LMFDB - Embedded newform 324.3.j.a.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(19,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 16]))

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

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

chi := DirichletCharacter("324.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.j (of order $18$, degree $6$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			19.10
Character	$\chi$	$=$	324.19
Dual form			324.3.j.a.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39865 + 1.42960i) q^{2} +(-0.0875399 - 3.99904i) q^{4} +(0.479555 + 2.71969i) q^{5} +(6.88504 - 8.20527i) q^{7} +(5.83949 + 5.46812i) q^{8} +O(q^{10})$	\(q+(-1.39865 + 1.42960i) q^{2} +(-0.0875399 - 3.99904i) q^{4} +(0.479555 + 2.71969i) q^{5} +(6.88504 - 8.20527i) q^{7} +(5.83949 + 5.46812i) q^{8} +(-4.55882 - 3.11833i) q^{10} +(-3.94539 - 0.695679i) q^{11} +(-12.6152 - 4.59155i) q^{13} +(2.10051 + 21.3192i) q^{14} +(-15.9847 + 0.700152i) q^{16} +(-14.6014 - 25.2904i) q^{17} +(5.56407 + 3.21242i) q^{19} +(10.8342 - 2.15584i) q^{20} +(6.51278 - 4.66734i) q^{22} +(-4.28210 - 5.10321i) q^{23} +(16.3256 - 5.94202i) q^{25} +(24.2084 - 11.6127i) q^{26} +(-33.4159 - 26.8153i) q^{28} +(26.7618 - 9.74049i) q^{29} +(-2.45869 - 2.93015i) q^{31} +(21.3561 - 23.8310i) q^{32} +(56.5776 + 14.4982i) q^{34} +(25.6176 + 14.7903i) q^{35} +(-21.2201 - 36.7544i) q^{37} +(-12.3747 + 3.46136i) q^{38} +(-12.0713 + 18.5039i) q^{40} +(-54.2511 - 19.7458i) q^{41} +(84.3675 + 14.8763i) q^{43} +(-2.43667 + 15.8387i) q^{44} +(13.2847 + 1.01591i) q^{46} +(15.9649 - 19.0263i) q^{47} +(-11.4139 - 64.7317i) q^{49} +(-14.3391 + 31.6499i) q^{50} +(-17.2575 + 50.8506i) q^{52} -6.37757 q^{53} -11.0639i q^{55} +(85.0726 - 10.2663i) q^{56} +(-23.5054 + 51.8823i) q^{58} +(61.5326 - 10.8499i) q^{59} +(25.8478 + 21.6889i) q^{61} +(7.62782 + 0.583312i) q^{62} +(4.19923 + 63.8621i) q^{64} +(6.43793 - 36.5113i) q^{65} +(-9.28610 + 25.5134i) q^{67} +(-99.8591 + 60.6056i) q^{68} +(-56.9744 + 15.9365i) q^{70} +(25.7260 - 14.8529i) q^{71} +(31.4586 - 54.4878i) q^{73} +(82.2239 + 21.0702i) q^{74} +(12.3595 - 22.5322i) q^{76} +(-32.8724 + 27.5832i) q^{77} +(-30.0773 - 82.6368i) q^{79} +(-9.56973 - 43.1376i) q^{80} +(104.107 - 49.9401i) q^{82} +(-28.4724 - 78.2273i) q^{83} +(61.7799 - 51.8395i) q^{85} +(-139.268 + 99.8055i) q^{86} +(-19.2350 - 25.6363i) q^{88} +(-67.2880 + 116.546i) q^{89} +(-124.531 + 71.8980i) q^{91} +(-20.0331 + 17.5710i) q^{92} +(4.87065 + 49.4347i) q^{94} +(-6.06851 + 16.6731i) q^{95} +(-24.5669 + 139.326i) q^{97} +(108.505 + 74.2198i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	$ 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−1.39865	+	1.42960i	−0.699326	+	0.714802i
$2$	−1.39865	+	1.42960i	−0.699326	+	0.714802i
$3$		0			0
$3$		0			0
$4$	−0.0875399	−	3.99904i	−0.0218850	−	0.999760i
$5$	0.479555	+	2.71969i	0.0959110	+	0.543938i	0.994464	+	0.105074i	$0.0335080\pi$
$5$	0.479555	+	2.71969i	0.0959110	+	0.543938i	−0.898553	+	0.438864i	$0.855381\pi$
$6$		0			0
$7$	6.88504	−	8.20527i	0.983577	−	1.17218i	−0.00148767	−	0.999999i	$-0.500474\pi$
$7$	6.88504	−	8.20527i	0.983577	−	1.17218i	0.985065	−	0.172183i	$-0.0550820\pi$
$8$	5.83949	+	5.46812i	0.729936	+	0.683516i
$9$		0			0
$10$	−4.55882	−	3.11833i	−0.455882	−	0.311833i
$11$	−3.94539	−	0.695679i	−0.358672	−	0.0632435i	−0.00859124	−	0.999963i	$-0.502735\pi$
$11$	−3.94539	−	0.695679i	−0.358672	−	0.0632435i	−0.350081	+	0.936720i	$0.613846\pi$
$12$		0			0
$13$	−12.6152	−	4.59155i	−0.970399	−	0.353196i	−0.192299	−	0.981336i	$-0.561594\pi$
$13$	−12.6152	−	4.59155i	−0.970399	−	0.353196i	−0.778100	+	0.628140i	$0.783817\pi$
$14$	2.10051	+	21.3192i	0.150037	+	1.52280i
$15$		0			0
$16$	−15.9847	+	0.700152i	−0.999042	+	0.0437595i
$17$	−14.6014	−	25.2904i	−0.858907	−	1.48767i	−0.872973	−	0.487769i	$-0.837811\pi$
$17$	−14.6014	−	25.2904i	−0.858907	−	1.48767i	0.0140658	−	0.999901i	$-0.495523\pi$
$18$		0			0
$19$	5.56407	+	3.21242i	0.292846	+	0.169075i	0.639225	−	0.769020i	$-0.279255\pi$
$19$	5.56407	+	3.21242i	0.292846	+	0.169075i	−0.346379	+	0.938095i	$0.612589\pi$
$20$	10.8342	−	2.15584i	0.541709	−	0.107792i
$21$		0			0
$22$	6.51278	−	4.66734i	0.296035	−	0.212152i
$23$	−4.28210	−	5.10321i	−0.186178	−	0.221879i	0.664880	−	0.746951i	$-0.268483\pi$
$23$	−4.28210	−	5.10321i	−0.186178	−	0.221879i	−0.851058	+	0.525072i	$0.824038\pi$
$24$		0			0
$25$	16.3256	−	5.94202i	0.653023	−	0.237681i
$26$	24.2084	−	11.6127i	0.931092	−	0.446644i
$27$		0			0
$28$	−33.4159	−	26.8153i	−1.19343	−	0.957689i
$29$	26.7618	−	9.74049i	0.922820	−	0.335879i	0.163460	−	0.986550i	$-0.447735\pi$
$29$	26.7618	−	9.74049i	0.922820	−	0.335879i	0.759360	+	0.650671i	$0.225512\pi$
$30$		0			0
$31$	−2.45869	−	2.93015i	−0.0793126	−	0.0945211i	0.724929	−	0.688824i	$-0.241873\pi$
$31$	−2.45869	−	2.93015i	−0.0793126	−	0.0945211i	−0.804242	+	0.594303i	$0.797428\pi$
$32$	21.3561	−	23.8310i	0.667377	−	0.744720i
$33$		0			0
$34$	56.5776	+	14.4982i	1.66405	+	0.426419i
$35$	25.6176	+	14.7903i	0.731931	+	0.422580i
$36$		0			0
$37$	−21.2201	−	36.7544i	−0.573518	−	0.993362i	−0.996201	−	0.0870841i	$-0.972245\pi$
$37$	−21.2201	−	36.7544i	−0.573518	−	0.993362i	0.422683	−	0.906277i	$-0.361088\pi$
$38$	−12.3747	+	3.46136i	−0.325650	+	0.0910885i
$39$		0			0
$40$	−12.0713	+	18.5039i	−0.301781	+	0.462597i
$41$	−54.2511	−	19.7458i	−1.32320	−	0.481604i	−0.418715	−	0.908118i	$-0.637519\pi$
$41$	−54.2511	−	19.7458i	−1.32320	−	0.481604i	−0.904481	+	0.426513i	$0.859742\pi$
$42$		0			0
$43$	84.3675	+	14.8763i	1.96204	+	0.345960i	0.996237	+	0.0866659i	$0.0276213\pi$
$43$	84.3675	+	14.8763i	1.96204	+	0.345960i	0.965798	+	0.259294i	$0.0834899\pi$
$44$	−2.43667	+	15.8387i	−0.0553789	+	0.359970i
$45$		0			0
$46$	13.2847	+	1.01591i	0.288799	+	0.0220849i
$47$	15.9649	−	19.0263i	0.339680	−	0.404815i	−0.568980	−	0.822351i	$-0.692662\pi$
$47$	15.9649	−	19.0263i	0.339680	−	0.404815i	0.908660	+	0.417537i	$0.137106\pi$
$48$		0			0
$49$	−11.4139	−	64.7317i	−0.232938	−	1.32106i
$50$	−14.3391	+	31.6499i	−0.286781	+	0.632999i
$51$		0			0
$52$	−17.2575	+	50.8506i	−0.331875	+	0.977896i
$53$	−6.37757			−0.120332			−0.0601658	−	0.998188i	$-0.519163\pi$
$53$	−6.37757			−0.120332			−0.0601658	+	0.998188i	$0.519163\pi$
$54$		0			0
$55$		−	11.0639i		−	0.201161i
$56$	85.0726	−	10.2663i	1.51915	−	0.183327i
$57$		0			0
$58$	−23.5054	+	51.8823i	−0.405265	+	0.894523i
$59$	61.5326	−	10.8499i	1.04292	−	0.183896i	0.374156	−	0.927366i	$-0.377933\pi$
$59$	61.5326	−	10.8499i	1.04292	−	0.183896i	0.668769	+	0.743470i	$0.266821\pi$
$60$		0			0
$61$	25.8478	+	21.6889i	0.423734	+	0.355555i	0.829581	−	0.558386i	$-0.188579\pi$
$61$	25.8478	+	21.6889i	0.423734	+	0.355555i	−0.405847	+	0.913941i	$0.633024\pi$
$62$	7.62782	+	0.583312i	0.123029	+	0.00940826i
$63$		0			0
$64$	4.19923	+	63.8621i	0.0656130	+	0.997845i
$65$	6.43793	−	36.5113i	0.0990451	−	0.561713i
$66$		0			0
$67$	−9.28610	+	25.5134i	−0.138599	+	0.380796i	−0.989501	−	0.144528i	$-0.953834\pi$
$67$	−9.28610	+	25.5134i	−0.138599	+	0.380796i	0.850902	+	0.525324i	$0.176056\pi$
$68$	−99.8591	+	60.6056i	−1.46852	+	0.891259i
$69$		0			0
$70$	−56.9744	+	15.9365i	−0.813920	+	0.227664i
$71$	25.7260	−	14.8529i	0.362339	−	0.209196i	−0.307768	−	0.951462i	$-0.599582\pi$
$71$	25.7260	−	14.8529i	0.362339	−	0.209196i	0.670106	+	0.742265i	$0.266249\pi$
$72$		0			0
$73$	31.4586	−	54.4878i	0.430939	−	0.746409i	−0.566015	−	0.824395i	$-0.691516\pi$
$73$	31.4586	−	54.4878i	0.430939	−	0.746409i	0.996954	+	0.0779862i	$0.0248490\pi$
$74$	82.2239	+	21.0702i	1.11113	+	0.284732i
$75$		0			0
$76$	12.3595	−	22.5322i	0.162625	−	0.296476i
$77$	−32.8724	+	27.5832i	−0.426914	+	0.358224i
$78$		0			0
$79$	−30.0773	−	82.6368i	−0.380726	−	1.04604i	−0.971052	−	0.238870i	$-0.923223\pi$
