LMFDB - Embedded newform 1050.3.q.e.649.15

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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.15
Character	$\chi$	$=$	1050.649
Dual form			1050.3.q.e.199.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-4.01037 - 5.73733i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-4.01037 - 5.73733i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(8.69259 + 15.0560i) q^{11} +(1.73205 - 3.00000i) q^{12} -7.22559 q^{13} +(-0.854777 - 9.86252i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(1.32600 + 2.29669i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(-2.20128 - 1.27091i) q^{19} +(-5.13291 + 10.9842i) q^{21} +24.5864i q^{22} +(-34.7289 - 20.0507i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-8.84951 - 5.10926i) q^{26} +5.19615 q^{27} +(5.92697 - 12.6835i) q^{28} -47.0080 q^{29} +(34.9025 - 20.1510i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(15.0560 - 26.0778i) q^{33} +3.75049i q^{34} -6.00000 q^{36} +(28.1482 + 16.2514i) q^{37} +(-1.79734 - 3.11308i) q^{38} +(6.25755 + 10.8384i) q^{39} +70.6679i q^{41} +(-14.0535 + 9.82336i) q^{42} +37.3732i q^{43} +(-17.3852 + 30.1120i) q^{44} +(-28.3560 - 49.1141i) q^{46} +(-16.7242 + 28.9672i) q^{47} +6.92820 q^{48} +(-16.8339 + 46.0176i) q^{49} +(2.29669 - 3.97799i) q^{51} +(-7.22559 - 12.5151i) q^{52} +(-61.3911 + 35.4442i) q^{53} +(6.36396 + 3.67423i) q^{54} +(16.2276 - 11.3430i) q^{56} +4.40256i q^{57} +(-57.5728 - 33.2397i) q^{58} +(-87.0863 + 50.2793i) q^{59} +(-11.1621 - 6.44446i) q^{61} +56.9955 q^{62} +(20.9216 - 1.81326i) q^{63} -8.00000 q^{64} +(36.8795 - 21.2924i) q^{66} +(-81.4689 + 47.0361i) q^{67} +(-2.65199 + 4.59339i) q^{68} +69.4578i q^{69} -11.5793 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-11.3345 - 19.6320i) q^{73} +(22.9829 + 39.8076i) q^{74} -5.08364i q^{76} +(51.5208 - 110.252i) q^{77} +17.6990i q^{78} +(-12.0542 + 20.8785i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-49.9698 + 86.5502i) q^{82} +111.664 q^{83} +(-24.1581 + 2.09377i) q^{84} +(-26.4268 + 45.7726i) q^{86} +(40.7101 + 70.5120i) q^{87} +(-42.5848 + 24.5864i) q^{88} +(110.770 + 63.9533i) q^{89} +(28.9773 + 41.4556i) q^{91} -80.2029i q^{92} +(-60.4529 - 34.9025i) q^{93} +(-40.9658 + 23.6516i) q^{94} +(8.48528 + 4.89898i) q^{96} +7.48256 q^{97} +(-53.1566 + 44.4565i) q^{98} -52.1556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 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
$7$	−4.01037	−	5.73733i	−0.572910	−	0.819618i
$7$	−4.01037	−	5.73733i	−0.572910	−	0.819618i
$8$			2.82843i			0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$		0			0
$11$	8.69259	+	15.0560i	0.790236	+	1.36873i	0.925821	+	0.377963i	$0.123375\pi$
$11$	8.69259	+	15.0560i	0.790236	+	1.36873i	−0.135585	+	0.990766i	$0.543291\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	−7.22559			−0.555815			−0.277907	−	0.960608i	$-0.589641\pi$
$13$	−7.22559			−0.555815			−0.277907	+	0.960608i	$0.589641\pi$
$14$	−0.854777	−	9.86252i	−0.0610555	−	0.704466i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	1.32600	+	2.29669i	0.0779998	+	0.135100i	0.902387	−	0.430927i	$-0.141813\pi$
$17$	1.32600	+	2.29669i	0.0779998	+	0.135100i	−0.824387	+	0.566027i	$0.808480\pi$
$18$	−3.67423	+	2.12132i	−0.204124	+	0.117851i
$19$	−2.20128	−	1.27091i	−0.115857	−	0.0668900i	0.440952	−	0.897531i	$-0.354641\pi$
$19$	−2.20128	−	1.27091i	−0.115857	−	0.0668900i	−0.556809	+	0.830641i	$0.687974\pi$
$20$		0			0
$21$	−5.13291	+	10.9842i	−0.244424	+	0.523058i
$22$			24.5864i			1.11756i
$23$	−34.7289	−	20.0507i	−1.50995	−	0.871771i	−0.999933	−	0.0116074i	$-0.996305\pi$
$23$	−34.7289	−	20.0507i	−1.50995	−	0.871771i	−0.510019	−	0.860163i	$-0.670361\pi$
$24$	4.24264	−	2.44949i	0.176777	−	0.102062i
$25$		0			0
$26$	−8.84951	−	5.10926i	−0.340366	−	0.196510i
$27$	5.19615			0.192450
$28$	5.92697	−	12.6835i	0.211678	−	0.452982i
$29$	−47.0080			−1.62096			−0.810482	−	0.585763i	$-0.800795\pi$
$29$	−47.0080			−1.62096			−0.810482	+	0.585763i	$0.800795\pi$
$30$		0			0
$31$	34.9025	−	20.1510i	1.12589	−	0.650031i	0.182990	−	0.983115i	$-0.441422\pi$
$31$	34.9025	−	20.1510i	1.12589	−	0.650031i	0.942897	+	0.333084i	$0.108089\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$	15.0560	−	26.0778i	0.456243	−	0.790236i
$34$			3.75049i			0.110308i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	28.1482	+	16.2514i	0.760762	+	0.439226i	0.829569	−	0.558404i	$-0.188586\pi$
$37$	28.1482	+	16.2514i	0.760762	+	0.439226i	−0.0688071	+	0.997630i	$0.521919\pi$
$38$	−1.79734	−	3.11308i	−0.0472984	−	0.0819232i
$39$	6.25755	+	10.8384i	0.160450	+	0.277907i
$40$		0			0
$41$			70.6679i			1.72361i	0.507241	+	0.861804i	$0.330665\pi$
$41$			70.6679i			1.72361i	−0.507241	+	0.861804i	$0.669335\pi$
$42$	−14.0535	+	9.82336i	−0.334608	+	0.233890i
$43$			37.3732i			0.869144i	0.900637	+	0.434572i	$0.143100\pi$
$43$			37.3732i			0.869144i	−0.900637	+	0.434572i	$0.856900\pi$
$44$	−17.3852	+	30.1120i	−0.395118	+	0.684364i
$45$		0			0
$46$	−28.3560	−	49.1141i	−0.616435	−	1.06770i
$47$	−16.7242	+	28.9672i	−0.355835	+	0.616324i	−0.987260	−	0.159113i	$-0.949137\pi$
$47$	−16.7242	+	28.9672i	−0.355835	+	0.616324i	0.631426	+	0.775436i	$0.282470\pi$
$48$	6.92820			0.144338
$49$	−16.8339	+	46.0176i	−0.343548	+	0.939135i
$50$		0			0
$51$	2.29669	−	3.97799i	0.0450332	−	0.0779998i
$52$	−7.22559	−	12.5151i	−0.138954	−	0.240675i
$53$	−61.3911	+	35.4442i	−1.15832	+	0.668758i	−0.950902	−	0.309493i	$-0.899841\pi$
$53$	−61.3911	+	35.4442i	−1.15832	+	0.668758i	−0.207422	+	0.978252i	$0.566507\pi$
$54$	6.36396	+	3.67423i	0.117851	+	0.0680414i
$55$		0			0
$56$	16.2276	−	11.3430i	0.289779	−	0.202554i
$57$			4.40256i			0.0772379i
$58$	−57.5728	−	33.2397i	−0.992634	−	0.573098i
$59$	−87.0863	+	50.2793i	−1.47604	+	0.852192i	−0.999635	−	0.0270340i	$-0.991394\pi$
$59$	−87.0863	+	50.2793i	−1.47604	+	0.852192i	−0.476405	+	0.879226i	$0.658060\pi$
$60$		0			0
$61$	−11.1621	−	6.44446i	−0.182986	−	0.105647i	0.405709	−	0.914002i	$-0.367025\pi$
$61$	−11.1621	−	6.44446i	−0.182986	−	0.105647i	−0.588695	+	0.808355i	$0.700358\pi$
$62$	56.9955			0.919283
$63$	20.9216	−	1.81326i	0.332088	−	0.0287819i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	36.8795	−	21.2924i	0.558781	−	0.322612i
$67$	−81.4689	+	47.0361i	−1.21595	+	0.702031i	−0.964050	−	0.265721i	$-0.914390\pi$
$67$	−81.4689	+	47.0361i	−1.21595	+	0.702031i	−0.251904	+	0.967752i	$0.581057\pi$
$68$	−2.65199	+	4.59339i	−0.0389999	+	0.0675498i
$69$			69.4578i			1.00663i
$70$		0			0
$71$	−11.5793			−0.163088			−0.0815440	−	0.996670i	$-0.525985\pi$
$71$	−11.5793			−0.163088			−0.0815440	+	0.996670i	$0.525985\pi$
$72$	−7.34847	−	4.24264i	−0.102062	−	0.0589256i
$73$	−11.3345	−	19.6320i	−0.155267	−	0.268931i	0.777889	−	0.628402i	$-0.216291\pi$
$73$	−11.3345	−	19.6320i	−0.155267	−	0.268931i	−0.933156	+	0.359471i	$0.882957\pi$
$74$	22.9829	+	39.8076i	0.310580	+	0.537940i
$75$		0			0
$76$		−	5.08364i		−	0.0668900i
$77$	51.5208	−	110.252i	0.669101	−	1.43185i
$78$			17.6990i			0.226910i
$79$	−12.0542	+	20.8785i	−0.152585	+	0.264285i	−0.932177	−	0.362003i	$-0.882093\pi$
$79$	−12.0542	+	20.8785i	−0.152585	+	0.264285i	0.779592	+	0.626287i	$0.215426\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−49.9698	+	86.5502i	−0.609388	+	1.05549i
$83$	111.664			1.34535			0.672676	−	0.739937i	$-0.265145\pi$
$83$	111.664			1.34535			0.672676	+	0.739937i	$0.265145\pi$
$84$	−24.1581	+	2.09377i	−0.287597	+	0.0249258i
$85$		0			0
$86$	−26.4268	+	45.7726i	−0.307289	+	0.532240i
$87$	40.7101	+	70.5120i	0.467932	+	0.810482i
$88$	−42.5848	+	24.5864i	−0.483919	+	0.279390i
