LMFDB - Embedded newform 1050.3.q.e.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1050.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
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			199.3
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.50174 + 2.59373i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.50174 + 2.59373i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.13478 + 8.89370i) q^{11} +(-1.73205 - 3.00000i) q^{12} -7.02340 q^{13} +(6.12892 - 7.77408i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.8741 - 27.4947i) q^{17} +(3.67423 + 2.12132i) q^{18} +(26.9408 - 15.5543i) q^{19} +(-1.74007 + 11.9988i) q^{21} -14.5234i q^{22} +(-20.5146 + 11.8441i) q^{23} +(4.24264 + 2.44949i) q^{24} +(8.60187 - 4.96629i) q^{26} -5.19615 q^{27} +(-2.00927 + 13.8551i) q^{28} -9.19673 q^{29} +(17.4511 + 10.0754i) q^{31} +(4.89898 + 2.82843i) q^{32} +(8.89370 + 15.4043i) q^{33} +44.8986i q^{34} -6.00000 q^{36} +(-41.7118 + 24.0823i) q^{37} +(-21.9971 + 38.1001i) q^{38} +(-6.08244 + 10.5351i) q^{39} +65.1226i q^{41} +(-6.35331 - 15.9259i) q^{42} -3.03497i q^{43} +(10.2696 + 17.7874i) q^{44} +(16.7501 - 29.0120i) q^{46} +(30.9732 + 53.6472i) q^{47} -6.92820 q^{48} +(35.5451 - 33.7275i) q^{49} +(-27.4947 - 47.6222i) q^{51} +(-7.02340 + 12.1649i) q^{52} +(-1.19642 - 0.690751i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-7.33617 - 18.3897i) q^{56} -53.8817i q^{57} +(11.2636 - 6.50307i) q^{58} +(95.1064 + 54.9097i) q^{59} +(-34.3741 + 19.8459i) q^{61} -28.4976 q^{62} +(16.4913 + 13.0014i) q^{63} -8.00000 q^{64} +(-21.7850 - 12.5776i) q^{66} +(13.7863 + 7.95952i) q^{67} +(-31.7481 - 54.9893i) q^{68} +41.0292i q^{69} +53.3489 q^{71} +(7.34847 - 4.24264i) q^{72} +(-36.1901 + 62.6830i) q^{73} +(34.0576 - 58.9894i) q^{74} -62.2172i q^{76} +(10.3171 - 71.1427i) q^{77} -17.2037i q^{78} +(53.2229 + 92.1847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.0486 - 79.7586i) q^{82} +49.4298 q^{83} +(19.0425 + 15.0127i) q^{84} +(2.14605 + 3.71707i) q^{86} +(-7.96460 + 13.7951i) q^{87} +(-25.1552 - 14.5234i) q^{88} +(142.807 - 82.4499i) q^{89} +(45.6643 - 18.2168i) q^{91} +47.3765i q^{92} +(30.2262 - 17.4511i) q^{93} +(-75.8686 - 43.8027i) q^{94} +(8.48528 - 4.89898i) q^{96} -49.4799 q^{97} +(-19.6848 + 66.4418i) q^{98} +30.8087 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
$7$	−6.50174	+	2.59373i	−0.928819	+	0.370533i
$7$	−6.50174	+	2.59373i	−0.928819	+	0.370533i
$8$			2.82843i			0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−5.13478	+	8.89370i	−0.466798	+	0.808518i	−0.999281	−	0.0379228i	$-0.987926\pi$
$11$	−5.13478	+	8.89370i	−0.466798	+	0.808518i	0.532482	+	0.846441i	$0.321259\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	−7.02340			−0.540261			−0.270131	−	0.962824i	$-0.587067\pi$
$13$	−7.02340			−0.540261			−0.270131	+	0.962824i	$0.587067\pi$
$14$	6.12892	−	7.77408i	0.437780	−	0.555291i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	15.8741	−	27.4947i	0.933768	−	1.61733i	0.156951	−	0.987606i	$-0.449833\pi$
$17$	15.8741	−	27.4947i	0.933768	−	1.61733i	0.776816	−	0.629727i	$-0.216833\pi$
$18$	3.67423	+	2.12132i	0.204124	+	0.117851i
$19$	26.9408	−	15.5543i	1.41794	−	0.818648i	0.421822	−	0.906679i	$-0.361391\pi$
$19$	26.9408	−	15.5543i	1.41794	−	0.818648i	0.996118	+	0.0880311i	$0.0280575\pi$
$20$		0			0
$21$	−1.74007	+	11.9988i	−0.0828607	+	0.571373i
$22$		−	14.5234i		−	0.660152i
$23$	−20.5146	+	11.8441i	−0.891940	+	0.514962i	−0.874576	−	0.484888i	$-0.838860\pi$
$23$	−20.5146	+	11.8441i	−0.891940	+	0.514962i	−0.0173632	+	0.999849i	$0.505527\pi$
$24$	4.24264	+	2.44949i	0.176777	+	0.102062i
$25$		0			0
$26$	8.60187	−	4.96629i	0.330841	−	0.191011i
$27$	−5.19615			−0.192450
$28$	−2.00927	+	13.8551i	−0.0717595	+	0.494824i
$29$	−9.19673			−0.317129			−0.158564	−	0.987349i	$-0.550687\pi$
$29$	−9.19673			−0.317129			−0.158564	+	0.987349i	$0.550687\pi$
$30$		0			0
$31$	17.4511	+	10.0754i	0.562940	+	0.325013i	0.754325	−	0.656502i	$-0.227965\pi$
$31$	17.4511	+	10.0754i	0.562940	+	0.325013i	−0.191385	+	0.981515i	$0.561298\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	8.89370	+	15.4043i	0.269506	+	0.466798i
$34$			44.8986i			1.32055i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	−41.7118	+	24.0823i	−1.12735	+	0.650874i	−0.943266	−	0.332037i	$-0.892264\pi$
$37$	−41.7118	+	24.0823i	−1.12735	+	0.650874i	−0.184081	+	0.982911i	$0.558931\pi$
$38$	−21.9971	+	38.1001i	−0.578871	+	1.00263i
$39$	−6.08244	+	10.5351i	−0.155960	+	0.270131i
$40$		0			0
$41$			65.1226i			1.58836i	0.607685	+	0.794178i	$0.292098\pi$
$41$			65.1226i			1.58836i	−0.607685	+	0.794178i	$0.707902\pi$
$42$	−6.35331	−	15.9259i	−0.151269	−	0.379189i
$43$		−	3.03497i		−	0.0705807i	−0.999377	−	0.0352904i	$-0.988764\pi$
$43$		−	3.03497i		−	0.0705807i	0.999377	−	0.0352904i	$-0.0112356\pi$
$44$	10.2696	+	17.7874i	0.233399	+	0.404259i
$45$		0			0
$46$	16.7501	−	29.0120i	0.364133	−	0.630697i
$47$	30.9732	+	53.6472i	0.659005	+	1.14143i	0.980874	+	0.194645i	$0.0623556\pi$
$47$	30.9732	+	53.6472i	0.659005	+	1.14143i	−0.321869	+	0.946784i	$0.604311\pi$
$48$	−6.92820			−0.144338
$49$	35.5451	−	33.7275i	0.725411	−	0.688316i
$50$		0			0
$51$	−27.4947	−	47.6222i	−0.539111	−	0.933768i
$52$	−7.02340	+	12.1649i	−0.135065	+	0.233940i
$53$	−1.19642	−	0.690751i	−0.0225739	−	0.0130330i	0.488671	−	0.872468i	$-0.337482\pi$
$53$	−1.19642	−	0.690751i	−0.0225739	−	0.0130330i	−0.511244	+	0.859435i	$0.670815\pi$
$54$	6.36396	−	3.67423i	0.117851	−	0.0680414i
$55$		0			0
$56$	−7.33617	−	18.3897i	−0.131003	−	0.328387i
$57$		−	53.8817i		−	0.945293i
$58$	11.2636	−	6.50307i	0.194201	−	0.112122i
$59$	95.1064	+	54.9097i	1.61197	+	0.930673i	0.988912	+	0.148500i	$0.0474445\pi$
$59$	95.1064	+	54.9097i	1.61197	+	0.930673i	0.623061	+	0.782173i	$0.285889\pi$
$60$		0			0
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	−0.754553	−	0.656239i	$-0.772146\pi$
$61$	−34.3741	+	19.8459i	−0.563510	+	0.325343i	0.191043	+	0.981582i	$0.438813\pi$
$62$	−28.4976			−0.459638
$63$	16.4913	+	13.0014i	0.261767	+	0.206372i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−21.7850	−	12.5776i	−0.330076	−	0.190570i
$67$	13.7863	+	7.95952i	0.205765	+	0.118799i	0.599342	−	0.800493i	$-0.295429\pi$
$67$	13.7863	+	7.95952i	0.205765	+	0.118799i	−0.393576	+	0.919292i	$0.628762\pi$
$68$	−31.7481	−	54.9893i	−0.466884	−	0.808667i
$69$			41.0292i			0.594626i
$70$		0			0
$71$	53.3489			0.751393			0.375696	−	0.926743i	$-0.377404\pi$
$71$	53.3489			0.751393			0.375696	+	0.926743i	$0.377404\pi$
$72$	7.34847	−	4.24264i	0.102062	−	0.0589256i
$73$	−36.1901	+	62.6830i	−0.495754	+	0.858672i	−0.999988	−	0.00489557i	$-0.998442\pi$
$73$	−36.1901	+	62.6830i	−0.495754	+	0.858672i	0.504234	+	0.863567i	$0.331775\pi$
$74$	34.0576	−	58.9894i	0.460237	−	0.797155i
$75$		0			0
$76$		−	62.2172i		−	0.818648i
$77$	10.3171	−	71.1427i	0.133989	−	0.923931i
$78$		−	17.2037i		−	0.220561i
$79$	53.2229	+	92.1847i	0.673707	+	1.16690i	0.976845	+	0.213948i	$0.0686325\pi$
$79$	53.2229	+	92.1847i	0.673707	+	1.16690i	−0.303138	+	0.952947i	$0.598034\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−46.0486	−	79.7586i	−0.561569	−	0.972666i
$83$	49.4298			0.595540			0.297770	−	0.954638i	$-0.403757\pi$
$83$	49.4298			0.595540			0.297770	+	0.954638i	$0.403757\pi$
$84$	19.0425	+	15.0127i	0.226697	+	0.178723i
$85$		0			0
$86$	2.14605	+	3.71707i	0.0249541	+	0.0432217i
$87$	−7.96460	+	13.7951i	−0.0915472	+	0.158564i
$88$	−25.1552	−	14.5234i	−0.285854	−	0.165038i
$89$	142.807	−	82.4499i	1.60458	−	0.926403i	0.614022	−	0.789289i	$-0.289551\pi$