$79$	−30.0773	−	82.6368i	−0.380726	−	1.04604i	0.590326	−	0.807165i	$-0.298999\pi$
$80$	−9.56973	−	43.1376i	−0.119622	−	0.539220i
$81$		0			0
$82$	104.107	−	49.9401i	1.26960	−	0.609026i
$83$	−28.4724	−	78.2273i	−0.343041	−	0.942498i	−0.984507	−	0.175346i	$-0.943896\pi$
$83$	−28.4724	−	78.2273i	−0.343041	−	0.942498i	0.641466	−	0.767152i	$-0.278327\pi$
$84$		0			0
$85$	61.7799	−	51.8395i	0.726822	−	0.609876i
$86$	−139.268	+	99.8055i	−1.61940	+	1.16053i
$87$		0			0
$88$	−19.2350	−	25.6363i	−0.218580	−	0.291322i
$89$	−67.2880	+	116.546i	−0.756044	+	1.30951i	0.188809	+	0.982014i	$0.439537\pi$
$89$	−67.2880	+	116.546i	−0.756044	+	1.30951i	−0.944853	+	0.327493i	$0.893796\pi$
$90$		0			0
$91$	−124.531	+	71.8980i	−1.36847	+	0.790088i
$92$	−20.0331	+	17.5710i	−0.217751	+	0.190989i
$93$		0			0
$94$	4.87065	+	49.4347i	0.0518154	+	0.525901i
$95$	−6.06851	+	16.6731i	−0.0638790	+	0.175506i
$96$		0			0
$97$	−24.5669	+	139.326i	−0.253267	+	1.43635i	0.547216	+	0.836991i	$0.315687\pi$
$97$	−24.5669	+	139.326i	−0.253267	+	1.43635i	−0.800483	+	0.599355i	$0.795424\pi$
$98$	108.505	+	74.2198i	1.10719	+	0.757344i
$99$		0			0
$100$	−25.1915	−	64.7665i	−0.251915	−	0.647665i
$101$	−82.2098	−	68.9822i	−0.813959	−	0.682993i	0.137590	−	0.990489i	$-0.456064\pi$
$101$	−82.2098	−	68.9822i	−0.813959	−	0.682993i	−0.951549	+	0.307497i	$0.900509\pi$
$102$		0			0
$103$	−89.0485	+	15.7017i	−0.864549	+	0.152443i	−0.588300	−	0.808643i	$-0.700203\pi$
$103$	−89.0485	+	15.7017i	−0.864549	+	0.152443i	−0.276249	+	0.961086i	$0.589091\pi$
$104$	−48.5591	−	95.7937i	−0.466914	−	0.921094i
$105$		0			0
$106$	8.92001	−	9.11741i	0.0841510	−	0.0860133i
$107$			119.136i			1.11342i	0.830707	+	0.556710i	$0.187937\pi$
$107$			119.136i			1.11342i	−0.830707	+	0.556710i	$0.812063\pi$
$108$		0			0
$109$	−56.5706			−0.518996			−0.259498	−	0.965744i	$-0.583557\pi$
$109$	−56.5706			−0.518996			−0.259498	+	0.965744i	$0.583557\pi$
$110$	15.8170	+	15.4745i	0.143790	+	0.140677i
$111$		0			0
$112$	−104.310	+	135.979i	−0.931341	+	1.21410i
$113$	−11.0426	−	62.6255i	−0.0977218	−	0.554208i	−0.993879	−	0.110472i	$-0.964764\pi$
$113$	−11.0426	−	62.6255i	−0.0977218	−	0.554208i	0.896158	−	0.443736i	$-0.146347\pi$
$114$		0			0
$115$	11.8256	−	14.0933i	0.102832	−	0.122550i
$116$	−41.2953	−	106.169i	−0.355994	−	0.915248i
$117$		0			0
$118$	−70.5517	+	103.142i	−0.597896	+	0.874088i
$119$	−308.046	−	54.3168i	−2.58862	−	0.456444i
$120$		0			0
$121$	−98.6207	−	35.8950i	−0.815047	−	0.296653i
$122$	−67.1586	+	6.61692i	−0.550480	+	0.0542370i
$123$		0			0
$124$	−11.5026	+	10.0889i	−0.0927627	+	0.0813622i
$125$	58.5101	+	101.342i	0.468080	+	0.810739i
$126$		0			0
$127$	134.846	+	77.8535i	1.06178	+	0.613019i	0.925924	−	0.377709i	$-0.123288\pi$
$127$	134.846	+	77.8535i	1.06178	+	0.613019i	0.135856	+	0.990729i	$0.456621\pi$
$128$	−97.1708	−	83.3177i	−0.759147	−	0.650919i
$129$		0			0
$130$	43.1923	+	60.2704i	0.332249	+	0.463618i
$131$	−35.7128	−	42.5609i	−0.272617	−	0.324892i	0.612314	−	0.790615i	$-0.290239\pi$
$131$	−35.7128	−	42.5609i	−0.272617	−	0.324892i	−0.884931	+	0.465723i	$0.845794\pi$
$132$		0			0
$133$	64.6676	−	23.5371i	0.486223	−	0.176971i
$134$	−23.4860	−	48.9598i	−0.175269	−	0.365372i
$135$		0			0
$136$	53.0262	−	227.525i	0.389899	−	1.67298i
$137$	134.712	−	49.0310i	0.983296	−	0.357890i	0.200175	−	0.979760i	$-0.435849\pi$
$137$	134.712	−	49.0310i	0.983296	−	0.357890i	0.783121	+	0.621870i	$0.213627\pi$
$138$		0			0
$139$	−42.8676	−	51.0876i	−0.308400	−	0.367537i	0.589475	−	0.807786i	$-0.299334\pi$
$139$	−42.8676	−	51.0876i	−0.308400	−	0.367537i	−0.897876	+	0.440249i	$0.854890\pi$
$140$	56.9045	−	103.740i	0.406461	−	0.741003i
$141$		0			0
$142$	−14.7480	+	57.5522i	−0.103859	+	0.405297i
$143$	46.5776	+	26.8916i	0.325718	+	0.188053i
$144$		0			0
$145$	39.3249	+	68.1127i	0.271206	+	0.469743i
$146$	33.8964	+	121.183i	0.232167	+	0.830020i
$147$		0			0
$148$	−145.125	+	88.0777i	−0.980572	+	0.595120i
$149$	172.018	+	62.6093i	1.15448	+	0.420196i	0.847123	−	0.531398i	$-0.178333\pi$
$149$	172.018	+	62.6093i	1.15448	+	0.420196i	0.307358	+	0.951594i	$0.400555\pi$
$150$		0			0
$151$	173.422	+	30.5789i	1.14849	+	0.202509i	0.715315	−	0.698802i	$-0.246283\pi$
$151$	173.422	+	30.5789i	1.14849	+	0.202509i	0.433172	+	0.901311i	$0.357394\pi$
$152$	14.9254	+	49.1839i	0.0981936	+	0.323578i
$153$		0			0
$154$	6.54398	−	85.5739i	0.0424934	−	0.555675i
$155$	6.79004	−	8.09205i	0.0438067	−	0.0522068i
$156$		0			0
$157$	51.6585	+	292.970i	0.329035	+	1.86605i	0.479652	+	0.877459i	$0.340763\pi$
$157$	51.6585	+	292.970i	0.329035	+	1.86605i	−0.150616	+	0.988592i	$0.548126\pi$
$158$	160.206	+	72.5815i	1.01396	+	0.459376i
$159$		0			0
$160$	75.0545	+	46.6536i	0.469091	+	0.291585i
$161$	−71.3556			−0.443203
$162$		0			0
$163$			14.5977i			0.0895565i	0.998997	+	0.0447782i	$0.0142581\pi$
$163$			14.5977i			0.0895565i	−0.998997	+	0.0447782i	$0.985742\pi$
$164$	−74.2150	+	218.681i	−0.452531	+	1.33342i
$165$		0			0
$166$	151.657	+	68.7086i	0.913597	+	0.413907i
$167$	49.1521	−	8.66683i	0.294324	−	0.0518972i	−0.0245366	−	0.999699i	$-0.507811\pi$
$167$	49.1521	−	8.66683i	0.294324	−	0.0518972i	0.318860	+	0.947802i	$0.396700\pi$
$168$		0			0
$169$	8.59914	+	7.21553i	0.0508825	+	0.0426955i
$170$	−12.2987	+	160.826i	−0.0723450	+	0.946037i
$171$		0			0
$172$	52.1053	−	338.692i	0.302938	−	1.96914i
$173$	−7.11493	+	40.3508i	−0.0411268	+	0.233242i	−0.998442	−	0.0558055i	$-0.982227\pi$
$173$	−7.11493	+	40.3508i	−0.0411268	+	0.233242i	0.957315	+	0.289047i	$0.0933384\pi$
$174$		0			0
$175$	63.6463	−	174.867i	0.363693	−	0.999239i
$176$	63.5529	+	8.35783i	0.361096	+	0.0474877i
$177$		0			0
$178$	−72.5024	−	259.203i	−0.407317	−	1.45620i
$179$	60.9506	−	35.1898i	0.340506	−	0.196591i	−0.319990	−	0.947421i	$-0.603679\pi$
$179$	60.9506	−	35.1898i	0.340506	−	0.196591i	0.660496	+	0.750830i	$0.270346\pi$
$180$		0			0
$181$	14.6168	−	25.3171i	0.0807559	−	0.139873i	−0.822819	−	0.568304i	$-0.807600\pi$
$181$	14.6168	−	25.3171i	0.0807559	−	0.139873i	0.903575	+	0.428430i	$0.140933\pi$
$182$	71.3899	−	278.591i	0.392252	−	1.53072i
$183$		0			0
$184$	2.89970	−	53.2152i	0.0157593	−	0.289213i
$185$	89.7843	−	75.3380i	0.485321	−	0.407233i
$186$		0			0
$187$	40.0143	+	109.938i	0.213980	+	0.587906i
$188$	−77.4845	−	62.1789i	−0.412152	−	0.330739i
$189$		0			0
$190$	−15.3482	−	31.9954i	−0.0807799	−	0.168397i
$191$	92.8174	+	255.014i	0.485955	+	1.33515i	0.904314	+	0.426869i	$0.140383\pi$
$191$	92.8174	+	255.014i	0.485955	+	1.33515i	−0.418359	+	0.908282i	$0.637394\pi$
$192$		0			0
$193$	−15.0244	+	12.6070i	−0.0778467	+	0.0653211i	−0.680881	−	0.732394i	$-0.738403\pi$
$193$	−15.0244	+	12.6070i	−0.0778467	+	0.0653211i	0.603034	+	0.797716i	$0.293958\pi$
$194$	−164.820	−	229.989i	−0.849588	−	1.18551i
$195$		0			0
$196$	−257.866	+	51.3115i	−1.31564	+	0.261793i
$197$	41.0263	−	71.0596i	0.208255	−	0.360709i	−0.742910	−	0.669392i	$-0.766555\pi$
$197$	41.0263	−	71.0596i	0.208255	−	0.360709i	0.951165	+	0.308683i	$0.0998882\pi$
$198$		0			0
$199$	−207.379	+	119.730i	−1.04210	+	0.601659i	−0.920428	−	0.390911i	$-0.872160\pi$
$199$	−207.379	+	119.730i	−1.04210	+	0.601659i	−0.121675	+	0.992570i	$0.538827\pi$
$200$	127.825	+	54.5719i	0.639123	+	0.272859i
$201$		0			0
$202$	213.600	−	21.0454i	1.05743	−	0.104185i
$203$	104.333	−	286.651i	0.513953	−	1.41208i
$204$		0			0
$205$	27.6860	−	157.015i	0.135054	−	0.765929i
$206$	102.101	−	149.265i	0.495635	−	0.724589i
$207$		0			0
$208$	204.864	+	64.5619i	0.984925	+	0.310394i
$209$	−19.7176	−	16.5450i	−0.0943427	−	0.0791629i
$210$		0			0
$211$	−275.960	+	48.6593i	−1.30787	+	0.230613i	−0.783774	−	0.621047i	$-0.786708\pi$
$211$	−275.960	+	48.6593i	−1.30787	+	0.230613i	−0.524096	+	0.851659i	$0.675597\pi$
