LMFDB - Embedded newform 1050.3.q.e.199.15

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			199.15
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.15

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

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

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			2.44949i			0.408248i
$7$	−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	−0.135585	−	0.990766i	$-0.543291\pi$
$11$	8.69259	−	15.0560i	0.790236	−	1.36873i	0.925821	−	0.377963i	$-0.123375\pi$
$12$	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	−0.824387	−	0.566027i	$-0.808480\pi$
$17$	1.32600	−	2.29669i	0.0779998	−	0.135100i	0.902387	+	0.430927i	$0.141813\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	−2.20128	+	1.27091i	−0.115857	+	0.0668900i	−0.556809	−	0.830641i	$-0.687974\pi$
$19$	−2.20128	+	1.27091i	−0.115857	+	0.0668900i	0.440952	+	0.897531i	$0.354641\pi$
$20$		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	−0.510019	+	0.860163i	$0.670361\pi$
$23$	−34.7289	+	20.0507i	−1.50995	+	0.871771i	−0.999933	+	0.0116074i	$0.996305\pi$
$24$	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	0.942897	−	0.333084i	$-0.108089\pi$
$31$	34.9025	+	20.1510i	1.12589	+	0.650031i	0.182990	+	0.983115i	$0.441422\pi$
$32$	−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	−0.0688071	−	0.997630i	$-0.521919\pi$
$37$	28.1482	−	16.2514i	0.760762	−	0.439226i	0.829569	+	0.558404i	$0.188586\pi$
$38$	−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	$-0.669335\pi$
$41$		−	70.6679i		−	1.72361i	0.507241	−	0.861804i	$-0.330665\pi$
$42$	−14.0535	−	9.82336i	−0.334608	−	0.233890i
$43$		−	37.3732i		−	0.869144i	−0.900637	−	0.434572i	$-0.856900\pi$
$43$		−	37.3732i		−	0.869144i	0.900637	−	0.434572i	$-0.143100\pi$
$44$	−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	0.631426	−	0.775436i	$-0.282470\pi$
$47$	−16.7242	−	28.9672i	−0.355835	−	0.616324i	−0.987260	+	0.159113i	$0.949137\pi$
$48$	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	−0.207422	−	0.978252i	$-0.566507\pi$
$53$	−61.3911	−	35.4442i	−1.15832	−	0.668758i	−0.950902	+	0.309493i	$0.899841\pi$
$54$	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	−0.476405	−	0.879226i	$-0.658060\pi$
$59$	−87.0863	−	50.2793i	−1.47604	−	0.852192i	−0.999635	+	0.0270340i	$0.991394\pi$
$60$		0			0
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	−0.588695	−	0.808355i	$-0.700358\pi$
$61$	−11.1621	+	6.44446i	−0.182986	+	0.105647i	0.405709	+	0.914002i	$0.367025\pi$
$62$	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	−0.251904	−	0.967752i	$-0.581057\pi$
$67$	−81.4689	−	47.0361i	−1.21595	−	0.702031i	−0.964050	+	0.265721i	$0.914390\pi$
$68$	−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	−0.933156	−	0.359471i	$-0.882957\pi$
$73$	−11.3345	+	19.6320i	−0.155267	+	0.268931i	0.777889	+	0.628402i	$0.216291\pi$
$74$	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	0.779592	−	0.626287i	$-0.215426\pi$
$79$	−12.0542	−	20.8785i	−0.152585	−	0.264285i	−0.932177	+	0.362003i	$0.882093\pi$
$80$		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	0.274582	−	0.961564i	$-0.411460\pi$
$89$	110.770	−	63.9533i	1.24461	−	0.718577i	0.970030	+	0.242987i	$0.0781272\pi$