$89$	142.807	−	82.4499i	1.60458	−	0.926403i	0.990555	−	0.137114i	$-0.0437826\pi$
$90$		0			0
$91$	45.6643	−	18.2168i	0.501805	−	0.200185i
$92$			47.3765i			0.514962i
$93$	30.2262	−	17.4511i	0.325013	−	0.187647i
$94$	−75.8686	−	43.8027i	−0.807113	−	0.465987i
$95$		0			0
$96$	8.48528	−	4.89898i	0.0883883	−	0.0510310i
$97$	−49.4799			−0.510102			−0.255051	−	0.966928i	$-0.582092\pi$
$97$	−49.4799			−0.510102			−0.255051	+	0.966928i	$0.582092\pi$
$98$	−19.6848	+	66.4418i	−0.200865	+	0.677977i
$99$	30.8087			0.311199
$100$		0			0
$101$	116.803	+	67.4364i	1.15647	+	0.667687i	0.950455	−	0.310863i	$-0.100618\pi$
$101$	116.803	+	67.4364i	1.15647	+	0.667687i	0.206012	+	0.978549i	$0.433951\pi$
$102$	67.3479	+	38.8833i	0.660274	+	0.381209i
$103$	−18.7010	−	32.3911i	−0.181563	−	0.314477i	0.760850	−	0.648928i	$-0.224782\pi$
$103$	−18.7010	−	32.3911i	−0.181563	−	0.314477i	−0.942413	+	0.334451i	$0.891449\pi$
$104$		−	19.8652i		−	0.191011i
$105$		0			0
$106$	1.95374			0.0184315
$107$	21.4739	−	12.3980i	0.200691	−	0.115869i	−0.396287	−	0.918127i	$-0.629701\pi$
$107$	21.4739	−	12.3980i	0.200691	−	0.115869i	0.596978	+	0.802258i	$0.296368\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−28.1448	+	48.7483i	−0.258209	+	0.447232i	−0.965762	−	0.259429i	$-0.916466\pi$
$109$	−28.1448	+	48.7483i	−0.258209	+	0.447232i	0.707553	+	0.706660i	$0.249799\pi$
$110$		0			0
$111$			83.4237i			0.751565i
$112$	21.9884	+	17.3352i	0.196325	+	0.154779i
$113$			74.9910i			0.663637i	0.943343	+	0.331818i	$0.107662\pi$
$113$			74.9910i			0.663637i	−0.943343	+	0.331818i	$0.892338\pi$
$114$	38.1001	+	65.9913i	0.334212	+	0.578871i
$115$		0			0
$116$	−9.19673	+	15.9292i	−0.0792822	+	0.137321i
$117$	10.5351	+	18.2473i	0.0900436	+	0.155960i
$118$	−155.308			−1.31617
$119$	−31.8952	+	219.936i	−0.268027	+	1.84820i
$120$		0			0
$121$	7.76807	+	13.4547i	0.0641989	+	0.111196i
$122$	28.0664	−	48.6124i	0.230052	−	0.398462i
$123$	97.6839	+	56.3978i	0.794178	+	0.458519i
$124$	34.9023	−	20.1508i	0.281470	−	0.162507i
$125$		0			0
$126$	−29.3910	−	4.26229i	−0.233262	−	0.0338277i
$127$		−	128.504i		−	1.01184i	−0.862580	−	0.505921i	$-0.831153\pi$
$127$		−	128.504i		−	1.01184i	0.862580	−	0.505921i	$-0.168847\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−4.55246	−	2.62836i	−0.0352904	−	0.0203749i
$130$		0			0
$131$	65.3818	−	37.7482i	0.499098	−	0.288154i	−0.229243	−	0.973369i	$-0.573625\pi$
$131$	65.3818	−	37.7482i	0.499098	−	0.288154i	0.728341	+	0.685215i	$0.240292\pi$
$132$	35.5748			0.269506
$133$	−134.819	+	171.007i	−1.01367	+	1.28577i
$134$	−22.5129			−0.168007
$135$		0			0
$136$	77.7667	+	44.8986i	0.571814	+	0.330137i
$137$	93.1121	+	53.7583i	0.679650	+	0.392396i	0.799723	−	0.600369i	$-0.204980\pi$
$137$	93.1121	+	53.7583i	0.679650	+	0.392396i	−0.120073	+	0.992765i	$0.538313\pi$
$138$	−29.0120	−	50.2503i	−0.210232	−	0.364133i
$139$		−	272.004i		−	1.95686i	−0.206576	−	0.978431i	$-0.566232\pi$
$139$		−	272.004i		−	1.95686i	0.206576	−	0.978431i	$-0.433768\pi$
$140$		0			0
$141$	107.294			0.760953
$142$	−65.3388	+	37.7234i	−0.460132	+	0.265658i
$143$	36.0636	−	62.4640i	0.252193	−	0.436811i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	102.361i		−	0.701102i
$147$	−19.8082	−	82.5266i	−0.134750	−	0.561405i
$148$			96.3294i			0.650874i
$149$	−41.7135	−	72.2498i	−0.279956	−	0.484898i	0.691417	−	0.722456i	$-0.256987\pi$
$149$	−41.7135	−	72.2498i	−0.279956	−	0.484898i	−0.971374	+	0.237557i	$0.923653\pi$
$150$		0			0
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	−0.995924	−	0.0901962i	$-0.971251\pi$
$151$	−63.3973	+	109.807i	−0.419850	+	0.727201i	0.576074	+	0.817397i	$0.304584\pi$
$152$	43.9942	+	76.2002i	0.289436	+	0.501317i
$153$	−95.2443			−0.622512
$154$	37.6696	+	94.4270i	0.244608	+	0.613162i
$155$		0			0
$156$	12.1649	+	21.0702i	0.0779800	+	0.135065i
$157$	−49.6184	+	85.9416i	−0.316041	+	0.547399i	−0.979658	−	0.200673i	$-0.935687\pi$
$157$	−49.6184	+	85.9416i	−0.316041	+	0.547399i	0.663617	+	0.748072i	$0.269020\pi$
$158$	−130.369	−	75.2685i	−0.825120	−	0.476383i
$159$	−2.07225	+	1.19642i	−0.0130330	+	0.00752463i
$160$		0			0
$161$	102.660	−	130.217i	0.637641	−	0.808799i
$162$		−	12.7279i		−	0.0785674i
$163$	241.603	−	139.490i	1.48223	−	0.855765i	0.482433	−	0.875933i	$-0.339753\pi$
$163$	241.603	−	139.490i	1.48223	−	0.855765i	0.999797	+	0.0201678i	$0.00642003\pi$
$164$	112.796	+	65.1226i	0.687779	+	0.397089i
$165$		0			0
$166$	−60.5389	+	34.9522i	−0.364692	+	0.210555i
$167$	29.9435			0.179302			0.0896511	−	0.995973i	$-0.471425\pi$
$167$	29.9435			0.179302			0.0896511	+	0.995973i	$0.471425\pi$
$168$	−33.9378	−	4.92167i	−0.202011	−	0.0292957i
$169$	−119.672			−0.708118
$170$		0			0
$171$	−80.8225	−	46.6629i	−0.472646	−	0.272883i
$172$	−5.25673	−	3.03497i	−0.0305624	−	0.0176452i
$173$	53.2530	+	92.2369i	0.307821	+	0.533161i	0.977885	−	0.209142i	$-0.0670670\pi$
$173$	53.2530	+	92.2369i	0.307821	+	0.533161i	−0.670065	+	0.742303i	$0.733734\pi$
$174$		−	22.5273i		−	0.129467i
$175$		0			0
$176$	41.0782			0.233399
$177$	164.729	−	95.1064i	0.930673	−	0.537324i
$178$	−116.602	+	201.960i	−0.655066	+	1.13461i
$179$	−119.986	+	207.822i	−0.670315	+	1.16102i	0.307500	+	0.951548i	$0.400508\pi$
$179$	−119.986	+	207.822i	−0.670315	+	1.16102i	−0.977815	+	0.209471i	$0.932826\pi$
$180$		0			0
$181$			309.322i			1.70896i	0.519482	+	0.854482i	$0.326125\pi$
$181$			309.322i			1.70896i	−0.519482	+	0.854482i	$0.673875\pi$
$182$	−43.0459	+	54.6004i	−0.236516	+	0.300002i
$183$			68.7483i			0.375674i
$184$	−33.5002	−	58.0241i	−0.182066	−	0.315348i
$185$		0			0
$186$	−24.6796	+	42.7464i	−0.132686	+	0.229819i
$187$	163.020	+	282.358i	0.871762	+	1.50994i
$188$	123.893			0.659005
$189$	33.7840	−	13.4774i	0.178751	−	0.0713091i
$190$		0			0
$191$	−1.54480	−	2.67567i	−0.00808796	−	0.0140088i	0.861953	−	0.506988i	$-0.169241\pi$
$191$	−1.54480	−	2.67567i	−0.00808796	−	0.0140088i	−0.870041	+	0.492979i	$0.835908\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	206.718	+	119.349i	1.07108	+	0.618387i	0.928476	−	0.371393i	$-0.121120\pi$
$193$	206.718	+	119.349i	1.07108	+	0.618387i	0.142602	+	0.989780i	$0.454453\pi$
$194$	60.6002	−	34.9875i	0.312372	−	0.180348i
$195$		0			0
$196$	−22.8726	−	95.2935i	−0.116697	−	0.486191i
$197$			291.539i			1.47989i	0.672666	+	0.739946i	$0.265149\pi$
$197$			291.539i			1.47989i	−0.672666	+	0.739946i	$0.734851\pi$
$198$	−37.7328	+	21.7850i	−0.190570	+	0.110025i
$199$	−209.224	−	120.796i	−1.05138	−	0.607013i	−0.128342	−	0.991730i	$-0.540966\pi$
$199$	−209.224	−	120.796i	−1.05138	−	0.607013i	−0.923034	+	0.384717i	$0.874299\pi$
$200$		0			0
$201$	23.8785	−	13.7863i	0.118799	−	0.0685885i
$202$	−190.739			−0.944252
$203$	59.7947	−	23.8538i	0.294555	−	0.117507i
$204$	−109.979			−0.539111
$205$		0			0
$206$	45.8080	+	26.4473i	0.222369	+	0.128385i
$207$	61.5438	+	35.5324i	0.297313	+	0.171654i
$208$	14.0468	+	24.3298i	0.0675327	+	0.116970i
$209$			319.472i			1.52857i
$210$		0			0
$211$	−263.018			−1.24653			−0.623266	−	0.782010i	$-0.714195\pi$
$211$	−263.018			−1.24653			−0.623266	+	0.782010i	$0.714195\pi$
$212$	−2.39283	+	1.38150i	−0.0112869	+	0.00651652i
$213$	46.2015	−	80.0234i	0.216908	−	0.375696i
$214$	−17.5334	+	30.3688i	−0.0819318	+	0.141910i
$215$		0			0
$216$		−	14.6969i		−	0.0680414i
$217$	−139.596	−	20.2442i	−0.643297	−	0.0932911i
$218$		−	79.6056i		−	0.365163i
$219$	62.6830	+	108.570i	0.286224	+	0.495754i
$220$		0			0
$221$	−111.490	+	193.106i	−0.504479	+	0.873783i
$222$	−58.9894	−	102.173i	−0.265718	−	0.460237i
$223$	−112.658			−0.505193			−0.252597	−	0.967572i	$-0.581285\pi$