$89$	110.770	+	63.9533i	1.24461	+	0.718577i	0.970030	−	0.242987i	$-0.0781272\pi$
$89$	110.770	+	63.9533i	1.24461	+	0.718577i	0.274582	+	0.961564i	$0.411460\pi$
$90$		0			0
$91$	28.9773	+	41.4556i	0.318432	+	0.455556i
$92$		−	80.2029i		−	0.871771i
$93$	−60.4529	−	34.9025i	−0.650031	−	0.375296i
$94$	−40.9658	+	23.6516i	−0.435807	+	0.251613i
$95$		0			0
$96$	8.48528	+	4.89898i	0.0883883	+	0.0510310i
$97$	7.48256			0.0771398			0.0385699	−	0.999256i	$-0.487720\pi$
$97$	7.48256			0.0771398			0.0385699	+	0.999256i	$0.487720\pi$
$98$	−53.1566	+	44.4565i	−0.542414	+	0.453638i
$99$	−52.1556			−0.526824
$100$		0			0
$101$	−81.9228	+	47.2982i	−0.811117	+	0.468299i	−0.847344	−	0.531045i	$-0.821799\pi$
$101$	−81.9228	+	47.2982i	−0.811117	+	0.468299i	0.0362267	+	0.999344i	$0.488466\pi$
$102$	5.62573	−	3.24802i	0.0551542	−	0.0318433i
$103$	29.9109	−	51.8072i	0.290397	−	0.502982i	−0.683507	−	0.729944i	$-0.739546\pi$
$103$	29.9109	−	51.8072i	0.290397	−	0.502982i	0.973904	+	0.226962i	$0.0728794\pi$
$104$		−	20.4371i		−	0.196510i
$105$		0			0
$106$	−100.251			−0.945767
$107$	5.59592	+	3.23081i	0.0522983	+	0.0301945i	0.525921	−	0.850533i	$-0.323721\pi$
$107$	5.59592	+	3.23081i	0.0522983	+	0.0301945i	−0.473623	+	0.880728i	$0.657054\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	−81.9201	−	141.890i	−0.751560	−	1.30174i	−0.947066	−	0.321038i	$-0.895968\pi$
$109$	−81.9201	−	141.890i	−0.751560	−	1.30174i	0.195506	−	0.980703i	$-0.437365\pi$
$110$		0			0
$111$		−	56.2964i		−	0.507175i
$112$	27.8954	−	2.41768i	0.249066	−	0.0215864i
$113$		−	105.434i		−	0.933040i	−0.884511	−	0.466520i	$-0.845508\pi$
$113$		−	105.434i		−	0.933040i	0.884511	−	0.466520i	$-0.154492\pi$
$114$	−3.11308	+	5.39202i	−0.0273077	+	0.0472984i
$115$		0			0
$116$	−47.0080	−	81.4202i	−0.405241	−	0.701898i
$117$	10.8384	−	18.7726i	0.0926358	−	0.160450i
$118$	−142.211			−1.20518
$119$	7.85915	−	16.8183i	0.0660433	−	0.141330i
$120$		0			0
$121$	−90.6223	+	156.962i	−0.748945	+	1.29721i
$122$	−9.11384	−	15.7856i	−0.0747036	−	0.129391i
$123$	106.002	−	61.2002i	0.861804	−	0.497563i
$124$	69.8050	+	40.3019i	0.562944	+	0.325016i
$125$		0			0
$126$	26.9058	+	12.5730i	0.213538	+	0.0997858i
$127$		−	53.7033i		−	0.422860i	−0.977393	−	0.211430i	$-0.932188\pi$
$127$		−	53.7033i		−	0.422860i	0.977393	−	0.211430i	$-0.0678121\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$	56.0598	−	32.3661i	0.434572	−	0.250900i
$130$		0			0
$131$	−50.6489	−	29.2421i	−0.386632	−	0.223222i	0.294068	−	0.955785i	$-0.404991\pi$
$131$	−50.6489	−	29.2421i	−0.386632	−	0.223222i	−0.680700	+	0.732562i	$0.738324\pi$
$132$	60.2240			0.456243
$133$	1.53632	+	17.7263i	0.0115513	+	0.133280i
$134$	−133.038			−0.992822
$135$		0			0
$136$	−6.49603	+	3.75049i	−0.0477650	+	0.0275771i
$137$	10.4936	−	6.05848i	0.0765956	−	0.0442225i	−0.461213	−	0.887289i	$-0.652586\pi$
$137$	10.4936	−	6.05848i	0.0765956	−	0.0442225i	0.537809	+	0.843067i	$0.319252\pi$
$138$	−49.1141	+	85.0680i	−0.355899	+	0.616435i
$139$			45.2562i			0.325584i	0.986660	+	0.162792i	$0.0520500\pi$
$139$			45.2562i			0.325584i	−0.986660	+	0.162792i	$0.947950\pi$
$140$		0			0
$141$	57.9344			0.410882
$142$	−14.1816	−	8.18777i	−0.0998706	−	0.0576603i
$143$	−62.8091	−	108.789i	−0.439225	−	0.760759i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$		0			0
$146$		−	32.0589i		−	0.219581i
$147$	83.6050	−	14.6016i	0.568741	−	0.0993309i
$148$			65.0055i			0.439226i
$149$	−25.4474	+	44.0762i	−0.170788	+	0.295814i	−0.938696	−	0.344747i	$-0.887965\pi$
$149$	−25.4474	+	44.0762i	−0.170788	+	0.295814i	0.767908	+	0.640561i	$0.221298\pi$
$150$		0			0
$151$	78.8476	+	136.568i	0.522169	+	0.904424i	0.999667	+	0.0257911i	$0.00821047\pi$
$151$	78.8476	+	136.568i	0.522169	+	0.904424i	−0.477498	+	0.878633i	$0.658456\pi$
$152$	3.59468	−	6.22616i	0.0236492	−	0.0409616i
$153$	−7.95598			−0.0519999
$154$	141.060	−	98.6004i	0.915974	−	0.640263i
$155$		0			0
$156$	−12.5151	+	21.6768i	−0.0802249	+	0.138954i
$157$	−83.9231	−	145.359i	−0.534542	−	0.925854i	−0.999185	−	0.0403562i	$-0.987151\pi$
$157$	−83.9231	−	145.359i	−0.534542	−	0.925854i	0.464643	−	0.885498i	$-0.346183\pi$
$158$	−29.5266	+	17.0472i	−0.186877	+	0.107894i
$159$	106.333	+	61.3911i	0.668758	+	0.386108i
$160$		0			0
$161$	24.2381	+	279.662i	0.150547	+	1.73703i
$162$		−	12.7279i		−	0.0785674i
$163$	−239.517	−	138.285i	−1.46943	−	0.848374i	−0.470015	−	0.882658i	$-0.655752\pi$
$163$	−239.517	−	138.285i	−1.46943	−	0.848374i	−0.999412	+	0.0342839i	$0.989085\pi$
$164$	−122.400	+	70.6679i	−0.746344	+	0.430902i
$165$		0			0
$166$	136.760	+	78.9586i	0.823857	+	0.475654i
$167$	48.4258			0.289975			0.144987	−	0.989433i	$-0.453686\pi$
$167$	48.4258			0.289975			0.144987	+	0.989433i	$0.453686\pi$
$168$	−31.0681	−	14.5181i	−0.184929	−	0.0864170i
$169$	−116.791			−0.691070
$170$		0			0
$171$	6.60384	−	3.81273i	0.0386190	−	0.0222967i
$172$	−64.7323	+	37.3732i	−0.376351	+	0.217286i
$173$	56.4843	−	97.8337i	0.326499	−	0.565513i	−0.655316	−	0.755355i	$-0.727464\pi$
$173$	56.4843	−	97.8337i	0.326499	−	0.565513i	0.981815	+	0.189842i	$0.0607977\pi$
$174$			115.146i			0.661756i
$175$		0			0
$176$	−69.5407			−0.395118
$177$	150.838	+	87.0863i	0.852192	+	0.492013i
$178$	90.4437	+	156.653i	0.508111	+	0.880073i
$179$	165.708	+	287.015i	0.925744	+	1.60344i	0.790360	+	0.612642i	$0.209893\pi$
$179$	165.708	+	287.015i	0.925744	+	1.60344i	0.135384	+	0.990793i	$0.456773\pi$
$180$		0			0
$181$		−	213.328i		−	1.17861i	−0.807912	−	0.589303i	$-0.799402\pi$
$181$		−	213.328i		−	1.17861i	0.807912	−	0.589303i	$-0.200598\pi$
$182$	6.17627	+	71.2626i	0.0339356	+	0.391553i
$183$			22.3243i			0.121991i
$184$	56.7120	−	98.2281i	0.308218	−	0.533848i
$185$		0			0
$186$	−49.3596	−	85.4933i	−0.265374	−	0.459642i
$187$	−23.0527	+	39.9285i	−0.123277	+	0.213521i
$188$	−66.8969			−0.355835
$189$	−20.8385	−	29.8120i	−0.110257	−	0.157736i
$190$		0			0
$191$	33.4517	−	57.9400i	0.175140	−	0.303351i	−0.765070	−	0.643947i	$-0.777296\pi$
$191$	33.4517	−	57.9400i	0.175140	−	0.303351i	0.940210	+	0.340596i	$0.110629\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	−97.5179	+	56.3020i	−0.505274	+	0.291720i	−0.730889	−	0.682497i	$-0.760894\pi$
$193$	−97.5179	+	56.3020i	−0.505274	+	0.291720i	0.225615	+	0.974217i	$0.427561\pi$
$194$	9.16422	+	5.29097i	0.0472383	+	0.0272730i
$195$		0			0
$196$	−96.5387	+	16.8605i	−0.492544	+	0.0860231i
$197$			61.0211i			0.309752i	0.987934	+	0.154876i	$0.0494978\pi$
$197$			61.0211i			0.309752i	−0.987934	+	0.154876i	$0.950502\pi$
$198$	−63.8772	−	36.8795i	−0.322612	−	0.186260i
$199$	165.554	−	95.5826i	0.831929	−	0.480314i	−0.0225837	−	0.999745i	$-0.507189\pi$
$199$	165.554	−	95.5826i	0.831929	−	0.480314i	0.854513	+	0.519431i	$0.173856\pi$
$200$		0			0
$201$	141.108	+	81.4689i	0.702031	+	0.405318i
$202$	−133.779			−0.662274
$203$	188.519	+	269.700i	0.928667	+	1.32857i
$204$	9.18678			0.0450332
$205$		0			0
$206$	73.2664	−	42.3004i	0.355662	−	0.205342i
$207$	104.187	−	60.1522i	0.503317	−	0.290590i
$208$	14.4512	−	25.0302i	0.0694768	−	0.120337i
$209$		−	44.1900i		−	0.211435i
$210$		0			0
$211$	280.115			1.32756			0.663781	−	0.747927i	$-0.268951\pi$
$211$	280.115			1.32756			0.663781	+	0.747927i	$0.268951\pi$
$212$	−122.782	−	70.8884i	−0.579162	−	0.334379i
$213$	10.0279	+	17.3689i	0.0470795	+	0.0815440i
$214$	4.56905	+	7.91383i	0.0213507	+	0.0369805i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	−255.585	−	119.434i	−1.17781	−	0.550388i
$218$		−	231.705i		−	1.06287i
$219$	−19.6320	+	34.0036i	−0.0896437	+	0.155267i
$220$		0			0
$221$	−9.58111	−	16.5950i	−0.0433535	−	0.0750904i