$212$	0.558292	+	25.5042i	0.00263345	+	0.120303i
$213$		0			0
$214$	−170.317	−	166.630i	−0.795876	−	0.778645i
$215$			236.588i			1.10041i
$216$		0			0
$217$	−40.9709			−0.188806
$218$	79.1226	−	80.8736i	0.362948	−	0.370980i
$219$		0			0
$220$	−44.2449	+	0.968530i	−0.201113	+	0.00440241i
$221$	68.0774	+	386.086i	0.308043	+	1.74700i
$222$		0			0
$223$	262.185	−	312.460i	1.17572	−	1.40117i	0.278010	−	0.960578i	$-0.410325\pi$
$223$	262.185	−	312.460i	1.17572	−	1.40117i	0.897709	−	0.440589i	$-0.145230\pi$
$224$	−48.5027	−	339.310i	−0.216530	−	1.51478i
$225$		0			0
$226$	104.974	+	71.8048i	0.464488	+	0.317720i
$227$	−140.975	−	24.8577i	−0.621035	−	0.109505i	−0.145727	−	0.989325i	$-0.546552\pi$
$227$	−140.975	−	24.8577i	−0.621035	−	0.109505i	−0.475308	+	0.879819i	$0.657663\pi$
$228$		0			0
$229$	−93.0432	−	33.8650i	−0.406302	−	0.147882i	0.130781	−	0.991411i	$-0.458252\pi$
$229$	−93.0432	−	33.8650i	−0.406302	−	0.147882i	−0.537083	+	0.843529i	$0.680474\pi$
$230$	3.60781	+	36.6176i	0.0156861	+	0.159207i
$231$		0			0
$232$	209.537	+	89.4572i	0.903178	+	0.385592i
$233$	−99.3139	−	172.017i	−0.426240	−	0.738269i	0.570295	−	0.821440i	$-0.306829\pi$
$233$	−99.3139	−	172.017i	−0.426240	−	0.738269i	−0.996535	+	0.0831703i	$0.973495\pi$
$234$		0			0
$235$	59.4017	+	34.2956i	0.252773	+	0.145939i
$236$	−48.7756	−	245.121i	−0.206676	−	1.03865i
$237$		0			0
$238$	508.501	−	364.414i	2.13656	−	1.53115i
$239$	191.617	+	228.360i	0.801744	+	0.955481i	0.999694	−	0.0247310i	$-0.00787293\pi$
$239$	191.617	+	228.360i	0.801744	+	0.955481i	−0.197950	+	0.980212i	$0.563428\pi$
$240$		0			0
$241$	−350.769	+	127.669i	−1.45547	+	0.529748i	−0.944114	−	0.329619i	$-0.893080\pi$
$241$	−350.769	+	127.669i	−1.45547	+	0.529748i	−0.511358	+	0.859368i	$0.670857\pi$
$242$	189.252	−	90.7840i	0.782032	−	0.375140i
$243$		0			0
$244$	84.4720	−	105.265i	0.346197	−	0.431414i
$245$	170.577	−	62.0848i	0.696231	−	0.253407i
$246$		0			0
$247$	−55.4418	−	66.0730i	−0.224461	−	0.267502i
$248$	1.66495	−	30.5550i	0.00671351	−	0.123206i
$249$		0			0
$250$	−226.715	−	58.0966i	−0.906859	−	0.232386i
$251$	203.533	+	117.510i	0.810889	+	0.468167i	0.847265	−	0.531171i	$-0.178248\pi$
$251$	203.533	+	117.510i	0.810889	+	0.468167i	−0.0363752	+	0.999338i	$0.511581\pi$
$252$		0			0
$253$	13.3444	+	23.1131i	0.0527445	+	0.0913561i
$254$	−299.903	+	83.8867i	−1.18072	+	0.330263i
$255$		0			0
$256$	255.020	−	22.3834i	0.996170	−	0.0874351i
$257$	61.4850	+	22.3787i	0.239241	+	0.0870767i	0.458858	−	0.888509i	$-0.348259\pi$
$257$	61.4850	+	22.3787i	0.239241	+	0.0870767i	−0.219617	+	0.975586i	$0.570481\pi$
$258$		0			0
$259$	−447.681	−	78.9383i	−1.72850	−	0.304781i
$260$	−146.574	−	22.5494i	−0.563746	−	0.0867283i
$261$		0			0
$262$	110.795	+	8.47268i	0.422882	+	0.0323385i
$263$	128.280	−	152.878i	0.487756	−	0.581285i	−0.464889	−	0.885369i	$-0.653906\pi$
$263$	128.280	−	152.878i	0.487756	−	0.581285i	0.952645	+	0.304084i	$0.0983504\pi$
$264$		0			0
$265$	−3.05840	−	17.3450i	−0.0115411	−	0.0654529i
$266$	−56.7988	+	125.369i	−0.213529	+	0.471313i
$267$		0			0
$268$	102.842	+	34.9021i	0.383738	+	0.130232i
$269$	175.681			0.653089			0.326544	−	0.945182i	$-0.394116\pi$
$269$	175.681			0.653089			0.326544	+	0.945182i	$0.394116\pi$
$270$		0			0
$271$			195.154i			0.720126i	0.932928	+	0.360063i	$0.117245\pi$
$271$			195.154i			0.720126i	−0.932928	+	0.360063i	$0.882755\pi$
$272$	251.106	+	394.035i	0.923184	+	1.44866i
$273$		0			0
$274$	−118.320	+	261.162i	−0.431824	+	0.953144i
$275$	−68.5445	+	12.0862i	−0.249253	+	0.0439500i
$276$		0			0
$277$	191.969	+	161.081i	0.693028	+	0.581520i	0.919781	−	0.392433i	$-0.128366\pi$
$277$	191.969	+	161.081i	0.693028	+	0.581520i	−0.226752	+	0.973952i	$0.572811\pi$
$278$	132.992	+	10.1701i	0.478389	+	0.0365832i
$279$		0			0
$280$	68.7182	+	226.448i	0.245422	+	0.808742i
$281$	−41.2615	+	234.006i	−0.146838	+	0.832760i	0.819035	+	0.573744i	$0.194509\pi$
$281$	−41.2615	+	234.006i	−0.146838	+	0.832760i	−0.965873	+	0.259016i	$0.916602\pi$
$282$		0			0
$283$	85.0094	−	233.561i	0.300387	−	0.825305i	−0.694046	−	0.719931i	$-0.744174\pi$
$283$	85.0094	−	233.561i	0.300387	−	0.825305i	0.994433	−	0.105375i	$-0.0336042\pi$
$284$	−61.6496	−	101.579i	−0.217076	−	0.357674i
$285$		0			0
$286$	−103.590	+	28.9756i	−0.362204	+	0.101313i
$287$	−535.540	+	309.194i	−1.86599	+	1.07733i
$288$		0			0
$289$	−281.903	+	488.270i	−0.975442	+	1.68951i
$290$	−152.376	−	39.0470i	−0.525435	−	0.134645i
$291$		0			0
$292$	−220.653	−	121.034i	−0.755661	−	0.414501i
$293$	70.3130	−	58.9996i	0.239976	−	0.201364i	−0.514866	−	0.857271i	$-0.672158\pi$
$293$	70.3130	−	58.9996i	0.239976	−	0.201364i	0.754842	+	0.655907i	$0.227714\pi$
$294$		0			0
$295$	59.0165	+	162.146i	0.200056	+	0.549649i
$296$	77.0627	−	330.661i	0.260347	−	1.11710i
$297$		0			0
$298$	−330.099	+	158.349i	−1.10772	+	0.531371i
$299$	30.5878	+	84.0394i	0.102300	+	0.281068i
$300$		0			0
$301$	702.938	−	589.835i	2.33534	−	1.95958i
$302$	−286.272	+	205.155i	−0.947922	+	0.679322i
$303$		0			0
$304$	−91.1890	−	47.4538i	−0.299964	−	0.156098i
$305$	−46.5916	+	80.6990i	−0.152759	+	0.264587i
$306$		0			0
$307$	303.723	−	175.354i	0.989324	−	0.571187i	0.0842519	−	0.996444i	$-0.473150\pi$
$307$	303.723	−	175.354i	0.989324	−	0.571187i	0.905072	+	0.425258i	$0.139817\pi$
$308$	113.184	+	129.044i	0.367481	+	0.418972i
$309$		0			0
$310$	2.07153	+	21.0251i	0.00668236	+	0.0678227i
$311$	121.780	−	334.587i	0.391575	−	1.07584i	−0.574708	−	0.818359i	$-0.694884\pi$
$311$	121.780	−	334.587i	0.391575	−	1.07584i	0.966283	−	0.257484i	$-0.0828934\pi$
$312$		0			0
$313$	−28.3513	+	160.788i	−0.0905793	+	0.513701i	0.905433	+	0.424489i	$0.139546\pi$
$313$	−28.3513	+	160.788i	−0.0905793	+	0.513701i	−0.996013	+	0.0892124i	$0.971565\pi$
$314$	−491.084	−	335.912i	−1.56396	−	1.06978i
$315$		0			0
$316$	−327.835	+	127.515i	−1.03745	+	0.403527i
$317$	−114.983	−	96.4823i	−0.362723	−	0.304361i	0.443152	−	0.896447i	$-0.353860\pi$
$317$	−114.983	−	96.4823i	−0.362723	−	0.304361i	−0.805875	+	0.592086i	$0.798305\pi$
$318$		0			0
$319$	−112.362	+	19.8124i	−0.352232	+	0.0621079i
$320$	−171.671	+	42.0460i	−0.536473	+	0.131394i
$321$		0			0
$322$	99.8017	−	102.010i	0.309943	−	0.316802i
$323$		−	187.623i		−	0.580877i
$324$		0			0
$325$	−233.233			−0.717641
$326$	−20.8690	−	20.4171i	−0.0640152	−	0.0626292i
$327$		0			0
$328$	−208.826	−	411.957i	−0.636665	−	1.25597i
$329$	−46.1965	−	261.994i	−0.140415	−	0.796333i
$330$		0			0
$331$	−72.2132	+	86.0604i	−0.218167	+	0.260001i	−0.864017	−	0.503463i	$-0.832059\pi$
$331$	−72.2132	+	86.0604i	−0.218167	+	0.260001i	0.645850	+	0.763465i	$0.276503\pi$
$332$	−310.342	+	120.710i	−0.934765	+	0.363586i
$333$		0			0
$334$	−56.3565	+	82.3899i	−0.168732	+	0.246676i
$335$	−73.8417	−	13.0203i	−0.220423	−	0.0388665i
$336$		0			0
$337$	−89.7083	−	32.6511i	−0.266197	−	0.0968877i	0.205474	−	0.978663i	$-0.434127\pi$
$337$	−89.7083	−	32.6511i	−0.266197	−	0.0968877i	−0.471670	+	0.881775i	$0.656349\pi$
$338$	−22.3426	+	2.20134i	−0.0661023	+	0.00651284i
$339$		0			0
$340$	−212.716	−	242.522i	−0.625637	−	0.713301i
$341$	7.66205	+	13.2711i	0.0224694	+	0.0389181i
$342$		0			0
$343$	−155.193	−	89.6009i	−0.452459	−	0.261227i
$344$	411.318	+	548.202i	1.19569	+	1.59361i
$345$		0			0
$346$	−47.7344	−	66.6083i	−0.137961	−	0.192510i
$347$	−211.714	−	252.311i	−0.610127	−	0.727121i	0.369212	−	0.929345i	$-0.379628\pi$
$347$	−211.714	−	252.311i	−0.610127	−	0.727121i	−0.979339	+	0.202224i	$0.935183\pi$
$348$		0			0
$349$	321.315	−	116.949i	0.920674	−	0.335098i	0.162167	−	0.986763i	$-0.448152\pi$
$349$	321.315	−	116.949i	0.920674	−	0.335098i	0.758506	+	0.651666i	$0.225929\pi$
$350$	160.971	+	335.567i	0.459918	+	0.958763i
$351$		0			0
$352$	−100.837	+	79.1658i	−0.286468	+	0.224903i