$223$	−112.658			−0.505193			−0.252597	+	0.967572i	$0.581285\pi$
$224$	−39.1880	−	5.68306i	−0.174947	−	0.0253708i
$225$		0			0
$226$	−53.0266	−	91.8448i	−0.234631	−	0.406393i
$227$	24.5102	−	42.4529i	0.107974	−	0.187017i	−0.806975	−	0.590585i	$-0.798897\pi$
$227$	24.5102	−	42.4529i	0.107974	−	0.187017i	0.914950	+	0.403568i	$0.132230\pi$
$228$	−93.3258	−	53.8817i	−0.409324	−	0.236323i
$229$	−24.3476	+	14.0571i	−0.106321	+	0.0613846i	−0.552218	−	0.833700i	$-0.686218\pi$
$229$	−24.3476	+	14.0571i	−0.106321	+	0.0613846i	0.445896	+	0.895085i	$0.352885\pi$
$230$		0			0
$231$	−97.7792	−	77.0871i	−0.423286	−	0.333710i
$232$		−	26.0123i		−	0.112122i
$233$	152.596	−	88.1014i	0.654919	−	0.378117i	−0.135420	−	0.990788i	$-0.543238\pi$
$233$	152.596	−	88.1014i	0.654919	−	0.378117i	0.790338	+	0.612671i	$0.209905\pi$
$234$	−25.8056	−	14.8989i	−0.110280	−	0.0636704i
$235$		0			0
$236$	190.213	−	109.819i	0.805987	−	0.465337i
$237$	184.369			0.777930
$238$	−116.455	−	291.919i	−0.489306	−	1.22655i
$239$	−34.7150			−0.145251			−0.0726255	−	0.997359i	$-0.523138\pi$
$239$	−34.7150			−0.145251			−0.0726255	+	0.997359i	$0.523138\pi$
$240$		0			0
$241$	−229.871	−	132.716i	−0.953823	−	0.550690i	−0.0595563	−	0.998225i	$-0.518969\pi$
$241$	−229.871	−	132.716i	−0.953823	−	0.550690i	−0.894266	+	0.447535i	$0.852302\pi$
$242$	−19.0278	−	10.9857i	−0.0786273	−	0.0453955i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			79.3837i			0.325343i
$245$		0			0
$246$	−159.517			−0.648444
$247$	−189.216	+	109.244i	−0.766058	+	0.442284i
$248$	−28.4976	+	49.3592i	−0.114910	+	0.199029i
$249$	42.8075	−	74.1447i	0.171918	−	0.297770i
$250$		0			0
$251$			24.1723i			0.0963040i	0.998840	+	0.0481520i	$0.0153332\pi$
$251$			24.1723i			0.0963040i	−0.998840	+	0.0481520i	$0.984667\pi$
$252$	39.0104	−	15.5624i	0.154803	−	0.0617555i
$253$		−	243.268i		−	0.961533i
$254$	90.8659	+	157.384i	0.357740	+	0.619624i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	4.76874	+	8.25969i	0.0185554	+	0.0321389i	0.875154	−	0.483844i	$-0.160760\pi$
$257$	4.76874	+	8.25969i	0.0185554	+	0.0321389i	−0.856599	+	0.515983i	$0.827427\pi$
$258$	7.43413			0.0288145
$259$	208.736	−	264.766i	0.805932	−	1.02226i
$260$		0			0
$261$	13.7951	+	23.8938i	0.0528548	+	0.0915472i
$262$	−53.3840	+	92.4639i	−0.203756	+	0.352916i
$263$	114.197	+	65.9316i	0.434209	+	0.250691i	0.701138	−	0.713026i	$-0.252676\pi$
$263$	114.197	+	65.9316i	0.434209	+	0.250691i	−0.266929	+	0.963716i	$0.586009\pi$
$264$	−43.5701	+	25.1552i	−0.165038	+	0.0952848i
$265$		0			0
$266$	44.1980	−	304.771i	0.166158	−	1.14576i
$267$		−	285.615i		−	1.06972i
$268$	27.5726	−	15.9190i	0.102883	−	0.0593994i
$269$	32.8041	+	18.9395i	0.121949	+	0.0704070i	0.559733	−	0.828673i	$-0.310904\pi$
$269$	32.8041	+	18.9395i	0.121949	+	0.0704070i	−0.437785	+	0.899080i	$0.644237\pi$
$270$		0			0
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.207128	−	0.978314i	$-0.433588\pi$
$271$	313.801	−	181.173i	1.15794	−	0.668535i	0.950809	+	0.309779i	$0.100255\pi$
$272$	−126.992			−0.466884
$273$	12.2212	−	84.2726i	0.0447664	−	0.308691i
$274$	−152.051			−0.554932
$275$		0			0
$276$	71.0647	+	41.0292i	0.257481	+	0.148657i
$277$	−98.1197	−	56.6495i	−0.354223	−	0.204511i	0.312321	−	0.949977i	$-0.398894\pi$
$277$	−98.1197	−	56.6495i	−0.354223	−	0.204511i	−0.666544	+	0.745466i	$0.732227\pi$
$278$	192.336	+	333.135i	0.691855	+	1.19833i
$279$		−	60.4525i		−	0.216676i
$280$		0			0
$281$	−178.735			−0.636069			−0.318034	−	0.948079i	$-0.603023\pi$
$281$	−178.735			−0.636069			−0.318034	+	0.948079i	$0.603023\pi$
$282$	−131.408	+	75.8686i	−0.465987	+	0.269038i
$283$	−21.5843	+	37.3850i	−0.0762695	+	0.132103i	−0.901638	−	0.432492i	$-0.857634\pi$
$283$	−21.5843	+	37.3850i	−0.0762695	+	0.132103i	0.825368	+	0.564595i	$0.190968\pi$
$284$	53.3489	−	92.4030i	0.187848	−	0.325363i
$285$		0			0
$286$			102.003i			0.356655i
$287$	−168.910	−	423.410i	−0.588538	−	1.47530i
$288$		−	16.9706i		−	0.0589256i
$289$	−359.471	−	622.622i	−1.24384	−	2.15440i
$290$		0			0
$291$	−42.8508	+	74.2198i	−0.147254	+	0.255051i
$292$	72.3801	+	125.366i	0.247877	+	0.429336i
$293$	−15.4426			−0.0527050			−0.0263525	−	0.999653i	$-0.508389\pi$
$293$	−15.4426			−0.0527050			−0.0263525	+	0.999653i	$0.508389\pi$
$294$	82.6151	+	87.0675i	0.281004	+	0.296148i
$295$		0			0
$296$	−68.1151	−	117.979i	−0.230119	−	0.398577i
$297$	26.6811	−	46.2130i	0.0898354	−	0.155599i
$298$	102.177	+	58.9917i	0.342875	+	0.197959i
$299$	144.082	−	83.1859i	0.481881	−	0.278214i
$300$		0			0
$301$	7.87189	+	19.7326i	0.0261525	+	0.0655568i
$302$		−	179.315i		−	0.593757i
$303$	202.309	−	116.803i	0.667687	−	0.385489i
$304$	−107.763	−	62.2172i	−0.354485	−	0.204662i
$305$		0			0
$306$	116.650	−	67.3479i	0.381209	−	0.220091i
$307$	−234.648			−0.764327			−0.382163	−	0.924095i	$-0.624821\pi$
$307$	−234.648			−0.764327			−0.382163	+	0.924095i	$0.624821\pi$
$308$	−112.906	−	89.0125i	−0.366577	−	0.289002i
$309$	−64.7823			−0.209651
$310$		0			0
$311$	−345.352	−	199.389i	−1.11045	−	0.641121i	−0.171508	−	0.985183i	$-0.554864\pi$
$311$	−345.352	−	199.389i	−1.11045	−	0.641121i	−0.938947	+	0.344061i	$0.888197\pi$
$312$	−29.7978	−	17.2037i	−0.0955056	−	0.0551402i
$313$	64.6002	+	111.891i	0.206390	+	0.357479i	0.950575	−	0.310495i	$-0.100495\pi$
$313$	64.6002	+	111.891i	0.206390	+	0.357479i	−0.744184	+	0.667974i	$0.767162\pi$
$314$		−	140.342i		−	0.446949i
$315$		0			0
$316$	212.892			0.673707
$317$	348.632	−	201.283i	1.09979	−	0.634961i	0.163621	−	0.986523i	$-0.447683\pi$
$317$	348.632	−	201.283i	1.09979	−	0.634961i	0.936165	+	0.351562i	$0.114349\pi$
$318$	1.69199	−	2.93061i	0.00532072	−	0.00921575i
$319$	47.2232	−	81.7930i	0.148035	−	0.256404i
$320$		0			0
$321$		−	42.9479i		−	0.133794i
$322$	−33.6554	+	232.074i	−0.104520	+	0.720726i
$323$		−	987.640i		−	3.05771i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	−197.268	+	341.679i	−0.605118	+	1.04809i
$327$	48.7483	+	84.4345i	0.149077	+	0.258209i
$328$	−184.195			−0.561569
$329$	−340.526	−	268.464i	−1.03503	−	0.815999i
$330$		0			0
$331$	83.4463	+	144.533i	0.252104	+	0.436656i	0.964105	−	0.265522i	$-0.0855443\pi$
$331$	83.4463	+	144.533i	0.252104	+	0.436656i	−0.712001	+	0.702178i	$0.752211\pi$
$332$	49.4298	−	85.6150i	0.148885	−	0.257876i
$333$	125.136	+	72.2470i	0.375782	+	0.216958i
$334$	−36.6731	+	21.1732i	−0.109800	+	0.0633929i
$335$		0			0
$336$	45.0453	−	17.9699i	0.134064	−	0.0534818i
$337$			541.392i			1.60651i	0.595638	+	0.803253i	$0.296899\pi$
$337$			541.392i			1.60651i	−0.595638	+	0.803253i	$0.703101\pi$
$338$	146.568	−	84.6208i	0.433632	−	0.250357i
$339$	112.486	+	64.9441i	0.331818	+	0.191575i
$340$		0			0
$341$	−179.215	+	103.470i	−0.525558	+	0.303431i
$342$	131.983			0.385914
$343$	−143.625	+	311.482i	−0.418732	+	0.908110i
$344$	8.58420			0.0249541
$345$		0			0
$346$	−130.443	−	75.3111i	−0.377002	−	0.217662i
$347$	371.251	+	214.342i	1.06989	+	0.617700i	0.928151	−	0.372204i	$-0.121398\pi$
$347$	371.251	+	214.342i	1.06989	+	0.617700i	0.141737	+	0.989904i	$0.454731\pi$
$348$	15.9292	+	27.5902i	0.0457736	+	0.0792822i
$349$		−	74.6851i		−	0.213998i	−0.994259	−	0.106999i	$-0.965876\pi$
$349$		−	74.6851i		−	0.213998i	0.994259	−	0.106999i	$-0.0341241\pi$
$350$		0			0
$351$	36.4946			0.103973
$352$	−50.3104	+	29.0467i	−0.142927	+	0.0825190i
$353$	−182.956	+	316.890i	−0.518290	+	0.897705i	0.481484	+	0.876455i	$0.340098\pi$
$353$	−182.956	+	316.890i	−0.518290	+	0.897705i	−0.999774	+	0.0212499i	$0.993235\pi$
$354$	−134.501	+	232.962i	−0.379946	+	0.658085i
$355$		0			0
$356$		−	329.799i		−	0.926403i
$357$	302.282	+	238.313i	0.846728	+	0.667543i