$90$		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	0.0362267	−	0.999344i	$-0.488466\pi$
$101$	−81.9228	−	47.2982i	−0.811117	−	0.468299i	−0.847344	+	0.531045i	$0.821799\pi$
$102$	5.62573	+	3.24802i	0.0551542	+	0.0318433i
$103$	29.9109	+	51.8072i	0.290397	+	0.502982i	0.973904	−	0.226962i	$-0.0728794\pi$
$103$	29.9109	+	51.8072i	0.290397	+	0.502982i	−0.683507	+	0.729944i	$0.739546\pi$
$104$			20.4371i			0.196510i
$105$		0			0
$106$	−100.251			−0.945767
$107$	5.59592	−	3.23081i	0.0522983	−	0.0301945i	−0.473623	−	0.880728i	$-0.657054\pi$
$107$	5.59592	−	3.23081i	0.0522983	−	0.0301945i	0.525921	+	0.850533i	$0.323721\pi$
$108$	5.19615	−	9.00000i	0.0481125	−	0.0833333i
$109$	−81.9201	+	141.890i	−0.751560	+	1.30174i	0.195506	+	0.980703i	$0.437365\pi$
$109$	−81.9201	+	141.890i	−0.751560	+	1.30174i	−0.947066	+	0.321038i	$0.895968\pi$
$110$		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	$0.154492\pi$
$113$			105.434i			0.933040i	−0.884511	+	0.466520i	$0.845508\pi$
$114$	−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	$0.0678121\pi$
$127$			53.7033i			0.422860i	−0.977393	+	0.211430i	$0.932188\pi$
$128$	−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	−0.680700	−	0.732562i	$-0.738324\pi$
$131$	−50.6489	+	29.2421i	−0.386632	+	0.223222i	0.294068	+	0.955785i	$0.404991\pi$
$132$	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	0.537809	−	0.843067i	$-0.319252\pi$
$137$	10.4936	+	6.05848i	0.0765956	+	0.0442225i	−0.461213	+	0.887289i	$0.652586\pi$
$138$	−49.1141	−	85.0680i	−0.355899	−	0.616435i
$139$		−	45.2562i		−	0.325584i	−0.986660	−	0.162792i	$-0.947950\pi$
$139$		−	45.2562i		−	0.325584i	0.986660	−	0.162792i	$-0.0520500\pi$
$140$		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	0.767908	−	0.640561i	$-0.221298\pi$
$149$	−25.4474	−	44.0762i	−0.170788	−	0.295814i	−0.938696	+	0.344747i	$0.887965\pi$
$150$		0			0
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	−0.477498	−	0.878633i	$-0.658456\pi$
$151$	78.8476	−	136.568i	0.522169	−	0.904424i	0.999667	−	0.0257911i	$-0.00821047\pi$
$152$	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	0.464643	+	0.885498i	$0.346183\pi$
$157$	−83.9231	+	145.359i	−0.534542	+	0.925854i	−0.999185	+	0.0403562i	$0.987151\pi$
$158$	−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	−0.999412	−	0.0342839i	$-0.989085\pi$
$163$	−239.517	+	138.285i	−1.46943	+	0.848374i	−0.470015	+	0.882658i	$0.655752\pi$
$164$	−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	0.981815	−	0.189842i	$-0.0607977\pi$
$173$	56.4843	+	97.8337i	0.326499	+	0.565513i	−0.655316	+	0.755355i	$0.727464\pi$
$174$		−	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	0.135384	−	0.990793i	$-0.456773\pi$
$179$	165.708	−	287.015i	0.925744	−	1.60344i	0.790360	−	0.612642i	$-0.209893\pi$
$180$		0			0
$181$			213.328i			1.17861i	0.807912	+	0.589303i	$0.200598\pi$
$181$			213.328i			1.17861i	−0.807912	+	0.589303i	$0.799402\pi$
$182$	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	0.940210	−	0.340596i	$-0.110629\pi$
$191$	33.4517	+	57.9400i	0.175140	+	0.303351i	−0.765070	+	0.643947i	$0.777296\pi$
$192$	6.92820	−	12.0000i	0.0360844	−	0.0625000i
$193$	−97.5179	−	56.3020i	−0.505274	−	0.291720i	0.225615	−	0.974217i	$-0.427561\pi$
