LMFDB - Embedded newform 756.2.bj.b.451.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(451,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("756.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bj (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.17
Character	$\chi$	$=$	756.451
Dual form			756.2.bj.b.523.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.514563 - 1.31728i) q^{2} +(-1.47045 + 1.35565i) q^{4} +(-2.53954 - 1.46621i) q^{5} +(2.33334 + 1.24720i) q^{7} +(2.54241 + 1.23943i) q^{8} +O(q^{10})$	\(q+(-0.514563 - 1.31728i) q^{2} +(-1.47045 + 1.35565i) q^{4} +(-2.53954 - 1.46621i) q^{5} +(2.33334 + 1.24720i) q^{7} +(2.54241 + 1.23943i) q^{8} +(-0.624647 + 4.09975i) q^{10} +(1.58550 - 0.915388i) q^{11} +(0.488438 - 0.282000i) q^{13} +(0.442264 - 3.71543i) q^{14} +(0.324441 - 3.98682i) q^{16} +(-0.330952 - 0.191075i) q^{17} +(-4.34210 - 7.52073i) q^{19} +(5.72193 - 1.28674i) q^{20} +(-2.02166 - 1.61752i) q^{22} +(-4.16067 - 2.40216i) q^{23} +(1.79952 + 3.11687i) q^{25} +(-0.622805 - 0.498302i) q^{26} +(-5.12183 + 1.32924i) q^{28} +(1.82266 - 3.15694i) q^{29} +0.654198 q^{31} +(-5.41870 + 1.62409i) q^{32} +(-0.0814037 + 0.534277i) q^{34} +(-4.09697 - 6.58849i) q^{35} +(3.63968 + 6.30411i) q^{37} +(-7.67262 + 9.58965i) q^{38} +(-4.63930 - 6.87527i) q^{40} +(-8.94130 + 5.16226i) q^{41} +(-5.57437 - 3.21836i) q^{43} +(-1.09045 + 3.49541i) q^{44} +(-1.02339 + 6.71682i) q^{46} -7.97727 q^{47} +(3.88897 + 5.82030i) q^{49} +(3.17982 - 3.97430i) q^{50} +(-0.335931 + 1.07682i) q^{52} +(3.65087 - 6.32349i) q^{53} -5.36859 q^{55} +(4.38648 + 6.06290i) q^{56} +(-5.09644 - 0.776506i) q^{58} +0.0693815 q^{59} -9.83174i q^{61} +(-0.336626 - 0.861761i) q^{62} +(4.92765 + 6.30224i) q^{64} -1.65388 q^{65} -1.81471i q^{67} +(0.745679 - 0.167688i) q^{68} +(-6.57073 + 8.78704i) q^{70} -9.64068i q^{71} +(-13.1397 - 7.58623i) q^{73} +(6.43143 - 8.03834i) q^{74} +(16.5803 + 5.17250i) q^{76} +(4.84118 - 0.158473i) q^{77} -6.31873i q^{79} +(-6.66944 + 9.64901i) q^{80} +(11.4010 + 9.12188i) q^{82} +(2.90035 - 5.02356i) q^{83} +(0.560312 + 0.970489i) q^{85} +(-1.37112 + 8.99905i) q^{86} +(5.16553 - 0.362179i) q^{88} +(1.91814 - 1.10744i) q^{89} +(1.49140 - 0.0488201i) q^{91} +(9.37453 - 2.10814i) q^{92} +(4.10481 + 10.5083i) q^{94} +25.4656i q^{95} +(1.59144 + 0.918820i) q^{97} +(5.66585 - 8.11777i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	$ 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.514563	−	1.31728i	−0.363851	−	0.931457i
$2$	−0.514563	−	1.31728i	−0.363851	−	0.931457i
$3$		0			0
$3$		0			0
$4$	−1.47045	+	1.35565i	−0.735225	+	0.677824i
$5$	−2.53954	−	1.46621i	−1.13572	−	0.655708i	−0.190352	−	0.981716i	$-0.560963\pi$
$5$	−2.53954	−	1.46621i	−1.13572	−	0.655708i	−0.945367	+	0.326008i	$0.894296\pi$
$6$		0			0
$7$	2.33334	+	1.24720i	0.881920	+	0.471399i
$7$	2.33334	+	1.24720i	0.881920	+	0.471399i
$8$	2.54241	+	1.23943i	0.898876	+	0.438203i
$9$		0			0
$10$	−0.624647	+	4.09975i	−0.197531	+	1.29645i
$11$	1.58550	−	0.915388i	0.478046	−	0.276000i	−0.241556	−	0.970387i	$-0.577658\pi$
$11$	1.58550	−	0.915388i	0.478046	−	0.276000i	0.719602	+	0.694387i	$0.244324\pi$
$12$		0			0
$13$	0.488438	−	0.282000i	0.135468	−	0.0782127i	−0.430734	−	0.902479i	$-0.641745\pi$
$13$	0.488438	−	0.282000i	0.135468	−	0.0782127i	0.566203	+	0.824266i	$0.308412\pi$
$14$	0.442264	−	3.71543i	0.118200	−	0.992990i
$15$		0			0
$16$	0.324441	−	3.98682i	0.0811103	−	0.996705i
$17$	−0.330952	−	0.191075i	−0.0802677	−	0.0463426i	0.459329	−	0.888266i	$-0.348090\pi$
$17$	−0.330952	−	0.191075i	−0.0802677	−	0.0463426i	−0.539597	+	0.841924i	$0.681423\pi$
$18$		0			0
$19$	−4.34210	−	7.52073i	−0.996145	−	1.72537i	−0.574038	−	0.818829i	$-0.694624\pi$
$19$	−4.34210	−	7.52073i	−0.996145	−	1.72537i	−0.422107	−	0.906546i	$-0.638709\pi$
$20$	5.72193	−	1.28674i	1.27946	−	0.287725i
$21$		0			0
$22$	−2.02166	−	1.61752i	−0.431020	−	0.344856i
$23$	−4.16067	−	2.40216i	−0.867559	−	0.500885i	−0.00102274	−	0.999999i	$-0.500326\pi$
$23$	−4.16067	−	2.40216i	−0.867559	−	0.500885i	−0.866536	+	0.499114i	$0.833659\pi$
$24$		0			0
$25$	1.79952	+	3.11687i	0.359905	+	0.623374i
$26$	−0.622805	−	0.498302i	−0.122142	−	0.0977251i
$27$		0			0
$28$	−5.12183	+	1.32924i	−0.967935	+	0.251202i
$29$	1.82266	−	3.15694i	0.338459	−	0.586229i	−0.645684	−	0.763605i	$-0.723428\pi$
$29$	1.82266	−	3.15694i	0.338459	−	0.586229i	0.984143	+	0.177376i	$0.0567609\pi$
$30$		0			0
$31$	0.654198			0.117497			0.0587487	−	0.998273i	$-0.481289\pi$
$31$	0.654198			0.117497			0.0587487	+	0.998273i	$0.481289\pi$
$32$	−5.41870	+	1.62409i	−0.957900	+	0.287102i
$33$		0			0
$34$	−0.0814037	+	0.534277i	−0.0139606	+	0.0916278i
$35$	−4.09697	−	6.58849i	−0.692514	−	1.11366i
$36$		0			0
$37$	3.63968	+	6.30411i	0.598360	+	1.03639i	0.993063	+	0.117581i	$0.0375141\pi$
$37$	3.63968	+	6.30411i	0.598360	+	1.03639i	−0.394703	+	0.918809i	$0.629153\pi$
$38$	−7.67262	+	9.58965i	−1.24466	+	1.55565i
$39$		0			0
$40$	−4.63930	−	6.87527i	−0.733537	−	1.08708i
$41$	−8.94130	+	5.16226i	−1.39640	+	0.806210i	−0.994013	−	0.109261i	$-0.965152\pi$
$41$	−8.94130	+	5.16226i	−1.39640	+	0.806210i	−0.402384	+	0.915471i	$0.631818\pi$
$42$		0			0
$43$	−5.57437	−	3.21836i	−0.850083	−	0.490796i	0.0105955	−	0.999944i	$-0.496627\pi$
$43$	−5.57437	−	3.21836i	−0.850083	−	0.490796i	−0.860679	+	0.509148i	$0.829961\pi$
$44$	−1.09045	+	3.49541i	−0.164392	+	0.526953i
$45$		0			0
$46$	−1.02339	+	6.71682i	−0.150891	+	0.990342i
$47$	−7.97727			−1.16360			−0.581802	−	0.813331i	$-0.697652\pi$
$47$	−7.97727			−1.16360			−0.581802	+	0.813331i	$0.697652\pi$
$48$		0			0
$49$	3.88897	+	5.82030i	0.555566	+	0.831472i
$50$	3.17982	−	3.97430i	0.449694	−	0.562051i
$51$		0			0
$52$	−0.335931	+	1.07682i	−0.0465852	+	0.149327i
$53$	3.65087	−	6.32349i	0.501485	−	0.868598i	−0.498513	−	0.866882i	$-0.666120\pi$