$358$		−	339.373i		−	0.947968i
$359$	−248.793	−	430.922i	−0.693017	−	1.20034i	−0.970845	−	0.239710i	$-0.922948\pi$
$359$	−248.793	−	430.922i	−0.693017	−	1.20034i	0.277828	−	0.960631i	$-0.410386\pi$
$360$		0			0
$361$	303.373	−	525.457i	0.840368	−	1.45556i
$362$	−218.724	−	378.841i	−0.604210	−	1.04652i
$363$	26.9094			0.0741305
$364$	14.1119	−	97.3096i	0.0387689	−	0.267334i
$365$		0			0
$366$	−48.6124	−	84.1991i	−0.132821	−	0.230052i
$367$	69.6861	−	120.700i	0.189880	−	0.328882i	−0.755330	−	0.655345i	$-0.772523\pi$
$367$	69.6861	−	120.700i	0.189880	−	0.328882i	0.945210	+	0.326462i	$0.105857\pi$
$368$	82.0584	+	47.3765i	0.222985	+	0.128740i
$369$	169.194	−	97.6839i	0.458519	−	0.264726i
$370$		0			0
$371$	9.57040	+	1.38790i	0.0257962	+	0.00374098i
$372$		−	69.8045i		−	0.187647i
$373$	300.961	−	173.760i	0.806865	−	0.465844i	−0.0390009	−	0.999239i	$-0.512418\pi$
$373$	300.961	−	173.760i	0.806865	−	0.465844i	0.845866	+	0.533395i	$0.179084\pi$
$374$	−399.315	−	230.544i	−1.06769	−	0.616429i
$375$		0			0
$376$	−151.737	+	87.6055i	−0.403556	+	0.232993i
$377$	64.5923			0.171332
$378$	−31.8468	+	40.3953i	−0.0842509	+	0.106866i
$379$	−307.387			−0.811048			−0.405524	−	0.914084i	$-0.632911\pi$
$379$	−307.387			−0.811048			−0.405524	+	0.914084i	$0.632911\pi$
$380$		0			0
$381$	−192.756	−	111.288i	−0.505921	−	0.292093i
$382$	3.78397	+	2.18468i	0.00990569	+	0.00571905i
$383$	−254.364	−	440.572i	−0.664136	−	1.15032i	−0.979519	−	0.201353i	$-0.935466\pi$
$383$	−254.364	−	440.572i	−0.664136	−	1.15032i	0.315382	−	0.948965i	$-0.397867\pi$
$384$		−	19.5959i		−	0.0510310i
$385$		0			0
$386$	−337.569			−0.874531
$387$	−7.88509	+	4.55246i	−0.0203749	+	0.0117635i
$388$	−49.4799	+	85.7016i	−0.127525	+	0.220880i
$389$	−85.4840	+	148.063i	−0.219753	+	0.380624i	−0.954732	−	0.297466i	$-0.903859\pi$
$389$	−85.4840	+	148.063i	−0.219753	+	0.380624i	0.734979	+	0.678090i	$0.237192\pi$
$390$		0			0
$391$			752.057i			1.92342i
$392$	95.3957	+	100.537i	0.243356	+	0.256472i
$393$		−	130.764i		−	0.332732i
$394$	−206.149	−	357.061i	−0.523221	−	0.906245i
$395$		0			0
$396$	30.8087	−	53.3622i	0.0777997	−	0.134753i
$397$	−318.249	−	551.223i	−0.801634	−	1.38847i	−0.918540	−	0.395328i	$-0.870631\pi$
$397$	−318.249	−	551.223i	−0.801634	−	1.38847i	0.116906	−	0.993143i	$-0.462702\pi$
$398$	341.661			0.858446
$399$	139.755	+	350.325i	0.350262	+	0.878006i
$400$		0			0
$401$	296.110	+	512.878i	0.738429	+	1.27900i	0.953202	+	0.302333i	$0.0977654\pi$
$401$	296.110	+	512.878i	0.738429	+	1.27900i	−0.214773	+	0.976664i	$0.568901\pi$
$402$	−19.4968	+	33.7694i	−0.0484994	+	0.0840034i
$403$	−122.566	−	70.7636i	−0.304135	−	0.175592i
$404$	233.606	−	134.873i	0.578234	−	0.333843i
$405$		0			0
$406$	−56.3661	+	71.4961i	−0.138833	+	0.176099i
$407$		−	494.630i		−	1.21531i
$408$	134.696	−	77.7667i	0.330137	−	0.190605i
$409$	245.717	+	141.865i	0.600776	+	0.346858i	0.769347	−	0.638831i	$-0.220582\pi$
$409$	245.717	+	141.865i	0.600776	+	0.346858i	−0.168571	+	0.985690i	$0.553915\pi$
$410$		0			0
$411$	161.275	−	93.1121i	0.392396	−	0.226550i
$412$	−74.8041			−0.181563
$413$	−760.778	−	110.328i	−1.84208	−	0.267138i
$414$	−100.501			−0.242755
$415$		0			0
$416$	−34.4075	−	19.8652i	−0.0827103	−	0.0477528i
$417$	−408.006	−	235.562i	−0.978431	−	0.564897i
$418$	−225.901	−	391.271i	−0.540432	−	0.936056i
$419$			482.511i			1.15158i	0.817599	+	0.575789i	$0.195305\pi$
$419$			482.511i			1.15158i	−0.817599	+	0.575789i	$0.804695\pi$
$420$		0			0
$421$	762.080			1.81017			0.905083	−	0.425234i	$-0.139808\pi$
$421$	762.080			1.81017			0.905083	+	0.425234i	$0.139808\pi$
$422$	322.130	−	185.982i	0.763342	−	0.440716i
$423$	92.9197	−	160.942i	0.219668	−	0.380476i
$424$	1.95374	−	3.38397i	0.00460787	−	0.00798107i
$425$		0			0
$426$			130.678i			0.306755i
$427$	172.017	−	218.190i	0.402849	−	0.510984i
$428$		−	49.5920i		−	0.115869i
$429$	−62.4640	−	108.191i	−0.145604	−	0.252193i
$430$		0			0
$431$	−128.008	+	221.717i	−0.297003	+	0.514424i	−0.975449	−	0.220226i	$-0.929320\pi$
$431$	−128.008	+	221.717i	−0.297003	+	0.514424i	0.678446	+	0.734650i	$0.262654\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	646.579			1.49325			0.746627	−	0.665243i	$-0.231672\pi$
$433$	646.579			1.49325			0.746627	+	0.665243i	$0.231672\pi$
$434$	185.284	−	73.9150i	0.426921	−	0.170311i
$435$		0			0
$436$	56.2897	+	97.4966i	0.129105	+	0.223616i
$437$	−368.454	+	638.181i	−0.843144	+	1.46037i
$438$	−153.541	−	88.6472i	−0.350551	−	0.202391i
$439$	−290.352	+	167.635i	−0.661394	+	0.381856i	−0.792808	−	0.609472i	$-0.791382\pi$
$439$	−290.352	+	167.635i	−0.661394	+	0.381856i	0.131414	+	0.991328i	$0.458048\pi$
$440$		0			0
$441$	−140.944	−	41.7578i	−0.319602	−	0.0946888i
$442$		−	315.341i		−	0.713441i
$443$	−243.400	+	140.527i	−0.549435	+	0.317216i	−0.748894	−	0.662690i	$-0.769415\pi$
$443$	−243.400	+	140.527i	−0.549435	+	0.317216i	0.199459	+	0.979906i	$0.436081\pi$
$444$	144.494	+	83.4237i	0.325437	+	0.187891i
$445$		0			0
$446$	137.977	−	79.6613i	0.309366	−	0.178613i
$447$	−144.500			−0.323265
$448$	52.0139	−	20.7498i	0.116102	−	0.0463166i
$449$	−47.2320			−0.105194			−0.0525969	−	0.998616i	$-0.516750\pi$
$449$	−47.2320			−0.105194			−0.0525969	+	0.998616i	$0.516750\pi$
$450$		0			0
$451$	−579.181	−	334.390i	−1.28422	−	0.741442i
$452$	129.888	+	74.9910i	0.287363	+	0.165909i
$453$	109.807	+	190.192i	0.242400	+	0.419850i
$454$			69.3253i			0.152699i
$455$		0			0
$456$	152.400			0.334212
$457$	−509.909	+	294.396i	−1.11578	+	0.644193i	−0.940319	−	0.340294i	$-0.889473\pi$
$457$	−509.909	+	294.396i	−1.11578	+	0.644193i	−0.175456	+	0.984487i	$0.556140\pi$
$458$	19.8797	−	34.4327i	0.0434055	−	0.0751805i
$459$	−82.4840	+	142.866i	−0.179704	+	0.311256i
$460$		0			0
$461$		−	60.5606i		−	0.131368i	−0.997840	−	0.0656839i	$-0.979077\pi$
$461$		−	60.5606i		−	0.131368i	0.997840	−	0.0656839i	$-0.0209229\pi$
$462$	174.263	+	25.2717i	0.377193	+	0.0547007i
$463$			88.7592i			0.191704i	0.995396	+	0.0958522i	$0.0305576\pi$
$463$			88.7592i			0.191704i	−0.995396	+	0.0958522i	$0.969442\pi$
$464$	18.3935	+	31.8584i	0.0396411	+	0.0686604i
$465$		0			0
$466$	−124.594	+	215.803i	−0.267369	+	0.463097i
$467$	−151.112	−	261.733i	−0.323580	−	0.560457i	0.657644	−	0.753329i	$-0.271553\pi$
$467$	−151.112	−	261.733i	−0.323580	−	0.560457i	−0.981224	+	0.192872i	$0.938220\pi$
$468$	42.1404			0.0900436
$469$	−110.280	−	15.9928i	−0.235138	−	0.0340997i
$470$		0			0
$471$	85.9416	+	148.855i	0.182466	+	0.316041i
$472$	−155.308	+	269.002i	−0.329043	+	0.569919i
$473$	26.9921	+	15.5839i	0.0570658	+	0.0329470i
$474$	−225.806	+	130.369i	−0.476383	+	0.275040i
$475$		0			0
$476$	349.045	+	275.180i	0.733288	+	0.578110i
$477$			4.14451i			0.00868869i
$478$	42.5170	−	24.5472i	0.0889478	−	0.0513540i
$479$	−30.4237	−	17.5651i	−0.0635151	−	0.0366704i	0.467906	−	0.883778i	$-0.345009\pi$
$479$	−30.4237	−	17.5651i	−0.0635151	−	0.0366704i	−0.531421	+	0.847108i	$0.678342\pi$
$480$		0			0
$481$	292.959	−	169.140i	0.609062	−	0.351642i
$482$	375.378			0.778793
$483$	−106.419	−	266.761i	−0.220329	−	0.552301i
$484$	31.0723			0.0641989
$485$		0			0
$486$	−19.0919	−	11.0227i	−0.0392837	−	0.0226805i
$487$	55.9741	+	32.3167i	0.114937	+	0.0663586i	0.556366	−	0.830937i	$-0.312195\pi$
$487$	55.9741	+	32.3167i	0.114937	+	0.0663586i	−0.441430	+	0.897296i	$0.645529\pi$
$488$	−56.1327	−	97.2247i	−0.115026	−	0.199231i
$489$		−	483.207i		−	0.988153i
$490$		0			0
$491$	241.365			0.491578			0.245789	−	0.969323i	$-0.420953\pi$
$491$	241.365			0.491578			0.245789	+	0.969323i	$0.420953\pi$
$492$	195.368	−	112.796i	0.397089	−	0.229260i