$193$	−97.5179	−	56.3020i	−0.505274	−	0.291720i	−0.730889	+	0.682497i	$0.760894\pi$
$194$	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	$-0.950502\pi$
$197$		−	61.0211i		−	0.309752i	0.987934	−	0.154876i	$-0.0494978\pi$
$198$	−63.8772	+	36.8795i	−0.322612	+	0.186260i
$199$	165.554	+	95.5826i	0.831929	+	0.480314i	0.854513	−	0.519431i	$-0.173856\pi$
$199$	165.554	+	95.5826i	0.831929	+	0.480314i	−0.0225837	+	0.999745i	$0.507189\pi$
$200$		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	−0.883183	−	0.469028i	$-0.844604\pi$
$227$	−8.03620	+	13.9191i	−0.0354018	+	0.0613176i	0.847782	+	0.530345i	$0.177938\pi$
$228$	−7.62546	−	4.40256i	−0.0334450	−	0.0193095i
$229$	−128.261	+	74.0517i	−0.560093	+	0.323370i	−0.753183	−	0.657811i	$-0.771482\pi$
$229$	−128.261	+	74.0517i	−0.560093	+	0.323370i	0.193090	+	0.981181i	$0.438149\pi$
$230$		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	0.172488	−	0.985012i	$-0.444819\pi$
$233$	259.044	−	149.559i	1.11178	−	0.641885i	0.939289	+	0.343127i	$0.111486\pi$
$234$	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	0.234399	−	0.972140i	$-0.424688\pi$
$241$	−118.162	−	68.2209i	−0.490299	−	0.283074i	−0.724699	+	0.689066i	$0.758021\pi$
$242$	−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	$0.364230\pi$
$251$			457.024i			1.82081i	−0.413717	+	0.910406i	$0.635770\pi$
$252$	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	0.910555	−	0.413388i	$-0.135655\pi$
$257$	24.9991	+	43.2997i	0.0972726	+	0.168481i	−0.813282	+	0.581869i	$0.802321\pi$
$258$	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	0.769127	−	0.639096i	$-0.220691\pi$
$263$	157.857	+	91.1388i	0.600217	+	0.346535i	−0.168910	+	0.985631i	$0.554025\pi$
$264$	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	0.559336	−	0.828941i	$-0.311056\pi$
$269$	32.5814	+	18.8109i	0.121120	+	0.0699289i	−0.438216	+	0.898870i	$0.644389\pi$
$270$		0			0
$271$	175.576	−	101.369i	0.647880	−	0.374054i	−0.139763	−	0.990185i	$-0.544634\pi$
$271$	175.576	−	101.369i	0.647880	−	0.374054i	0.787644	+	0.616131i	$0.211301\pi$
$272$	−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	0.0427390	−	0.999086i	$-0.486392\pi$
$277$	−221.912	−	128.121i	−0.801126	−	0.462530i	−0.843865	+	0.536556i	$0.819725\pi$
$278$	−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	0.237562	−	0.971372i	$-0.423652\pi$
$283$	271.684	−	470.571i	0.960014	−	1.66279i	0.722452	−	0.691421i	$-0.243015\pi$
$284$	−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	0.281865	−	0.959454i	$-0.409047\pi$
$311$	−126.924	−	73.2794i	−0.408115	−	0.235625i	−0.689979	+	0.723829i	$0.742380\pi$
$312$	−30.6556	−	17.6990i	−0.0982551	−	0.0567276i
$313$	−112.435	−	194.744i	−0.359218	−	0.622184i	0.628612	−	0.777719i	$-0.283623\pi$
$313$	−112.435	−	194.744i	−0.359218	−	0.622184i	−0.987830	+	0.155535i	$0.950290\pi$
$314$			237.370i			0.755957i
$315$		0			0
$316$	−48.2168			−0.152585
$317$	−195.918	+	113.113i	−0.618038	+	0.356825i	−0.776105	−	0.630604i	$-0.782807\pi$
$317$	−195.918	+	113.113i	−0.618038	+	0.356825i	0.158067	+	0.987428i	$0.449474\pi$
$318$	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	0.740888	−	0.671628i	$-0.234405\pi$