$353$	−150.584	+	54.8083i	−0.426585	+	0.155264i	−0.546386	−	0.837534i	$-0.683997\pi$
$353$	−150.584	+	54.8083i	−0.426585	+	0.155264i	0.119801	+	0.992798i	$0.461774\pi$
$354$		0			0
$355$	52.7325	+	62.8441i	0.148542	+	0.177026i
$356$	471.963	+	258.885i	1.32574	+	0.727205i
$357$		0			0
$358$	−34.9412	+	136.354i	−0.0976010	+	0.380876i
$359$	−386.417	−	223.098i	−1.07637	−	0.621443i	−0.146456	−	0.989217i	$-0.546787\pi$
$359$	−386.417	−	223.098i	−1.07637	−	0.621443i	−0.929915	+	0.367774i	$0.880120\pi$
$360$		0			0
$361$	−159.861	−	276.887i	−0.442828	−	0.767000i
$362$	15.7496	+	56.3061i	0.0435071	+	0.155542i
$363$		0			0
$364$	298.425	+	491.711i	0.819848	+	1.35085i
$365$	163.276	+	59.4277i	0.447332	+	0.162816i
$366$		0			0
$367$	136.104	+	23.9988i	0.370855	+	0.0653918i	0.355970	−	0.934497i	$-0.384151\pi$
$367$	136.104	+	23.9988i	0.370855	+	0.0653918i	0.0148853	+	0.999889i	$0.495262\pi$
$368$	72.0210	+	78.5750i	0.195709	+	0.213519i
$369$		0			0
$370$	−17.8736	+	233.728i	−0.0483069	+	0.631697i
$371$	−43.9098	+	52.3297i	−0.118355	+	0.141050i
$372$		0			0
$373$	62.3471	+	353.588i	0.167150	+	0.947957i	0.946820	+	0.321765i	$0.104276\pi$
$373$	62.3471	+	353.588i	0.167150	+	0.947957i	−0.779669	+	0.626192i	$0.784613\pi$
$374$	−213.135	−	96.5610i	−0.569879	−	0.258185i
$375$		0			0
$376$	197.265	−	23.8054i	0.524642	−	0.0633123i
$377$	−382.329			−1.01413
$378$		0			0
$379$			362.853i			0.957397i	0.877979	+	0.478698i	$0.158891\pi$
$379$			362.853i			0.957397i	−0.877979	+	0.478698i	$0.841109\pi$
$380$	67.2076	+	22.8087i	0.176862	+	0.0600228i
$381$		0			0
$382$	−494.388	−	223.984i	−1.29421	−	0.586344i
$383$	380.114	−	67.0243i	0.992464	−	0.174998i	0.346240	−	0.938146i	$-0.387458\pi$
$383$	380.114	−	67.0243i	0.992464	−	0.174998i	0.646224	+	0.763148i	$0.276347\pi$
$384$		0			0
$385$	−90.7820	−	76.1752i	−0.235797	−	0.197858i
$386$	2.99094	−	39.1118i	0.00774855	−	0.101326i
$387$		0			0
$388$	559.320	+	86.0474i	1.44155	+	0.221772i
$389$	−67.4685	+	382.633i	−0.173441	+	0.983633i	0.766487	+	0.642260i	$0.222003\pi$
$389$	−67.4685	+	382.633i	−0.173441	+	0.983633i	−0.939928	+	0.341373i	$0.889108\pi$
$390$		0			0
$391$	−66.5374	+	182.810i	−0.170172	+	0.467545i
$392$	287.309	−	440.413i	0.732932	−	1.12350i
$393$		0			0
$394$	44.2056	+	158.039i	0.112197	+	0.401115i
$395$	210.323	−	121.430i	0.532463	−	0.307418i
$396$		0			0
$397$	109.298	−	189.310i	0.275310	−	0.476850i	−0.694904	−	0.719103i	$-0.744553\pi$
$397$	109.298	−	189.310i	0.275310	−	0.476850i	0.970213	+	0.242253i	$0.0778863\pi$
$398$	118.884	−	463.930i	0.298704	−	1.16565i
$399$		0			0
$400$	−256.799	+	106.412i	−0.641996	+	0.266029i
$401$	−394.305	+	330.861i	−0.983304	+	0.825090i	−0.984585	−	0.174909i	$-0.944037\pi$
$401$	−394.305	+	330.861i	−0.983304	+	0.825090i	0.00128077	+	0.999999i	$0.499592\pi$
$402$		0			0
$403$	17.5629	+	48.2537i	0.0435804	+	0.119736i
$404$	−268.666	+	334.799i	−0.665015	+	0.828711i
$405$		0			0
$406$	263.873	+	550.080i	0.649934	+	1.35488i
$407$	58.1525	+	159.773i	0.142881	+	0.392562i
$408$		0			0
$409$	74.5657	−	62.5681i	0.182312	−	0.152978i	−0.547064	−	0.837091i	$-0.684255\pi$
$409$	74.5657	−	62.5681i	0.182312	−	0.152978i	0.729377	+	0.684112i	$0.239810\pi$
$410$	185.747	+	259.190i	0.453041	+	0.632171i
$411$		0			0
$412$	70.5869	+	354.734i	0.171327	+	0.861006i
$413$	334.628	−	579.593i	0.810238	−	1.40337i
$414$		0			0
$415$	199.100	−	114.951i	0.479759	−	0.276989i
$416$	−378.832	+	202.575i	−0.910655	+	0.486960i
$417$		0			0
$418$	51.2310	−	5.04763i	0.122562	−	0.0120757i
$419$	−268.045	+	736.447i	−0.639725	+	1.75763i	0.0128628	+	0.999917i	$0.495906\pi$
$419$	−268.045	+	736.447i	−0.639725	+	1.75763i	−0.652588	+	0.757713i	$0.726317\pi$
$420$		0			0
$421$	62.9563	−	357.043i	0.149540	−	0.848082i	−0.814069	−	0.580768i	$-0.802753\pi$
$421$	62.9563	−	357.043i	0.149540	−	0.848082i	0.963609	−	0.267315i	$-0.0861364\pi$
$422$	316.409	−	462.572i	0.749785	−	1.09614i
$423$		0			0
$424$	−37.2417	−	34.8733i	−0.0878343	−	0.0822485i
$425$	−388.652	−	326.118i	−0.914476	−	0.767337i
$426$		0			0
$427$	355.926	−	62.7594i	0.833551	−	0.146977i
$428$	476.430	−	10.4292i	1.11315	−	0.0243672i
$429$		0			0
$430$	−338.227	−	330.904i	−0.786574	−	0.769544i
$431$		−	391.570i		−	0.908516i	−0.890870	−	0.454258i	$-0.849904\pi$
$431$		−	391.570i		−	0.908516i	0.890870	−	0.454258i	$-0.150096\pi$
$432$		0			0
$433$	109.591			0.253097			0.126548	−	0.991960i	$-0.459610\pi$
$433$	109.591			0.253097			0.126548	+	0.991960i	$0.459610\pi$
$434$	57.3041	−	58.5722i	0.132037	−	0.134959i
$435$		0			0
$436$	4.95219	+	226.228i	0.0113582	+	0.518872i
$437$	−7.43227	−	42.1505i	−0.0170075	−	0.0964542i
$438$		0			0
$439$	−322.727	+	384.611i	−0.735141	+	0.876107i	−0.996008	−	0.0892681i	$-0.971547\pi$
$439$	−322.727	+	384.611i	−0.735141	+	0.876107i	0.260867	+	0.965375i	$0.415992\pi$
$440$	60.4986	−	64.6073i	0.137497	−	0.146835i
$441$		0			0
$442$	−647.168	−	442.677i	−1.46418	−	1.00153i
$443$	117.936	+	20.7954i	0.266222	+	0.0469422i	0.305166	−	0.952299i	$-0.401288\pi$
$443$	117.936	+	20.7954i	0.266222	+	0.0469422i	−0.0389435	+	0.999241i	$0.512399\pi$
$444$		0			0
$445$	−349.238	−	127.112i	−0.784804	−	0.285645i
$446$	79.9885	+	811.845i	0.179346	+	1.82028i
$447$		0			0
$448$	552.918	+	405.237i	1.23419	+	0.904547i
$449$	−174.179	−	301.687i	−0.387927	−	0.671909i	0.604244	−	0.796800i	$-0.293475\pi$
$449$	−174.179	−	301.687i	−0.387927	−	0.671909i	−0.992171	+	0.124891i	$0.960142\pi$
$450$		0			0
$451$	200.305	+	115.646i	0.444135	+	0.256422i
$452$	−249.475	+	49.6419i	−0.551936	+	0.109827i
$453$		0			0
$454$	232.712	−	166.771i	0.512581	−	0.367338i
$455$	−255.260	−	304.207i	−0.561011	−	0.668587i
$456$		0			0
$457$	103.935	−	37.8291i	0.227428	−	0.0827770i	−0.225793	−	0.974175i	$-0.572497\pi$
$457$	103.935	−	37.8291i	0.227428	−	0.0827770i	0.453221	+	0.891398i	$0.350275\pi$
$458$	178.549	−	85.6497i	0.389844	−	0.187008i
$459$		0			0
$460$	−57.3947	−	46.0575i	−0.124771	−	0.100125i
$461$	−32.3753	+	11.7837i	−0.0702284	+	0.0255611i	−0.376895	−	0.926256i	$-0.623008\pi$
$461$	−32.3753	+	11.7837i	−0.0702284	+	0.0255611i	0.306667	+	0.951817i	$0.400786\pi$
$462$		0			0
$463$	321.730	+	383.423i	0.694881	+	0.828127i	0.991937	−	0.126733i	$-0.0404492\pi$
$463$	321.730	+	383.423i	0.694881	+	0.828127i	−0.297056	+	0.954860i	$0.596005\pi$
$464$	−420.958	+	174.436i	−0.907238	+	0.375939i
$465$		0			0
$466$	384.822	+	98.6121i	0.825798	+	0.211614i
$467$	54.0741	+	31.2197i	0.115790	+	0.0668516i	0.556777	−	0.830662i	$-0.312038\pi$
$467$	54.0741	+	31.2197i	0.115790	+	0.0668516i	−0.440986	+	0.897514i	$0.645371\pi$
$468$		0			0
$469$	145.409	+	251.856i	0.310040	+	0.537005i
$470$	−132.112	+	36.9533i	−0.281088	+	0.0786241i
$471$		0			0
$472$	418.647	+	273.110i	0.886964	+	0.578623i
$473$	−322.514	−	117.385i	−0.681847	−	0.248172i
$474$		0			0
$475$	109.925	+	19.3827i	0.231421	+	0.0408057i
$476$	−190.249	+	1236.64i	−0.399683	+	2.59799i
$477$		0			0
$478$	−594.470	−	45.4601i	−1.24366	−	0.0951048i
$479$	374.570	−	446.396i	0.781984	−	0.931932i	−0.217037	−	0.976163i	$-0.569639\pi$
$479$	374.570	−	446.396i	0.781984	−	0.931932i	0.999021	+	0.0442311i	$0.0140838\pi$
$480$		0			0
$481$	98.9365	+	561.097i	0.205689	+	1.16652i
$482$	308.087	−	680.026i	0.639185	−	1.41084i
$483$		0			0
$484$	−134.912	+	397.530i	−0.278744	+	0.821344i
$485$	−390.704			−0.805575
$486$		0			0
$487$		−	132.281i		−	0.271624i	−0.990735	−	0.135812i	$-0.956636\pi$
$487$		−	132.281i		−	0.271624i	0.990735	−	0.135812i	$-0.0433644\pi$
$488$	32.3404	+	267.991i	0.0662713	+	0.549161i
$489$		0			0
$490$	−149.821	+	330.692i	−0.305757	+	0.674882i
$491$	−341.355	+	60.1901i	−0.695225	+	0.122587i	−0.510083	−	0.860125i	$-0.670385\pi$
$491$	−341.355	+	60.1901i	−0.695225	+	0.122587i	−0.185141	+	0.982712i	$0.559274\pi$
$492$		0			0
$493$	−637.101	−	534.591i	−1.29229	−	1.08436i