$53$	3.65087	−	6.32349i	0.501485	−	0.868598i	0.999999	−	0.00171612i	$-0.000546258\pi$
$54$		0			0
$55$	−5.36859			−0.723901
$56$	4.38648	+	6.06290i	0.586168	+	0.810189i
$57$		0			0
$58$	−5.09644	−	0.776506i	−0.669196	−	0.101960i
$59$	0.0693815			0.00903270			0.00451635	−	0.999990i	$-0.498562\pi$
$59$	0.0693815			0.00903270			0.00451635	+	0.999990i	$0.498562\pi$
$60$		0			0
$61$		−	9.83174i		−	1.25883i	−0.777071	−	0.629413i	$-0.783295\pi$
$61$		−	9.83174i		−	1.25883i	0.777071	−	0.629413i	$-0.216705\pi$
$62$	−0.336626	−	0.861761i	−0.0427516	−	0.109444i
$63$		0			0
$64$	4.92765	+	6.30224i	0.615956	+	0.787781i
$65$	−1.65388			−0.205139
$66$		0			0
$67$		−	1.81471i		−	0.221702i	−0.993837	−	0.110851i	$-0.964642\pi$
$67$		−	1.81471i		−	0.221702i	0.993837	−	0.110851i	$-0.0353576\pi$
$68$	0.745679	−	0.167688i	0.0904269	−	0.0203351i
$69$		0			0
$70$	−6.57073	+	8.78704i	−0.785353	+	1.05025i
$71$		−	9.64068i		−	1.14414i	−0.820205	−	0.572069i	$-0.806141\pi$
$71$		−	9.64068i		−	1.14414i	0.820205	−	0.572069i	$-0.193859\pi$
$72$		0			0
$73$	−13.1397	−	7.58623i	−1.53789	−	0.887901i	−0.998962	−	0.0455481i	$-0.985497\pi$
$73$	−13.1397	−	7.58623i	−1.53789	−	0.887901i	−0.538927	−	0.842353i	$-0.681170\pi$
$74$	6.43143	−	8.03834i	0.747639	−	0.934438i
$75$		0			0
$76$	16.5803	+	5.17250i	1.90189	+	0.593327i
$77$	4.84118	−	0.158473i	0.551704	−	0.0180597i
$78$		0			0
$79$		−	6.31873i		−	0.710913i	−0.934693	−	0.355456i	$-0.884325\pi$
$79$		−	6.31873i		−	0.710913i	0.934693	−	0.355456i	$-0.115675\pi$
$80$	−6.66944	+	9.64901i	−0.745666	+	1.07879i
$81$		0			0
$82$	11.4010	+	9.12188i	1.25903	+	1.00734i
$83$	2.90035	−	5.02356i	0.318355	−	0.551407i	−0.661790	−	0.749689i	$-0.730203\pi$
$83$	2.90035	−	5.02356i	0.318355	−	0.551407i	0.980145	+	0.198282i	$0.0635363\pi$
$84$		0			0
$85$	0.560312	+	0.970489i	0.0607744	+	0.105264i
$86$	−1.37112	+	8.99905i	−0.147851	+	0.970393i
$87$		0			0
$88$	5.16553	−	0.362179i	0.550648	−	0.0386085i
$89$	1.91814	−	1.10744i	0.203323	−	0.117389i	−0.394882	−	0.918732i	$-0.629214\pi$
$89$	1.91814	−	1.10744i	0.203323	−	0.117389i	0.598204	+	0.801343i	$0.295881\pi$
$90$		0			0
$91$	1.49140	−	0.0488201i	0.156342	−	0.00511774i
$92$	9.37453	−	2.10814i	0.977363	−	0.219789i
$93$		0			0
$94$	4.10481	+	10.5083i	0.423379	+	1.08385i
$95$			25.4656i			2.61272i
$96$		0			0
$97$	1.59144	+	0.918820i	0.161587	+	0.0932921i	0.578613	−	0.815602i	$-0.303594\pi$
$97$	1.59144	+	0.918820i	0.161587	+	0.0932921i	−0.417026	+	0.908895i	$0.636928\pi$
$98$	5.66585	−	8.11777i	0.572337	−	0.820018i
$99$		0			0
$100$	−6.87148	−	2.14368i	−0.687148	−	0.214368i
$101$	3.91963	−	2.26300i	0.390018	−	0.225177i	−0.292150	−	0.956372i	$-0.594371\pi$
$101$	3.91963	−	2.26300i	0.390018	−	0.225177i	0.682168	+	0.731196i	$0.261037\pi$
$102$		0			0
$103$	7.02725	−	12.1716i	0.692416	−	1.19930i	−0.278628	−	0.960399i	$-0.589880\pi$
$103$	7.02725	−	12.1716i	0.692416	−	1.19930i	0.971044	−	0.238900i	$-0.0767869\pi$
$104$	1.59132	−	0.111575i	0.156042	−	0.0109408i
$105$		0			0
$106$	−10.2084	−	1.55538i	−0.991528	−	0.151072i
$107$	−7.78206	+	4.49298i	−0.752320	+	0.434352i	−0.826532	−	0.562890i	$-0.809689\pi$
$107$	−7.78206	+	4.49298i	−0.752320	+	0.434352i	0.0742113	+	0.997243i	$0.476356\pi$
$108$		0			0
$109$	1.49757	−	2.59388i	0.143442	−	0.248448i	−0.785349	−	0.619054i	$-0.787516\pi$
$109$	1.49757	−	2.59388i	0.143442	−	0.248448i	0.928790	+	0.370605i	$0.120850\pi$
$110$	2.76248	+	7.07193i	0.263392	+	0.674283i
$111$		0			0
$112$	5.72941	−	8.89797i	0.541378	−	0.840779i
$113$	4.05327	+	7.02047i	0.381299	+	0.660430i	0.991248	−	0.132011i	$-0.0421434\pi$
$113$	4.05327	+	7.02047i	0.381299	+	0.660430i	−0.609949	+	0.792441i	$0.708810\pi$
$114$		0			0
$115$	7.04413	+	12.2008i	0.656869	+	1.13773i
$116$	1.59957	+	7.11300i	0.148516	+	0.660425i
$117$		0			0
$118$	−0.0357012	−	0.0913948i	−0.00328656	−	0.00841357i
$119$	−0.533915	−	0.858609i	−0.0489439	−	0.0787086i
$120$		0			0
$121$	−3.82413	+	6.62359i	−0.347648	+	0.602144i
$122$	−12.9512	+	5.05906i	−1.17254	+	0.458025i
$123$		0			0
$124$	−0.961965	+	0.886861i	−0.0863870	+	0.0796425i
$125$			4.10817i			0.367446i
$126$		0			0
$127$		−	5.68040i		−	0.504054i	−0.967720	−	0.252027i	$-0.918903\pi$
$127$		−	5.68040i		−	0.504054i	0.967720	−	0.252027i	$-0.0810972\pi$
$128$	5.76623	−	9.73399i	0.509667	−	0.860371i
$129$		0			0
$130$	0.851026	+	2.17862i	0.0746399	+	0.191078i
$131$	3.88155	−	6.72304i	0.339133	−	0.587395i	−0.645137	−	0.764067i	$-0.723200\pi$
$131$	3.88155	−	6.72304i	0.339133	−	0.587395i	0.984270	+	0.176672i	$0.0565331\pi$
$132$		0			0
$133$	−0.751709	−	22.9639i	−0.0651814	−	1.99122i
$134$	−2.39048	+	0.933783i	−0.206506	+	0.0806665i
$135$		0			0
$136$	−0.604591	−	0.895982i	−0.0518433	−	0.0768298i
$137$	9.44452	+	16.3584i	0.806900	+	1.39759i	0.915001	+	0.403452i	$0.132190\pi$
$137$	9.44452	+	16.3584i	0.806900	+	1.39759i	−0.108101	+	0.994140i	$0.534477\pi$
$138$		0			0
$139$	3.57292	+	6.18848i	0.303051	+	0.524900i	0.976826	−	0.214037i	$-0.0686613\pi$
$139$	3.57292	+	6.18848i	0.303051	+	0.524900i	−0.673774	+	0.738937i	$0.735328\pi$
$140$	14.9560	+	4.13400i	1.26402	+	0.349387i
$141$		0			0
$142$	−12.6995	+	4.96074i	−1.06572	+	0.416296i
$143$	0.516278	−	0.894220i	0.0431734	−	0.0747785i
$144$		0			0
$145$	−9.25745	+	5.34479i	−0.768789	+	0.443861i
$146$	−3.23196	+	21.2123i	−0.267479	+	1.75554i
$147$		0			0
$148$	−13.8981	−	4.33575i	−1.14242	−	0.356397i
$149$	4.90778	−	8.50053i	0.402061	−	0.696390i	−0.591913	−	0.806002i	$-0.701627\pi$
$149$	4.90778	−	8.50053i	0.402061	−	0.696390i	0.993975	+	0.109611i	$0.0349606\pi$
$150$		0			0
$151$	−3.24987	+	1.87632i	−0.264471	+	0.152692i	−0.626372	−	0.779524i	$-0.715461\pi$
$151$	−3.24987	+	1.87632i	−0.264471	+	0.152692i	0.361901	+	0.932216i	$0.382128\pi$
$152$	−1.71798	−	24.5025i	−0.139347	−	1.98741i
$153$		0			0
$154$	−2.69985	−	6.29565i	−0.217560	−	0.507318i
$155$	−1.66136	−	0.959189i	−0.133444	−	0.0770439i