$331$	−69.9082	−	121.085i	−0.211203	−	0.365814i	−0.952091	+	0.305814i	$0.901071\pi$
$332$	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	$0.0142261\pi$
$337$			30.1128i			0.0893556i	−0.999001	+	0.0446778i	$0.985774\pi$
$338$	−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	0.919266	−	0.393636i	$-0.128783\pi$
$347$	360.186	+	207.954i	1.03800	+	0.599290i	0.118734	+	0.992926i	$0.462116\pi$
$348$	−81.4202	−	141.024i	−0.233966	−	0.405241i
$349$			594.950i			1.70473i	0.522950	+	0.852363i	$0.324831\pi$
$349$			594.950i			1.70473i	−0.522950	+	0.852363i	$0.675169\pi$
$350$		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	−0.483795	−	0.875181i	$-0.660742\pi$
$353$	182.159	−	315.509i	0.516031	−	0.893793i	0.999827	−	0.0186116i	$-0.00592459\pi$
$354$	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	−0.878094	−	0.478488i	$-0.841185\pi$
$359$	−306.381	−	530.668i	−0.853430	−	1.47818i	0.0246647	−	0.999696i	$-0.492148\pi$
$360$		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	−0.305738	−	0.952116i	$-0.598903\pi$
$367$	246.509	−	426.967i	0.671687	−	1.16340i	0.977425	−	0.211281i	$-0.0677635\pi$
$368$	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	−0.679570	−	0.733611i	$-0.737834\pi$
$373$	−143.243	+	82.7013i	−0.384029	+	0.221719i	0.295541	+	0.955330i	$0.404500\pi$
$374$	−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	0.635098	−	0.772432i	$-0.280960\pi$
$383$	−134.585	−	233.108i	−0.351396	−	0.608636i	−0.986494	+	0.163795i	$0.947626\pi$
$384$		−	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	0.382487	+	0.923961i	$0.375068\pi$
$389$	−236.874	+	410.277i	−0.608930	+	1.05470i	−0.991417	+	0.130737i	$0.958266\pi$
$390$		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	−0.983772	−	0.179424i	$-0.942577\pi$
$397$	−256.967	−	445.080i	−0.647271	−	1.12111i	0.336500	−	0.941683i	$-0.390757\pi$
$398$	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	0.999966	+	0.00827591i	$0.00263433\pi$
$401$	203.367	+	352.242i	0.507150	+	0.878410i	−0.492816	+	0.870134i	$0.664032\pi$
$402$	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	0.917617	−	0.397467i	$-0.130111\pi$
$409$	422.173	+	243.742i	1.03221	+	0.595946i	0.114592	+	0.993413i	$0.463444\pi$
$410$		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	$0.229028\pi$
$419$			552.257i			1.31804i	−0.752127	+	0.659018i	$0.770972\pi$
$420$		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	0.435027	+	0.900417i	$0.356739\pi$
$431$	−242.339	+	419.743i	−0.562271	+	0.973881i	−0.997298	+	0.0734641i	$0.976595\pi$
$432$	−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	−0.631614	−	0.775283i	$-0.717607\pi$
$439$	−121.167	+	69.9559i	−0.276007	+	0.159353i	0.355607	+	0.934635i	$0.384274\pi$
$440$		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	−0.484188	−	0.874964i	$-0.660885\pi$
$443$	13.9364	−	8.04616i	0.0314591	−	0.0181629i	0.515647	+	0.856801i	$0.327552\pi$
$444$	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	−0.732494	+	0.680773i	$0.761644\pi$
$457$	−771.557	+	445.459i	−1.68831	+	0.974745i	−0.955814	+	0.293972i	$0.905023\pi$
$458$	−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	$-0.803367\pi$
$461$		−	534.019i		−	1.15839i	0.815188	−	0.579196i	$-0.196633\pi$
$462$	−270.062	+	126.200i	−0.584550	+	0.273159i