$222$	39.8076	−	68.9487i	0.179313	−	0.310580i
$223$	272.759			1.22313			0.611567	−	0.791192i	$-0.290539\pi$
$223$	272.759			1.22313			0.611567	+	0.791192i	$0.290539\pi$
$224$	35.8743	+	16.7640i	0.160153	+	0.0748393i
$225$		0			0
$226$	74.5528	−	129.129i	0.329879	−	0.571368i
$227$	−8.03620	−	13.9191i	−0.0354018	−	0.0613176i	0.847782	−	0.530345i	$-0.177938\pi$
$227$	−8.03620	−	13.9191i	−0.0354018	−	0.0613176i	−0.883183	+	0.469028i	$0.844604\pi$
$228$	−7.62546	+	4.40256i	−0.0334450	+	0.0193095i
$229$	−128.261	−	74.0517i	−0.560093	−	0.323370i	0.193090	−	0.981181i	$-0.438149\pi$
$229$	−128.261	−	74.0517i	−0.560093	−	0.323370i	−0.753183	+	0.657811i	$0.771482\pi$
$230$		0			0
$231$	−209.997	+	18.2003i	−0.909078	+	0.0787891i
$232$		−	132.959i		−	0.573098i
$233$	259.044	+	149.559i	1.11178	+	0.641885i	0.939289	−	0.343127i	$-0.111486\pi$
$233$	259.044	+	149.559i	1.11178	+	0.641885i	0.172488	+	0.985012i	$0.444819\pi$
$234$	26.5485	−	15.3278i	0.113455	−	0.0655034i
$235$		0			0
$236$	−174.173	−	100.559i	−0.738020	−	0.426096i
$237$	41.7570			0.176190
$238$	21.5178	−	15.0408i	0.0904108	−	0.0631968i
$239$	114.253			0.478046			0.239023	−	0.971014i	$-0.423173\pi$
$239$	114.253			0.478046			0.239023	+	0.971014i	$0.423173\pi$
$240$		0			0
$241$	−118.162	+	68.2209i	−0.490299	+	0.283074i	−0.724699	−	0.689066i	$-0.758021\pi$
$241$	−118.162	+	68.2209i	−0.490299	+	0.283074i	0.234399	+	0.972140i	$0.424688\pi$
$242$	−221.978	+	128.159i	−0.917266	+	0.529584i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$		−	25.7778i		−	0.105647i
$245$		0			0
$246$	173.100			0.703660
$247$	15.9056	+	9.18308i	0.0643950	+	0.0371785i
$248$	56.9955	+	98.7192i	0.229821	+	0.398061i
$249$	−96.7041	−	167.496i	−0.388370	−	0.672676i
$250$		0			0
$251$		−	457.024i		−	1.82081i	−0.413717	−	0.910406i	$-0.635770\pi$
$251$		−	457.024i		−	1.82081i	0.413717	−	0.910406i	$-0.364230\pi$
$252$	24.0622	+	34.4240i	0.0954850	+	0.136603i
$253$		−	697.171i		−	2.75562i
$254$	37.9739	−	65.7728i	0.149504	−	0.258948i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	24.9991	−	43.2997i	0.0972726	−	0.168481i	−0.813282	−	0.581869i	$-0.802321\pi$
$257$	24.9991	−	43.2997i	0.0972726	−	0.168481i	0.910555	+	0.413388i	$0.135655\pi$
$258$	91.5453			0.354827
$259$	−19.6453	−	226.669i	−0.0758505	−	0.875172i
$260$		0			0
$261$	70.5120	−	122.130i	0.270161	−	0.467932i
$262$	−41.3546	−	71.6283i	−0.157842	−	0.273390i
$263$	157.857	−	91.1388i	0.600217	−	0.346535i	−0.168910	−	0.985631i	$-0.554025\pi$
$263$	157.857	−	91.1388i	0.600217	−	0.346535i	0.769127	+	0.639096i	$0.220691\pi$
$264$	73.7591	+	42.5848i	0.279390	+	0.161306i
$265$		0			0
$266$	−10.6528	+	22.7965i	−0.0400480	+	0.0857012i
$267$		−	221.541i		−	0.829741i
$268$	−162.938	−	94.0722i	−0.607977	−	0.351016i
$269$	32.5814	−	18.8109i	0.121120	−	0.0699289i	−0.438216	−	0.898870i	$-0.644389\pi$
$269$	32.5814	−	18.8109i	0.121120	−	0.0699289i	0.559336	+	0.828941i	$0.311056\pi$
$270$		0			0
$271$	175.576	+	101.369i	0.647880	+	0.374054i	0.787644	−	0.616131i	$-0.211301\pi$
$271$	175.576	+	101.369i	0.647880	+	0.374054i	−0.139763	+	0.990185i	$0.544634\pi$
$272$	−10.6080			−0.0389999
$273$	37.0883	−	79.3675i	0.135855	−	0.290724i
$274$	17.1360			0.0625401
$275$		0			0
$276$	−120.304	+	69.4578i	−0.435885	+	0.251659i
$277$	−221.912	+	128.121i	−0.801126	+	0.462530i	−0.843865	−	0.536556i	$-0.819725\pi$
$277$	−221.912	+	128.121i	−0.801126	+	0.462530i	0.0427390	+	0.999086i	$0.486392\pi$
$278$	−32.0010	+	55.4273i	−0.115111	+	0.199379i
$279$			120.906i			0.433354i
$280$		0			0
$281$	−141.462			−0.503423			−0.251711	−	0.967802i	$-0.580993\pi$
$281$	−141.462			−0.503423			−0.251711	+	0.967802i	$0.580993\pi$
$282$	70.9549	+	40.9658i	0.251613	+	0.145269i
$283$	271.684	+	470.571i	0.960014	+	1.66279i	0.722452	+	0.691421i	$0.243015\pi$
$283$	271.684	+	470.571i	0.960014	+	1.66279i	0.237562	+	0.971372i	$0.423652\pi$
$284$	−11.5793	−	20.0559i	−0.0407720	−	0.0706192i
$285$		0			0
$286$		−	177.651i		−	0.621157i
$287$	405.445	−	283.405i	1.41270	−	0.987472i
$288$		−	16.9706i		−	0.0589256i
$289$	140.983	−	244.191i	0.487832	−	0.844950i
$290$		0			0
$291$	−6.48008	−	11.2238i	−0.0222683	−	0.0385699i
$292$	22.6690	−	39.2639i	0.0776337	−	0.134466i
$293$	−375.289			−1.28085			−0.640424	−	0.768021i	$-0.721241\pi$
$293$	−375.289			−1.28085			−0.640424	+	0.768021i	$0.721241\pi$
$294$	112.720	+	41.2344i	0.383400	+	0.140253i
$295$		0			0
$296$	−45.9658	+	79.6151i	−0.155290	+	0.268970i
$297$	45.1680	+	78.2333i	0.152081	+	0.263412i
$298$	−62.3332	+	35.9881i	−0.209172	+	0.120765i
$299$	250.937	+	144.878i	0.839253	+	0.484543i
$300$		0			0
$301$	214.422	−	149.880i	0.712367	−	0.497942i
$302$			223.015i			0.738459i
$303$	141.894	+	81.9228i	0.468299	+	0.270372i
$304$	8.80512	−	5.08364i	0.0289642	−	0.0167225i
$305$		0			0
$306$	−9.74405	−	5.62573i	−0.0318433	−	0.0183847i
$307$	−41.3436			−0.134670			−0.0673349	−	0.997730i	$-0.521450\pi$
$307$	−41.3436			−0.134670			−0.0673349	+	0.997730i	$0.521450\pi$
$308$	242.484	−	21.0159i	0.787284	−	0.0682333i
$309$	−103.614			−0.335321
$310$		0			0
$311$	−126.924	+	73.2794i	−0.408115	+	0.235625i	−0.689979	−	0.723829i	$-0.742380\pi$
$311$	−126.924	+	73.2794i	−0.408115	+	0.235625i	0.281865	+	0.959454i	$0.409047\pi$
$312$	−30.6556	+	17.6990i	−0.0982551	+	0.0567276i
$313$	−112.435	+	194.744i	−0.359218	+	0.622184i	−0.987830	−	0.155535i	$-0.950290\pi$
$313$	−112.435	+	194.744i	−0.359218	+	0.622184i	0.628612	+	0.777719i	$0.283623\pi$
$314$		−	237.370i		−	0.755957i
$315$		0			0
$316$	−48.2168			−0.152585
$317$	−195.918	−	113.113i	−0.618038	−	0.356825i	0.158067	−	0.987428i	$-0.449474\pi$
$317$	−195.918	−	113.113i	−0.618038	−	0.356825i	−0.776105	+	0.630604i	$0.782807\pi$
$318$	86.8202	+	150.377i	0.273019	+	0.472884i
$319$	−408.621	−	707.753i	−1.28094	−	2.21866i
$320$		0			0
$321$		−	11.1918i		−	0.0348656i
$322$	−168.065	+	359.653i	−0.521942	+	1.11694i
$323$		−	6.74089i		−	0.0208696i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−195.565	−	338.728i	−0.599891	−	1.03904i
$327$	−141.890	+	245.760i	−0.433914	+	0.751560i
$328$	−199.879			−0.609388
$329$	233.265	−	20.2169i	0.709011	−	0.0614495i
$330$		0			0
$331$	−69.9082	+	121.085i	−0.211203	+	0.365814i	−0.952091	−	0.305814i	$-0.901071\pi$
$331$	−69.9082	+	121.085i	−0.211203	+	0.365814i	0.740888	+	0.671628i	$0.234405\pi$
$332$	111.664	+	193.408i	0.336338	+	0.582555i
$333$	−84.4446	+	48.7541i	−0.253587	+	0.146409i
$334$	59.3093	+	34.2422i	0.177573	+	0.102522i
$335$		0			0
$336$	−27.7847	−	39.7494i	−0.0826924	−	0.118302i
$337$		−	30.1128i		−	0.0893556i	−0.999001	−	0.0446778i	$-0.985774\pi$
$337$		−	30.1128i		−	0.0893556i	0.999001	−	0.0446778i	$-0.0142261\pi$
$338$	−143.039	−	82.5836i	−0.423192	−	0.244330i
$339$	−158.150	+	91.3081i	−0.466520	+	0.269345i
$340$		0			0
$341$	606.786	+	350.328i	1.77943	+	1.02736i
$342$	10.7840			0.0315323
$343$	331.528	−	87.9664i	0.966554	−	0.256462i
$344$	−105.707			−0.307289
$345$		0			0
$346$	138.358	−	79.8809i	0.399878	−	0.230870i
$347$	360.186	−	207.954i	1.03800	−	0.599290i	0.118734	−	0.992926i	$-0.462116\pi$
$347$	360.186	−	207.954i	1.03800	−	0.599290i	0.919266	+	0.393636i	$0.128783\pi$
$348$	−81.4202	+	141.024i	−0.233966	+	0.405241i
$349$		−	594.950i		−	1.70473i	−0.522950	−	0.852363i	$-0.675169\pi$
$349$		−	594.950i		−	1.70473i	0.522950	−	0.852363i	$-0.324831\pi$
$350$		0			0
$351$	−37.5453			−0.106967
$352$	−85.1697	−	49.1727i	−0.241959	−	0.139695i
$353$	182.159	+	315.509i	0.516031	+	0.893793i	0.999827	+	0.0186116i	$0.00592459\pi$
$353$	182.159	+	315.509i	0.516031	+	0.893793i	−0.483795	+	0.875181i	$0.660742\pi$