$156$		0			0
$157$			6.54953i			0.522709i	0.965243	+	0.261355i	$0.0841692\pi$
$157$			6.54953i			0.522709i	−0.965243	+	0.261355i	$0.915831\pi$
$158$	−8.32353	+	3.25139i	−0.662185	+	0.258666i
$159$		0			0
$160$	16.1423	+	3.82048i	1.27616	+	0.302036i
$161$	−6.71227	−	10.7943i	−0.529001	−	0.850707i
$162$		0			0
$163$	11.1236	−	6.42221i	0.871268	−	0.503027i	0.00349827	−	0.999994i	$-0.498886\pi$
$163$	11.1236	−	6.42221i	0.871268	−	0.503027i	0.867769	+	0.496967i	$0.165553\pi$
$164$	6.14952	−	19.7121i	0.480197	−	1.53926i
$165$		0			0
$166$	−8.10984	−	1.23564i	−0.629446	−	0.0959039i
$167$	−1.76904	−	3.06407i	−0.136893	−	0.237105i	0.789426	−	0.613846i	$-0.210378\pi$
$167$	−1.76904	−	3.06407i	−0.136893	−	0.237105i	−0.926319	+	0.376740i	$0.877045\pi$
$168$		0			0
$169$	−6.34095	+	10.9829i	−0.487766	+	0.844835i
$170$	0.990089	−	1.23747i	0.0759364	−	0.0949093i
$171$		0			0
$172$	12.5598	−	2.82444i	0.957675	−	0.215361i
$173$			9.95747i			0.757052i	0.925591	+	0.378526i	$0.123569\pi$
$173$			9.95747i			0.757052i	−0.925591	+	0.378526i	$0.876431\pi$
$174$		0			0
$175$	0.311536	+	9.51709i	0.0235499	+	0.719425i
$176$	−3.13509	−	6.61809i	−0.236316	−	0.498857i
$177$		0			0
$178$	−2.44582	−	1.95688i	−0.183322	−	0.146675i
$179$	−0.147551	−	0.0851888i	−0.0110285	−	0.00636731i	0.494476	−	0.869192i	$-0.335360\pi$
$179$	−0.147551	−	0.0851888i	−0.0110285	−	0.00636731i	−0.505504	+	0.862824i	$0.668693\pi$
$180$		0			0
$181$		−	15.4196i		−	1.14613i	−0.819511	−	0.573064i	$-0.805755\pi$
$181$		−	15.4196i		−	1.14613i	0.819511	−	0.573064i	$-0.194245\pi$
$182$	−0.831731	−	1.93947i	−0.0616520	−	0.143763i
$183$		0			0
$184$	−7.60080	−	11.2641i	−0.560338	−	0.830401i
$185$		−	21.3461i		−	1.56940i
$186$		0			0
$187$	−0.699633			−0.0511622
$188$	11.7302	−	10.8144i	0.855510	−	0.788718i
$189$		0			0
$190$	33.5454	−	13.1037i	2.43364	−	0.950642i
$191$			14.4684i			1.04689i	0.852058	+	0.523447i	$0.175354\pi$
$191$			14.4684i			1.04689i	−0.852058	+	0.523447i	$0.824646\pi$
$192$		0			0
$193$	19.8723			1.43044			0.715218	−	0.698901i	$-0.246327\pi$
$193$	19.8723			1.43044			0.715218	+	0.698901i	$0.246327\pi$
$194$	0.391444	−	2.56917i	0.0281041	−	0.184455i
$195$		0			0
$196$	−13.6088	−	3.28640i	−0.972058	−	0.234743i
$197$	18.7081			1.33289			0.666447	−	0.745553i	$-0.267814\pi$
$197$	18.7081			1.33289			0.666447	+	0.745553i	$0.267814\pi$
$198$		0			0
$199$	−1.44143	+	2.49663i	−0.102180	+	0.176981i	−0.912583	−	0.408892i	$-0.865915\pi$
$199$	−1.44143	+	2.49663i	−0.102180	+	0.176981i	0.810402	+	0.585874i	$0.199249\pi$
$200$	0.711994	+	10.1547i	0.0503456	+	0.718047i
$201$		0			0
$202$	−4.99790	−	3.99879i	−0.351651	−	0.281354i
$203$	8.19023	−	5.09299i	0.574841	−	0.357458i
$204$		0			0
$205$	30.2758			2.11455
$206$	−19.6493	−	2.99382i	−1.36903	−	0.208589i
$207$		0			0
$208$	−0.965813	−	2.03881i	−0.0669671	−	0.141366i
$209$	−13.7688	−	7.94941i	−0.952406	−	0.549872i
$210$		0			0
$211$	−16.7550	+	9.67350i	−1.15346	+	0.665951i	−0.949728	−	0.313075i	$-0.898641\pi$
$211$	−16.7550	+	9.67350i	−1.15346	+	0.665951i	−0.203733	+	0.979026i	$0.565307\pi$
$212$	3.20401	+	14.2477i	0.220052	+	0.978534i
$213$		0			0
$214$	9.92287	+	7.93923i	0.678313	+	0.542715i
$215$	9.43757	+	16.3464i	0.643637	+	1.11481i
$216$		0			0
$217$	1.52647	+	0.815918i	0.103623	+	0.0553881i
$218$	−4.18746	−	0.638011i	−0.283610	−	0.0432115i
$219$		0			0
$220$	7.89424	−	7.27792i	0.532230	−	0.490677i
$221$	−0.215533			−0.0144983
$222$		0			0
$223$	9.86207	−	17.0816i	0.660413	−	1.14387i	−0.320095	−	0.947386i	$-0.603715\pi$
$223$	9.86207	−	17.0816i	0.660413	−	1.14387i	0.980507	−	0.196483i	$-0.0629520\pi$
$224$	−14.6693	−	2.96866i	−0.980131	−	0.198352i
$225$		0			0
$226$	7.16225	−	8.95176i	0.476426	−	0.595462i
$227$	0.648829	+	1.12380i	0.0430643	+	0.0745895i	0.886754	−	0.462241i	$-0.152955\pi$
$227$	0.648829	+	1.12380i	0.0430643	+	0.0745895i	−0.843690	+	0.536831i	$0.819621\pi$
$228$		0			0
$229$	11.2908	+	6.51872i	0.746114	+	0.430769i	0.824288	−	0.566171i	$-0.191576\pi$
$229$	11.2908	+	6.51872i	0.746114	+	0.430769i	−0.0781741	+	0.996940i	$0.524909\pi$
$230$	12.4472	−	15.5572i	0.820744	−	1.02581i
$231$		0			0
$232$	8.54673	−	5.76716i	0.561120	−	0.378633i
$233$	8.17297	+	14.1560i	0.535429	+	0.927390i	0.999142	+	0.0414048i	$0.0131833\pi$
$233$	8.17297	+	14.1560i	0.535429	+	0.927390i	−0.463714	+	0.885985i	$0.653483\pi$
$234$		0			0
$235$	20.2586	+	11.6963i	1.32153	+	0.762984i
$236$	−0.102022	+	0.0940568i	−0.00664106	+	0.00612258i
$237$		0			0
$238$	−0.856295	+	1.14512i	−0.0555054	+	0.0742273i
$239$	−7.08294	+	4.08934i	−0.458157	+	0.264517i	−0.711269	−	0.702920i	$-0.751879\pi$
$239$	−7.08294	+	4.08934i	−0.458157	+	0.264517i	0.253112	+	0.967437i	$0.418546\pi$
$240$		0			0
$241$	7.30903	−	4.21987i	0.470816	−	0.271826i	−0.245765	−	0.969329i	$-0.579039\pi$
$241$	7.30903	−	4.21987i	0.470816	−	0.271826i	0.716581	+	0.697504i	$0.245706\pi$
$242$	10.6929	+	1.62919i	0.687364	+	0.104728i
$243$		0			0
$244$	13.3284	+	14.4571i	0.853262	+	0.925520i
$245$	−1.34243	−	20.4830i	−0.0857647	−	1.30861i
$246$		0			0
$247$	−4.24169	−	2.44894i	−0.269892	−	0.155822i
$248$	1.66324	+	0.810830i	0.105616	+	0.0514877i
$249$		0			0
$250$	5.41160	−	2.11391i	0.342260	−	0.133696i
$251$	13.3180			0.840622			0.420311	−	0.907380i	$-0.361921\pi$
$251$	13.3180			0.840622			0.420311	+	0.907380i	$0.361921\pi$
$252$		0			0
$253$	−8.79564			−0.552977
$254$	−7.48267	+	2.92293i	−0.469505	+	0.183401i
$255$		0			0
$256$	−15.7895	−	2.58698i	−0.986842	−	0.161686i
$257$	−2.00922	−	1.16003i	−0.125332	−	0.0723604i	0.436023	−	0.899935i	$-0.356387\pi$
$257$	−2.00922	−	1.16003i	−0.125332	−	0.0723604i	−0.561355	+	0.827575i	$0.689720\pi$
$258$		0			0
$259$	0.630106	+	19.2491i	0.0391529	+	1.19608i
$260$	2.43195	−	2.24208i	0.150823	−	0.139048i
$261$		0			0
$262$	−10.8534	−	1.65365i	−0.670527	−	0.102163i