$463$		−	158.679i		−	0.342719i	−0.985209	−	0.171359i	$-0.945184\pi$
$463$		−	158.679i		−	0.342719i	0.985209	−	0.171359i	$-0.0548159\pi$
$464$	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	0.799690	−	0.600413i	$-0.204997\pi$
$467$	−56.0995	−	97.1671i	−0.120127	−	0.208067i	−0.919818	+	0.392346i	$0.871664\pi$
$468$	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	0.971076	−	0.238772i	$-0.0767450\pi$
$479$	598.669	+	345.642i	1.24983	+	0.721590i	0.278755	+	0.960362i	$0.410078\pi$
$480$		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	−0.304643	−	0.952467i	$-0.598537\pi$
$487$	−624.248	−	360.410i	−1.28182	−	0.740062i	−0.977182	+	0.212405i	$0.931870\pi$
$488$	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	−0.854135	−	0.520052i	$-0.825913\pi$
$499$	−437.845	−	758.370i	−0.877445	−	1.51978i	−0.0233104	−	0.999728i	$-0.507421\pi$
$500$		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	0.312921	−	0.949779i	$-0.398692\pi$
$509$	657.585	−	379.657i	1.29191	−	0.745887i	0.978993	+	0.203892i	$0.0653591\pi$
$510$		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	0.345220	−	0.938522i	$-0.387804\pi$
$521$	−153.671	−	88.7220i	−0.294954	−	0.170292i	−0.640174	+	0.768230i	$0.721138\pi$
$522$	172.718	+	99.7190i	0.330878	+	0.191033i
$523$	−52.6094	−	91.1221i	−0.100592	−	0.174230i	0.811337	−	0.584579i	$-0.198740\pi$
$523$	−52.6094	−	91.1221i	−0.100592	−	0.174230i	−0.911929	+	0.410349i	$0.865407\pi$
$524$			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	0.965009	−	0.262216i	$-0.0844534\pi$
$541$	138.181	+	239.337i	0.255419	+	0.442398i	−0.709591	+	0.704614i	$0.751120\pi$
$542$	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	$0.317150\pi$
$547$			918.409i			1.67899i	−0.543366	+	0.839496i	$0.682850\pi$
$548$	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	−0.195675	−	0.980669i	$-0.562690\pi$
$557$	−636.538	−	367.505i	−1.14280	−	0.659794i	−0.947122	+	0.320875i	$0.896023\pi$
$558$	−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	−0.221056	−	0.975261i	$-0.570950\pi$
$563$	413.283	−	715.827i	0.734073	−	1.27145i	0.955129	−	0.296191i	$-0.0957164\pi$
$564$	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	0.610571	−	0.791961i	$-0.290940\pi$
$569$	−216.546	−	375.069i	−0.380573	−	0.659172i	−0.991144	+	0.132790i	$0.957607\pi$
$570$		0			0
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	−0.995976	−	0.0896166i	$-0.971436\pi$
$571$	−240.036	+	415.754i	−0.420378	+	0.728116i	0.575598	+	0.817733i	$0.304769\pi$
$572$	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	−0.825798	−	0.563966i	$-0.809275\pi$
$577$	43.5695	−	75.4646i	0.0755104	−	0.130788i	0.901308	+	0.433179i	$0.142608\pi$
$578$	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	0.716585	−	0.697499i	$-0.245704\pi$
$593$	−145.735	−	252.421i	−0.245760	−	0.425668i	−0.962345	+	0.271831i	$0.912371\pi$
$594$		−	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	−0.501103	−	0.865388i	$-0.667072\pi$
$599$	298.839	−	517.604i	0.498896	−	0.864114i	0.999999	+	0.00127378i	$0.000405456\pi$
$600$		0			0
$601$			447.444i			0.744499i	0.928133	+	0.372250i	$0.121413\pi$
$601$			447.444i			0.744499i	−0.928133	+	0.372250i	$0.878587\pi$