$494$	172.002	+	13.1533i	0.348182	+	0.0266261i
$495$		0			0
$496$	41.3529	+	45.1161i	0.0833729	+	0.0909599i
$497$	55.2525	−	313.352i	0.111172	−	0.630487i
$498$		0			0
$499$	282.637	−	776.540i	0.566408	−	1.55619i	−0.243663	−	0.969860i	$-0.578349\pi$
$499$	282.637	−	776.540i	0.566408	−	1.55619i	0.810070	−	0.586333i	$-0.199429\pi$
$500$	400.151	−	242.856i	0.800301	−	0.485711i
$501$		0			0
$502$	−452.665	+	126.616i	−0.901723	+	0.252224i
$503$	738.784	−	426.537i	1.46876	−	0.847987i	0.469369	−	0.883002i	$-0.344481\pi$
$503$	738.784	−	426.537i	1.46876	−	0.847987i	0.999387	+	0.0350156i	$0.0111481\pi$
$504$		0			0
$505$	148.186	−	256.666i	0.293438	−	0.508250i
$506$	−51.7067	−	13.2501i	−0.102187	−	0.0261859i
$507$		0			0
$508$	299.535	−	546.071i	0.589635	−	1.07494i
$509$	226.507	−	190.062i	0.445005	−	0.373403i	−0.392574	−	0.919721i	$-0.628415\pi$
$509$	226.507	−	190.062i	0.445005	−	0.373403i	0.837578	+	0.546317i	$0.183971\pi$
$510$		0			0
$511$	−230.494	−	633.277i	−0.451065	−	1.23929i
$512$	−324.684	+	395.884i	−0.634149	+	0.773211i
$513$		0			0
$514$	−117.989	+	56.5992i	−0.229550	+	0.110115i
$515$	−85.4074	−	234.655i	−0.165840	−	0.455640i
$516$		0			0
$517$	−76.2241	+	63.9597i	−0.147435	+	0.123713i
$518$	739.001	−	529.600i	1.42664	−	1.02239i
$519$		0			0
$520$	237.243	−	178.004i	0.456236	−	0.342315i
$521$	80.1249	−	138.780i	0.153791	−	0.266373i	−0.778827	−	0.627238i	$-0.784185\pi$
$521$	80.1249	−	138.780i	0.153791	−	0.266373i	0.932618	+	0.360865i	$0.117519\pi$
$522$		0			0
$523$	393.607	−	227.249i	0.752594	−	0.434510i	−0.0740363	−	0.997256i	$-0.523588\pi$
$523$	393.607	−	227.249i	0.752594	−	0.434510i	0.826630	+	0.562745i	$0.190255\pi$
$524$	−167.076	+	146.543i	−0.318848	+	0.279662i
$525$		0			0
$526$	39.1361	+	397.213i	0.0744032	+	0.755157i
$527$	−38.2044	+	104.966i	−0.0724941	+	0.199176i
$528$		0			0
$529$	84.1535	−	477.258i	0.159080	−	0.902190i
$530$	29.0742	+	19.8874i	0.0548569	+	0.0375233i
$531$		0			0
$532$	−99.7868	−	256.548i	−0.187569	−	0.482233i
$533$	593.724	+	498.193i	1.11393	+	0.934697i
$534$		0			0
$535$	−324.013	+	57.1323i	−0.605632	+	0.106789i
$536$	−193.736	+	98.2074i	−0.361448	+	0.183223i
$537$		0			0
$538$	−245.717	+	251.154i	−0.456722	+	0.466829i
$539$			263.332i			0.488557i
$540$		0			0
$541$	871.728			1.61133			0.805663	−	0.592374i	$-0.201809\pi$
$541$	871.728			1.61133			0.805663	+	0.592374i	$0.201809\pi$
$542$	−278.994	−	272.953i	−0.514748	−	0.503604i
$543$		0			0
$544$	−914.525	−	192.137i	−1.68111	−	0.353192i
$545$	−27.1287	−	153.855i	−0.0497774	−	0.282302i
$546$		0			0
$547$	−311.684	+	371.451i	−0.569807	+	0.679069i	−0.971591	−	0.236665i	$-0.923946\pi$
$547$	−311.684	+	371.451i	−0.569807	+	0.679069i	0.401784	+	0.915734i	$0.368390\pi$
$548$	−207.870	−	534.425i	−0.379324	−	0.975228i
$549$		0			0
$550$	78.5914	−	114.896i	0.142893	−	0.208902i
$551$	180.195	+	31.7732i	0.327032	+	0.0576647i
$552$		0			0
$553$	−885.141	−	322.165i	−1.60062	−	0.582577i
$554$	−498.780	+	49.1432i	−0.900325	+	0.0887061i
$555$		0			0
$556$	−200.549	+	175.902i	−0.360700	+	0.316370i
$557$	497.888	+	862.368i	0.893875	+	1.54824i	0.835191	+	0.549961i	$0.185357\pi$
$557$	497.888	+	862.368i	0.893875	+	1.54824i	0.0586846	+	0.998277i	$0.481309\pi$
$558$		0			0
$559$	−996.007	−	575.045i	−1.78177	−	1.02870i
$560$	−419.844	−	218.482i	−0.749721	−	0.390147i
$561$		0			0
$562$	−276.825	−	386.280i	−0.492571	−	0.687332i
$563$	452.656	+	539.454i	0.804007	+	0.958178i	0.999747	−	0.0224778i	$-0.00715550\pi$
$563$	452.656	+	539.454i	0.804007	+	0.958178i	−0.195741	+	0.980656i	$0.562711\pi$
$564$		0			0
$565$	165.026	−	60.0647i	0.292082	−	0.106309i
$566$	215.002	+	448.201i	0.379862	+	0.791875i
$567$		0			0
$568$	231.445	+	53.9396i	0.407473	+	0.0949642i
$569$	−80.5126	+	29.3042i	−0.141498	+	0.0515012i	−0.411799	−	0.911275i	$-0.635099\pi$
$569$	−80.5126	+	29.3042i	−0.141498	+	0.0515012i	0.270300	+	0.962776i	$0.412877\pi$
$570$		0			0
$571$	362.943	+	432.539i	0.635627	+	0.757511i	0.983673	−	0.179966i	$-0.0575989\pi$
$571$	362.943	+	432.539i	0.635627	+	0.757511i	−0.348045	+	0.937478i	$0.613154\pi$
$572$	103.463	−	188.620i	0.180880	−	0.329755i
$573$		0			0
$574$	307.009	−	1198.07i	0.534859	−	2.08722i
$575$	−100.231	−	57.8684i	−0.174315	−	0.100641i
$576$		0			0
$577$	−58.9669	−	102.134i	−0.102196	−	0.177008i	0.810393	−	0.585886i	$-0.199253\pi$
$577$	−58.9669	−	102.134i	−0.102196	−	0.177008i	−0.912589	+	0.408878i	$0.865920\pi$
$578$	−303.749	−	1085.93i	−0.525517	−	1.87877i
$579$		0			0
$580$	268.943	−	163.224i	0.463695	−	0.281421i
$581$	−837.910	−	304.974i	−1.44219	−	0.524913i
$582$		0			0
$583$	25.1620	+	4.43674i	0.0431595	+	0.00761019i
$584$	481.648	−	146.162i	0.824740	−	0.250277i
$585$		0			0
$586$	−13.9974	+	183.040i	−0.0238863	+	0.312355i
$587$	−215.284	+	256.566i	−0.366753	+	0.437079i	−0.917587	−	0.397536i	$-0.869865\pi$
$587$	−215.284	+	256.566i	−0.366753	+	0.437079i	0.550833	+	0.834615i	$0.314310\pi$
$588$		0			0
$589$	−4.26745	−	24.2019i	−0.00724525	−	0.0410899i
$590$	−314.349	−	142.416i	−0.532795	−	0.241384i
$591$		0			0
$592$	364.931	+	572.649i	0.616437	+	0.967313i
$593$	745.762			1.25761			0.628804	−	0.777564i	$-0.283545\pi$
$593$	745.762			1.25761			0.628804	+	0.777564i	$0.283545\pi$
$594$		0			0
$595$		−	863.838i		−	1.45183i
$596$	235.319	−	693.386i	0.394830	−	1.16340i
$597$		0			0
$598$	−162.925	−	73.8134i	−0.272450	−	0.123434i
$599$	−111.446	+	19.6509i	−0.186053	+	0.0328062i	−0.265898	−	0.964001i	$-0.585669\pi$
$599$	−111.446	+	19.6509i	−0.186053	+	0.0328062i	0.0798450	+	0.996807i	$0.474557\pi$
$600$		0			0
$601$	−236.295	−	198.275i	−0.393170	−	0.329909i	0.424676	−	0.905345i	$-0.360388\pi$
$601$	−236.295	−	198.275i	−0.393170	−	0.329909i	−0.817847	+	0.575436i	$0.804832\pi$
$602$	−139.935	+	1829.90i	−0.232451	+	3.03970i
$603$		0			0
$604$	107.105	−	696.197i	0.177326	−	1.15264i
$605$	50.3293	−	285.431i	0.0831889	−	0.471788i
$606$		0			0
$607$	−208.225	+	572.094i	−0.343040	+	0.942495i	0.641467	+	0.767150i	$0.278326\pi$
$607$	−208.225	+	572.094i	−0.343040	+	0.942495i	−0.984507	+	0.175344i	$0.943896\pi$
$608$	195.382	−	63.9929i	0.321352	−	0.105252i
$609$		0			0
$610$	−50.2022	−	179.477i	−0.0822987	−	0.294225i
$611$	−288.761	+	166.716i	−0.472604	+	0.272858i
$612$		0			0
$613$	534.388	−	925.588i	0.871759	−	1.50993i	0.0115838	−	0.999933i	$-0.496313\pi$
$613$	534.388	−	925.588i	0.871759	−	1.50993i	0.860175	−	0.509998i	$-0.170354\pi$
$614$	−174.115	+	679.463i	−0.283575	+	1.10662i
$615$		0			0
$616$	−342.787	−	18.6785i	−0.556472	−	0.0303223i
$617$	343.955	−	288.612i	0.557463	−	0.467767i	−0.319996	−	0.947419i	$-0.603682\pi$
$617$	343.955	−	288.612i	0.557463	−	0.467767i	0.877459	+	0.479652i	$0.159237\pi$
$618$		0			0
$619$	37.8961	+	104.119i	0.0612215	+	0.168205i	0.966532	−	0.256545i	$-0.0825842\pi$
$619$	37.8961	+	104.119i	0.0612215	+	0.168205i	−0.905311	+	0.424750i	$0.860362\pi$
$620$	−32.9549	−	26.4453i	−0.0531530	−	0.0426537i
$621$		0			0
$622$	308.000	+	642.068i	0.495176	+	1.03226i
$623$	493.013	+	1354.54i	0.791353	+	2.17422i
$624$		0			0
$625$	85.1568	−	71.4550i	0.136251	−	0.114328i
$626$	−190.210	−	265.418i	−0.303850	−	0.423991i
$627$		0			0
$628$	1167.08	−	232.231i	1.85840	−	0.369795i
$629$	−619.688	+	1073.33i	−0.985196	+	1.70641i
$630$		0			0
$631$	89.1012	−	51.4426i	0.141206	−	0.0815255i	−0.427732	−	0.903905i	$-0.640687\pi$
$631$	89.1012	−	51.4426i	0.141206	−	0.0815255i	0.568939	+	0.822380i	$0.307354\pi$
$632$	276.232	−	647.023i	0.437076	−	1.02377i
$633$		0			0
$634$	298.753	−	29.4352i	0.471220	−	0.0464278i
$635$	−147.071	+	404.075i	−0.231608	+	0.636339i
$636$		0			0
$637$	−153.230	+	869.010i	−0.240549	+	1.36422i
$638$	128.831	−	188.344i	0.201930	−	0.295210i
$639$		0			0
$640$	180.000	−	304.230i	0.281249	−	0.475360i