$263$	24.6237	−	14.2165i	1.51836	−	0.876626i	0.518593	−	0.855021i	$-0.326456\pi$
$263$	24.6237	−	14.2165i	1.51836	−	0.876626i	0.999767	−	0.0216045i	$-0.00687747\pi$
$264$		0			0
$265$	−18.5431	+	10.7059i	−1.13909	+	0.657656i
$266$	−29.8631	+	12.8066i	−1.83102	+	0.785223i
$267$		0			0
$268$	2.46011	+	2.66844i	0.150275	+	0.163001i
$269$	−13.5982	−	7.85090i	−0.829094	−	0.478678i	0.0244481	−	0.999701i	$-0.492217\pi$
$269$	−13.5982	−	7.85090i	−0.829094	−	0.478678i	−0.853542	+	0.521023i	$0.825550\pi$
$270$		0			0
$271$	0.243398	+	0.421578i	0.0147854	+	0.0256091i	0.873323	−	0.487141i	$-0.161960\pi$
$271$	0.243398	+	0.421578i	0.0147854	+	0.0256091i	−0.858538	+	0.512750i	$0.828627\pi$
$272$	−0.869158	+	1.25745i	−0.0527004	+	0.0762444i
$273$		0			0
$274$	16.6888	−	20.8585i	1.00820	−	1.26011i
$275$	5.70629	+	3.29453i	0.344102	+	0.198667i
$276$		0			0
$277$	3.72114	+	6.44520i	0.223581	+	0.387254i	0.955893	−	0.293715i	$-0.0948918\pi$
$277$	3.72114	+	6.44520i	0.223581	+	0.387254i	−0.732311	+	0.680970i	$0.761558\pi$
$278$	6.31347	−	7.89090i	0.378657	−	0.473265i
$279$		0			0
$280$	−2.25020	−	21.8285i	−0.134475	−	1.30450i
$281$	−13.2312	+	22.9172i	−0.789310	+	1.36712i	0.137081	+	0.990560i	$0.456228\pi$
$281$	−13.2312	+	22.9172i	−0.789310	+	1.36712i	−0.926390	+	0.376565i	$0.877105\pi$
$282$		0			0
$283$	−29.4011			−1.74771			−0.873857	−	0.486184i	$-0.838389\pi$
$283$	−29.4011			−1.74771			−0.873857	+	0.486184i	$0.838389\pi$
$284$	13.0694	+	14.1761i	0.775524	+	0.841198i
$285$		0			0
$286$	−1.44360	−	0.219950i	−0.0853616	−	0.0130059i
$287$	−27.3015	+	0.893697i	−1.61156	+	0.0527533i
$288$		0			0
$289$	−8.42698	−	14.5960i	−0.495705	−	0.858586i
$290$	11.8041	+	9.44441i	0.693162	+	0.554595i
$291$		0			0
$292$	29.6056	−	6.65768i	1.73253	−	0.389611i
$293$	−13.7086	+	7.91467i	−0.800866	+	0.462380i	−0.843774	−	0.536699i	$-0.819671\pi$
$293$	−13.7086	+	7.91467i	−0.800866	+	0.462380i	0.0429080	+	0.999079i	$0.486338\pi$
$294$		0			0
$295$	−0.176197	−	0.101728i	−0.0102586	−	0.00592281i
$296$	1.44006	+	20.5387i	0.0837021	+	1.19379i
$297$		0			0
$298$	−13.7229	−	2.09086i	−0.794948	−	0.121120i
$299$	−2.70964			−0.156702
$300$		0			0
$301$	−8.99295	−	14.4619i	−0.518345	−	0.833571i
$302$	4.14390	+	3.31551i	0.238454	+	0.190786i
$303$		0			0
$304$	−31.3926	+	14.8711i	−1.80049	+	0.852918i
$305$	−14.4154	+	24.9682i	−0.825422	+	1.42967i
$306$		0			0
$307$	−2.28683			−0.130517			−0.0652583	−	0.997868i	$-0.520787\pi$
$307$	−2.28683			−0.130517			−0.0652583	+	0.997868i	$0.520787\pi$
$308$	−6.90388	+	6.79596i	−0.393385	+	0.387236i
$309$		0			0
$310$	−0.408643	+	2.68204i	−0.0232094	+	0.152330i
$311$	−5.60173			−0.317645			−0.158822	−	0.987307i	$-0.550770\pi$
$311$	−5.60173			−0.317645			−0.158822	+	0.987307i	$0.550770\pi$
$312$		0			0
$313$			8.81602i			0.498311i	0.968464	+	0.249155i	$0.0801530\pi$
$313$			8.81602i			0.498311i	−0.968464	+	0.249155i	$0.919847\pi$
$314$	8.62755	−	3.37015i	0.486881	−	0.190188i
$315$		0			0
$316$	8.56597	+	9.29137i	0.481873	+	0.522681i
$317$	3.20647			0.180094			0.0900468	−	0.995938i	$-0.471298\pi$
$317$	3.20647			0.180094			0.0900468	+	0.995938i	$0.471298\pi$
$318$		0			0
$319$		−	6.67376i		−	0.373659i
$320$	−3.27359	−	23.2298i	−0.182999	−	1.29858i
$321$		0			0
$322$	−10.7652	+	14.3963i	−0.599920	+	0.802273i
$323$			3.31867i			0.184656i
$324$		0			0
$325$	1.75791	+	1.01493i	0.0975114	+	0.0562983i
$326$	−14.1836	−	11.3483i	−0.785559	−	0.628521i
$327$		0			0
$328$	−29.1307	+	2.04248i	−1.60847	+	0.112777i
$329$	−18.6137	−	9.94928i	−1.02621	−	0.548521i
$330$		0			0
$331$			15.5698i			0.855794i	0.903827	+	0.427897i	$0.140745\pi$
$331$			15.5698i			0.855794i	−0.903827	+	0.427897i	$0.859255\pi$
$332$	2.54535	+	11.3187i	0.139694	+	0.621197i
$333$		0			0
$334$	−3.12596	+	3.90699i	−0.171045	+	0.213781i
$335$	−2.66074	+	4.60853i	−0.145372	+	0.251791i
$336$		0			0
$337$	−1.89825	−	3.28787i	−0.103404	−	0.179102i	0.809681	−	0.586871i	$-0.199640\pi$
$337$	−1.89825	−	3.28787i	−0.103404	−	0.179102i	−0.913085	+	0.407769i	$0.866307\pi$
$338$	17.7303	+	2.70143i	0.964401	+	0.146939i
$339$		0			0
$340$	−2.13955	−	0.667469i	−0.116033	−	0.0361986i
$341$	1.03723	−	0.598845i	0.0561691	−	0.0324293i
$342$		0			0
$343$	1.81518	+	18.4311i	0.0980104	+	0.995185i
$344$	−10.1834	−	15.0914i	−0.549051	−	0.813674i
$345$		0			0
$346$	13.1168	−	5.12375i	0.705162	−	0.275454i
$347$		−	16.5711i		−	0.889586i	−0.895633	−	0.444793i	$-0.853277\pi$
$347$		−	16.5711i		−	0.889586i	0.895633	−	0.444793i	$-0.146723\pi$
$348$		0			0
$349$	−22.4588	−	12.9666i	−1.20219	−	0.694087i	−0.241152	−	0.970487i	$-0.577525\pi$
$349$	−22.4588	−	12.9666i	−1.20219	−	0.694087i	−0.961043	+	0.276400i	$0.910859\pi$
$350$	12.3764	−	5.30753i	0.661544	−	0.283699i
$351$		0			0
$352$	−7.10467	+	7.53521i	−0.378680	+	0.401628i
$353$	−0.184978	+	0.106797i	−0.00984539	+	0.00568424i	−0.504915	−	0.863169i	$-0.668476\pi$
$353$	−0.184978	+	0.106797i	−0.00984539	+	0.00568424i	0.495069	+	0.868854i	$0.335143\pi$
$354$		0			0
$355$	−14.1352	+	24.4829i	−0.750220	+	1.29942i
$356$	−1.31923	+	4.22876i	−0.0699193	+	0.224124i
$357$		0			0
$358$	−0.0362929	+	0.238201i	−0.00191814	+	0.0125893i
$359$	23.6659	−	13.6635i	1.24904	−	0.721133i	0.278121	−	0.960546i	$-0.410288\pi$
$359$	23.6659	−	13.6635i	1.24904	−	0.721133i	0.970918	+	0.239413i	$0.0769551\pi$
$360$		0			0
$361$	−28.2076	+	48.8570i	−1.48461	+	2.57142i
$362$	−20.3119	+	7.93435i	−1.06757	+	0.417020i
$363$		0			0
$364$	−2.12685	+	2.09360i	−0.111477	+	0.109735i
$365$	22.2460	+	38.5311i	1.16441	+	2.01681i
$366$		0			0
$367$	14.0722	+	24.3737i	0.734562	+	1.27230i	0.954915	+	0.296878i	$0.0959455\pi$
$367$	14.0722	+	24.3737i	0.734562	+	1.27230i	−0.220354	+	0.975420i	$0.570721\pi$
$368$	−10.9269	+	15.8085i	−0.569603	+	0.824074i
$369$		0			0
$370$	−28.1188	+	10.9839i	−1.46183	+	0.571027i
$371$	16.4054	−	10.2015i	0.851726	−	0.529635i
$372$		0			0