$354$	123.159	+	213.317i	0.347906	+	0.602591i
$355$		0			0
$356$			255.813i			0.718577i
$357$	−32.0336	+	2.77633i	−0.0897301	+	0.00777684i
$358$			468.693i			1.30920i
$359$	−306.381	+	530.668i	−0.853430	+	1.47818i	0.0246647	+	0.999696i	$0.492148\pi$
$359$	−306.381	+	530.668i	−0.853430	+	1.47818i	−0.878094	+	0.478488i	$0.841185\pi$
$360$		0			0
$361$	−177.270	−	307.040i	−0.491051	−	0.850526i
$362$	150.846	−	261.272i	0.416700	−	0.721746i
$363$	313.925			0.864807
$364$	−42.8259	+	91.6457i	−0.117654	+	0.251774i
$365$		0			0
$366$	−15.7856	+	27.3415i	−0.0431302	+	0.0747036i
$367$	246.509	+	426.967i	0.671687	+	1.16340i	0.977425	+	0.211281i	$0.0677635\pi$
$367$	246.509	+	426.967i	0.671687	+	1.16340i	−0.305738	+	0.952116i	$0.598903\pi$
$368$	138.916	−	80.2029i	0.377488	−	0.217943i
$369$	−183.601	−	106.002i	−0.497563	−	0.287268i
$370$		0			0
$371$	449.556	+	210.077i	1.21174	+	0.566245i
$372$		−	139.610i		−	0.375296i
$373$	−143.243	−	82.7013i	−0.384029	−	0.221719i	0.295541	−	0.955330i	$-0.404500\pi$
$373$	−143.243	−	82.7013i	−0.384029	−	0.221719i	−0.679570	+	0.733611i	$0.737834\pi$
$374$	−56.4674	+	32.6015i	−0.150982	+	0.0871697i
$375$		0			0
$376$	−81.9317	−	47.3033i	−0.217903	−	0.125807i
$377$	339.660			0.900956
$378$	−4.44155	−	51.2472i	−0.0117501	−	0.135575i
$379$	179.349			0.473215			0.236608	−	0.971605i	$-0.423964\pi$
$379$	179.349			0.473215			0.236608	+	0.971605i	$0.423964\pi$
$380$		0			0
$381$	−80.5549	+	46.5084i	−0.211430	+	0.122069i
$382$	81.9395	−	47.3078i	0.214501	−	0.123842i
$383$	−134.585	+	233.108i	−0.351396	+	0.608636i	−0.986494	−	0.163795i	$-0.947626\pi$
$383$	−134.585	+	233.108i	−0.351396	+	0.608636i	0.635098	+	0.772432i	$0.280960\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	−159.246			−0.412554
$387$	−97.0984	−	56.0598i	−0.250900	−	0.144857i
$388$	7.48256	+	12.9602i	0.0192849	+	0.0334025i
$389$	−236.874	−	410.277i	−0.608930	−	1.05470i	−0.991417	−	0.130737i	$-0.958266\pi$
$389$	−236.874	−	410.277i	−0.608930	−	1.05470i	0.382487	−	0.923961i	$-0.375068\pi$
$390$		0			0
$391$		−	106.349i		−	0.271992i
$392$	−130.157	−	47.6133i	−0.332034	−	0.121463i
$393$			101.298i			0.257755i
$394$	−43.1484	+	74.7353i	−0.109514	+	0.189683i
$395$		0			0
$396$	−52.1556	−	90.3361i	−0.131706	−	0.228121i
$397$	−256.967	+	445.080i	−0.647271	+	1.12111i	0.336500	+	0.941683i	$0.390757\pi$
$397$	−256.967	+	445.080i	−0.647271	+	1.12111i	−0.983772	+	0.179424i	$0.942577\pi$
$398$	270.348			0.679267
$399$	25.2589	−	17.6559i	0.0633056	−	0.0442504i
$400$		0			0
$401$	203.367	−	352.242i	0.507150	−	0.878410i	−0.492816	−	0.870134i	$-0.664032\pi$
$401$	203.367	−	352.242i	0.507150	−	0.878410i	0.999966	−	0.00827591i	$-0.00263433\pi$
$402$	115.214	+	199.557i	0.286603	+	0.496411i
$403$	−252.191	+	145.603i	−0.625785	+	0.361297i
$404$	−163.846	−	94.5963i	−0.405558	−	0.234149i
$405$		0			0
$406$	40.1814	+	463.617i	0.0989689	+	1.14191i
$407$			565.066i			1.38837i
$408$	11.2515	+	6.49603i	0.0275771	+	0.0159217i
$409$	422.173	−	243.742i	1.03221	−	0.595946i	0.114592	−	0.993413i	$-0.463444\pi$
$409$	422.173	−	243.742i	1.03221	−	0.595946i	0.917617	+	0.397467i	$0.130111\pi$
$410$		0			0
$411$	−18.1755	−	10.4936i	−0.0442225	−	0.0255319i
$412$	119.643			0.290397
$413$	637.717	+	298.004i	1.54411	+	0.721560i
$414$	170.136			0.410957
$415$		0			0
$416$	35.3980	−	20.4371i	0.0850914	−	0.0491275i
$417$	67.8843	−	39.1930i	0.162792	−	0.0939881i
$418$	31.2471	−	54.1215i	0.0747537	−	0.129477i
$419$		−	552.257i		−	1.31804i	−0.752127	−	0.659018i	$-0.770972\pi$
$419$		−	552.257i		−	1.31804i	0.752127	−	0.659018i	$-0.229028\pi$
$420$		0			0
$421$	−74.6870			−0.177404			−0.0887019	−	0.996058i	$-0.528272\pi$
$421$	−74.6870			−0.177404			−0.0887019	+	0.996058i	$0.528272\pi$
$422$	343.070	+	198.072i	0.812962	+	0.469364i
$423$	−50.1727	−	86.9016i	−0.118612	−	0.205441i
$424$	−100.251	−	173.640i	−0.236442	−	0.409529i
$425$		0			0
$426$			28.3633i			0.0665804i
$427$	7.79031	+	89.8855i	0.0182443	+	0.210505i
$428$			12.9232i			0.0301945i
$429$	−108.789	+	188.427i	−0.253586	+	0.439225i
$430$		0			0
$431$	−242.339	−	419.743i	−0.562271	−	0.973881i	−0.997298	−	0.0734641i	$-0.976595\pi$
$431$	−242.339	−	419.743i	−0.562271	−	0.973881i	0.435027	−	0.900417i	$-0.356739\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	458.196			1.05819			0.529094	−	0.848563i	$-0.322532\pi$
$433$	458.196			1.05819			0.529094	+	0.848563i	$0.322532\pi$
$434$	−228.573	−	327.002i	−0.526667	−	0.753461i
$435$		0			0
$436$	163.840	−	283.779i	0.375780	−	0.650870i
$437$	50.9653	+	88.2746i	0.116626	+	0.202001i
$438$	−48.0883	+	27.7638i	−0.109791	+	0.0633877i
$439$	−121.167	−	69.9559i	−0.276007	−	0.159353i	0.355607	−	0.934635i	$-0.384274\pi$
$439$	−121.167	−	69.9559i	−0.276007	−	0.159353i	−0.631614	+	0.775283i	$0.717607\pi$
$440$		0			0
$441$	−94.3065	−	112.762i	−0.213847	−	0.255696i
$442$		−	27.0995i		−	0.0613110i
$443$	13.9364	+	8.04616i	0.0314591	+	0.0181629i	0.515647	−	0.856801i	$-0.327552\pi$
$443$	13.9364	+	8.04616i	0.0314591	+	0.0181629i	−0.484188	+	0.874964i	$0.660885\pi$
$444$	97.5082	−	56.2964i	0.219613	−	0.126794i
$445$		0			0
$446$	334.060	+	192.870i	0.749014	+	0.432444i
$447$	88.1524			0.197209
$448$	32.0830	+	45.8986i	0.0716138	+	0.102452i
$449$	329.314			0.733439			0.366720	−	0.930332i	$-0.380481\pi$
$449$	329.314			0.733439			0.366720	+	0.930332i	$0.380481\pi$
$450$		0			0
$451$	−1063.98	+	614.288i	−2.35915	+	1.36206i
$452$	182.616	−	105.434i	0.404018	−	0.233260i
$453$	136.568	−	236.543i	0.301475	−	0.522169i
$454$		−	22.7298i		−	0.0500657i
$455$		0			0
$456$	−12.4523			−0.0273077
$457$	−771.557	−	445.459i	−1.68831	−	0.974745i	−0.955814	−	0.293972i	$-0.905023\pi$
$457$	−771.557	−	445.459i	−1.68831	−	0.974745i	−0.732494	−	0.680773i	$-0.761644\pi$
$458$	−104.725	−	181.389i	−0.228657	−	0.396046i
$459$	6.89008	+	11.9340i	0.0150111	+	0.0259999i
$460$		0			0
$461$			534.019i			1.15839i	0.815188	+	0.579196i	$0.196633\pi$
$461$			534.019i			1.15839i	−0.815188	+	0.579196i	$0.803367\pi$
$462$	−270.062	−	126.200i	−0.584550	−	0.273159i
$463$			158.679i			0.342719i	0.985209	+	0.171359i	$0.0548159\pi$
$463$			158.679i			0.342719i	−0.985209	+	0.171359i	$0.945184\pi$
$464$	94.0160	−	162.840i	0.202621	−	0.350949i
$465$		0			0
$466$	211.509	+	366.344i	0.453881	+	0.786145i
$467$	−56.0995	+	97.1671i	−0.120127	+	0.208067i	−0.919818	−	0.392346i	$-0.871664\pi$
$467$	−56.0995	+	97.1671i	−0.120127	+	0.208067i	0.799690	+	0.600413i	$0.204997\pi$
$468$	43.3535			0.0926358
$469$	596.582	+	278.782i	1.27203	+	0.594417i
$470$		0			0
$471$	−145.359	+	251.769i	−0.308618	+	0.534542i
$472$	−142.211	−	246.317i	−0.301295	−	0.521859i
$473$	−562.691	+	324.870i	−1.18962	+	0.686829i
$474$	51.1416	+	29.5266i	0.107894	+	0.0622925i
$475$		0			0
$476$	36.9893	−	3.20583i	0.0777085	−	0.00673494i
$477$		−	212.665i		−	0.445839i
$478$	139.931	+	80.7891i	0.292742	+	0.169015i
$479$	598.669	−	345.642i	1.24983	−	0.721590i	0.278755	−	0.960362i	$-0.410078\pi$
$479$	598.669	−	345.642i	1.24983	−	0.721590i	0.971076	+	0.238772i	$0.0767450\pi$
$480$		0			0
$481$	−203.387	−	117.426i	−0.422843	−	0.244128i
$482$	−192.958			−0.400328
$483$	398.502	−	278.551i	0.825056	−	0.576711i
$484$	−362.489			−0.748945
$485$		0			0
$486$	−19.0919	+	11.0227i	−0.0392837	+	0.0226805i
$487$	−624.248	+	360.410i	−1.28182	+	0.740062i	−0.977182	−	0.212405i	$-0.931870\pi$
$487$	−624.248	+	360.410i	−1.28182	+	0.740062i	−0.304643	+	0.952467i	$0.598537\pi$
$488$	18.2277	−	31.5713i	0.0373518	−	0.0646953i
$489$			479.033i			0.979618i
$490$		0			0
$491$	589.995			1.20162			0.600809	−	0.799392i	$-0.294845\pi$
$491$	589.995			1.20162			0.600809	+	0.799392i	$0.294845\pi$