$641$	−571.595	−	479.625i	−0.891724	−	0.748245i	0.0768313	−	0.997044i	$-0.475520\pi$
$641$	−571.595	−	479.625i	−0.891724	−	0.748245i	−0.968555	+	0.248799i	$0.919964\pi$
$642$		0			0
$643$	56.2528	−	9.91888i	0.0874849	−	0.0154259i	−0.129734	−	0.991549i	$-0.541412\pi$
$643$	56.2528	−	9.91888i	0.0874849	−	0.0154259i	0.217219	+	0.976123i	$0.430301\pi$
$644$	6.24647	+	285.354i	0.00969948	+	0.443096i
$645$		0			0
$646$	268.227	+	262.420i	0.415213	+	0.406223i
$647$		−	1171.96i		−	1.81137i	−0.423949	−	0.905686i	$-0.639357\pi$
$647$		−	1171.96i		−	1.81137i	0.423949	−	0.905686i	$-0.360643\pi$
$648$		0			0
$649$	−250.318			−0.385698
$650$	326.212	−	333.431i	0.501865	−	0.512971i
$651$		0			0
$652$	58.3768	−	1.27788i	0.0895350	−	0.00195994i
$653$	−52.2667	−	296.419i	−0.0800408	−	0.453934i	−0.998317	−	0.0579936i	$-0.981530\pi$
$653$	−52.2667	−	296.419i	−0.0800408	−	0.453934i	0.918276	−	0.395941i	$-0.129581\pi$
$654$		0			0
$655$	98.6262	−	117.538i	0.150574	−	0.179448i
$656$	881.011	+	277.646i	1.34300	+	0.423240i
$657$		0			0
$658$	439.160	+	300.395i	0.667417	+	0.456528i
$659$	1253.24	+	220.980i	1.90173	+	0.335326i	0.996061	−	0.0886691i	$-0.0282614\pi$
$659$	1253.24	+	220.980i	1.90173	+	0.335326i	0.905665	+	0.423995i	$0.139372\pi$
$660$		0			0
$661$	−538.965	−	196.167i	−0.815379	−	0.296774i	−0.0995351	−	0.995034i	$-0.531736\pi$
$661$	−538.965	−	196.167i	−0.815379	−	0.296774i	−0.715844	+	0.698260i	$0.753958\pi$
$662$	−22.0311	−	223.605i	−0.0332796	−	0.337772i
$663$		0			0
$664$	261.492	−	612.498i	0.393814	−	0.922437i
$665$	95.0253	+	164.589i	0.142895	+	0.247502i
$666$		0			0
$667$	−164.304	−	94.8611i	−0.246333	−	0.142221i
$668$	−38.9618	−	195.802i	−0.0583260	−	0.293117i
$669$		0			0
$670$	121.893	−	87.3536i	0.181929	−	0.130378i
$671$	−86.8911	−	103.553i	−0.129495	−	0.154326i
$672$		0			0
$673$	−635.898	+	231.448i	−0.944870	+	0.343905i	−0.768087	−	0.640345i	$-0.778791\pi$
$673$	−635.898	+	231.448i	−0.944870	+	0.343905i	−0.176783	+	0.984250i	$0.556569\pi$
$674$	172.149	−	82.5798i	0.255414	−	0.122522i
$675$		0			0
$676$	28.1024	−	35.0200i	0.0415717	−	0.0518047i
$677$	258.562	−	94.1090i	0.381924	−	0.139009i	−0.143922	−	0.989589i	$-0.545971\pi$
$677$	258.562	−	94.1090i	0.381924	−	0.139009i	0.525845	+	0.850580i	$0.323749\pi$
$678$		0			0
$679$	974.061	+	1160.84i	1.43455	+	1.70963i
$680$	644.228	+	35.1041i	0.947394	+	0.0516237i
$681$		0			0
$682$	−29.6889	−	7.60791i	−0.0435322	−	0.0111553i
$683$	155.102	+	89.5482i	0.227089	+	0.131110i	0.609229	−	0.792995i	$-0.291479\pi$
$683$	155.102	+	89.5482i	0.227089	+	0.131110i	−0.382139	+	0.924105i	$0.624813\pi$
$684$		0			0
$685$	197.951	+	342.861i	0.288979	+	0.500527i
$686$	345.156	−	96.5446i	0.503142	−	0.140736i
$687$		0			0
$688$	−1359.00	−	178.722i	−1.97530	−	0.259771i
$689$	80.4543	+	29.2830i	0.116770	+	0.0425007i
$690$		0			0
$691$	112.470	+	19.8314i	0.162764	+	0.0286996i	0.254436	−	0.967090i	$-0.418110\pi$
$691$	112.470	+	19.8314i	0.162764	+	0.0286996i	−0.0916725	+	0.995789i	$0.529221\pi$
$692$	161.987	+	24.9206i	0.234086	+	0.0360124i
$693$		0			0
$694$	656.820	+	50.2281i	0.946426	+	0.0723747i
$695$	118.385	−	141.086i	0.170338	−	0.203002i
$696$		0			0
$697$	292.764	+	1660.35i	0.420034	+	2.38213i
$698$	−282.217	+	622.925i	−0.404323	+	0.892442i
$699$		0			0
$700$	−704.871	−	239.216i	−1.00696	−	0.341738i
$701$	899.374			1.28299			0.641494	−	0.767128i	$-0.278315\pi$
$701$	899.374			1.28299			0.641494	+	0.767128i	$0.278315\pi$
$702$		0			0
$703$		−	272.672i		−	0.387869i
$704$	27.8599	−	254.882i	0.0395737	−	0.362049i
$705$		0			0
$706$	132.261	−	291.934i	0.187339	−	0.413504i
$707$	−1132.04	+	199.609i	−1.60118	+	0.282332i
$708$		0			0
$709$	977.405	+	820.140i	1.37857	+	1.15676i	0.969738	+	0.244146i	$0.0785077\pi$
$709$	977.405	+	820.140i	1.37857	+	1.15676i	0.408830	+	0.912610i	$0.365937\pi$
$710$	−163.597	−	12.5105i	−0.230418	−	0.0176204i
$711$		0			0
$712$	−1030.22	+	312.631i	−1.44693	+	0.439088i
$713$	−4.42482	+	25.0944i	−0.00620592	+	0.0351955i
$714$		0			0
$715$	−50.8003	+	139.573i	−0.0710494	+	0.195207i
$716$	−146.061	−	240.663i	−0.203996	−	0.336122i
$717$		0			0
$718$	859.405	−	240.387i	1.19694	−	0.334801i
$719$	6.70417	−	3.87065i	0.00932429	−	0.00538338i	−0.495331	−	0.868705i	$-0.664953\pi$
$719$	6.70417	−	3.87065i	0.00932429	−	0.00538338i	0.504655	+	0.863321i	$0.331620\pi$
$720$		0			0
$721$	−484.266	+	838.774i	−0.671659	+	1.16335i
$722$	619.429	+	158.731i	0.857934	+	0.219849i
$723$		0			0
$724$	−102.524	−	56.2370i	−0.141607	−	0.0776754i
$725$	379.023	−	318.038i	0.522790	−	0.438673i
$726$		0			0
$727$	24.9037	+	68.4224i	0.0342554	+	0.0941160i	0.955641	−	0.294533i	$-0.0951641\pi$
$727$	24.9037	+	68.4224i	0.0342554	+	0.0941160i	−0.921386	+	0.388649i	$0.872942\pi$
$728$	−1120.34	−	261.104i	−1.53894	−	0.358659i
$729$		0			0
$730$	−313.325	+	150.302i	−0.429212	+	0.205893i
$731$	−855.659	−	2350.90i	−1.17053	−	3.21601i
$732$		0			0
$733$	319.658	−	268.225i	0.436096	−	0.365928i	−0.398150	−	0.917320i	$-0.630348\pi$
$733$	319.658	−	268.225i	0.436096	−	0.365928i	0.834246	+	0.551392i	$0.185903\pi$
$734$	−224.671	+	161.009i	−0.306091	+	0.219358i
$735$		0			0
$736$	−213.063	−	6.93759i	−0.289488	−	0.00942607i
$737$	54.3864	−	94.2000i	0.0737943	−	0.127815i
$738$		0			0
$739$	288.257	−	166.425i	0.390063	−	0.225203i	−0.292124	−	0.956380i	$-0.594362\pi$
$739$	288.257	−	166.425i	0.390063	−	0.225203i	0.682188	+	0.731177i	$0.261029\pi$
$740$	−309.140	−	352.456i	−0.417756	−	0.476292i
$741$		0			0
$742$	−13.3962	−	135.965i	−0.0180541	−	0.183241i
$743$	−228.523	+	627.863i	−0.307569	+	0.845038i	0.685561	+	0.728016i	$0.259557\pi$
$743$	−228.523	+	627.863i	−0.307569	+	0.845038i	−0.993129	+	0.117022i	$0.962665\pi$
$744$		0			0
$745$	−87.7860	+	497.859i	−0.117834	+	0.668268i
$746$	−592.693	−	405.415i	−0.794494	−	0.543452i
$747$		0			0
$748$	436.145	−	169.643i	0.583082	−	0.226795i
$749$	977.544	+	820.256i	1.30513	+	1.09514i
$750$		0			0
$751$	319.336	−	56.3076i	0.425215	−	0.0749768i	0.0430541	−	0.999073i	$-0.486291\pi$
$751$	319.336	−	56.3076i	0.425215	−	0.0749768i	0.382161	+	0.924096i	$0.375180\pi$
$752$	−241.873	+	315.307i	−0.321640	+	0.419291i
$753$		0			0
$754$	534.745	−	546.579i	0.709211	−	0.724906i
$755$			486.318i			0.644129i
$756$		0			0
$757$	480.106			0.634222			0.317111	−	0.948388i	$-0.397287\pi$
$757$	480.106			0.634222			0.317111	+	0.948388i	$0.397287\pi$
$758$	−518.737	−	507.506i	−0.684350	−	0.669533i
$759$		0			0
$760$	−126.607	+	64.1789i	−0.166589	+	0.0844460i
$761$	−41.2739	−	234.076i	−0.0542364	−	0.307590i	0.945607	−	0.325313i	$-0.105470\pi$
$761$	−41.2739	−	234.076i	−0.0542364	−	0.307590i	−0.999843	+	0.0177226i	$0.994358\pi$
$762$		0			0
$763$	−389.491	+	464.177i	−0.510473	+	0.608358i
$764$	1011.69	−	393.505i	1.32420	−	0.515058i
$765$		0			0
$766$	−435.829	+	637.156i	−0.568967	+	0.831797i
$767$	−826.063	−	145.657i	−1.07700	−	0.189905i
$768$		0			0
$769$	−573.990	−	208.915i	−0.746411	−	0.271671i	−0.0593164	−	0.998239i	$-0.518892\pi$
$769$	−573.990	−	208.915i	−0.746411	−	0.271671i	−0.687095	+	0.726568i	$0.741114\pi$
$770$	235.873	−	23.2398i	0.306328	−	0.0301816i
$771$		0			0
$772$	51.7311	+	58.9796i	0.0670092	+	0.0763985i
$773$	−216.951	−	375.770i	−0.280661	−	0.486119i	0.690887	−	0.722963i	$-0.257220\pi$
$773$	−216.951	−	375.770i	−0.280661	−	0.486119i	−0.971548	+	0.236844i	$0.923887\pi$
$774$		0			0
$775$	−57.5506	−	33.2268i	−0.0742588	−	0.0428733i
$776$	−905.308	+	679.256i	−1.16663	+	0.875329i
$777$		0			0
$778$	−452.649	−	631.624i	−0.581811	−	0.811856i
$779$	−238.425	−	284.144i	−0.306066	−	0.364755i
$780$		0			0
$781$	−111.832	+	40.7036i	−0.143191	+	0.0521173i
$782$	−168.283	−	350.810i	−0.215196	−	0.448606i
$783$		0			0
$784$	227.770	+	1026.72i	0.290523	+	1.30960i
$785$	−772.015	+	280.991i	−0.983459	+	0.357950i