$373$	−3.41247	+	5.91057i	−0.176691	+	0.306038i	−0.940745	−	0.339114i	$-0.889873\pi$
$373$	−3.41247	+	5.91057i	−0.176691	+	0.306038i	0.764054	+	0.645152i	$0.223206\pi$
$374$	0.360005	+	0.921611i	0.0186154	+	0.0476554i
$375$		0			0
$376$	−20.2814	−	9.88723i	−1.04594	−	0.509895i
$377$		−	2.05596i		−	0.105887i
$378$		0			0
$379$		−	24.6134i		−	1.26431i	−0.774843	−	0.632153i	$-0.782171\pi$
$379$		−	24.6134i		−	1.26431i	0.774843	−	0.632153i	$-0.217829\pi$
$380$	−34.5224	−	37.4459i	−1.77096	−	1.92094i
$381$		0			0
$382$	19.0589	−	7.44489i	0.975137	−	0.380914i
$383$	15.5567	−	26.9450i	0.794911	−	1.37683i	−0.127985	−	0.991776i	$-0.540851\pi$
$383$	15.5567	−	26.9450i	0.794911	−	1.37683i	0.922896	−	0.385050i	$-0.125816\pi$
$384$		0			0
$385$	−12.5268	−	6.69573i	−0.638423	−	0.341246i
$386$	−10.2255	−	26.1773i	−0.520466	−	1.33239i
$387$		0			0
$388$	−3.58573	+	0.806357i	−0.182038	+	0.0409366i
$389$	−7.19219	−	12.4572i	−0.364658	−	0.631607i	0.624063	−	0.781374i	$-0.285481\pi$
$389$	−7.19219	−	12.4572i	−0.364658	−	0.631607i	−0.988721	+	0.149767i	$0.952148\pi$
$390$		0			0
$391$	0.917988	+	1.59000i	0.0464247	+	0.0804099i
$392$	2.67349	+	19.6177i	0.135032	+	0.990841i
$393$		0			0
$394$	−9.62648	−	24.6437i	−0.484975	−	1.24153i
$395$	−9.26457	+	16.0467i	−0.466151	+	0.807397i
$396$		0			0
$397$	3.00720	−	1.73621i	0.150927	−	0.0871377i	−0.422635	−	0.906300i	$-0.638895\pi$
$397$	3.00720	−	1.73621i	0.150927	−	0.0871377i	0.573562	+	0.819162i	$0.305561\pi$
$398$	4.03046	+	0.614091i	0.202029	+	0.0307816i
$399$		0			0
$400$	13.0102	−	6.16314i	0.650512	−	0.308157i
$401$	16.9918	−	29.4307i	0.848530	−	1.46970i	−0.0339901	−	0.999422i	$-0.510821\pi$
$401$	16.9918	−	29.4307i	0.848530	−	1.46970i	0.882520	−	0.470275i	$-0.155845\pi$
$402$		0			0
$403$	0.319535	−	0.184484i	0.0159172	−	0.00918978i
$404$	−2.69579	+	8.64126i	−0.134120	+	0.429919i
$405$		0			0
$406$	−10.9233	−	8.16816i	−0.542113	−	0.405379i
$407$	11.5414	+	6.66344i	0.572087	+	0.330295i
$408$		0			0
$409$			14.2902i			0.706603i	0.935510	+	0.353301i	$0.114941\pi$
$409$			14.2902i			0.706603i	−0.935510	+	0.353301i	$0.885059\pi$
$410$	−15.5788	−	39.8817i	−0.769382	−	1.96961i
$411$		0			0
$412$	6.16712	+	27.4241i	0.303832	+	1.35109i
$413$	0.161891	+	0.0865328i	0.00796612	+	0.00425800i
$414$		0			0
$415$	−14.7311	+	8.50503i	−0.723124	+	0.417496i
$416$	−2.18871	+	2.32134i	−0.107310	+	0.113813i
$417$		0			0
$418$	−3.38668	+	22.2278i	−0.165648	+	1.08720i
$419$	−3.26093	−	5.64810i	−0.159307	−	0.275928i	0.775312	−	0.631579i	$-0.217593\pi$
$419$	−3.26093	−	5.64810i	−0.159307	−	0.275928i	−0.934619	+	0.355651i	$0.884259\pi$
$420$		0			0
$421$	−3.51243	+	6.08371i	−0.171185	+	0.296502i	−0.938835	−	0.344369i	$-0.888093\pi$
$421$	−3.51243	+	6.08371i	−0.171185	+	0.296502i	0.767649	+	0.640870i	$0.221426\pi$
$422$	21.3642	+	17.0934i	1.03999	+	0.832093i
$423$		0			0
$424$	17.1195	−	11.5519i	0.831396	−	0.561010i
$425$		−	1.37538i		−	0.0667157i
$426$		0			0
$427$	12.2622	−	22.9408i	0.593409	−	1.11018i
$428$	5.35224	−	17.1564i	0.258710	−	0.829287i
$429$		0			0
$430$	16.6765	−	20.8432i	0.804212	−	1.00515i
$431$	16.8002	+	9.69959i	0.809236	+	0.467213i	0.846691	−	0.532086i	$-0.178592\pi$
$431$	16.8002	+	9.69959i	0.809236	+	0.467213i	−0.0374543	+	0.999298i	$0.511925\pi$
$432$		0			0
$433$		−	20.5238i		−	0.986309i	−0.869942	−	0.493154i	$-0.835844\pi$
$433$		−	20.5238i		−	0.986309i	0.869942	−	0.493154i	$-0.164156\pi$
$434$	0.289328	−	2.43062i	0.0138882	−	0.116674i
$435$		0			0
$436$	1.31427	+	5.84435i	0.0629422	+	0.279893i
$437$			41.7217i			1.99582i
$438$		0			0
$439$	−6.99396			−0.333803			−0.166902	−	0.985974i	$-0.553376\pi$
$439$	−6.99396			−0.333803			−0.166902	+	0.985974i	$0.553376\pi$
$440$	−13.6491	−	6.65397i	−0.650697	−	0.317216i
$441$		0			0
$442$	0.110905	+	0.283917i	0.00527523	+	0.0135046i
$443$		−	3.23523i		−	0.153710i	−0.997042	−	0.0768552i	$-0.975512\pi$
$443$		−	3.23523i		−	0.153710i	0.997042	−	0.0768552i	$-0.0244879\pi$
$444$		0			0
$445$	−6.49495			−0.307890
$446$	−27.5759	−	4.20153i	−1.30576	−	0.198948i
$447$		0			0
$448$	3.63770	+	20.8511i	0.171865	+	0.985120i
$449$	−15.0764			−0.711500			−0.355750	−	0.934581i	$-0.615775\pi$
$449$	−15.0764			−0.711500			−0.355750	+	0.934581i	$0.615775\pi$
$450$		0			0
$451$	−9.45095	+	16.3695i	−0.445028	+	0.770811i
$452$	−15.4774	−	4.82844i	−0.727996	−	0.227111i
$453$		0			0
$454$	1.14650	−	1.43296i	0.0538079	−	0.0672520i
$455$	−3.85907	−	2.06273i	−0.180916	−	0.0967021i
$456$		0			0
$457$	26.9060			1.25861			0.629304	−	0.777159i	$-0.283340\pi$
$457$	26.9060			1.25861			0.629304	+	0.777159i	$0.283340\pi$
$458$	2.77717	−	18.2274i	0.129768	−	0.851709i
$459$		0			0
$460$	−26.8980	−	8.39129i	−1.25413	−	0.391246i
$461$	13.3994	+	7.73613i	0.624071	+	0.360307i	0.778452	−	0.627704i	$-0.216005\pi$
$461$	13.3994	+	7.73613i	0.624071	+	0.360307i	−0.154381	+	0.988011i	$0.549338\pi$
$462$		0			0
$463$	5.18126	−	2.99140i	0.240793	−	0.139022i	−0.374748	−	0.927127i	$-0.622271\pi$
$463$	5.18126	−	2.99140i	0.240793	−	0.139022i	0.615541	+	0.788105i	$0.288937\pi$
$464$	−11.9948	−	8.29085i	−0.556845	−	0.384893i
$465$		0			0
$466$	14.4419	−	18.0502i	0.669008	−	0.836161i
$467$	16.0086	+	27.7278i	0.740791	+	1.28309i	0.952136	+	0.305676i	$0.0988824\pi$
$467$	16.0086	+	27.7278i	0.740791	+	1.28309i	−0.211345	+	0.977412i	$0.567784\pi$
$468$		0			0
$469$	2.26331	−	4.23434i	0.104510	−	0.195523i
$470$	4.98298	−	32.7048i	0.229848	−	1.50856i
$471$		0			0
$472$	0.176396	+	0.0859932i	0.00811928	+	0.00395816i
$473$	−11.7842			−0.541838
$474$		0			0
$475$	15.6274	−	27.0675i	0.717035	−	1.24194i
$476$	1.94907	+	0.538741i	0.0893353	+	0.0246932i
$477$		0			0
$478$	9.03142	+	7.22599i	0.413088	+	0.330509i
$479$	11.9382	+	20.6776i	0.545470	+	0.944782i	0.998577	+	0.0533262i	$0.0169823\pi$
$479$	11.9382	+	20.6776i	0.545470	+	0.944782i	−0.453107	+	0.891456i	$0.649684\pi$
$480$		0			0