$493$	−145.989	+	252.861i	−0.296125	+	0.512903i
$494$	154.494	−	267.592i	0.312742	−	0.541685i
$495$		0			0
$496$		−	80.6033i		−	0.162507i
$497$	−346.860	+	138.373i	−0.697908	+	0.278416i
$498$			121.078i			0.243128i
$499$	−95.8123	−	165.952i	−0.192009	−	0.332569i	0.753907	−	0.656981i	$-0.228167\pi$
$499$	−95.8123	−	165.952i	−0.192009	−	0.332569i	−0.945916	+	0.324412i	$0.894834\pi$
$500$		0			0
$501$	25.9318	−	44.9152i	0.0517601	−	0.0896511i
$502$	−17.0924	−	29.6049i	−0.0340486	−	0.0589739i
$503$	919.711			1.82845			0.914226	−	0.405205i	$-0.132800\pi$
$503$	919.711			1.82845			0.914226	+	0.405205i	$0.132800\pi$
$504$	−36.7735	+	46.6445i	−0.0729634	+	0.0925485i
$505$		0			0
$506$	172.016	+	297.941i	0.339953	+	0.588816i
$507$	−103.639	+	179.508i	−0.204416	+	0.354059i
$508$	−222.575	−	128.504i	−0.438140	−	0.252960i
$509$	−250.976	+	144.901i	−0.493076	+	0.284678i	−0.725850	−	0.687853i	$-0.758553\pi$
$509$	−250.976	+	144.901i	−0.493076	+	0.284678i	0.232773	+	0.972531i	$0.425220\pi$
$510$		0			0
$511$	72.7154	−	501.416i	0.142300	−	0.981244i
$512$		−	22.6274i		−	0.0441942i
$513$	−139.989	+	80.8225i	−0.272883	+	0.157549i
$514$	−11.6810	−	6.74401i	−0.0227256	−	0.0131206i
$515$		0			0
$516$	−9.10492	+	5.25673i	−0.0176452	+	0.0101875i
$517$	−636.163			−1.23049
$518$	−68.4307	+	471.870i	−0.132106	+	0.910946i
$519$	184.474			0.355441
$520$		0			0
$521$	−653.176	−	377.112i	−1.25370	−	0.723823i	−0.281856	−	0.959457i	$-0.590950\pi$
$521$	−653.176	−	377.112i	−1.25370	−	0.723823i	−0.971842	+	0.235634i	$0.924283\pi$
$522$	−33.7909	−	19.5092i	−0.0647336	−	0.0373740i
$523$	37.8638	+	65.5821i	0.0723974	+	0.125396i	0.899952	−	0.435990i	$-0.143602\pi$
$523$	37.8638	+	65.5821i	0.0723974	+	0.125396i	−0.827554	+	0.561386i	$0.810268\pi$
$524$		−	150.993i		−	0.288154i
$525$		0			0
$526$	−186.483			−0.354530
$527$	554.040	−	319.875i	1.05131	−	0.606974i
$528$	35.5748	−	61.6174i	0.0673765	−	0.116700i
$529$	16.0662	−	27.8275i	0.0303709	−	0.0526039i
$530$		0			0
$531$		−	329.458i		−	0.620449i
$532$	161.375	+	404.520i	0.303336	+	0.760376i
$533$		−	457.382i		−	0.858128i
$534$	201.960	+	349.805i	0.378202	+	0.655066i
$535$		0			0
$536$	−22.5129	+	38.9935i	−0.0420017	+	0.0727491i
$537$	207.822	+	359.959i	0.387007	+	0.670315i
$538$	−53.5689			−0.0995705
$539$	117.446	+	489.311i	0.217895	+	0.907813i
$540$		0			0
$541$	−493.177	−	854.207i	−0.911602	−	1.57894i	−0.811802	−	0.583933i	$-0.801513\pi$
$541$	−493.177	−	854.207i	−0.911602	−	1.57894i	−0.0998002	−	0.995007i	$-0.531820\pi$
$542$	−256.217	+	443.782i	−0.472726	+	0.818785i
$543$	463.984	+	267.881i	0.854482	+	0.493335i
$544$	155.533	−	89.7972i	0.285907	−	0.165068i
$545$		0			0
$546$	44.6218	+	111.854i	0.0817250	+	0.204861i
$547$		−	346.700i		−	0.633820i	−0.948456	−	0.316910i	$-0.897355\pi$
$547$		−	346.700i		−	0.633820i	0.948456	−	0.316910i	$-0.102645\pi$
$548$	186.224	−	107.517i	0.339825	−	0.196198i
$549$	103.122	+	59.5377i	0.187837	+	0.108448i
$550$		0			0
$551$	−247.768	+	143.049i	−0.449669	+	0.259617i
$552$	−116.048			−0.210232
$553$	−585.143	−	461.315i	−1.05813	−	0.834204i
$554$	160.229			0.289222
$555$		0			0
$556$	−471.124	−	272.004i	−0.847346	−	0.489215i
$557$	−132.891	−	76.7246i	−0.238583	−	0.137746i	0.375942	−	0.926643i	$-0.377319\pi$
$557$	−132.891	−	76.7246i	−0.238583	−	0.137746i	−0.614525	+	0.788897i	$0.710652\pi$
$558$	42.7464	+	74.0389i	0.0766064	+	0.132686i
$559$			21.3158i			0.0381320i
$560$		0			0
$561$	564.716			1.00662
$562$	218.905	−	126.385i	0.389511	−	0.224884i
$563$	−87.0695	+	150.809i	−0.154653	+	0.267866i	−0.932933	−	0.360051i	$-0.882759\pi$
$563$	−87.0695	+	150.809i	−0.154653	+	0.267866i	0.778280	+	0.627918i	$0.216093\pi$
$564$	107.294	−	185.839i	0.190238	−	0.329502i
$565$		0			0
$566$		−	61.0495i		−	0.107861i
$567$	9.04169	−	62.3478i	0.0159465	−	0.109961i
$568$			150.893i			0.265658i
$569$	−109.591	−	189.817i	−0.192603	−	0.333597i	0.753509	−	0.657437i	$-0.228359\pi$
$569$	−109.591	−	189.817i	−0.192603	−	0.333597i	−0.946112	+	0.323840i	$0.895026\pi$
$570$		0			0
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	0.0522282	+	0.998635i	$0.483368\pi$
$571$	−478.914	+	829.504i	−0.838729	+	1.45272i	−0.890958	+	0.454087i	$0.849966\pi$
$572$	−72.1272	−	124.928i	−0.126097	−	0.218406i
$573$	−5.35135			−0.00933917
$574$	506.268	+	399.132i	0.882001	+	0.695351i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−518.944	+	898.838i	−0.899384	+	1.55778i	−0.0710997	+	0.997469i	$0.522651\pi$
$577$	−518.944	+	898.838i	−0.899384	+	1.55778i	−0.828284	+	0.560309i	$0.810682\pi$
$578$	880.521	+	508.369i	1.52339	+	0.879531i
$579$	358.046	−	206.718i	0.618387	−	0.357026i
$580$		0			0
$581$	−321.380	+	128.208i	−0.553149	+	0.220667i
$582$		−	121.200i		−	0.208248i
$583$	12.2867	−	7.09371i	0.0210749	−	0.0121676i
$584$	−177.294	−	102.361i	−0.303586	−	0.175276i
$585$		0			0
$586$	18.9132	−	10.9195i	0.0322751	−	0.0186340i
$587$	819.162			1.39551			0.697753	−	0.716339i	$-0.254183\pi$
$587$	819.162			1.39551			0.697753	+	0.716339i	$0.254183\pi$
$588$	−162.748	−	48.2177i	−0.276783	−	0.0820029i
$589$	626.864			1.06429
$590$		0			0
$591$	437.308	+	252.480i	0.739946	+	0.427208i
$592$	166.847	+	96.3294i	0.281837	+	0.162719i
$593$	266.689	+	461.919i	0.449729	+	0.778953i	0.998368	−	0.0571059i	$-0.0181873\pi$
$593$	266.689	+	461.919i	0.449729	+	0.778953i	−0.548639	+	0.836059i	$0.684854\pi$
$594$			75.4655i			0.127046i
$595$		0			0
$596$	−166.854			−0.279956
$597$	−362.387	+	209.224i	−0.607013	+	0.350459i
$598$	−117.643	+	203.763i	−0.196727	+	0.340741i
$599$	−171.452	+	296.963i	−0.286230	+	0.495765i	−0.972907	−	0.231198i	$-0.925735\pi$
$599$	−171.452	+	296.963i	−0.286230	+	0.495765i	0.686677	+	0.726963i	$0.259069\pi$
$600$		0			0
$601$		−	418.941i		−	0.697073i	−0.937295	−	0.348536i	$-0.886679\pi$
$601$		−	418.941i		−	0.697073i	0.937295	−	0.348536i	$-0.113321\pi$
$602$	−23.5941	−	18.6011i	−0.0391929	−	0.0308989i
$603$		−	47.7571i		−	0.0791992i
$604$	126.795	+	219.615i	0.209925	+	0.363601i
$605$		0			0
$606$	−165.185	+	286.108i	−0.272582	+	0.472126i
$607$	−70.7875	−	122.608i	−0.116619	−	0.201989i	0.801807	−	0.597583i	$-0.203872\pi$
$607$	−70.7875	−	122.608i	−0.116619	−	0.201989i	−0.918426	+	0.395594i	$0.870539\pi$
$608$	175.977			0.289436
$609$	16.0030	−	110.350i	0.0262775	−	0.181199i
$610$		0			0
$611$	−217.537	−	376.786i	−0.356035	−	0.616670i
$612$	−95.2443	+	164.968i	−0.155628	+	0.269556i
$613$	257.244	+	148.520i	0.419647	+	0.242284i	0.694926	−	0.719081i	$-0.255437\pi$
$613$	257.244	+	148.520i	0.419647	+	0.242284i	−0.275279	+	0.961364i	$0.588770\pi$
$614$	287.384	−	165.921i	0.468053	−	0.270230i
$615$		0			0
$616$	201.222	+	29.1813i	0.326659	+	0.0473722i
$617$			674.329i			1.09292i	0.837486	+	0.546458i	$0.184024\pi$
$617$			674.329i			1.09292i	−0.837486	+	0.546458i	$0.815976\pi$
$618$	79.3418	−	45.8080i	0.128385	−	0.0741230i
$619$	833.055	+	480.965i	1.34581	+	0.777003i	0.987653	−	0.156659i	$-0.0500724\pi$
$619$	833.055	+	480.965i	1.34581	+	0.777003i	0.358156	+	0.933662i	$0.383406\pi$
$620$		0			0
$621$	106.597	−	61.5438i	0.171654	−	0.0991044i
$622$	563.957			0.906683
$623$	−714.643	+	906.471i	−1.14710	+	1.45501i
$624$	48.6595			0.0779800
$625$		0			0
$626$	−158.238	−	91.3585i	−0.252776	−	0.145940i
$627$	479.208	+	276.671i	0.764287	+	0.441261i
$628$	99.2368	+	171.883i	0.158020	+	0.273699i
$629$			1529.14i			2.43106i
$630$		0			0
$631$	1185.17			1.87824			0.939122	−	0.343584i	$-0.111641\pi$
$631$	1185.17			1.87824			0.939122	+	0.343584i	$0.111641\pi$
$632$	−260.738	+	150.537i	−0.412560	+	0.238191i
$633$	−227.781	+	394.527i	−0.359843	+	0.623266i