$602$	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	0.999961	+	0.00887709i	$0.00282570\pi$
$607$	308.155	+	533.739i	0.507668	+	0.879307i	−0.492293	+	0.870430i	$0.663841\pi$
$608$	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	0.407542	−	0.913186i	$-0.366386\pi$
$613$	−110.052	−	63.5384i	−0.179530	−	0.103651i	−0.587072	+	0.809535i	$0.699719\pi$
$614$	−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	$0.0176949\pi$
$617$			68.5630i			0.111123i	−0.998455	+	0.0555616i	$0.982305\pi$
$618$	−126.901	+	73.2664i	−0.205342	+	0.118554i
$619$	−833.529	−	481.238i	−1.34657	−	0.777445i	−0.358812	−	0.933410i	$-0.616818\pi$
$619$	−833.529	−	481.238i	−1.34657	−	0.777445i	−0.987763	+	0.155965i	$0.950151\pi$
$620$		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	−0.805000	−	0.593275i	$-0.797835\pi$
$641$	71.3374	−	123.560i	0.111291	−	0.192761i	0.916291	+	0.400513i	$0.131168\pi$
$642$	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	−0.802810	−	0.596235i	$-0.796663\pi$
$647$	74.3724	−	128.817i	0.114950	−	0.199098i	0.917760	+	0.397136i	$0.129996\pi$
$648$	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	−0.678680	−	0.734434i	$-0.737448\pi$
$653$	−249.434	+	144.011i	−0.381982	+	0.220537i	0.296698	+	0.954971i	$0.404114\pi$
$654$	−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	−0.0434835	−	0.999054i	$-0.513846\pi$
$661$	−615.015	−	355.079i	−0.930432	−	0.537185i	−0.886948	+	0.461869i	$0.847179\pi$
$662$	−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	$0.336855\pi$
$673$			1173.04i			1.74301i	−0.490389	+	0.871504i	$0.663145\pi$
$674$	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	1.00000		0.000393478i	$0.000125248\pi$
$677$	338.731	+	586.699i	0.500341	+	0.866616i	−0.499659	+	0.866222i	$0.666541\pi$
$678$	−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	−0.130032	−	0.991510i	$-0.541508\pi$
$683$	−719.691	−	415.514i	−1.05372	−	0.608366i	−0.923689	+	0.383144i	$0.874841\pi$
$684$	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	−0.0541345	−	0.998534i	$-0.517240\pi$
$691$	541.436	−	312.598i	0.783554	−	0.452385i	0.837688	+	0.546149i	$0.183907\pi$
$692$	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	0.534955	−	0.844881i	$-0.320329\pi$
$709$	−329.126	−	570.062i	−0.464211	−	0.804037i	−0.999166	+	0.0408438i	$0.986995\pi$
$710$		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	0.636975	−	0.770884i	$-0.280185\pi$
$719$	1166.99	−	673.760i	1.62307	−	0.937079i	0.986093	−	0.166195i	$-0.0531481\pi$
$720$		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	0.581476	−	0.813564i	$-0.302476\pi$
$733$	−303.337	−	525.395i	−0.413829	−	0.716773i	−0.995305	+	0.0967907i	$0.969142\pi$
$734$		−	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	−0.364817	−	0.931079i	$-0.618868\pi$
$739$	461.084	−	798.622i	0.623930	−	1.08068i	0.988747	−	0.149599i	$-0.0477984\pi$
$740$		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	$-0.997130\pi$
$743$		−	13.3994i		−	0.0180342i	0.999959	−	0.00901712i	$-0.00287028\pi$
$744$	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	−0.962389	−	0.271676i	$-0.912422\pi$
$751$	−538.071	−	931.967i	−0.716473	−	1.24097i	0.245916	−	0.969291i	$-0.420911\pi$