$481$	3.55552	+	2.05278i	0.162118	+	0.0935987i
$482$	−9.31971	−	7.45665i	−0.424501	−	0.339641i
$483$		0			0
$484$	−3.35606	−	14.9238i	−0.152548	−	0.678355i
$485$	−2.69436	−	4.66677i	−0.122345	−	0.211907i
$486$		0			0
$487$	−3.70986	−	2.14189i	−0.168110	−	0.0970582i	0.413585	−	0.910466i	$-0.364277\pi$
$487$	−3.70986	−	2.14189i	−0.168110	−	0.0970582i	−0.581694	+	0.813408i	$0.697610\pi$
$488$	12.1857	−	24.9963i	0.551622	−	1.13153i
$489$		0			0
$490$	−26.2910	+	12.3081i	−1.18771	+	0.556025i
$491$	−6.60375	+	3.81268i	−0.298023	+	0.172064i	−0.641555	−	0.767077i	$-0.721710\pi$
$491$	−6.60375	+	3.81268i	−0.298023	+	0.172064i	0.343531	+	0.939141i	$0.388377\pi$
$492$		0			0
$493$	−1.20643	+	0.696531i	−0.0543347	+	0.0313702i
$494$	−1.04332	+	6.84763i	−0.0469412	+	0.308089i
$495$		0			0
$496$	0.212249	−	2.60817i	0.00953025	−	0.117110i
$497$	12.0239	−	22.4950i	0.539345	−	1.00904i
$498$		0			0
$499$	18.0408	+	10.4159i	0.807617	+	0.466278i	0.846128	−	0.532980i	$-0.178928\pi$
$499$	18.0408	+	10.4159i	0.807617	+	0.466278i	−0.0385104	+	0.999258i	$0.512261\pi$
$500$	−5.56923	−	6.04085i	−0.249063	−	0.270155i
$501$		0			0
$502$	−6.85293	−	17.5435i	−0.305861	−	0.783003i
$503$	−13.9678			−0.622792			−0.311396	−	0.950280i	$-0.600796\pi$
$503$	−13.9678			−0.622792			−0.311396	+	0.950280i	$0.600796\pi$
$504$		0			0
$505$	−13.2721			−0.590600
$506$	4.52591	+	11.5863i	0.201201	+	0.515075i
$507$		0			0
$508$	7.70062	+	8.35274i	0.341660	+	0.370593i
$509$	23.8817	+	13.7881i	1.05854	+	0.611146i	0.925027	−	0.379902i	$-0.124042\pi$
$509$	23.8817	+	13.7881i	1.05854	+	0.611146i	0.133509	+	0.991048i	$0.457376\pi$
$510$		0			0
$511$	−21.1979	−	34.0892i	−0.937740	−	1.50802i
$512$	4.71691	+	22.1303i	0.208460	+	0.978031i
$513$		0			0
$514$	−0.494205	+	3.24361i	−0.0217984	+	0.143070i
$515$	−35.6920	+	20.6068i	−1.57278	+	0.908045i
$516$		0			0
$517$	−12.6479	+	7.30229i	−0.556256	+	0.321154i
$518$	25.0322	−	10.7349i	1.09985	−	0.471664i
$519$		0			0
$520$	−4.20483	−	2.04986i	−0.184394	−	0.0898924i
$521$	−25.2177	−	14.5594i	−1.10481	−	0.637860i	−0.167327	−	0.985901i	$-0.553514\pi$
$521$	−25.2177	−	14.5594i	−1.10481	−	0.637860i	−0.937479	+	0.348041i	$0.886847\pi$
$522$		0			0
$523$	2.77500	+	4.80644i	0.121342	+	0.210171i	0.920297	−	0.391220i	$-0.127947\pi$
$523$	2.77500	+	4.80644i	0.121342	+	0.210171i	−0.798955	+	0.601391i	$0.794613\pi$
$524$	3.40645	+	15.1479i	0.148812	+	0.661739i
$525$		0			0
$526$	−31.3975	−	25.1210i	−1.36900	−	1.09533i
$527$	−0.216508	−	0.125001i	−0.00943125	−	0.00544513i
$528$		0			0
$529$	0.0407669	+	0.0706104i	0.00177247	+	0.00307002i
$530$	23.6442	+	18.9176i	1.02704	+	0.821727i
$531$		0			0
$532$	32.2363	+	32.7482i	1.39762	+	1.41982i
$533$	−2.91151	+	5.04289i	−0.126112	+	0.218432i
$534$		0			0
$535$	26.3505			1.13923
$536$	2.24920	−	4.61373i	0.0971505	−	0.199283i
$537$		0			0
$538$	−3.34471	+	21.9524i	−0.144201	+	0.946433i
$539$	11.4938	+	5.66817i	0.495072	+	0.244145i
$540$		0			0
$541$	15.4643	+	26.7849i	0.664862	+	1.15157i	0.979323	+	0.202304i	$0.0648430\pi$
$541$	15.4643	+	26.7849i	0.664862	+	1.15157i	−0.314461	+	0.949270i	$0.601824\pi$
$542$	0.430092	−	0.537552i	0.0184741	−	0.0230898i
$543$		0			0
$544$	2.10366	+	0.497884i	0.0901935	+	0.0213466i
$545$	−7.60632	+	4.39151i	−0.325819	+	0.188112i
$546$		0			0
$547$	8.81420	+	5.08888i	0.376868	+	0.217585i	0.676455	−	0.736484i	$-0.263515\pi$
$547$	8.81420	+	5.08888i	0.376868	+	0.217585i	−0.299587	+	0.954069i	$0.596849\pi$
$548$	−36.0639	−	11.2507i	−1.54057	−	0.480608i
$549$		0			0
$550$	1.40357	−	9.21202i	0.0598482	−	0.392802i
$551$	−31.6566			−1.34862
$552$		0			0
$553$	7.88075	−	14.7438i	0.335123	−	0.626968i
$554$	6.57537	−	8.21824i	0.279361	−	0.349160i
$555$		0			0
$556$	−13.6432	−	4.25623i	−0.578601	−	0.180504i
$557$	8.10369	−	14.0360i	0.343364	−	0.594724i	−0.641691	−	0.766963i	$-0.721767\pi$
$557$	8.10369	−	14.0360i	0.343364	−	0.594724i	0.985055	+	0.172239i	$0.0551002\pi$
$558$		0			0
$559$	−3.63031			−0.153546
$560$	−27.5964	+	14.1963i	−1.16616	+	0.599903i
$561$		0			0
$562$	36.9966	+	5.63690i	1.56061	+	0.237778i
$563$	−7.19905			−0.303404			−0.151702	−	0.988426i	$-0.548475\pi$
$563$	−7.19905			−0.303404			−0.151702	+	0.988426i	$0.548475\pi$
$564$		0			0
$565$		−	23.7717i		−	1.00008i
$566$	15.1287	+	38.7294i	0.635908	+	1.62792i
$567$		0			0
$568$	11.9489	−	24.5105i	0.501365	−	1.02844i
$569$	7.67327			0.321680			0.160840	−	0.986980i	$-0.448580\pi$
$569$	7.67327			0.321680			0.160840	+	0.986980i	$0.448580\pi$
$570$		0			0
$571$		−	36.3426i		−	1.52089i	−0.649401	−	0.760446i	$-0.724980\pi$
$571$		−	36.3426i		−	1.52089i	0.649401	−	0.760446i	$-0.275020\pi$
$572$	0.453086	+	2.01480i	0.0189445	+	0.0842429i
$573$		0			0
$574$	15.2256	+	35.5038i	0.635504	+	1.48190i
$575$		−	17.2910i		−	0.721085i
$576$		0			0
$577$	33.2642	+	19.2051i	1.38481	+	0.799520i	0.992724	−	0.120410i	$-0.0384208\pi$
$577$	33.2642	+	19.2051i	1.38481	+	0.799520i	0.392084	+	0.919929i	$0.371754\pi$
$578$	−14.8907	+	18.6112i	−0.619373	+	0.774125i
$579$		0			0
$580$	6.36696	−	20.4091i	0.264373	−	0.847441i
$581$	13.0329	−	8.10434i	0.540696	−	0.336225i
$582$		0			0
$583$		−	13.3678i		−	0.553640i
$584$	−24.0040	−	35.5730i	−0.993291	−	1.47202i
$585$		0			0
$586$	17.4798	+	13.9855i	0.722083	+	0.577735i
$587$	1.74472	−	3.02195i	0.0720124	−	0.124729i	−0.827771	−	0.561066i	$-0.810391\pi$
$587$	1.74472	−	3.02195i	0.0720124	−	0.124729i	0.899783	+	0.436337i	$0.143725\pi$
$588$		0			0
$589$	−2.84059	−	4.92005i	−0.117044	−	0.202727i
$590$	−0.0433389	+	0.284446i	−0.00178424	+	0.0117105i
$591$		0			0
$592$	26.3142	−	12.4654i	1.08151	−	0.512327i
$593$	8.09945	−	4.67622i	0.332604	−	0.192029i	−0.324392	−	0.945923i	$-0.605160\pi$
$593$	8.09945	−	4.67622i	0.332604	−	0.192029i	0.656997	+	0.753893i	$0.271826\pi$
$594$		0			0
$595$	0.0970019	+	2.96331i	0.00397669	+	0.121484i
$596$	4.30707	+	19.1528i	0.176425	+	0.784530i