$492$	212.004	+	122.400i	0.430902	+	0.248781i
$493$	−62.3325	−	107.963i	−0.126435	−	0.218992i
$494$	12.9868	+	22.4939i	0.0262891	+	0.0455341i
$495$		0			0
$496$			161.208i			0.325016i
$497$	46.4371	+	66.4340i	0.0934348	+	0.133670i
$498$		−	273.521i		−	0.549238i
$499$	−437.845	+	758.370i	−0.877445	+	1.51978i	−0.0233104	+	0.999728i	$0.507421\pi$
$499$	−437.845	+	758.370i	−0.877445	+	1.51978i	−0.854135	+	0.520052i	$0.825913\pi$
$500$		0			0
$501$	−41.9380	−	72.6387i	−0.0837085	−	0.144987i
$502$	323.165	−	559.737i	0.643754	−	1.11501i
$503$	−817.809			−1.62586			−0.812931	−	0.582360i	$-0.802129\pi$
$503$	−817.809			−1.62586			−0.812931	+	0.582360i	$0.802129\pi$
$504$	5.12866	+	59.1751i	0.0101759	+	0.117411i
$505$		0			0
$506$	492.974	−	853.857i	0.974258	−	1.68746i
$507$	101.144	+	175.186i	0.199495	+	0.345535i
$508$	93.0168	−	53.7033i	0.183104	−	0.105715i
$509$	657.585	+	379.657i	1.29191	+	0.745887i	0.978993	−	0.203892i	$-0.0653591\pi$
$509$	657.585	+	379.657i	1.29191	+	0.745887i	0.312921	+	0.949779i	$0.398692\pi$
$510$		0			0
$511$	−67.1794	+	143.761i	−0.131467	+	0.281333i
$512$		−	22.6274i		−	0.0441942i
$513$	−11.4382	−	6.60384i	−0.0222967	−	0.0128730i
$514$	61.2350	−	35.3540i	0.119134	−	0.0687821i
$515$		0			0
$516$	112.120	+	64.7323i	0.217286	+	0.125450i
$517$	−581.508			−1.12477
$518$	136.219	−	291.504i	0.262971	−	0.562748i
$519$	−195.667			−0.377009
$520$		0			0
$521$	−153.671	+	88.7220i	−0.294954	+	0.170292i	−0.640174	−	0.768230i	$-0.721138\pi$
$521$	−153.671	+	88.7220i	−0.294954	+	0.170292i	0.345220	+	0.938522i	$0.387804\pi$
$522$	172.718	−	99.7190i	0.330878	−	0.191033i
$523$	−52.6094	+	91.1221i	−0.100592	+	0.174230i	−0.911929	−	0.410349i	$-0.865407\pi$
$523$	−52.6094	+	91.1221i	−0.100592	+	0.174230i	0.811337	+	0.584579i	$0.198740\pi$
$524$		−	116.969i		−	0.223222i
$525$		0			0
$526$	257.780			0.490075
$527$	92.5612	+	53.4403i	0.175638	+	0.101405i
$528$	60.2240	+	104.311i	0.114061	+	0.197559i
$529$	539.563	+	934.551i	1.01997	+	1.76664i
$530$		0			0
$531$		−	301.676i		−	0.568128i
$532$	−29.1665	+	20.3873i	−0.0548243	+	0.0383220i
$533$		−	510.618i		−	0.958007i
$534$	156.653	−	271.331i	0.293358	−	0.508111i
$535$		0			0
$536$	−133.038	−	230.429i	−0.248206	−	0.429905i
$537$	287.015	−	497.125i	0.534479	−	0.925744i
$538$	53.2051			0.0988943
$539$	−839.172	+	146.562i	−1.55690	+	0.271914i
$540$		0			0
$541$	138.181	−	239.337i	0.255419	−	0.442398i	−0.709591	−	0.704614i	$-0.751120\pi$
$541$	138.181	−	239.337i	0.255419	−	0.442398i	0.965009	+	0.262216i	$0.0844534\pi$
$542$	143.357	+	248.301i	0.264496	+	0.458121i
$543$	−319.992	+	184.747i	−0.589303	+	0.340234i
$544$	−12.9921	−	7.50097i	−0.0238825	−	0.0137886i
$545$		0			0
$546$	101.545	−	70.9796i	0.185980	−	0.129999i
$547$		−	918.409i		−	1.67899i	−0.543366	−	0.839496i	$-0.682850\pi$
$547$		−	918.409i		−	1.67899i	0.543366	−	0.839496i	$-0.317150\pi$
$548$	20.9872	+	12.1170i	0.0382978	+	0.0221113i
$549$	33.4864	−	19.3334i	0.0609953	−	0.0352156i
$550$		0			0
$551$	103.478	+	59.7429i	0.187800	+	0.108426i
$552$	−196.456			−0.355899
$553$	168.128	−	14.5716i	0.304030	−	0.0263500i
$554$	−362.380			−0.654116
$555$		0			0
$556$	−78.3861	+	45.2562i	−0.140982	+	0.0813961i
$557$	−636.538	+	367.505i	−1.14280	+	0.659794i	−0.947122	−	0.320875i	$-0.896023\pi$
$557$	−636.538	+	367.505i	−1.14280	+	0.659794i	−0.195675	+	0.980669i	$0.562690\pi$
$558$	−85.4933	+	148.079i	−0.153214	+	0.265374i
$559$		−	270.044i		−	0.483083i
$560$		0			0
$561$	79.8569			0.142347
$562$	−173.255	−	100.029i	−0.308282	−	0.177987i
$563$	413.283	+	715.827i	0.734073	+	1.27145i	0.955129	+	0.296191i	$0.0957164\pi$
$563$	413.283	+	715.827i	0.734073	+	1.27145i	−0.221056	+	0.975261i	$0.570950\pi$
$564$	57.9344	+	100.345i	0.102721	+	0.177917i
$565$		0			0
$566$			768.438i			1.35767i
$567$	−26.6714	+	57.0757i	−0.0470395	+	0.100663i
$568$		−	32.7511i		−	0.0576603i
$569$	−216.546	+	375.069i	−0.380573	+	0.659172i	−0.991144	−	0.132790i	$-0.957607\pi$
$569$	−216.546	+	375.069i	−0.380573	+	0.659172i	0.610571	+	0.791961i	$0.290940\pi$
$570$		0			0
$571$	−240.036	−	415.754i	−0.420378	−	0.728116i	0.575598	−	0.817733i	$-0.304769\pi$
$571$	−240.036	−	415.754i	−0.420378	−	0.728116i	−0.995976	+	0.0896166i	$0.971436\pi$
$572$	125.618	−	217.577i	0.219612	−	0.380380i
$573$	−115.880			−0.202234
$574$	696.964	−	60.4054i	1.21422	−	0.105236i
$575$		0			0
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	43.5695	+	75.4646i	0.0755104	+	0.130788i	0.901308	−	0.433179i	$-0.142608\pi$
$577$	43.5695	+	75.4646i	0.0755104	+	0.130788i	−0.825798	+	0.563966i	$0.809275\pi$
$578$	345.338	−	199.381i	0.597470	−	0.344949i
$579$	168.906	+	97.5179i	0.291720	+	0.168425i
$580$		0			0
$581$	−447.815	−	640.655i	−0.770766	−	1.10268i
$582$		−	18.3284i		−	0.0314922i
$583$	−1067.30	−	616.204i	−1.83070	−	1.05695i
$584$	55.5276	−	32.0589i	0.0950815	−	0.0548953i
$585$		0			0
$586$	−459.633	−	265.369i	−0.784356	−	0.452848i
$587$	−104.332			−0.177737			−0.0888687	−	0.996043i	$-0.528325\pi$
$587$	−104.332			−0.177737			−0.0888687	+	0.996043i	$0.528325\pi$
$588$	108.896	+	130.206i	0.185197	+	0.221439i
$589$	−102.440			−0.173922
$590$		0			0
$591$	91.5316	−	52.8458i	0.154876	−	0.0894176i
$592$	−112.593	+	65.0055i	−0.190191	+	0.109807i
$593$	−145.735	+	252.421i	−0.245760	+	0.425668i	−0.962345	−	0.271831i	$-0.912371\pi$
$593$	−145.735	+	252.421i	−0.245760	+	0.425668i	0.716585	+	0.697499i	$0.245704\pi$
$594$			127.754i			0.215075i
$595$		0			0
$596$	−101.790			−0.170788
$597$	−286.748	−	165.554i	−0.480314	−	0.277310i
$598$	204.889	+	354.878i	0.342624	+	0.593442i
$599$	298.839	+	517.604i	0.498896	+	0.864114i	0.999999	−	0.00127378i	$-0.000405456\pi$
$599$	298.839	+	517.604i	0.498896	+	0.864114i	−0.501103	+	0.865388i	$0.667072\pi$
$600$		0			0
$601$		−	447.444i		−	0.744499i	−0.928133	−	0.372250i	$-0.878587\pi$
$601$		−	447.444i		−	0.744499i	0.928133	−	0.372250i	$-0.121413\pi$
$602$	368.594	−	31.9458i	0.612283	−	0.0530661i
$603$		−	282.217i		−	0.468021i
$604$	−157.695	+	273.136i	−0.261085	+	0.452212i
$605$		0			0
$606$	115.856	+	200.669i	0.191182	+	0.331137i
$607$	308.155	−	533.739i	0.507668	−	0.879307i	−0.492293	−	0.870430i	$-0.663841\pi$
$607$	308.155	−	533.739i	0.507668	−	0.879307i	0.999961	−	0.00887709i	$-0.00282570\pi$
$608$	14.3787			0.0236492
$609$	241.288	−	516.346i	0.396203	−	0.847859i
$610$		0			0
$611$	120.842	−	209.305i	0.197778	−	0.342562i
$612$	−7.95598	−	13.7802i	−0.0130000	−	0.0225166i
$613$	−110.052	+	63.5384i	−0.179530	+	0.103651i	−0.587072	−	0.809535i	$-0.699719\pi$
$613$	−110.052	+	63.5384i	−0.179530	+	0.103651i	0.407542	+	0.913186i	$0.366386\pi$
$614$	−50.6354	−	29.2344i	−0.0824681	−	0.0476130i
$615$		0			0
$616$	311.841	+	145.723i	0.506235	+	0.236563i
$617$		−	68.5630i		−	0.111123i	−0.998455	−	0.0555616i	$-0.982305\pi$
$617$		−	68.5630i		−	0.111123i	0.998455	−	0.0555616i	$-0.0176949\pi$
$618$	−126.901	−	73.2664i	−0.205342	−	0.118554i
$619$	−833.529	+	481.238i	−1.34657	+	0.777445i	−0.987763	−	0.155965i	$-0.950151\pi$
$619$	−833.529	+	481.238i	−1.34657	+	0.777445i	−0.358812	+	0.933410i	$0.616818\pi$
$620$		0			0
$621$	−180.457	−	104.187i	−0.290590	−	0.167772i
$622$	−207.265			−0.333224
$623$	−77.3092	−	892.003i	−0.124092	−	1.43179i
$624$	−50.0604			−0.0802249
$625$		0			0
$626$	−275.409	+	159.008i	−0.439951	+	0.254006i
$627$	−66.2850	+	38.2697i	−0.105718	+	0.0610362i
$628$	167.846	−	290.718i	0.267271	−	0.462927i
$629$			86.1971i			0.137038i
$630$		0			0
$631$	412.586			0.653860			0.326930	−	0.945048i	$-0.393986\pi$
$631$	412.586			0.653860			0.326930	+	0.945048i	$0.393986\pi$
$632$	−59.0533	−	34.0944i	−0.0934387	−	0.0539469i