$752$	−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	$-0.946319\pi$
$757$		−	254.117i		−	0.335690i	0.985813	−	0.167845i	$-0.0536807\pi$
$758$	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	−0.877283	−	0.479973i	$-0.840646\pi$
$761$	−685.095	+	395.540i	−0.900256	+	0.519763i	−0.0229729	+	0.999736i	$0.507313\pi$
$762$	−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	$-0.902362\pi$
$769$		−	464.403i		−	0.603905i	0.953323	−	0.301952i	$-0.0976384\pi$
$770$		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	−0.495377	−	0.868678i	$-0.664970\pi$
$773$	390.063	−	675.608i	0.504609	−	0.874008i	0.999986	−	0.00533002i	$-0.00169661\pi$
$774$	−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	0.223449	+	0.974716i	$0.428268\pi$
$787$	−576.402	+	998.358i	−0.732404	+	1.26856i	−0.955853	+	0.293845i	$0.905065\pi$
$788$	−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	−0.870247	−	0.492616i	$-0.836041\pi$
$809$	−6.88050	+	11.9174i	−0.00850495	+	0.0147310i	0.861742	+	0.507347i	$0.169374\pi$
$810$		0			0
$811$			1274.65i			1.57170i	0.618416	+	0.785851i	$0.287775\pi$
$811$			1274.65i			1.57170i	−0.618416	+	0.785851i	$0.712225\pi$
$812$	−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	0.631316	−	0.775526i	$-0.282515\pi$
$821$	−292.249	−	506.190i	−0.355967	−	0.616553i	−0.987283	+	0.158973i	$0.949182\pi$
$822$	−14.8402	+	25.7040i	−0.0180538	+	0.0312700i
$823$	−70.1196	−	40.4835i	−0.0851999	−	0.0491902i	0.456795	−	0.889572i	$-0.348997\pi$
$823$	−70.1196	−	40.4835i	−0.0851999	−	0.0491902i	−0.541995	+	0.840382i	$0.682331\pi$
$824$	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	$-0.556016\pi$
$827$		−	1628.46i		−	1.96911i	0.175072	−	0.984556i	$-0.443984\pi$
$828$	208.373	−	120.304i	0.251659	−	0.145295i
$829$	761.982	+	439.931i	0.919158	+	0.530676i	0.883366	−	0.468683i	$-0.155271\pi$
$829$	761.982	+	439.931i	0.919158	+	0.530676i	0.0357920	+	0.999359i	$0.488605\pi$
$830$		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	$-0.873922\pi$
$839$		−	647.389i		−	0.771619i	0.922578	−	0.385810i	$-0.126078\pi$
$840$		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	−0.989961	−	0.141339i	$-0.954859\pi$
$857$	−319.299	+	553.041i	−0.372577	+	0.645322i	0.617384	+	0.786662i	$0.288192\pi$
$858$	−266.477	−	153.850i	−0.310579	−	0.179313i
$859$	−1097.36	+	633.562i	−1.27749	+	0.737558i	−0.976386	−	0.216034i	$-0.930688\pi$
$859$	−1097.36	+	633.562i	−1.27749	+	0.737558i	−0.301102	+	0.953592i	$0.597355\pi$
$860$		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	−0.393047	−	0.919518i	$-0.628579\pi$
$863$	178.430	−	103.017i	0.206756	−	0.119371i	0.599803	+	0.800148i	$0.295246\pi$
$864$	−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	−0.0341955	−	0.999415i	$-0.510887\pi$
$877$	714.076	−	412.272i	0.814226	−	0.470093i	0.848421	+	0.529322i	$0.177554\pi$
$878$	−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	$-0.924070\pi$
$881$		−	416.337i		−	0.472574i	0.971683	−	0.236287i	$-0.0759305\pi$
$882$	−35.7666	+	204.790i	−0.0405517	+	0.232188i
$883$		−	650.529i		−	0.736726i	−0.929682	−	0.368363i	$-0.879918\pi$
$883$		−	650.529i		−	0.736726i	0.929682	−	0.368363i	$-0.120082\pi$
$884$	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	0.751724	−	0.659478i	$-0.229223\pi$