$786$		0			0
$787$	−316.793	−	377.539i	−0.402533	−	0.479720i	0.526258	−	0.850325i	$-0.323595\pi$
$787$	−316.793	−	377.539i	−0.402533	−	0.479720i	−0.928790	+	0.370605i	$0.879150\pi$
$788$	−287.762	−	157.845i	−0.365180	−	0.200311i
$789$		0			0
$790$	−120.572	+	470.517i	−0.152623	+	0.595591i
$791$	−589.888	−	340.572i	−0.745749	−	0.430558i
$792$		0			0
$793$	−226.489	−	392.291i	−0.285610	−	0.494692i
$794$	117.768	+	421.031i	0.148322	+	0.530266i
$795$		0			0
$796$	496.960	+	818.835i	0.624321	+	1.02869i
$797$	772.427	+	281.140i	0.969168	+	0.352748i	0.777620	−	0.628735i	$-0.216427\pi$
$797$	772.427	+	281.140i	0.969168	+	0.352748i	0.191548	+	0.981483i	$0.438649\pi$
$798$		0			0
$799$	−714.293	−	125.949i	−0.893984	−	0.157633i
$800$	207.045	−	515.953i	0.258807	−	0.644942i
$801$		0			0
$802$	78.4951	−	1026.46i	0.0978741	−	1.27988i
$803$	−162.022	+	193.091i	−0.201771	+	0.240462i
$804$		0			0
$805$	−34.2189	−	194.065i	−0.0425080	−	0.241075i
$806$	−93.5481	−	42.3821i	−0.116065	−	0.0525833i
$807$		0			0
$808$	−102.860	−	852.355i	−0.127302	−	1.05489i
$809$	516.017			0.637845			0.318922	−	0.947781i	$-0.396679\pi$
$809$	516.017			0.637845			0.318922	+	0.947781i	$0.396679\pi$
$810$		0			0
$811$		−	134.169i		−	0.165437i	−0.996573	−	0.0827183i	$-0.973640\pi$
$811$		−	134.169i		−	0.165437i	0.996573	−	0.0827183i	$-0.0263602\pi$
$812$	−1155.46	−	392.137i	−1.42299	−	0.482927i
$813$		0			0
$814$	−309.747	−	140.332i	−0.380525	−	0.172397i
$815$	−39.7013	+	7.00040i	−0.0487132	+	0.00858945i
$816$		0			0
$817$	421.638	+	353.796i	0.516081	+	0.433043i
$818$	−14.8440	+	194.111i	−0.0181466	+	0.237299i
$819$		0			0
$820$	−630.335	−	96.9725i	−0.768701	−	0.118259i
$821$	−63.0494	+	357.571i	−0.0767959	+	0.435531i	0.922031	+	0.387115i	$0.126528\pi$
$821$	−63.0494	+	357.571i	−0.0767959	+	0.435531i	−0.998827	+	0.0484160i	$0.984583\pi$
$822$		0			0
$823$	−58.8132	+	161.588i	−0.0714620	+	0.196340i	−0.970282	−	0.241979i	$-0.922204\pi$
$823$	−58.8132	+	161.588i	−0.0714620	+	0.196340i	0.898820	+	0.438319i	$0.144426\pi$
$824$	−605.856	−	395.239i	−0.735263	−	0.479659i
$825$		0			0
$826$	360.560	+	1289.04i	0.436514	+	1.56058i
$827$	−110.416	+	63.7485i	−0.133513	+	0.0770840i	−0.565269	−	0.824907i	$-0.691228\pi$
$827$	−110.416	+	63.7485i	−0.133513	+	0.0770840i	0.431756	+	0.901991i	$0.357894\pi$
$828$		0			0
$829$	−348.608	+	603.807i	−0.420517	+	0.728356i	−0.995990	−	0.0894643i	$-0.971485\pi$
$829$	−348.608	+	603.807i	−0.420517	+	0.728356i	0.575473	+	0.817821i	$0.304818\pi$
$830$	−114.138	+	445.410i	−0.137516	+	0.536639i
$831$		0			0
$832$	240.252	−	824.913i	0.288765	−	0.991482i
$833$	−1470.43	+	1233.84i	−1.76522	+	1.48120i
$834$		0			0
$835$	47.1422	+	129.522i	0.0564578	+	0.155116i
$836$	−64.4383	+	80.2999i	−0.0770793	+	0.0960526i
$837$		0			0
$838$	−677.927	−	1413.23i	−0.808982	−	1.68643i
$839$	179.495	+	493.157i	0.213939	+	0.587792i	0.999520	−	0.0309662i	$-0.00985843\pi$
$839$	179.495	+	493.157i	0.213939	+	0.587792i	−0.785582	+	0.618758i	$0.787636\pi$
$840$		0			0
$841$	−22.9280	+	19.2389i	−0.0272628	+	0.0228762i
$842$	422.376	+	589.381i	0.501634	+	0.699978i
$843$		0			0
$844$	218.748	+	1099.32i	0.259180	+	1.30251i
$845$	−15.5003	+	26.8472i	−0.0183435	+	0.0317719i
$846$		0			0
$847$	−973.536	+	562.071i	−1.14939	+	0.663602i
$848$	101.943	−	4.46527i	0.120216	−	0.00526565i
$849$		0			0
$850$	1009.81	−	99.4933i	1.18801	−	0.117051i
$851$	−96.6984	+	265.677i	−0.113629	+	0.312193i
$852$		0			0
$853$	−19.4406	+	110.253i	−0.0227908	+	0.129253i	−0.994080	−	0.108647i	$-0.965348\pi$
$853$	−19.4406	+	110.253i	−0.0227908	+	0.129253i	0.971290	+	0.237900i	$0.0764592\pi$
$854$	−408.096	+	596.612i	−0.477864	+	0.698609i
$855$		0			0
$856$	−651.451	+	695.693i	−0.761040	+	0.812726i
$857$	1229.55	+	1031.71i	1.43471	+	1.20387i	0.942860	+	0.333188i	$0.108124\pi$
$857$	1229.55	+	1031.71i	1.43471	+	1.20387i	0.491852	+	0.870679i	$0.336320\pi$
$858$		0			0
$859$	−1502.90	+	265.002i	−1.74959	+	0.308500i	−0.954550	−	0.298052i	$-0.903663\pi$
$859$	−1502.90	+	265.002i	−1.74959	+	0.308500i	−0.795043	+	0.606553i	$0.792552\pi$
$860$	946.124	−	20.7109i	1.10014	−	0.0240824i
$861$		0			0
$862$	559.791	+	547.671i	0.649409	+	0.635349i
$863$			223.078i			0.258491i	0.991613	+	0.129246i	$0.0412555\pi$
$863$			223.078i			0.258491i	−0.991613	+	0.129246i	$0.958744\pi$
$864$		0			0
$865$	−113.154			−0.130814
$866$	−153.280	+	156.672i	−0.176997	+	0.180914i
$867$		0			0
$868$	3.58659	+	163.844i	0.00413202	+	0.188761i
$869$	61.1782	+	346.959i	0.0704006	+	0.399262i
$870$		0			0
$871$	234.292	−	279.218i	0.268992	−	0.320572i
$872$	−330.343	−	309.335i	−0.378834	−	0.354742i
$873$		0			0
$874$	70.6537	+	48.3287i	0.0808395	+	0.0552960i
$875$	1234.39	+	217.656i	1.41073	+	0.248749i
$876$		0			0
$877$	458.826	+	166.999i	0.523177	+	0.190421i	0.590089	−	0.807338i	$-0.299093\pi$
$877$	458.826	+	166.999i	0.523177	+	0.190421i	−0.0669123	+	0.997759i	$0.521315\pi$
$878$	−98.4587	−	999.309i	−0.112140	−	1.13817i
$879$		0			0
$880$	7.74638	+	176.852i	0.00880271	+	0.200968i
$881$	−219.502	−	380.189i	−0.249151	−	0.431543i	0.714139	−	0.700004i	$-0.246818\pi$
$881$	−219.502	−	380.189i	−0.249151	−	0.431543i	−0.963291	+	0.268461i	$0.913485\pi$
$882$		0			0
$883$	149.149	+	86.1113i	0.168912	+	0.0975213i	0.582073	−	0.813137i	$-0.302242\pi$
$883$	149.149	+	86.1113i	0.168912	+	0.0975213i	−0.413161	+	0.910658i	$0.635575\pi$
$884$	1538.02	−	306.042i	1.73984	−	0.346202i
$885$		0			0
$886$	−194.681	+	139.517i	−0.219731	+	0.157468i
$887$	925.651	+	1103.15i	1.04358	+	1.24368i	0.969153	+	0.246458i	$0.0792667\pi$
$887$	925.651	+	1103.15i	1.04358	+	1.24368i	0.0744220	+	0.997227i	$0.476289\pi$
$888$		0			0
$889$	1567.23	−	570.425i	1.76291	−	0.641648i
$890$	670.183	−	321.486i	0.753014	−	0.361221i
$891$		0			0
$892$	−1272.49	−	1021.14i	−1.42656	−	1.14477i
$893$	149.950	−	54.5775i	0.167918	−	0.0611170i
$894$		0			0
$895$	124.935	+	148.891i	0.139592	+	0.166359i
$896$	−1352.67	+	223.668i	−1.50968	+	0.249629i
$897$		0			0
$898$	674.910	+	172.948i	0.751570	+	0.192593i
$899$	−94.3401	−	54.4673i	−0.104939	−	0.0605865i
$900$		0			0
$901$	93.1216	+	161.291i	0.103354	+	0.179014i
$902$	−445.485	+	124.608i	−0.493886	+	0.138146i
$903$		0			0
$904$	277.961	−	426.083i	0.307479	−	0.471330i
$905$	75.8642	+	27.6123i	0.0838278	+	0.0305108i
$906$		0			0
$907$	−914.986	−	161.337i	−1.00880	−	0.177879i	−0.355260	−	0.934768i	$-0.615608\pi$
$907$	−914.986	−	161.337i	−1.00880	−	0.177879i	−0.653544	+	0.756888i	$0.726719\pi$
$908$	−87.0660	+	565.941i	−0.0958877	+	0.623283i
$909$		0			0
$910$	791.916	+	60.5591i	0.870237	+	0.0665485i
$911$	−1152.56	+	1373.56i	−1.26515	+	1.50775i	−0.496580	+	0.867991i	$0.665411\pi$
$911$	−1152.56	+	1373.56i	−1.26515	+	1.50775i	−0.768574	+	0.639761i	$0.779033\pi$
$912$		0			0
$913$	57.9137	+	328.445i	0.0634323	+	0.359743i
$914$	−91.2877	+	201.495i	−0.0998771	+	0.220454i
$915$		0			0
$916$	−127.282	+	375.048i	−0.138955	+	0.409441i
$917$	−595.108			−0.648973
$918$		0			0
$919$		−	793.239i		−	0.863154i	−0.902076	−	0.431577i	$-0.857957\pi$
$919$		−	793.239i		−	0.863154i	0.902076	−	0.431577i	$-0.142043\pi$
$920$	146.119	−	17.6333i	0.158825	−	0.0191666i
$921$		0			0
$922$	28.4359	−	62.7651i	0.0308415	−	0.0680750i
$923$	−392.737	+	69.2501i	−0.425500	+	0.0750272i
$924$		0			0
$925$	−564.826	−	473.945i	−0.610623	−	0.512373i
$926$	−998.132	−	76.3288i	−1.07790	−	0.0824285i
$927$		0			0
$928$	339.400	−	845.779i	0.365733	−	0.911400i
$929$	73.9324	−	419.292i	0.0795828	−	0.451336i	−0.918812	−	0.394696i	$-0.870850\pi$
$929$	73.9324	−	419.292i	0.0795828	−	0.451336i	0.998395	−	0.0566406i	$-0.0180389\pi$
$930$		0			0
$931$	144.437	−	396.838i	0.155142	−	0.426249i
$932$	−679.208	+	412.219i	−0.728764	+	0.442295i
$933$		0			0
$934$	−120.263	+	33.6391i	−0.128761	+	0.0360161i