$633$	−242.587	−	420.173i	−0.383234	−	0.663781i
$634$	−159.966	−	277.070i	−0.252313	−	0.437019i
$635$		0			0
$636$			245.565i			0.386108i
$637$	121.635	−	332.504i	0.190949	−	0.521985i
$638$		−	1155.76i		−	1.81153i
$639$	17.3689	−	30.0838i	0.0271813	−	0.0470795i
$640$		0			0
$641$	71.3374	+	123.560i	0.111291	+	0.192761i	0.916291	−	0.400513i	$-0.131168\pi$
$641$	71.3374	+	123.560i	0.111291	+	0.192761i	−0.805000	+	0.593275i	$0.797835\pi$
$642$	7.91383	−	13.7072i	0.0123268	−	0.0213507i
$643$	−239.942			−0.373160			−0.186580	−	0.982440i	$-0.559740\pi$
$643$	−239.942			−0.373160			−0.186580	+	0.982440i	$0.559740\pi$
$644$	−460.150	+	321.643i	−0.714519	+	0.499446i
$645$		0			0
$646$	4.76653	−	8.25588i	0.00737853	−	0.0127800i
$647$	74.3724	+	128.817i	0.114950	+	0.199098i	0.917760	−	0.397136i	$-0.129996\pi$
$647$	74.3724	+	128.817i	0.114950	+	0.199098i	−0.802810	+	0.596235i	$0.796663\pi$
$648$	22.0454	−	12.7279i	0.0340207	−	0.0196419i
$649$	−1514.01	−	874.115i	−2.33284	−	1.34686i
$650$		0			0
$651$	42.1915	+	486.810i	0.0648102	+	0.747788i
$652$		−	553.140i		−	0.848374i
$653$	−249.434	−	144.011i	−0.381982	−	0.220537i	0.296698	−	0.954971i	$-0.404114\pi$
$653$	−249.434	−	144.011i	−0.381982	−	0.220537i	−0.678680	+	0.734434i	$0.737448\pi$
$654$	−347.557	+	200.662i	−0.531433	+	0.306823i
$655$		0			0
$656$	−244.801	−	141.336i	−0.373172	−	0.215451i
$657$	68.0071			0.103512
$658$	299.985	+	140.183i	0.455905	+	0.213043i
$659$	175.647			0.266536			0.133268	−	0.991080i	$-0.457453\pi$
$659$	175.647			0.266536			0.133268	+	0.991080i	$0.457453\pi$
$660$		0			0
$661$	−615.015	+	355.079i	−0.930432	+	0.537185i	−0.886948	−	0.461869i	$-0.847179\pi$
$661$	−615.015	+	355.079i	−0.930432	+	0.537185i	−0.0434835	+	0.999054i	$0.513846\pi$
$662$	−171.239	+	98.8651i	−0.258670	+	0.149343i
$663$	−16.5950	+	28.7433i	−0.0250301	+	0.0433535i
$664$			315.834i			0.475654i
$665$		0			0
$666$	−137.897			−0.207053
$667$	1632.53	+	942.544i	2.44758	+	1.41311i
$668$	48.4258	+	83.8760i	0.0724937	+	0.125563i
$669$	−236.216	−	409.139i	−0.353089	−	0.611567i
$670$		0			0
$671$		−	224.076i		−	0.333944i
$672$	−5.92207	−	68.3296i	−0.00881261	−	0.101681i
$673$		−	1173.04i		−	1.74301i	−0.490389	−	0.871504i	$-0.663145\pi$
$673$		−	1173.04i		−	1.74301i	0.490389	−	0.871504i	$-0.336855\pi$
$674$	21.2930	−	36.8806i	0.0315920	−	0.0547189i
$675$		0			0
$676$	−116.791	−	202.288i	−0.172768	−	0.299242i
$677$	338.731	−	586.699i	0.500341	−	0.866616i	−0.499659	−	0.866222i	$-0.666541\pi$
$677$	338.731	−	586.699i	0.500341	−	0.866616i	1.00000		0.000393478i	$-0.000125248\pi$
$678$	−258.258			−0.380912
$679$	−30.0078	−	42.9299i	−0.0441941	−	0.0632252i
$680$		0			0
$681$	−13.9191	+	24.1086i	−0.0204392	+	0.0354018i
$682$	495.439	+	858.126i	0.726450	+	1.25825i
$683$	−719.691	+	415.514i	−1.05372	+	0.608366i	−0.923689	−	0.383144i	$-0.874841\pi$
$683$	−719.691	+	415.514i	−1.05372	+	0.608366i	−0.130032	+	0.991510i	$0.541508\pi$
$684$	13.2077	+	7.62546i	0.0193095	+	0.0111483i
$685$		0			0
$686$	468.239	+	126.689i	0.682564	+	0.184679i
$687$			256.523i			0.373395i
$688$	−129.465	−	74.7464i	−0.188175	−	0.108643i
$689$	443.587	−	256.105i	0.643813	−	0.371706i
$690$		0			0
$691$	541.436	+	312.598i	0.783554	+	0.452385i	0.837688	−	0.546149i	$-0.183907\pi$
$691$	541.436	+	312.598i	0.783554	+	0.452385i	−0.0541345	+	0.998534i	$0.517240\pi$
$692$	225.937			0.326499
$693$	209.163	+	299.233i	0.301823	+	0.431794i
$694$	588.181			0.847524
$695$		0			0
$696$	−199.438	+	115.146i	−0.286549	+	0.165439i
$697$	−162.303	+	93.7055i	−0.232859	+	0.134441i
$698$	420.693	−	728.661i	0.602712	−	1.04393i
$699$		−	518.088i		−	0.741185i
$700$		0			0
$701$	1030.02			1.46936			0.734678	−	0.678416i	$-0.237333\pi$
$701$	1030.02			1.46936			0.734678	+	0.678416i	$0.237333\pi$
$702$	−45.9834	−	26.5485i	−0.0655034	−	0.0378184i
$703$	−41.3081	−	71.5477i	−0.0587597	−	0.101775i
$704$	−69.5407	−	120.448i	−0.0987795	−	0.171091i
$705$		0			0
$706$			515.224i			0.729779i
$707$	599.906	+	280.335i	0.848523	+	0.396513i
$708$			348.345i			0.492013i
$709$	−329.126	+	570.062i	−0.464211	+	0.804037i	−0.999166	−	0.0408438i	$-0.986995\pi$
$709$	−329.126	+	570.062i	−0.464211	+	0.804037i	0.534955	+	0.844881i	$0.320329\pi$
$710$		0			0
$711$	−36.1626	−	62.6354i	−0.0508616	−	0.0880949i
$712$	−180.887	+	313.306i	−0.254055	+	0.440037i
$713$	−1616.17			−2.26671
$714$	−41.1962	−	19.2509i	−0.0576978	−	0.0269621i
$715$		0			0
$716$	−331.416	+	574.030i	−0.462872	+	0.801718i
$717$	−98.9461	−	171.380i	−0.138000	−	0.239023i
$718$	−750.478	+	433.288i	−1.04523	+	0.603466i
$719$	1166.99	+	673.760i	1.62307	+	0.937079i	0.986093	+	0.166195i	$0.0531481\pi$
$719$	1166.99	+	673.760i	1.62307	+	0.937079i	0.636975	+	0.770884i	$0.280185\pi$
$720$		0			0
$721$	−417.188	+	36.1574i	−0.578625	+	0.0501490i
$722$		−	501.394i		−	0.694452i
$723$	204.663	+	118.162i	0.283074	+	0.163433i
$724$	369.495	−	213.328i	0.510352	−	0.294652i
$725$		0			0
$726$	384.478	+	221.978i	0.529584	+	0.305755i
$727$	1126.18			1.54907			0.774536	−	0.632530i	$-0.217983\pi$
$727$	1126.18			1.54907			0.774536	+	0.632530i	$0.217983\pi$
$728$	−117.254	+	81.9602i	−0.161063	+	0.112583i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−85.8348	+	49.5568i	−0.117421	+	0.0677931i
$732$	−38.6668	+	22.3243i	−0.0528235	+	0.0304976i
$733$	−303.337	+	525.395i	−0.413829	+	0.716773i	−0.995305	−	0.0967907i	$-0.969142\pi$
$733$	−303.337	+	525.395i	−0.413829	+	0.716773i	0.581476	+	0.813564i	$0.302476\pi$
$734$			697.233i			0.949909i
$735$		0			0
$736$	226.848			0.308218
$737$	−1416.35	−	817.731i	−1.92178	−	1.10954i
$738$	−149.909	−	259.651i	−0.203129	−	0.351830i
$739$	461.084	+	798.622i	0.623930	+	1.08068i	0.988747	+	0.149599i	$0.0477984\pi$
$739$	461.084	+	798.622i	0.623930	+	1.08068i	−0.364817	+	0.931079i	$0.618868\pi$
$740$		0			0
$741$		−	31.8111i		−	0.0429300i
$742$	402.045	+	575.175i	0.541840	+	0.775168i
$743$			13.3994i			0.0180342i	0.999959	+	0.00901712i	$0.00287028\pi$
$743$			13.3994i			0.0180342i	−0.999959	+	0.00901712i	$0.997130\pi$
$744$	98.7192	−	170.987i	0.132687	−	0.229821i
$745$		0			0
$746$	−116.957	−	202.576i	−0.156779	−	0.271550i
$747$	−167.496	+	290.112i	−0.224225	+	0.388370i
$748$	−92.2108			−0.123277
$749$	−3.90552	−	45.0624i	−0.00521431	−	0.0601634i
$750$		0			0
$751$	−538.071	+	931.967i	−0.716473	+	1.24097i	0.245916	+	0.969291i	$0.420911\pi$
$751$	−538.071	+	931.967i	−0.716473	+	1.24097i	−0.962389	+	0.271676i	$0.912422\pi$
$752$	−66.8969	−	115.869i	−0.0889587	−	0.154081i
$753$	−685.536	+	395.794i	−0.910406	+	0.525623i
$754$	415.997	+	240.176i	0.551721	+	0.318536i
$755$		0			0
$756$	30.7975	−	65.9054i	0.0407374	−	0.0871764i
$757$			254.117i			0.335690i	0.985813	+	0.167845i	$0.0536807\pi$
$757$			254.117i			0.335690i	−0.985813	+	0.167845i	$0.946319\pi$
$758$	219.656	+	126.819i	0.289784	+	0.167307i
$759$	−1045.76	+	603.768i	−1.37781	+	0.795478i
$760$		0			0
$761$	−685.095	−	395.540i	−0.900256	−	0.519763i	−0.0229729	−	0.999736i	$-0.507313\pi$
$761$	−685.095	−	395.540i	−0.900256	−	0.519763i	−0.877283	+	0.479973i	$0.840646\pi$
$762$	−131.546			−0.172632
$763$	−485.538	+	1039.03i	−0.636354	+	1.36177i
$764$	133.807			0.175140
$765$		0			0
$766$	−329.664	+	190.332i	−0.430371	+	0.248475i
$767$	629.250	−	363.298i	0.820405	−	0.473661i
$768$	−13.8564	+	24.0000i	−0.0180422	+	0.0312500i
$769$			464.403i			0.603905i	0.953323	+	0.301952i	$0.0976384\pi$
$769$			464.403i			0.603905i	−0.953323	+	0.301952i	$0.902362\pi$
$770$		0			0
$771$	−86.5993			−0.112321
$772$	−195.036	−	112.604i	−0.252637	−	0.145860i
$773$	390.063	+	675.608i	0.504609	+	0.874008i	0.999986	+	0.00533002i	$0.00169661\pi$