$887$	−173.198	−	299.987i	−0.195262	−	0.338204i	−0.946987	+	0.321273i	$0.895889\pi$
$888$	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	0.285802	−	0.958289i	$-0.407740\pi$
$907$	−363.888	−	210.091i	−0.401199	−	0.231633i	−0.687001	+	0.726656i	$0.741073\pi$
$908$	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	0.831828	−	0.555034i	$-0.187295\pi$
$919$	−59.5137	−	103.081i	−0.0647592	−	0.112166i	−0.896587	+	0.442867i	$0.853961\pi$
$920$		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	−0.666059	−	0.745899i	$-0.732020\pi$
$929$	−328.049	+	189.399i	−0.353121	+	0.203874i	0.312938	+	0.949773i	$0.398687\pi$
$930$		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	−0.293414	−	0.955985i	$-0.594791\pi$
$941$	−1193.22	−	688.903i	−1.26803	−	0.732097i	−0.974615	+	0.223889i	$0.928125\pi$
$942$	−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	−0.266916	−	0.963720i	$-0.586005\pi$
$947$	411.218	−	237.417i	0.434232	−	0.250704i	0.701148	+	0.713016i	$0.252671\pi$
$948$	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	$0.0289045\pi$
$953$			172.839i			0.181363i	−0.995880	+	0.0906813i	$0.971096\pi$
$954$	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	$-0.784861\pi$
$967$		−	1209.88i		−	1.25117i	0.780158	−	0.625583i	$-0.215139\pi$
$968$	−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	−0.805923	−	0.592020i	$-0.798330\pi$
$971$	−675.990	+	390.283i	−0.696180	+	0.401939i	0.109743	+	0.993960i	$0.464997\pi$
$972$	−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	−0.413955	−	0.910297i	$-0.635853\pi$
$977$	−1376.86	−	794.931i	−1.40927	−	0.813644i	−0.995318	+	0.0966527i	$0.969186\pi$
$978$	−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	−0.630582	−	0.776123i	$-0.717184\pi$
$983$	350.785	−	607.577i	0.356851	−	0.618084i	0.987433	+	0.158039i	$0.0505171\pi$
$984$	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	−0.950198	−	0.311646i	$-0.899120\pi$
$991$	−203.359	+	352.228i	−0.205206	+	0.355427i	0.744992	+	0.667073i	$0.232453\pi$
$992$	−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	−0.611474	−	0.791264i	$-0.709423\pi$
$997$	378.379	−	655.372i	0.379518	−	0.657344i	0.990992	+	0.133920i	$0.0427565\pi$
$998$	−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.199.15		32
5.2	odd	4		1050.3.p.i.451.5		16
5.3	odd	4		210.3.o.b.31.2	✓	16
5.4	even	2	inner	1050.3.q.e.199.2		32
7.5	odd	6	inner	1050.3.q.e.649.2		32
15.8	even	4		630.3.v.c.451.8		16
35.3	even	12		1470.3.f.d.391.11		16
35.12	even	12		1050.3.p.i.901.5		16
35.18	odd	12		1470.3.f.d.391.13		16
35.19	odd	6	inner	1050.3.q.e.649.15		32
35.33	even	12		210.3.o.b.61.2	yes	16
105.68	odd	12		630.3.v.c.271.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.2	✓	16	5.3	odd	4
210.3.o.b.61.2	yes	16	35.33	even	12
630.3.v.c.271.8		16	105.68	odd	12
630.3.v.c.451.8		16	15.8	even	4
1050.3.p.i.451.5		16	5.2	odd	4
1050.3.p.i.901.5		16	35.12	even	12
1050.3.q.e.199.2		32	5.4	even	2	inner
1050.3.q.e.199.15		32	1.1	even	1	trivial
1050.3.q.e.649.2		32	7.5	odd	6	inner
1050.3.q.e.649.15		32	35.19	odd	6	inner
1470.3.f.d.391.11		16	35.3	even	12
1470.3.f.d.391.13		16	35.18	odd	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

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