$935$	−279.809	+	161.548i	−0.299261	+	0.172779i
$936$		0			0
$937$	315.711	−	546.828i	0.336938	−	0.583594i	−0.646917	−	0.762561i	$-0.723942\pi$
$937$	315.711	−	546.828i	0.336938	−	0.583594i	0.983855	+	0.178966i	$0.0572753\pi$
$938$	−563.430	−	144.381i	−0.600672	−	0.153925i
$939$		0			0
$940$	131.949	−	240.552i	0.140372	−	0.255907i
$941$	−607.699	+	509.920i	−0.645802	+	0.541892i	−0.905794	−	0.423719i	$-0.860725\pi$
$941$	−607.699	+	509.920i	−0.645802	+	0.541892i	0.259992	+	0.965611i	$0.416280\pi$
$942$		0			0
$943$	131.542	+	361.408i	0.139493	+	0.383253i
$944$	−975.981	+	216.513i	−1.03388	+	0.229357i
$945$		0			0
$946$	618.900	−	296.886i	0.654228	−	0.313833i
$947$	47.7790	+	131.272i	0.0504530	+	0.138618i	0.962360	−	0.271779i	$-0.0876121\pi$
$947$	47.7790	+	131.272i	0.0504530	+	0.138618i	−0.911907	+	0.410398i	$0.865390\pi$
$948$		0			0
$949$	−647.039	+	542.931i	−0.681812	+	0.572108i
$950$	−181.456	+	130.039i	−0.191007	+	0.136884i
$951$		0			0
$952$	−1501.82	−	2001.62i	−1.57754	−	2.10254i
$953$	384.189	−	665.436i	0.403137	−	0.698253i	−0.590966	−	0.806697i	$-0.701253\pi$
$953$	384.189	−	665.436i	0.403137	−	0.698253i	0.994103	+	0.108443i	$0.0345865\pi$
$954$		0			0
$955$	−649.048	+	374.728i	−0.679631	+	0.392385i
$956$	896.447	−	786.274i	0.937706	−	0.822462i
$957$		0			0
$958$	114.275	+	1159.84i	0.119285	+	1.21069i
$959$	525.182	−	1442.92i	0.547635	−	1.50461i
$960$		0			0
$961$	164.335	−	931.992i	0.171004	−	0.969814i
$962$	−940.525	−	643.340i	−0.977676	−	0.668752i
$963$		0			0
$964$	541.261	+	1391.56i	0.561475	+	1.44353i
$965$	−41.4921	−	34.8160i	−0.0429970	−	0.0360788i
$966$		0			0
$967$	443.889	−	78.2696i	0.459037	−	0.0809407i	0.0606523	−	0.998159i	$-0.480682\pi$
$967$	443.889	−	78.2696i	0.459037	−	0.0809407i	0.398385	+	0.917218i	$0.369571\pi$
$968$	−379.616	−	748.878i	−0.392165	−	0.773635i
$969$		0			0
$970$	546.459	−	558.552i	0.563360	−	0.575827i
$971$		−	796.807i		−	0.820605i	−0.911950	−	0.410302i	$-0.865423\pi$
$971$		−	796.807i		−	0.820605i	0.911950	−	0.410302i	$-0.134577\pi$
$972$		0			0
$973$	−714.333			−0.734156
$974$	189.110	+	185.015i	0.194158	+	0.189954i
$975$		0			0
$976$	−428.354	−	328.592i	−0.438887	−	0.336672i
$977$	65.1805	+	369.657i	0.0667149	+	0.378359i	0.999824	+	0.0187655i	$0.00597358\pi$
$977$	65.1805	+	369.657i	0.0667149	+	0.378359i	−0.933109	+	0.359594i	$0.882915\pi$
$978$		0			0
$979$	346.556	−	413.009i	0.353990	−	0.421869i
$980$	−263.212	−	676.708i	−0.268584	−	0.690519i
$981$		0			0
$982$	391.389	−	572.188i	0.398564	−	0.582676i
$983$	548.248	+	96.6709i	0.557729	+	0.0983427i	0.445406	−	0.895329i	$-0.353060\pi$
$983$	548.248	+	96.6709i	0.557729	+	0.0983427i	0.112324	+	0.993672i	$0.464171\pi$
$984$		0			0
$985$	212.935	+	77.5019i	0.216177	+	0.0786821i
$986$	1655.34	−	163.095i	1.67884	−	0.165411i
$987$		0			0
$988$	−259.375	+	227.498i	−0.262526	+	0.230261i
$989$	−285.353	−	494.247i	−0.288527	−	0.499744i
$990$		0			0
$991$	695.394	+	401.486i	0.701710	+	0.405132i	0.807984	−	0.589205i	$-0.200559\pi$
$991$	695.394	+	401.486i	0.701710	+	0.405132i	−0.106274	+	0.994337i	$0.533892\pi$
$992$	−122.337	−	3.98342i	−0.123323	−	0.00401554i
$993$		0			0
$994$	370.691	+	517.260i	0.372928	+	0.520383i
$995$	−425.079	−	506.589i	−0.427215	−	0.509135i
$996$		0			0
$997$	−1432.55	+	521.406i	−1.43686	+	0.522975i	−0.938890	−	0.344217i	$-0.888144\pi$
$997$	−1432.55	+	521.406i	−1.43686	+	0.522975i	−0.497973	+	0.867193i	$0.665922\pi$
$998$	714.834	+	1490.17i	0.716266	+	1.49316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.j.a.19.10		204
3.2	odd	2		108.3.j.a.7.25	✓	204
4.3	odd	2	inner	324.3.j.a.19.2		204
12.11	even	2		108.3.j.a.7.33	yes	204
27.4	even	9	inner	324.3.j.a.307.2		204
27.23	odd	18		108.3.j.a.31.33	yes	204
108.23	even	18		108.3.j.a.31.25	yes	204
108.31	odd	18	inner	324.3.j.a.307.10		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.3.j.a.7.25	✓	204	3.2	odd	2
108.3.j.a.7.33	yes	204	12.11	even	2
108.3.j.a.31.25	yes	204	108.23	even	18
108.3.j.a.31.33	yes	204	27.23	odd	18
324.3.j.a.19.2		204	4.3	odd	2	inner
324.3.j.a.19.10		204	1.1	even	1	trivial
324.3.j.a.307.2		204	27.4	even	9	inner
324.3.j.a.307.10		204	108.31	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.j (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39865 + 1.42960i) q^{2} +(-0.0875399 - 3.99904i) q^{4} +(0.479555 + 2.71969i) q^{5} +(6.88504 - 8.20527i) q^{7} +(5.83949 + 5.46812i) q^{8} +O(q^{10})\)	\(q+(-1.39865 + 1.42960i) q^{2} +(-0.0875399 - 3.99904i) q^{4} +(0.479555 + 2.71969i) q^{5} +(6.88504 - 8.20527i) q^{7} +(5.83949 + 5.46812i) q^{8} +(-4.55882 - 3.11833i) q^{10} +(-3.94539 - 0.695679i) q^{11} +(-12.6152 - 4.59155i) q^{13} +(2.10051 + 21.3192i) q^{14} +(-15.9847 + 0.700152i) q^{16} +(-14.6014 - 25.2904i) q^{17} +(5.56407 + 3.21242i) q^{19} +(10.8342 - 2.15584i) q^{20} +(6.51278 - 4.66734i) q^{22} +(-4.28210 - 5.10321i) q^{23} +(16.3256 - 5.94202i) q^{25} +(24.2084 - 11.6127i) q^{26} +(-33.4159 - 26.8153i) q^{28} +(26.7618 - 9.74049i) q^{29} +(-2.45869 - 2.93015i) q^{31} +(21.3561 - 23.8310i) q^{32} +(56.5776 + 14.4982i) q^{34} +(25.6176 + 14.7903i) q^{35} +(-21.2201 - 36.7544i) q^{37} +(-12.3747 + 3.46136i) q^{38} +(-12.0713 + 18.5039i) q^{40} +(-54.2511 - 19.7458i) q^{41} +(84.3675 + 14.8763i) q^{43} +(-2.43667 + 15.8387i) q^{44} +(13.2847 + 1.01591i) q^{46} +(15.9649 - 19.0263i) q^{47} +(-11.4139 - 64.7317i) q^{49} +(-14.3391 + 31.6499i) q^{50} +(-17.2575 + 50.8506i) q^{52} -6.37757 q^{53} -11.0639i q^{55} +(85.0726 - 10.2663i) q^{56} +(-23.5054 + 51.8823i) q^{58} +(61.5326 - 10.8499i) q^{59} +(25.8478 + 21.6889i) q^{61} +(7.62782 + 0.583312i) q^{62} +(4.19923 + 63.8621i) q^{64} +(6.43793 - 36.5113i) q^{65} +(-9.28610 + 25.5134i) q^{67} +(-99.8591 + 60.6056i) q^{68} +(-56.9744 + 15.9365i) q^{70} +(25.7260 - 14.8529i) q^{71} +(31.4586 - 54.4878i) q^{73} +(82.2239 + 21.0702i) q^{74} +(12.3595 - 22.5322i) q^{76} +(-32.8724 + 27.5832i) q^{77} +(-30.0773 - 82.6368i) q^{79} +(-9.56973 - 43.1376i) q^{80} +(104.107 - 49.9401i) q^{82} +(-28.4724 - 78.2273i) q^{83} +(61.7799 - 51.8395i) q^{85} +(-139.268 + 99.8055i) q^{86} +(-19.2350 - 25.6363i) q^{88} +(-67.2880 + 116.546i) q^{89} +(-124.531 + 71.8980i) q^{91} +(-20.0331 + 17.5710i) q^{92} +(4.87065 + 49.4347i) q^{94} +(-6.06851 + 16.6731i) q^{95} +(-24.5669 + 139.326i) q^{97} +(108.505 + 74.2198i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8}+O(q^{10}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8	\( 204 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 3 q^{8} - 3 q^{10} - 12 q^{13} - 39 q^{14} - 6 q^{16} + 6 q^{17} + 69 q^{20} - 6 q^{22} - 12 q^{25} + 174 q^{26} - 12 q^{28} - 60 q^{29} + 96 q^{32} + 6 q^{34} - 6 q^{37} - 72 q^{38} + 69 q^{40} + 192 q^{41} + 219 q^{44} - 3 q^{46} - 12 q^{49} + 165 q^{50} + 21 q^{52} + 24 q^{53} - 99 q^{56} - 141 q^{58} - 12 q^{61} - 294 q^{62} - 3 q^{64} + 156 q^{65} - 375 q^{68} - 165 q^{70} - 6 q^{73} - 447 q^{74} - 54 q^{76} - 132 q^{77} - 798 q^{80} - 12 q^{82} + 138 q^{85} - 606 q^{86} - 198 q^{88} + 114 q^{89} - 723 q^{92} - 357 q^{94} + 168 q^{97} - 510 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 3 * q^8 - 3 * q^10 - 12 * q^13 - 39 * q^14 - 6 * q^16 + 6 * q^17 + 69 * q^20 - 6 * q^22 - 12 * q^25 + 174 * q^26 - 12 * q^28 - 60 * q^29 + 96 * q^32 + 6 * q^34 - 6 * q^37 - 72 * q^38 + 69 * q^40 + 192 * q^41 + 219 * q^44 - 3 * q^46 - 12 * q^49 + 165 * q^50 + 21 * q^52 + 24 * q^53 - 99 * q^56 - 141 * q^58 - 12 * q^61 - 294 * q^62 - 3 * q^64 + 156 * q^65 - 375 * q^68 - 165 * q^70 - 6 * q^73 - 447 * q^74 - 54 * q^76 - 132 * q^77 - 798 * q^80 - 12 * q^82 + 138 * q^85 - 606 * q^86 - 198 * q^88 + 114 * q^89 - 723 * q^92 - 357 * q^94 + 168 * q^97 - 510 * q^98

Introduction

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