$597$		0			0
$598$	1.39428	+	3.56935i	0.0570163	+	0.145962i
$599$			6.99197i			0.285684i	0.989745	+	0.142842i	$0.0456241\pi$
$599$			6.99197i			0.285684i	−0.989745	+	0.142842i	$0.954376\pi$
$600$		0			0
$601$	5.17769	+	2.98934i	0.211202	+	0.121938i	0.601870	−	0.798594i	$-0.294423\pi$
$601$	5.17769	+	2.98934i	0.211202	+	0.121938i	−0.390668	+	0.920532i	$0.627756\pi$
$602$	−14.4229	+	19.2878i	−0.587835	+	0.786112i
$603$		0			0
$604$	2.23515	−	7.16471i	0.0909470	−	0.291528i
$605$	19.4231	−	11.2139i	0.789661	−	0.455911i
$606$		0			0
$607$	−13.1158	+	22.7173i	−0.532356	+	0.922067i	0.466931	+	0.884294i	$0.345360\pi$
$607$	−13.1158	+	22.7173i	−0.532356	+	0.922067i	−0.999286	+	0.0377732i	$0.987974\pi$
$608$	35.7429	+	33.7006i	1.44957	+	1.36674i
$609$		0			0
$610$	40.3077	+	6.14137i	1.63201	+	0.248657i
$611$	−3.89640	+	2.24959i	−0.157631	+	0.0910086i
$612$		0			0
$613$	−0.414372	+	0.717713i	−0.0167363	+	0.0289882i	−0.874272	−	0.485436i	$-0.838661\pi$
$613$	−0.414372	+	0.717713i	−0.0167363	+	0.0289882i	0.857536	+	0.514424i	$0.171994\pi$
$614$	1.17672	+	3.01240i	0.0474886	+	0.121571i
$615$		0			0
$616$	12.5047	+	5.59739i	0.503827	+	0.225525i
$617$	−3.69129	−	6.39349i	−0.148606	−	0.257392i	0.782107	−	0.623144i	$-0.214145\pi$
$617$	−3.69129	−	6.39349i	−0.148606	−	0.257392i	−0.930712	+	0.365752i	$0.880812\pi$
$618$		0			0
$619$	−10.0811	−	17.4609i	−0.405192	−	0.701813i	0.589152	−	0.808022i	$-0.299462\pi$
$619$	−10.0811	−	17.4609i	−0.405192	−	0.701813i	−0.994344	+	0.106209i	$0.966129\pi$
$620$	3.74327	−	0.841785i	0.150334	−	0.0338069i
$621$		0			0
$622$	2.88244	+	7.37904i	0.115575	+	0.295872i
$623$	5.85689	−	0.191722i	0.234651	−	0.00768116i
$624$		0			0
$625$	15.0210	−	26.0172i	0.600842	−	1.04069i
$626$	11.6132	−	4.53640i	0.464155	−	0.181311i
$627$		0			0
$628$	−8.87885	−	9.63074i	−0.354305	−	0.384309i
$629$		−	2.78181i		−	0.110918i
$630$		0			0
$631$			8.38135i			0.333656i	0.985986	+	0.166828i	$0.0533525\pi$
$631$			8.38135i			0.333656i	−0.985986	+	0.166828i	$0.946647\pi$
$632$	7.83160	−	16.0648i	0.311524	−	0.639022i
$633$		0			0
$634$	−1.64993	−	4.22382i	−0.0655272	−	0.167749i
$635$	−8.32864	+	14.4256i	−0.330512	+	0.572464i
$636$		0			0
$637$	3.54084	+	1.74617i	0.140293	+	0.0691858i
$638$	−8.79120	+	3.43407i	−0.348047	+	0.135956i
$639$		0			0
$640$	−28.9156	+	16.2654i	−1.14299	+	0.642947i
$641$	−6.70139	−	11.6072i	−0.264689	−	0.458455i	0.702793	−	0.711394i	$-0.251936\pi$
$641$	−6.70139	−	11.6072i	−0.264689	−	0.458455i	−0.967482	+	0.252939i	$0.918603\pi$
$642$		0			0
$643$	7.76497	+	13.4493i	0.306220	+	0.530389i	0.977532	−	0.210786i	$-0.0676022\pi$
$643$	7.76497	+	13.4493i	0.306220	+	0.530389i	−0.671312	+	0.741175i	$0.734269\pi$
$644$	24.5033	+	6.77295i	0.965564	+	0.266891i
$645$		0			0
$646$	4.37162	−	1.70767i	0.171999	−	0.0671873i
$647$	21.2347	−	36.7795i	0.834821	−	1.44595i	−0.0593553	−	0.998237i	$-0.518904\pi$
$647$	21.2347	−	36.7795i	0.834821	−	1.44595i	0.894176	−	0.447715i	$-0.147762\pi$
$648$		0			0
$649$	0.110004	−	0.0635110i	0.00431804	−	0.00249302i
$650$	0.432390	−	2.83791i	0.0169598	−	0.111312i
$651$		0			0
$652$	−7.65043	+	24.5232i	−0.299614	+	0.960403i
$653$	22.8981	−	39.6607i	0.896072	−	1.55204i	0.0635988	−	0.997976i	$-0.479742\pi$
$653$	22.8981	−	39.6607i	0.896072	−	1.55204i	0.832473	−	0.554066i	$-0.186924\pi$
$654$		0			0
$655$	−19.7147	+	11.3823i	−0.770319	+	0.444744i
$656$	17.6801	+	37.3222i	0.690291	+	1.45719i
$657$		0			0
$658$	−3.52805	+	29.6390i	−0.137538	+	1.15545i
$659$	−37.8619	−	21.8596i	−1.47489	−	0.851527i	−0.475289	−	0.879830i	$-0.657657\pi$
$659$	−37.8619	−	21.8596i	−1.47489	−	0.851527i	−0.999599	+	0.0283024i	$0.990990\pi$
$660$		0			0
$661$		−	35.1632i		−	1.36769i	−0.729628	−	0.683845i	$-0.760307\pi$
$661$		−	35.1632i		−	1.36769i	0.729628	−	0.683845i	$-0.239693\pi$
$662$	20.5098	−	8.01165i	0.797135	−	0.311382i
$663$		0			0
$664$	13.6002	−	9.17715i	0.527790	−	0.356142i
$665$	−31.7609	+	59.4201i	−1.23163	+	2.30421i
$666$		0			0
$667$	−15.1670	+	8.75664i	−0.587267	+	0.339059i
$668$	6.75509	+	2.10737i	0.261362	+	0.0815364i
$669$		0			0
$670$	7.43985	+	1.13355i	0.287426	+	0.0437930i
$671$	−8.99986	−	15.5882i	−0.347436	−	0.601776i
$672$		0			0
$673$	−14.6335	+	25.3459i	−0.564078	+	0.977012i	0.433057	+	0.901367i	$0.357435\pi$
$673$	−14.6335	+	25.3459i	−0.564078	+	0.977012i	−0.997135	+	0.0756454i	$0.975898\pi$
$674$	−3.35427	+	4.19235i	−0.129202	+	0.161483i
$675$		0			0
$676$	−5.56482	−	24.7458i	−0.214032	−	0.951762i
$677$		−	7.19408i		−	0.276491i	−0.990398	−	0.138246i	$-0.955854\pi$
$677$		−	7.19408i		−	0.276491i	0.990398	−	0.138246i	$-0.0441463\pi$
$678$		0			0
$679$	2.56742	+	4.12878i	0.0985287	+	0.158448i
$680$	0.221691	+	3.16184i	0.00850147	+	0.121251i
$681$		0			0
$682$	−1.32257	−	1.05818i	−0.0506437	−	0.0405197i
$683$	−34.3959	−	19.8585i	−1.31612	−	0.759863i	−0.333020	−	0.942920i	$-0.608068\pi$
$683$	−34.3959	−	19.8585i	−1.31612	−	0.759863i	−0.983102	+	0.183056i	$0.941401\pi$
$684$		0			0
$685$		−	55.3905i		−	2.11636i
$686$	23.3449	−	11.8751i	0.891311	−	0.453392i
$687$		0			0
$688$	−14.6396	+	21.1798i	−0.558129	+	0.807474i
$689$		−	4.11818i		−	0.156890i
$690$		0			0
$691$	−7.77944			−0.295944			−0.147972	−	0.988992i	$-0.547275\pi$
$691$	−7.77944			−0.295944			−0.147972	+	0.988992i	$0.547275\pi$
$692$	−13.4988	−	14.6420i	−0.513148	−	0.556604i
$693$		0			0
$694$	−21.8288	+	8.52690i	−0.828611	+	0.323677i
$695$		−	20.9546i		−	0.794852i
$696$		0			0
$697$	3.94553			0.149447
$698$	−5.52416	+	36.2567i	−0.209093	+	1.37234i
$699$		0			0
$700$	−13.3599	−	13.5721i	−0.504957	−	0.512976i
$701$	17.1899			0.649253			0.324626	−	0.945842i	$-0.394761\pi$
$701$	17.1899			0.649253			0.324626	+	0.945842i	$0.394761\pi$
$702$		0			0
$703$	31.6077	−	54.7462i	1.19211	−	2.06479i
$704$	13.5818	+	5.48149i	0.511882	+	0.206591i
$705$		0			0
$706$	0.235865	+	0.188714i	0.00887688	+	0.00710234i