$773$	390.063	+	675.608i	0.504609	+	0.874008i	−0.495377	+	0.868678i	$0.664970\pi$
$774$	−79.2805	−	137.318i	−0.102430	−	0.177413i
$775$		0			0
$776$			21.1639i			0.0272730i
$777$	−322.991	+	225.769i	−0.415690	+	0.290566i
$778$		−	669.980i		−	0.861157i
$779$	89.8126	−	155.560i	0.115292	−	0.199692i
$780$		0			0
$781$	−100.654	−	174.337i	−0.128878	−	0.223223i
$782$	75.2000	−	130.250i	0.0961637	−	0.166560i
$783$	−244.261			−0.311955
$784$	−125.742	−	150.349i	−0.160385	−	0.191772i
$785$		0			0
$786$	−71.6283	+	124.064i	−0.0911302	+	0.157842i
$787$	−576.402	−	998.358i	−0.732404	−	1.26856i	−0.955853	−	0.293845i	$-0.905065\pi$
$787$	−576.402	−	998.358i	−0.732404	−	1.26856i	0.223449	−	0.974716i	$-0.428268\pi$
$788$	−105.692	+	61.0211i	−0.134126	+	0.0774379i
$789$	−273.416	−	157.857i	−0.346535	−	0.200072i
$790$		0			0
$791$	−604.907	+	422.827i	−0.764737	+	0.534548i
$792$		−	147.518i		−	0.186260i
$793$	80.6530	+	46.5650i	0.101706	+	0.0587201i
$794$	−629.437	+	363.406i	−0.792742	+	0.457690i
$795$		0			0
$796$	331.108	+	191.165i	0.415964	+	0.240157i
$797$	−1475.63			−1.85148			−0.925742	−	0.378156i	$-0.876558\pi$
$797$	−1475.63			−1.85148			−0.925742	+	0.378156i	$0.876558\pi$
$798$	43.4204	−	3.76321i	0.0544115	−	0.00471580i
$799$	−88.7051			−0.111020
$800$		0			0
$801$	−332.311	+	191.860i	−0.414871	+	0.239526i
$802$	498.146	−	287.605i	0.621129	−	0.358609i
$803$	197.053	−	341.305i	0.245396	−	0.425038i
$804$			325.876i			0.405318i
$805$		0			0
$806$	−411.827			−0.510951
$807$	−56.4326	−	32.5814i	−0.0699289	−	0.0403734i
$808$	−133.779	−	231.713i	−0.165569	−	0.286773i
$809$	−6.88050	−	11.9174i	−0.00850495	−	0.0147310i	0.861742	−	0.507347i	$-0.169374\pi$
$809$	−6.88050	−	11.9174i	−0.00850495	−	0.0147310i	−0.870247	+	0.492616i	$0.836041\pi$
$810$		0			0
$811$		−	1274.65i		−	1.57170i	−0.618416	−	0.785851i	$-0.712225\pi$
$811$		−	1274.65i		−	1.57170i	0.618416	−	0.785851i	$-0.287775\pi$
$812$	−278.615	+	596.225i	−0.343122	+	0.734268i
$813$		−	351.151i		−	0.431920i
$814$	−399.562	+	692.062i	−0.490863	+	0.850199i
$815$		0			0
$816$	9.18678	+	15.9120i	0.0112583	+	0.0195000i
$817$	47.4980	−	82.2689i	0.0581371	−	0.100696i
$818$	689.406			0.842795
$819$	−151.171	+	13.1019i	−0.184580	+	0.0159974i
$820$		0			0
$821$	−292.249	+	506.190i	−0.355967	+	0.616553i	−0.987283	−	0.158973i	$-0.949182\pi$
$821$	−292.249	+	506.190i	−0.355967	+	0.616553i	0.631316	+	0.775526i	$0.282515\pi$
$822$	−14.8402	−	25.7040i	−0.0180538	−	0.0312700i
$823$	−70.1196	+	40.4835i	−0.0851999	+	0.0491902i	−0.541995	−	0.840382i	$-0.682331\pi$
$823$	−70.1196	+	40.4835i	−0.0851999	+	0.0491902i	0.456795	+	0.889572i	$0.348997\pi$
$824$	146.533	+	84.6007i	0.177831	+	0.102671i
$825$		0			0
$826$	570.320	+	815.913i	0.690461	+	0.987789i
$827$			1628.46i			1.96911i	0.175072	+	0.984556i	$0.443984\pi$
$827$			1628.46i			1.96911i	−0.175072	+	0.984556i	$0.556016\pi$
$828$	208.373	+	120.304i	0.251659	+	0.145295i
$829$	761.982	−	439.931i	0.919158	−	0.530676i	0.0357920	−	0.999359i	$-0.488605\pi$
$829$	761.982	−	439.931i	0.919158	−	0.530676i	0.883366	+	0.468683i	$0.155271\pi$
$830$		0			0
$831$	384.362	+	221.912i	0.462530	+	0.267042i
$832$	57.8047			0.0694768
$833$	−128.010	+	22.3570i	−0.153674	+	0.0268391i
$834$	110.855			0.132919
$835$		0			0
$836$	76.5394	−	44.1900i	0.0915543	−	0.0528589i
$837$	181.359	−	104.708i	0.216677	−	0.125099i
$838$	390.505	−	676.374i	0.465996	−	0.807129i
$839$			647.389i			0.771619i	0.922578	+	0.385810i	$0.126078\pi$
$839$			647.389i			0.771619i	−0.922578	+	0.385810i	$0.873922\pi$
$840$		0			0
$841$	1368.75			1.62753
$842$	−91.4725	−	52.8117i	−0.108637	−	0.0627217i
$843$	122.510	+	212.193i	0.145326	+	0.251711i
$844$	280.115	+	485.174i	0.331890	+	0.574851i
$845$		0			0
$846$		−	141.910i		−	0.167742i
$847$	1263.97	−	109.548i	1.49230	−	0.129336i
$848$		−	283.554i		−	0.334379i
$849$	470.571	−	815.052i	0.554264	−	0.960014i
$850$		0			0
$851$	−651.704	−	1128.78i	−0.765809	−	1.32642i
$852$	−20.0559	+	34.7378i	−0.0235397	+	0.0407720i
$853$	−569.518			−0.667665			−0.333833	−	0.942632i	$-0.608342\pi$
$853$	−569.518			−0.667665			−0.333833	+	0.942632i	$0.608342\pi$
$854$	−54.0175	+	115.595i	−0.0632524	+	0.135358i
$855$		0			0
$856$	−9.13810	+	15.8277i	−0.0106754	+	0.0184903i
$857$	−319.299	−	553.041i	−0.372577	−	0.645322i	0.617384	−	0.786662i	$-0.288192\pi$
$857$	−319.299	−	553.041i	−0.372577	−	0.645322i	−0.989961	+	0.141339i	$0.954859\pi$
$858$	−266.477	+	153.850i	−0.310579	+	0.179313i
$859$	−1097.36	−	633.562i	−1.27749	−	0.737558i	−0.301102	−	0.953592i	$-0.597355\pi$
$859$	−1097.36	−	633.562i	−1.27749	−	0.737558i	−0.976386	+	0.216034i	$0.930688\pi$
$860$		0			0
$861$	−776.233	−	362.732i	−0.901548	−	0.421292i
$862$		−	685.437i		−	0.795171i
$863$	178.430	+	103.017i	0.206756	+	0.119371i	0.599803	−	0.800148i	$-0.295246\pi$
$863$	178.430	+	103.017i	0.206756	+	0.119371i	−0.393047	+	0.919518i	$0.628579\pi$
$864$	−25.4558	+	14.6969i	−0.0294628	+	0.0170103i
$865$		0			0
$866$	561.173	+	323.993i	0.648006	+	0.374126i
$867$	−488.381			−0.563300
$868$	−48.7185	−	562.120i	−0.0561273	−	0.647604i
$869$	−419.129			−0.482312
$870$		0			0
$871$	588.661	−	339.864i	0.675845	−	0.390199i
$872$	401.325	−	231.705i	0.460235	−	0.265717i
$873$	−11.2238	+	19.4403i	−0.0128566	+	0.0222683i
$874$			144.152i			0.164933i
$875$		0			0
$876$	−78.5279			−0.0896437
$877$	714.076	+	412.272i	0.814226	+	0.470093i	0.848421	−	0.529322i	$-0.177554\pi$
$877$	714.076	+	412.272i	0.814226	+	0.470093i	−0.0341955	+	0.999415i	$0.510887\pi$
$878$	−98.9325	−	171.356i	−0.112679	−	0.195167i
$879$	325.009	+	562.933i	0.369749	+	0.640424i
$880$		0			0
$881$			416.337i			0.472574i	0.971683	+	0.236287i	$0.0759305\pi$
$881$			416.337i			0.472574i	−0.971683	+	0.236287i	$0.924070\pi$
$882$	−35.7666	−	204.790i	−0.0405517	−	0.232188i
$883$			650.529i			0.736726i	0.929682	+	0.368363i	$0.120082\pi$
$883$			650.529i			0.736726i	−0.929682	+	0.368363i	$0.879918\pi$
$884$	19.1622	−	33.1900i	0.0216767	−	0.0375452i
$885$		0			0
$886$	11.3790	+	19.7090i	0.0128431	+	0.0222449i
$887$	−173.198	+	299.987i	−0.195262	+	0.338204i	−0.946987	−	0.321273i	$-0.895889\pi$
$887$	−173.198	+	299.987i	−0.195262	+	0.338204i	0.751724	+	0.659478i	$0.229223\pi$
$888$	159.230			0.179313
$889$	−308.113	+	215.370i	−0.346584	+	0.242261i
$890$		0			0
$891$	78.2333	−	135.504i	0.0878040	−	0.152081i
$892$	272.759	+	472.433i	0.305784	+	0.529633i
$893$	73.6295	−	42.5100i	0.0824518	−	0.0476036i
$894$	107.964	+	62.3332i	0.120765	+	0.0697239i
$895$		0			0
$896$	6.83822	+	78.9002i	0.00763194	+	0.0880582i
$897$		−	501.873i		−	0.559502i
$898$	403.326	+	232.860i	0.449138	+	0.259310i
$899$	−1640.70	+	947.256i	−1.82502	+	1.05368i
$900$		0			0
$901$	−162.809	−	93.9978i	−0.180698	−	0.104326i
$902$	−1737.47			−1.92624
$903$	−410.516	−	191.833i	−0.454613	−	0.212440i
$904$	298.211			0.329879
$905$		0			0
$906$	334.522	−	193.136i	0.369230	−	0.213175i
$907$	−363.888	+	210.091i	−0.401199	+	0.231633i	−0.687001	−	0.726656i	$-0.741073\pi$
$907$	−363.888	+	210.091i	−0.401199	+	0.231633i	0.285802	+	0.958289i	$0.407740\pi$
$908$	16.0724	−	27.8382i	0.0177009	−	0.0306588i
$909$		−	283.789i		−	0.312199i
$910$		0			0
$911$	717.087			0.787142			0.393571	−	0.919294i	$-0.371239\pi$
$911$	717.087			0.787142			0.393571	+	0.919294i	$0.371239\pi$
$912$	−15.2509	−	8.80512i	−0.0167225	−	0.00965474i
$913$	970.652	+	1681.22i	1.06315	+	1.84142i
$914$	−629.974	−	1091.15i	−0.689249	−	1.19381i
$915$		0			0
$916$		−	296.207i		−	0.323370i
$917$	35.3490	+	407.861i	0.0385485	+	0.444777i
$918$			19.4881i			0.0212289i