$634$	−284.657	+	493.040i	−0.448985	+	0.777666i
$635$		0			0
$636$			4.78566i			0.00752463i
$637$	−249.648	+	236.882i	−0.391912	+	0.371871i
$638$			133.567i			0.209353i
$639$	−80.0234	−	138.605i	−0.125232	−	0.216908i
$640$		0			0
$641$	−203.549	+	352.557i	−0.317549	+	0.550011i	−0.979976	−	0.199115i	$-0.936193\pi$
$641$	−203.549	+	352.557i	−0.317549	+	0.550011i	0.662427	+	0.749126i	$0.269526\pi$
$642$	30.3688	+	52.6002i	0.0473034	+	0.0819318i
$643$	−1077.83			−1.67626			−0.838128	−	0.545474i	$-0.816350\pi$
$643$	−1077.83			−1.67626			−0.838128	+	0.545474i	$0.816350\pi$
$644$	−122.882	−	308.029i	−0.190810	−	0.478306i
$645$		0			0
$646$	698.367	+	1209.61i	1.08106	+	1.87246i
$647$	588.349	−	1019.05i	0.909350	−	1.57504i	0.0943805	−	0.995536i	$-0.469913\pi$
$647$	588.349	−	1019.05i	0.909350	−	1.57504i	0.814969	−	0.579504i	$-0.196754\pi$
$648$	−22.0454	−	12.7279i	−0.0340207	−	0.0196419i
$649$	−976.701	+	563.899i	−1.50493	+	0.868873i
$650$		0			0
$651$	−151.260	+	191.861i	−0.232349	+	0.294718i
$652$		−	557.959i		−	0.855765i
$653$	−761.345	+	439.563i	−1.16592	+	0.673144i	−0.952715	−	0.303864i	$-0.901723\pi$
$653$	−761.345	+	439.563i	−1.16592	+	0.673144i	−0.213204	+	0.977008i	$0.568390\pi$
$654$	−119.408	−	68.9405i	−0.182582	−	0.105414i
$655$		0			0
$656$	225.591	−	130.245i	0.343889	−	0.198545i
$657$	217.140			0.330503
$658$	606.890	+	88.0113i	0.922325	+	0.133756i
$659$	−65.1550			−0.0988696			−0.0494348	−	0.998777i	$-0.515742\pi$
$659$	−65.1550			−0.0988696			−0.0494348	+	0.998777i	$0.515742\pi$
$660$		0			0
$661$	22.0376	+	12.7234i	0.0333397	+	0.0192487i	0.516577	−	0.856241i	$-0.327206\pi$
$661$	22.0376	+	12.7234i	0.0333397	+	0.0192487i	−0.483237	+	0.875489i	$0.660539\pi$
$662$	−204.401	−	118.011i	−0.308762	−	0.178264i
$663$	193.106	+	334.469i	0.291261	+	0.504479i
$664$			139.809i			0.210555i
$665$		0			0
$666$	−204.345			−0.306825
$667$	188.667	−	108.927i	0.282860	−	0.163309i
$668$	29.9435	−	51.8636i	0.0448256	−	0.0776401i
$669$	−97.5647	+	168.987i	−0.145837	+	0.252597i
$670$		0			0
$671$		−	407.618i		−	0.607478i
$672$	−42.4624	+	53.8604i	−0.0631881	+	0.0801494i
$673$			23.1893i			0.0344566i	0.999852	+	0.0172283i	$0.00548420\pi$
$673$			23.1893i			0.0344566i	−0.999852	+	0.0172283i	$0.994516\pi$
$674$	−382.822	−	663.068i	−0.567986	−	0.983780i
$675$		0			0
$676$	−119.672	+	207.278i	−0.177029	+	0.306624i
$677$	71.0658	+	123.090i	0.104972	+	0.181816i	0.913727	−	0.406330i	$-0.133191\pi$
$677$	71.0658	+	123.090i	0.104972	+	0.181816i	−0.808755	+	0.588146i	$0.799858\pi$
$678$	−183.690			−0.270929
$679$	321.705	−	128.337i	0.473792	−	0.189009i
$680$		0			0
$681$	−42.4529	−	73.5306i	−0.0623391	−	0.107974i
$682$	146.329	−	253.449i	0.214558	−	0.371626i
$683$	−568.722	−	328.352i	−0.832682	−	0.480749i	0.0220879	−	0.999756i	$-0.492969\pi$
$683$	−568.722	−	328.352i	−0.832682	−	0.480749i	−0.854770	+	0.519007i	$0.826302\pi$
$684$	−161.645	+	93.3258i	−0.236323	+	0.136441i
$685$		0			0
$686$	−44.3466	−	483.044i	−0.0646452	−	0.704146i
$687$			48.6951i			0.0708808i
$688$	−10.5135	+	6.06994i	−0.0152812	+	0.00882259i
$689$	8.40290	+	4.85142i	0.0121958	+	0.00704125i
$690$		0			0
$691$	212.350	−	122.600i	0.307308	−	0.177425i	−0.338413	−	0.940998i	$-0.609890\pi$
$691$	212.350	−	122.600i	0.307308	−	0.177425i	0.645721	+	0.763573i	$0.276557\pi$
$692$	213.012			0.307821
$693$	−200.310	+	79.9094i	−0.289047	+	0.115309i
$694$	−606.250			−0.873560
$695$		0			0
$696$	−39.0184	−	22.5273i	−0.0560610	−	0.0323668i
$697$	1790.52	+	1033.76i	2.56890	+	1.48316i
$698$	52.8104	+	91.4702i	0.0756595	+	0.131046i
$699$		−	305.192i		−	0.436612i
$700$		0			0
$701$	379.419			0.541254			0.270627	−	0.962684i	$-0.412769\pi$
$701$	379.419			0.541254			0.270627	+	0.962684i	$0.412769\pi$
$702$	−44.6966	+	25.8056i	−0.0636704	+	0.0367601i
$703$	−749.168	+	1297.60i	−1.06567	+	1.84580i
$704$	41.0782	−	71.1496i	0.0583498	−	0.101065i
$705$		0			0
$706$		−	517.479i		−	0.732973i
$707$	−934.335	−	135.498i	−1.32155	−	0.191651i
$708$		−	380.426i		−	0.537324i
$709$	−442.054	−	765.661i	−0.623490	−	1.07992i	−0.988831	−	0.149042i	$-0.952381\pi$
$709$	−442.054	−	765.661i	−0.623490	−	1.07992i	0.365341	−	0.930874i	$-0.380952\pi$
$710$		0			0
$711$	159.669	−	276.554i	0.224569	−	0.388965i
$712$	233.203	+	403.920i	0.327533	+	0.567304i
$713$	−477.337			−0.669477
$714$	−538.731	−	78.1269i	−0.754525	−	0.109421i
$715$		0			0
$716$	239.973	+	415.645i	0.335157	+	0.580510i
$717$	−30.0641	+	52.0725i	−0.0419304	+	0.0726255i
$718$	609.416	+	351.847i	0.848769	+	0.490037i
$719$	825.831	−	476.794i	1.14858	−	0.663135i	0.200042	−	0.979787i	$-0.435892\pi$
$719$	825.831	−	476.794i	1.14858	−	0.663135i	0.948542	+	0.316653i	$0.102559\pi$
$720$		0			0
$721$	205.603	+	162.093i	0.285164	+	0.224817i
$722$			858.068i			1.18846i
$723$	−398.149	+	229.871i	−0.550690	+	0.317941i
$724$	535.762	+	309.322i	0.740003	+	0.427241i
$725$		0			0
$726$	−32.9571	+	19.0278i	−0.0453955	+	0.0262091i
$727$	1110.82			1.52795			0.763974	−	0.645248i	$-0.223246\pi$
$727$	1110.82			1.52795			0.763974	+	0.645248i	$0.223246\pi$
$728$	51.5249	+	129.158i	0.0707759	+	0.177415i
$729$	27.0000			0.0370370
$730$		0			0
$731$	−83.4455	−	48.1773i	−0.114153	−	0.0659060i
$732$	119.075	+	68.7483i	0.162671	+	0.0939184i
$733$	20.3571	+	35.2595i	0.0277722	+	0.0481029i	0.879577	−	0.475756i	$-0.157825\pi$
$733$	20.3571	+	35.2595i	0.0277722	+	0.0481029i	−0.851805	+	0.523859i	$0.824492\pi$
$734$			197.102i			0.268531i
$735$		0			0
$736$	−134.001			−0.182066
$737$	−141.579	+	81.7407i	−0.192102	+	0.110910i
$738$	−138.146	+	239.276i	−0.187190	+	0.324222i
$739$	422.735	−	732.199i	0.572037	−	0.990797i	−0.424320	−	0.905512i	$-0.639487\pi$
$739$	422.735	−	732.199i	0.572037	−	0.990797i	0.996357	−	0.0852847i	$-0.0271800\pi$
$740$		0			0
$741$			378.433i			0.510705i
$742$	−12.7027	+	5.06747i	−0.0171195	+	0.00682947i
$743$			355.319i			0.478222i	0.970992	+	0.239111i	$0.0768559\pi$
$743$			355.319i			0.478222i	−0.970992	+	0.239111i	$0.923144\pi$
$744$	49.3592	+	85.4927i	0.0663431	+	0.114910i
$745$		0			0
$746$	−245.733	+	425.623i	−0.329401	+	0.570540i
$747$	−74.1447	−	128.422i	−0.0992567	−	0.171918i
$748$	652.078			0.871762
$749$	−107.461	+	136.306i	−0.143473	+	0.181984i
$750$		0			0
$751$	−108.768	−	188.392i	−0.144831	−	0.250855i	0.784479	−	0.620156i	$-0.212931\pi$
$751$	−108.768	−	188.392i	−0.144831	−	0.250855i	−0.929310	+	0.369300i	$0.879597\pi$
$752$	123.893	−	214.589i	0.164751	−	0.285357i
$753$	36.2584	+	20.9338i	0.0481520	+	0.0278006i
$754$	−79.1091	+	45.6737i	−0.104919	+	0.0605751i
$755$		0			0
$756$	10.4404	−	71.9930i	0.0138101	−	0.0952289i
$757$		−	1178.25i		−	1.55647i	−0.627975	−	0.778233i	$-0.716116\pi$
$757$		−	1178.25i		−	1.55647i	0.627975	−	0.778233i	$-0.283884\pi$
$758$	376.471	−	217.356i	0.496663	−	0.286749i
$759$	−364.902	−	210.676i	−0.480766	−	0.277571i
$760$		0			0
$761$	711.636	−	410.863i	0.935133	−	0.539899i	0.0467017	−	0.998909i	$-0.485129\pi$
$761$	711.636	−	410.863i	0.935133	−	0.539899i	0.888431	+	0.459010i	$0.151796\pi$
$762$	314.769			0.413082
$763$	56.5504	−	389.948i	0.0741159	−	0.511073i
$764$	−6.17920			−0.00808796
$765$		0			0
$766$	623.063	+	359.725i	0.813398	+	0.469615i
$767$	−667.970	−	385.653i	−0.870887	−	0.502807i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$			230.888i			0.300244i	0.988667	+	0.150122i	$0.0479667\pi$
$769$			230.888i			0.300244i	−0.988667	+	0.150122i	$0.952033\pi$
$770$		0			0
$771$	16.5194			0.0214259
$772$	413.436	−	238.697i	0.535539	−	0.309193i
$773$	−337.234	+	584.107i	−0.436267	+	0.755636i	−0.997398	−	0.0720908i	$-0.977033\pi$
$773$	−337.234	+	584.107i	−0.436267	+	0.755636i	0.561131	+	0.827727i	$0.310366\pi$
$774$	6.43815	−	11.1512i	0.00831802	−	0.0144072i
$775$		0			0
$776$		−	139.950i		−	0.180348i
$777$	−216.378	−	542.399i	−0.278479	−	0.698068i
$778$		−	241.785i		−	0.310778i
$779$	1012.94	+	1754.46i	1.30030	+	2.25219i
$780$		0			0
$781$	−273.935	+	474.469i	−0.350749	+	0.607515i
$782$	−531.784	−	921.077i	−0.680031	−	1.17785i
$783$	47.7876			0.0610314
$784$	−187.926	−	55.6770i	−0.239701	−	0.0710166i
$785$		0			0
$786$	92.4639	+	160.152i	0.117639	+	0.203756i
$787$	311.445	−	539.438i	0.395737	−	0.685436i	−0.597458	−	0.801900i	$-0.703823\pi$
$787$	311.445	−	539.438i	0.395737	−	0.685436i	0.993195	+	0.116464i	$0.0371560\pi$
$788$	504.960	+	291.539i	0.640812	+	0.369973i
$789$	197.795	−	114.197i	0.250691	−	0.144736i
$790$		0			0
$791$	−194.506	−	487.571i	−0.245899	−	0.616399i
$792$			87.1401i			0.110025i
$793$	241.423	−	139.386i	0.304443	−	0.175770i
$794$	779.547	+	450.072i	0.981797	+	0.566841i
$795$		0			0
$796$	−418.448	+	241.591i	−0.525688	+	0.303506i
$797$	−1322.28			−1.65907			−0.829537	−	0.558452i	$-0.811396\pi$
$797$	−1322.28			−1.65907			−0.829537	+	0.558452i	$0.811396\pi$
$798$	−418.881	−	330.237i	−0.524913	−	0.413831i
$799$	1966.68			2.46143
$800$		0			0
$801$	−428.422	−	247.350i	−0.534859	−	0.308801i
$802$	−725.319	−	418.763i	−0.904387	−	0.522148i
$803$	−371.656	−	643.727i	−0.462834	−	0.801653i
$804$		−	55.1451i		−	0.0685885i
$805$		0			0
$806$	200.150			0.248325
$807$	56.8185	−	32.8041i	0.0704070	−	0.0406495i
$808$	−190.739	+	330.369i	−0.236063	+	0.408873i
$809$	521.105	−	902.581i	0.644135	−	1.11567i	−0.340366	−	0.940293i	$-0.610551\pi$
$809$	521.105	−	902.581i	0.644135	−	1.11567i	0.984501	−	0.175381i	$-0.0561158\pi$
$810$		0			0
$811$			782.292i			0.964602i	0.876006	+	0.482301i	$0.160199\pi$
$811$			782.292i			0.964602i	−0.876006	+	0.482301i	$0.839801\pi$
$812$	18.4787	−	127.421i	0.0227570	−	0.156923i
$813$		−	627.602i		−	0.771958i
$814$	349.756	+	605.796i	0.429676	+	0.744221i
$815$		0			0
$816$	−109.979	+	190.489i	−0.134778	+	0.233442i
$817$	−47.2069	−	81.7647i	−0.0577808	−	0.100079i
$818$	−401.255			−0.490532
$819$	−115.825	−	91.3141i	−0.141423	−	0.111495i
$820$		0			0
$821$	505.805	+	876.080i	0.616084	+	1.06709i	0.990193	+	0.139704i	$0.0446153\pi$
$821$	505.805	+	876.080i	0.616084	+	1.06709i	−0.374109	+	0.927385i	$0.622051\pi$
$822$	−131.680	+	228.077i	−0.160195	+	0.277466i
$823$	965.106	+	557.204i	1.17267	+	0.677040i	0.954307	−	0.298828i	$-0.0965956\pi$
$823$	965.106	+	557.204i	1.17267	+	0.677040i	0.218361	+	0.975868i	$0.429929\pi$
$824$	91.6160	−	52.8945i	0.111184	−	0.0641924i
$825$		0			0
$826$	1009.77	−	402.827i	1.22249	−	0.487684i
$827$			1267.52i			1.53267i	0.642440	+	0.766336i	$0.277922\pi$
$827$			1267.52i			1.53267i	−0.642440	+	0.766336i	$0.722078\pi$
$828$	123.088	−	71.0647i	0.148657	−	0.0858269i
$829$	180.535	+	104.232i	0.217775	+	0.125732i	0.604919	−	0.796287i	$-0.293205\pi$
$829$	180.535	+	104.232i	0.217775	+	0.125732i	−0.387145	+	0.922019i	$0.626539\pi$
$830$		0			0
$831$	−169.948	+	98.1197i	−0.204511	+	0.118074i
$832$	56.1872			0.0675327
$833$	−363.081	−	1512.69i	−0.435871	−	1.81596i
$834$	666.270			0.798885
$835$		0			0
$836$	553.341	+	319.472i	0.661892	+	0.382143i
$837$	−90.6787	−	52.3534i	−0.108338	−	0.0625488i
$838$	−341.187	−	590.953i	−0.407144	−	0.705194i
$839$		−	389.239i		−	0.463932i	−0.972724	−	0.231966i	$-0.925484\pi$
$839$		−	389.239i		−	0.463932i	0.972724	−	0.231966i	$-0.0745159\pi$
$840$		0			0
$841$	−756.420			−0.899429
$842$	−933.354	+	538.872i	−1.10850	+	0.639991i
$843$	−154.789	+	268.103i	−0.183617	+	0.318034i
$844$	−263.018	+	455.561i	−0.311633	+	0.539764i
$845$		0			0
$846$			262.816i			0.310658i
$847$	−85.4037	−	67.3305i	−0.100831	−	0.0794930i
$848$			5.52601i			0.00651652i
$849$	37.3850	+	64.7528i	0.0440342	+	0.0762695i
$850$		0			0
$851$	570.468	−	988.080i	0.670350	−	1.16108i
$852$	−92.4030	−	160.047i	−0.108454	−	0.187848i
$853$	−1239.21			−1.45277			−0.726386	−	0.687287i	$-0.758801\pi$
$853$	−1239.21			−1.45277			−0.726386	+	0.687287i	$0.758801\pi$
$854$	−56.3928	+	388.861i	−0.0660337	+	0.455341i
$855$		0			0
$856$	35.0668	+	60.7375i	0.0409659	+	0.0709550i
$857$	91.1334	−	157.848i	0.106340	−	0.184186i	−0.807945	−	0.589258i	$-0.799420\pi$
$857$	91.1334	−	157.848i	0.106340	−	0.184186i	0.914285	+	0.405072i	$0.132753\pi$
$858$	153.005	+	88.3374i	0.178327	+	0.102957i
$859$	366.992	−	211.883i	0.427232	−	0.246662i	−0.270935	−	0.962598i	$-0.587333\pi$
$859$	366.992	−	211.883i	0.427232	−	0.246662i	0.698167	+	0.715935i	$0.253999\pi$
$860$		0			0
$861$	−781.396	−	113.318i	−0.907544	−	0.131612i
$862$		−	362.062i		−	0.420026i
$863$	−14.9502	+	8.63152i	−0.0173236	+	0.0100018i	−0.508637	−	0.860981i	$-0.669850\pi$
$863$	−14.9502	+	8.63152i	−0.0173236	+	0.0100018i	0.491313	+	0.870983i	$0.336517\pi$
$864$	−25.4558	−	14.6969i	−0.0294628	−	0.0170103i
$865$		0			0
$866$	−791.895	+	457.201i	−0.914428	+	0.527945i
$867$	−1245.24			−1.43627
$868$	−174.659	+	221.542i	−0.201221	+	0.255233i
$869$	−1093.15			−1.25794
$870$		0			0
$871$	−96.8266	−	55.9028i	−0.111167	−	0.0641824i
$872$	−137.881	−	79.6056i	−0.158120	−	0.0912908i
$873$	74.2198	+	128.552i	0.0850169	+	0.147254i
$874$		−	1042.15i		−	1.19239i
$875$		0			0
$876$	250.732			0.286224
$877$	318.122	−	183.668i	0.362739	−	0.209428i	−0.307542	−	0.951534i	$-0.599507\pi$
$877$	318.122	−	183.668i	0.362739	−	0.209428i	0.670282	+	0.742107i	$0.266173\pi$
$878$	237.071	−	410.620i	0.270013	−	0.467676i
$879$	−13.3737	+	23.1638i	−0.0152146	+	0.0263525i
$880$		0			0
$881$			376.890i			0.427798i	0.976856	+	0.213899i	$0.0686164\pi$
$881$			376.890i			0.427798i	−0.976856	+	0.213899i	$0.931384\pi$
$882$	202.148	−	48.5201i	0.229193	−	0.0550114i
$883$		−	1101.06i		−	1.24695i	−0.781842	−	0.623476i	$-0.785720\pi$
$883$		−	1101.06i		−	1.24695i	0.781842	−	0.623476i	$-0.214280\pi$
$884$	222.980	+	386.212i	0.252239	+	0.436891i
$885$		0			0
$886$	198.735	−	344.219i	0.224306	−	0.388509i
$887$	60.6873	+	105.113i	0.0684186	+	0.118504i	0.898205	−	0.439576i	$-0.144871\pi$
$887$	60.6873	+	105.113i	0.0684186	+	0.118504i	−0.829787	+	0.558081i	$0.811538\pi$
$888$	−235.958			−0.265718
$889$	333.304	+	835.498i	0.374920	+	0.939818i
$890$		0			0
$891$	−46.2130	−	80.0433i	−0.0518665	−	0.0898354i
$892$	−112.658	+	195.129i	−0.126298	+	0.218755i
$893$	1668.89	+	963.534i	1.86886	+	1.07899i
$894$	176.975	−	102.177i	0.197959	−	0.114292i
$895$		0			0
$896$	−49.0314	+	62.1926i	−0.0547225	+	0.0694114i
$897$		−	288.165i		−	0.321254i
$898$	57.8472	−	33.3981i	0.0644178	−	0.0371916i
$899$	−160.493	−	92.6609i	−0.178524	−	0.103071i
$900$		0			0
$901$	−37.9839	+	21.9300i	−0.0421575	+	0.0243397i
$902$	945.799			1.04856
$903$	36.4161	+	5.28108i	0.0403279	+	0.00584837i
$904$	−212.106			−0.234631
$905$		0			0
$906$	−268.972	−	155.291i	−0.296879	−	0.171403i
$907$	67.6459	+	39.0554i	0.0745820	+	0.0430599i	0.536827	−	0.843692i	$-0.319623\pi$
$907$	67.6459	+	39.0554i	0.0745820	+	0.0430599i	−0.462245	+	0.886752i	$0.652956\pi$
$908$	−49.0204	−	84.9058i	−0.0539872	−	0.0935086i
$909$		−	404.618i		−	0.445124i
$910$		0			0
$911$	863.281			0.947619			0.473809	−	0.880627i	$-0.342879\pi$
$911$	863.281			0.947619			0.473809	+	0.880627i	$0.342879\pi$
$912$	−186.652	+	107.763i	−0.204662	+	0.118162i
$913$	−253.811	+	439.614i	−0.277997	+	0.481505i
$914$	416.339	−	721.121i	0.455513	−	0.788973i
$915$		0			0
$916$			56.2283i			0.0613846i
$917$	−327.187	+	415.012i	−0.356801	+	0.452575i
$918$		−	233.300i		−	0.254139i
$919$	678.926	+	1175.93i	0.738766	+	1.27958i	0.953051	+	0.302810i	$0.0979247\pi$