$919$	−59.5137	+	103.081i	−0.0647592	+	0.112166i	−0.896587	−	0.442867i	$-0.853961\pi$
$919$	−59.5137	+	103.081i	−0.0647592	+	0.112166i	0.831828	+	0.555034i	$0.187295\pi$
$920$		0			0
$921$	35.8046	+	62.0154i	0.0388758	+	0.0673349i
$922$	−377.608	+	654.037i	−0.409553	+	0.709367i
$923$	83.6669			0.0906467
$924$	−241.521	−	345.525i	−0.261386	−	0.373945i
$925$		0			0
$926$	−112.203	+	194.341i	−0.121169	+	0.209872i
$927$	89.7326	+	155.421i	0.0967989	+	0.167661i
$928$	230.291	−	132.959i	0.248159	−	0.143274i
$929$	−328.049	−	189.399i	−0.353121	−	0.203874i	0.312938	−	0.949773i	$-0.398687\pi$
$929$	−328.049	−	189.399i	−0.353121	−	0.203874i	−0.666059	+	0.745899i	$0.732020\pi$
$930$		0			0
$931$	95.5403	−	79.9034i	0.102621	−	0.0858253i
$932$			598.237i			0.641885i
$933$	219.838	+	126.924i	0.235625	+	0.136038i
$934$	−137.415	+	79.3366i	−0.147125	+	0.0849429i
$935$		0			0
$936$	53.0970	+	30.6556i	0.0567276	+	0.0327517i
$937$	365.585			0.390165			0.195083	−	0.980787i	$-0.437503\pi$
$937$	365.585			0.390165			0.195083	+	0.980787i	$0.437503\pi$
$938$	533.532	+	763.284i	0.568798	+	0.813735i
$939$	389.487			0.414790
$940$		0			0
$941$	−1193.22	+	688.903i	−1.26803	+	0.732097i	−0.974615	−	0.223889i	$-0.928125\pi$
$941$	−1193.22	+	688.903i	−1.26803	+	0.732097i	−0.293414	+	0.955985i	$0.594791\pi$
$942$	−356.056	+	205.569i	−0.377978	+	0.218226i
$943$	1416.94	−	2454.22i	1.50259	−	2.60256i
$944$		−	402.235i		−	0.426096i
$945$		0			0
$946$	−918.871			−0.971323
$947$	411.218	+	237.417i	0.434232	+	0.250704i	0.701148	−	0.713016i	$-0.252671\pi$
$947$	411.218	+	237.417i	0.434232	+	0.250704i	−0.266916	+	0.963720i	$0.586005\pi$
$948$	41.7570	+	72.3252i	0.0440474	+	0.0762924i
$949$	81.8986	+	141.853i	0.0862999	+	0.149476i
$950$		0			0
$951$			391.836i			0.412025i
$952$	47.5693	+	22.2290i	0.0499677	+	0.0233498i
$953$		−	172.839i		−	0.181363i	−0.995880	−	0.0906813i	$-0.971096\pi$
$953$		−	172.839i		−	0.181363i	0.995880	−	0.0906813i	$-0.0289045\pi$
$954$	150.377	−	260.461i	0.157628	−	0.273019i
$955$		0			0
$956$	114.253	+	197.892i	0.119512	+	0.207000i
$957$	−707.753	+	1225.86i	−0.739554	+	1.28094i
$958$	977.622			1.02048
$959$	−76.8427	−	35.9085i	−0.0801280	−	0.0374437i
$960$		0			0
$961$	331.623	−	574.388i	0.345081	−	0.597698i
$962$	−166.065	−	287.633i	−0.172625	−	0.298995i
$963$	−16.7878	+	9.69242i	−0.0174328	+	0.0100648i
$964$	−236.324	−	136.442i	−0.245150	−	0.141537i
$965$		0			0
$966$	685.029	−	59.3709i	0.709139	−	0.0614606i
$967$			1209.88i			1.25117i	0.780158	+	0.625583i	$0.215139\pi$
$967$			1209.88i			1.25117i	−0.780158	+	0.625583i	$0.784861\pi$
$968$	−443.957	−	256.319i	−0.458633	−	0.264792i
$969$	−10.1113	+	5.83779i	−0.0104348	+	0.00602455i
$970$		0			0
$971$	−675.990	−	390.283i	−0.696180	−	0.401939i	0.109743	−	0.993960i	$-0.464997\pi$
$971$	−675.990	−	390.283i	−0.696180	−	0.401939i	−0.805923	+	0.592020i	$0.798330\pi$
$972$	−31.1769			−0.0320750
$973$	259.650	−	181.494i	0.266855	−	0.186531i
$974$	−1019.39			−1.04661
$975$		0			0
$976$	44.6485	−	25.7778i	0.0457465	−	0.0264117i
$977$	−1376.86	+	794.931i	−1.40927	+	0.813644i	−0.995318	−	0.0966527i	$-0.969186\pi$
$977$	−1376.86	+	794.931i	−1.40927	+	0.813644i	−0.413955	+	0.910297i	$0.635853\pi$
$978$	−338.728	+	586.694i	−0.346347	+	0.599891i
$979$			2223.68i			2.27138i
$980$		0			0
$981$	491.520			0.501040
$982$	722.593	+	417.189i	0.735838	+	0.424836i
$983$	350.785	+	607.577i	0.356851	+	0.618084i	0.987433	−	0.158039i	$-0.0505171\pi$
$983$	350.785	+	607.577i	0.356851	+	0.618084i	−0.630582	+	0.776123i	$0.717184\pi$
$984$	173.100	+	299.819i	0.175915	+	0.304694i
$985$		0			0
$986$		−	176.303i		−	0.178806i
$987$	−232.339	−	332.389i	−0.235399	−	0.336767i
$988$			36.7323i			0.0371785i
$989$	749.360	−	1297.93i	0.757695	−	1.31237i
$990$		0			0
$991$	−203.359	−	352.228i	−0.205206	−	0.355427i	0.744992	−	0.667073i	$-0.232453\pi$
$991$	−203.359	−	352.228i	−0.205206	−	0.355427i	−0.950198	+	0.311646i	$0.899120\pi$
$992$	−113.991	+	197.438i	−0.114910	+	0.199031i
$993$	242.169			0.243876
$994$	9.89768	+	114.201i	0.00995743	+	0.114890i
$995$		0			0
$996$	193.408	−	334.993i	0.194185	−	0.336338i
$997$	378.379	+	655.372i	0.379518	+	0.657344i	0.990992	−	0.133920i	$-0.0427565\pi$
$997$	378.379	+	655.372i	0.379518	+	0.657344i	−0.611474	+	0.791264i	$0.709423\pi$
$998$	−1072.50	+	619.207i	−1.07465	+	0.620448i
$999$	146.262	+	84.4446i	0.146409	+	0.0845291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.649.15		32
5.2	odd	4		210.3.o.b.61.2	yes	16
5.3	odd	4		1050.3.p.i.901.5		16
5.4	even	2	inner	1050.3.q.e.649.2		32
7.3	odd	6	inner	1050.3.q.e.199.2		32
15.2	even	4		630.3.v.c.271.8		16
35.2	odd	12		1470.3.f.d.391.11		16
35.3	even	12		1050.3.p.i.451.5		16
35.12	even	12		1470.3.f.d.391.13		16
35.17	even	12		210.3.o.b.31.2	✓	16
35.24	odd	6	inner	1050.3.q.e.199.15		32
105.17	odd	12		630.3.v.c.451.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.2	✓	16	35.17	even	12
210.3.o.b.61.2	yes	16	5.2	odd	4
630.3.v.c.271.8		16	15.2	even	4
630.3.v.c.451.8		16	105.17	odd	12
1050.3.p.i.451.5		16	35.3	even	12
1050.3.p.i.901.5		16	5.3	odd	4
1050.3.q.e.199.2		32	7.3	odd	6	inner
1050.3.q.e.199.15		32	35.24	odd	6	inner
1050.3.q.e.649.2		32	5.4	even	2	inner
1050.3.q.e.649.15		32	1.1	even	1	trivial
1470.3.f.d.391.11		16	35.2	odd	12
1470.3.f.d.391.13		16	35.12	even	12

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)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-4.01037 - 5.73733i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.44949i q^{6} +(-4.01037 - 5.73733i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(8.69259 + 15.0560i) q^{11} +(1.73205 - 3.00000i) q^{12} -7.22559 q^{13} +(-0.854777 - 9.86252i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(1.32600 + 2.29669i) q^{17} +(-3.67423 + 2.12132i) q^{18} +(-2.20128 - 1.27091i) q^{19} +(-5.13291 + 10.9842i) q^{21} +24.5864i q^{22} +(-34.7289 - 20.0507i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-8.84951 - 5.10926i) q^{26} +5.19615 q^{27} +(5.92697 - 12.6835i) q^{28} -47.0080 q^{29} +(34.9025 - 20.1510i) q^{31} +(-4.89898 + 2.82843i) q^{32} +(15.0560 - 26.0778i) q^{33} +3.75049i q^{34} -6.00000 q^{36} +(28.1482 + 16.2514i) q^{37} +(-1.79734 - 3.11308i) q^{38} +(6.25755 + 10.8384i) q^{39} +70.6679i q^{41} +(-14.0535 + 9.82336i) q^{42} +37.3732i q^{43} +(-17.3852 + 30.1120i) q^{44} +(-28.3560 - 49.1141i) q^{46} +(-16.7242 + 28.9672i) q^{47} +6.92820 q^{48} +(-16.8339 + 46.0176i) q^{49} +(2.29669 - 3.97799i) q^{51} +(-7.22559 - 12.5151i) q^{52} +(-61.3911 + 35.4442i) q^{53} +(6.36396 + 3.67423i) q^{54} +(16.2276 - 11.3430i) q^{56} +4.40256i q^{57} +(-57.5728 - 33.2397i) q^{58} +(-87.0863 + 50.2793i) q^{59} +(-11.1621 - 6.44446i) q^{61} +56.9955 q^{62} +(20.9216 - 1.81326i) q^{63} -8.00000 q^{64} +(36.8795 - 21.2924i) q^{66} +(-81.4689 + 47.0361i) q^{67} +(-2.65199 + 4.59339i) q^{68} +69.4578i q^{69} -11.5793 q^{71} +(-7.34847 - 4.24264i) q^{72} +(-11.3345 - 19.6320i) q^{73} +(22.9829 + 39.8076i) q^{74} -5.08364i q^{76} +(51.5208 - 110.252i) q^{77} +17.6990i q^{78} +(-12.0542 + 20.8785i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-49.9698 + 86.5502i) q^{82} +111.664 q^{83} +(-24.1581 + 2.09377i) q^{84} +(-26.4268 + 45.7726i) q^{86} +(40.7101 + 70.5120i) q^{87} +(-42.5848 + 24.5864i) q^{88} +(110.770 + 63.9533i) q^{89} +(28.9773 + 41.4556i) q^{91} -80.2029i q^{92} +(-60.4529 - 34.9025i) q^{93} +(-40.9658 + 23.6516i) q^{94} +(8.48528 + 4.89898i) q^{96} +7.48256 q^{97} +(-53.1566 + 44.4565i) q^{98} -52.1556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Introduction

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