$919$	678.926	+	1175.93i	0.738766	+	1.27958i	−0.214285	+	0.976771i	$0.568742\pi$
$920$		0			0
$921$	−203.211	+	351.973i	−0.220642	+	0.382163i
$922$	42.8228	+	74.1712i	0.0464455	+	0.0804460i
$923$	−374.691			−0.405949
$924$	−231.298	+	92.2714i	−0.250322	+	0.0998608i
$925$		0			0
$926$	−62.7622	−	108.707i	−0.0677778	−	0.117395i
$927$	−56.1031	+	97.1734i	−0.0605211	+	0.104826i
$928$	−45.0546	−	26.0123i	−0.0485502	−	0.0280305i
$929$	−800.920	+	462.411i	−0.862131	+	0.497752i	−0.864725	−	0.502245i	$-0.832508\pi$
$929$	−800.920	+	462.411i	−0.862131	+	0.497752i	0.00259410	+	0.999997i	$0.499174\pi$
$930$		0			0
$931$	433.009	−	1461.53i	0.465101	−	1.56985i
$932$		−	352.405i		−	0.378117i
$933$	−598.166	+	345.352i	−0.641121	+	0.370152i
$934$	370.147	+	213.704i	0.396303	+	0.228806i
$935$		0			0
$936$	−51.6112	+	29.7978i	−0.0551402	+	0.0318352i
$937$	270.668			0.288867			0.144433	−	0.989515i	$-0.453864\pi$
$937$	270.668			0.288867			0.144433	+	0.989515i	$0.453864\pi$
$938$	146.373	−	58.3924i	0.156048	−	0.0622520i
$939$	223.782			0.238319
$940$		0			0
$941$	−395.174	−	228.154i	−0.419952	−	0.242459i	0.275105	−	0.961414i	$-0.411287\pi$
$941$	−395.174	−	228.154i	−0.419952	−	0.242459i	−0.695057	+	0.718955i	$0.744621\pi$
$942$	−210.513	−	121.540i	−0.223475	−	0.129023i
$943$	−771.320	−	1335.97i	−0.817943	−	1.41672i
$944$		−	439.278i		−	0.465337i
$945$		0			0
$946$	−44.0780			−0.0465940
$947$	860.460	−	496.787i	0.908617	−	0.524590i	0.0286308	−	0.999590i	$-0.490885\pi$
$947$	860.460	−	496.787i	0.908617	−	0.524590i	0.879986	+	0.475000i	$0.157552\pi$
$948$	184.369	−	319.337i	0.194483	−	0.336854i
$949$	254.177	−	440.248i	0.267837	−	0.463907i
$950$		0			0
$951$		−	697.264i		−	0.733190i
$952$	−622.073	−	90.2132i	−0.653438	−	0.0947618i
$953$		−	206.385i		−	0.216563i	−0.994120	−	0.108281i	$-0.965465\pi$
$953$		−	206.385i		−	0.216563i	0.994120	−	0.108281i	$-0.0345348\pi$
$954$	−2.93061	−	5.07596i	−0.00307192	−	0.00532072i
$955$		0			0
$956$	−34.7150	+	60.1282i	−0.0363128	+	0.0628956i
$957$	−81.7930	−	141.670i	−0.0854681	−	0.148035i
$958$	49.6817			0.0518598
$959$	−744.825	−	108.015i	−0.776668	−	0.112633i
$960$		0			0
$961$	−277.472	−	480.596i	−0.288733	−	0.500100i
$962$	−239.200	+	414.306i	−0.248649	+	0.430672i
$963$	−64.4218	−	37.1940i	−0.0668970	−	0.0386230i
$964$	−459.743	+	265.432i	−0.476911	+	0.275345i
$965$		0			0
$966$	318.964	+	251.465i	0.330191	+	0.260316i
$967$		−	169.282i		−	0.175058i	−0.996162	−	0.0875292i	$-0.972103\pi$
$967$		−	169.282i		−	0.175058i	0.996162	−	0.0875292i	$-0.0278971\pi$
$968$	−38.0556	+	21.9714i	−0.0393136	+	0.0226977i
$969$	−1481.46	−	855.321i	−1.52885	−	0.882684i
$970$		0			0
$971$	−122.891	+	70.9512i	−0.126561	+	0.0730702i	−0.561944	−	0.827175i	$-0.689946\pi$
$971$	−122.891	+	70.9512i	−0.126561	+	0.0730702i	0.435383	+	0.900245i	$0.356613\pi$
$972$	31.1769			0.0320750
$973$	705.504	+	1768.50i	0.725081	+	1.81757i
$974$	−91.4053			−0.0938453
$975$		0			0
$976$	137.497	+	79.3837i	0.140878	+	0.0813357i
$977$	−1219.19	−	703.901i	−1.24789	−	0.720472i	−0.277204	−	0.960811i	$-0.589408\pi$
$977$	−1219.19	−	703.901i	−1.24789	−	0.720472i	−0.970689	+	0.240339i	$0.922741\pi$
$978$	341.679	+	591.805i	0.349365	+	0.605118i
$979$			1693.45i			1.72977i
$980$		0			0
$981$	168.869			0.172140
$982$	−295.610	+	170.671i	−0.301029	+	0.173799i
$983$	−448.890	+	777.500i	−0.456653	+	0.790946i	−0.998782	−	0.0493494i	$-0.984285\pi$
$983$	−448.890	+	777.500i	−0.456653	+	0.790946i	0.542129	+	0.840296i	$0.317619\pi$
$984$	−159.517	+	276.292i	−0.162111	+	0.280784i
$985$		0			0
$986$		−	412.920i		−	0.418783i
$987$	−697.600	+	278.293i	−0.706788	+	0.281958i
$988$			436.976i			0.442284i
$989$	35.9466	+	62.2613i	0.0363464	+	0.0629538i
$990$		0			0
$991$	−762.140	+	1320.06i	−0.769061	+	1.33205i	0.169011	+	0.985614i	$0.445943\pi$
$991$	−762.140	+	1320.06i	−0.769061	+	1.33205i	−0.938072	+	0.346439i	$0.887391\pi$
$992$	56.9951	+	98.7185i	0.0574548	+	0.0995146i
$993$	289.066			0.291104
$994$	326.971	−	414.739i	0.328945	−	0.417242i
$995$		0			0
$996$	−85.6150	−	148.289i	−0.0859588	−	0.148885i
$997$	444.935	−	770.649i	0.446273	−	0.772968i	−0.551866	−	0.833932i	$-0.686084\pi$
$997$	444.935	−	770.649i	0.446273	−	0.772968i	0.998140	+	0.0609641i	$0.0194175\pi$
$998$	234.691	+	135.499i	0.235162	+	0.135771i
$999$	216.741	−	125.136i	0.216958	−	0.125261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.q.e.199.3		32
5.2	odd	4		210.3.o.b.31.1	✓	16
5.3	odd	4		1050.3.p.i.451.7		16
5.4	even	2	inner	1050.3.q.e.199.14		32
7.5	odd	6	inner	1050.3.q.e.649.13		32
15.2	even	4		630.3.v.c.451.7		16
35.12	even	12		210.3.o.b.61.1	yes	16
35.17	even	12		1470.3.f.d.391.12		16
35.19	odd	6	inner	1050.3.q.e.649.3		32
35.32	odd	12		1470.3.f.d.391.14		16
35.33	even	12		1050.3.p.i.901.7		16
105.47	odd	12		630.3.v.c.271.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.b.31.1	✓	16	5.2	odd	4
210.3.o.b.61.1	yes	16	35.12	even	12
630.3.v.c.271.7		16	105.47	odd	12
630.3.v.c.451.7		16	15.2	even	4
1050.3.p.i.451.7		16	5.3	odd	4
1050.3.p.i.901.7		16	35.33	even	12
1050.3.q.e.199.3		32	1.1	even	1	trivial
1050.3.q.e.199.14		32	5.4	even	2	inner
1050.3.q.e.649.3		32	35.19	odd	6	inner
1050.3.q.e.649.13		32	7.5	odd	6	inner
1470.3.f.d.391.12		16	35.17	even	12
1470.3.f.d.391.14		16	35.32	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)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.50174 + 2.59373i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(-6.50174 + 2.59373i) q^{7} +2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.13478 + 8.89370i) q^{11} +(-1.73205 - 3.00000i) q^{12} -7.02340 q^{13} +(6.12892 - 7.77408i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(15.8741 - 27.4947i) q^{17} +(3.67423 + 2.12132i) q^{18} +(26.9408 - 15.5543i) q^{19} +(-1.74007 + 11.9988i) q^{21} -14.5234i q^{22} +(-20.5146 + 11.8441i) q^{23} +(4.24264 + 2.44949i) q^{24} +(8.60187 - 4.96629i) q^{26} -5.19615 q^{27} +(-2.00927 + 13.8551i) q^{28} -9.19673 q^{29} +(17.4511 + 10.0754i) q^{31} +(4.89898 + 2.82843i) q^{32} +(8.89370 + 15.4043i) q^{33} +44.8986i q^{34} -6.00000 q^{36} +(-41.7118 + 24.0823i) q^{37} +(-21.9971 + 38.1001i) q^{38} +(-6.08244 + 10.5351i) q^{39} +65.1226i q^{41} +(-6.35331 - 15.9259i) q^{42} -3.03497i q^{43} +(10.2696 + 17.7874i) q^{44} +(16.7501 - 29.0120i) q^{46} +(30.9732 + 53.6472i) q^{47} -6.92820 q^{48} +(35.5451 - 33.7275i) q^{49} +(-27.4947 - 47.6222i) q^{51} +(-7.02340 + 12.1649i) q^{52} +(-1.19642 - 0.690751i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-7.33617 - 18.3897i) q^{56} -53.8817i q^{57} +(11.2636 - 6.50307i) q^{58} +(95.1064 + 54.9097i) q^{59} +(-34.3741 + 19.8459i) q^{61} -28.4976 q^{62} +(16.4913 + 13.0014i) q^{63} -8.00000 q^{64} +(-21.7850 - 12.5776i) q^{66} +(13.7863 + 7.95952i) q^{67} +(-31.7481 - 54.9893i) q^{68} +41.0292i q^{69} +53.3489 q^{71} +(7.34847 - 4.24264i) q^{72} +(-36.1901 + 62.6830i) q^{73} +(34.0576 - 58.9894i) q^{74} -62.2172i q^{76} +(10.3171 - 71.1427i) q^{77} -17.2037i q^{78} +(53.2229 + 92.1847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-46.0486 - 79.7586i) q^{82} +49.4298 q^{83} +(19.0425 + 15.0127i) q^{84} +(2.14605 + 3.71707i) q^{86} +(-7.96460 + 13.7951i) q^{87} +(-25.1552 - 14.5234i) q^{88} +(142.807 - 82.4499i) q^{89} +(45.6643 - 18.2168i) q^{91} +47.3765i q^{92} +(30.2262 - 17.4511i) q^{93} +(-75.8686 - 43.8027i) q^{94} +(8.48528 - 4.89898i) q^{96} -49.4799 q^{97} +(-19.6848 + 66.4418i) q^{98} +30.8087 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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