$707$	11.9683	−	0.391773i	0.450112	−	0.0147341i
$708$		0			0
$709$	−24.9909			−0.938552			−0.469276	−	0.883051i	$-0.655485\pi$
$709$	−24.9909			−0.938552			−0.469276	+	0.883051i	$0.655485\pi$
$710$	39.5243	+	6.02202i	1.48332	+	0.226002i
$711$		0			0
$712$	6.24929	−	0.438167i	0.234202	−	0.0164210i
$713$	−2.72190	−	1.57149i	−0.101936	−	0.0588527i
$714$		0			0
$715$	−2.62222	+	1.51394i	−0.0980656	+	0.0566182i
$716$	0.332453	−	0.0747618i	0.0124243	−	0.00279398i
$717$		0			0
$718$	−30.1763	−	24.1439i	−1.12617	−	0.901041i
$719$	−14.2772	−	24.7289i	−0.532451	−	0.922233i	−0.999282	−	0.0378861i	$-0.987938\pi$
$719$	−14.2772	−	24.7289i	−0.532451	−	0.922233i	0.466831	−	0.884347i	$-0.345396\pi$
$720$		0			0
$721$	31.5774	−	19.6360i	1.17600	−	0.731282i
$722$	78.8729	+	12.0173i	2.93535	+	0.447237i
$723$		0			0
$724$	20.9035	+	22.6737i	0.776873	+	0.842662i
$725$	13.1197			0.487253
$726$		0			0
$727$	−5.98570	+	10.3675i	−0.221997	+	0.384511i	−0.955414	−	0.295268i	$-0.904591\pi$
$727$	−5.98570	+	10.3675i	−0.221997	+	0.384511i	0.733417	+	0.679779i	$0.237924\pi$
$728$	3.85226	+	1.72436i	0.142774	+	0.0639092i
$729$		0			0
$730$	39.3093	−	49.1308i	1.45490	−	1.81841i
$731$	1.22990	+	2.13025i	0.0454895	+	0.0787901i
$732$		0			0
$733$	13.5239	+	7.80801i	0.499515	+	0.288395i	0.728513	−	0.685032i	$-0.240212\pi$
$733$	13.5239	+	7.80801i	0.499515	+	0.288395i	−0.228998	+	0.973427i	$0.573545\pi$
$734$	24.8660	−	31.0788i	0.917820	−	1.14714i
$735$		0			0
$736$	26.4467	+	6.25929i	0.974840	+	0.230721i
$737$	−1.66116	−	2.87722i	−0.0611897	−	0.105984i
$738$		0			0
$739$	−14.6499	−	8.45814i	−0.538906	−	0.311138i	0.205729	−	0.978609i	$-0.434043\pi$
$739$	−14.6499	−	8.45814i	−0.538906	−	0.311138i	−0.744635	+	0.667471i	$0.767377\pi$
$740$	28.9378	+	31.3884i	1.06377	+	1.15386i
$741$		0			0
$742$	−21.8798	−	16.3612i	−0.803234	−	0.600638i
$743$	−11.3689	+	6.56386i	−0.417086	+	0.240805i	−0.693830	−	0.720139i	$-0.744078\pi$
$743$	−11.3689	+	6.56386i	−0.417086	+	0.240805i	0.276744	+	0.960944i	$0.410745\pi$
$744$		0			0
$745$	−24.9271	+	14.3916i	−0.913257	+	0.527269i
$746$	9.54181	+	1.45381i	0.349350	+	0.0532279i
$747$		0			0
$748$	1.02877	−	0.948455i	0.0376157	−	0.0346789i
$749$	−23.7619	+	0.777829i	−0.868240	+	0.0284213i
$750$		0			0
$751$	16.4284	+	9.48495i	0.599481	+	0.346111i	0.768837	−	0.639444i	$-0.220836\pi$
$751$	16.4284	+	9.48495i	0.599481	+	0.346111i	−0.169356	+	0.985555i	$0.554169\pi$
$752$	−2.58816	+	31.8039i	−0.0943803	+	1.15977i
$753$		0			0
$754$	−2.70827	+	1.05792i	−0.0986294	+	0.0385272i
$755$	11.0043			0.400486
$756$		0			0
$757$	30.3460			1.10294			0.551471	−	0.834194i	$-0.314067\pi$
$757$	30.3460			1.10294			0.551471	+	0.834194i	$0.314067\pi$
$758$	−32.4227	+	12.6652i	−1.17765	+	0.460019i
$759$		0			0
$760$	−31.5628	+	64.7440i	−1.14490	+	2.34851i
$761$	−21.2843	−	12.2885i	−0.771556	−	0.445458i	0.0618737	−	0.998084i	$-0.480292\pi$
$761$	−21.2843	−	12.2885i	−0.771556	−	0.445458i	−0.833429	+	0.552626i	$0.813626\pi$
$762$		0			0
$763$	6.72945	−	4.18462i	0.243622	−	0.151493i
$764$	−19.6140	−	21.2750i	−0.709610	−	0.769702i
$765$		0			0
$766$	−43.4990	−	6.62762i	−1.57168	−	0.239466i
$767$	0.0338885	−	0.0195656i	0.00122364	−	0.000706472i
$768$		0			0
$769$	11.7047	−	6.75773i	0.422083	−	0.243690i	−0.273885	−	0.961762i	$-0.588309\pi$
$769$	11.7047	−	6.75773i	0.422083	−	0.243690i	0.695968	+	0.718073i	$0.254975\pi$
$770$	−2.37433	+	19.9466i	−0.0855650	+	0.718826i
$771$		0			0
$772$	−29.2211	+	26.9398i	−1.05169	+	0.969583i
$773$	41.3688	+	23.8843i	1.48793	+	0.859059i	0.999905	−	0.0137693i	$-0.00438304\pi$
$773$	41.3688	+	23.8843i	1.48793	+	0.859059i	0.488028	+	0.872828i	$0.337716\pi$
$774$		0			0
$775$	1.17725	+	2.03905i	0.0422879	+	0.0732448i
$776$	2.90728	+	4.30849i	0.104365	+	0.154666i
$777$		0			0
$778$	−12.7088	+	15.8842i	−0.455633	+	0.569475i
$779$	77.6480	+	44.8301i	2.78203	+	1.60620i
$780$		0			0
$781$	−8.82496	−	15.2853i	−0.315782	−	0.546950i
$782$	1.62211	−	2.02740i	0.0580067	−	0.0724998i
$783$		0			0
$784$	24.4663	−	13.6163i	0.873795	−	0.486295i
$785$	9.60296	−	16.6328i	0.342744	−	0.593651i
$786$		0			0
$787$	7.94020			0.283038			0.141519	−	0.989936i	$-0.454801\pi$
$787$	7.94020			0.283038			0.141519	+	0.989936i	$0.454801\pi$
$788$	−27.5092	+	25.3615i	−0.979976	+	0.903467i
$789$		0			0
$790$	25.9052	+	3.94698i	0.921665	+	0.140427i
$791$	0.701706	+	21.4364i	0.0249498	+	0.762190i
$792$		0			0
$793$	−2.77255	−	4.80220i	−0.0984561	−	0.170531i
$794$	−3.83446	−	3.06793i	−0.136080	−	0.108877i
$795$		0			0
$796$	−1.26500	−	5.62523i	−0.0448367	−	0.199381i
$797$	−22.6742	+	13.0910i	−0.803162	+	0.463706i	−0.844576	−	0.535436i	$-0.820147\pi$
$797$	−22.6742	+	13.0910i	−0.803162	+	0.463706i	0.0414133	+	0.999142i	$0.486814\pi$
$798$		0			0
$799$	2.64009	+	1.52426i	0.0933998	+	0.0539244i
$800$	−14.8132	−	13.9668i	−0.523725	−	0.493800i
$801$		0			0
$802$	−47.5118	−	7.23901i	−1.67770	−	0.255618i
$803$	−27.7774			−0.980242
$804$		0			0
$805$	1.21949	+	37.2541i	0.0429813	+	1.31303i
$806$	−0.407437	−	0.325988i	−0.0143514	−	0.0114825i
$807$		0			0
$808$	12.7701	−	0.895371i	0.449251	−	0.0314990i
$809$	20.3769	−	35.2939i	0.716414	−	1.24087i	−0.245997	−	0.969271i	$-0.579115\pi$
$809$	20.3769	−	35.2939i	0.716414	−	1.24087i	0.962412	−	0.271595i	$-0.0875513\pi$
$810$		0			0
$811$	3.31693			0.116473			0.0582367	−	0.998303i	$-0.481452\pi$
$811$	3.31693			0.116473			0.0582367	+	0.998303i	$0.481452\pi$
$812$	−5.13902	+	18.5920i	−0.180344	+	0.652453i
$813$		0			0
$814$	2.83882	−	18.6320i	0.0995007	−	0.653053i
$815$	−37.6652			−1.31935
$816$		0			0
$817$			55.8978i			1.95562i
$818$	18.8241	−	7.35319i	0.658170	−	0.257098i
$819$		0			0
$820$	−44.5190	+	41.0433i	−1.55467	+	1.43329i
$821$	−40.0076			−1.39627			−0.698137	−	0.715964i	$-0.745988\pi$
$821$	−40.0076			−1.39627			−0.698137	+	0.715964i	$0.745988\pi$
$822$		0			0
$823$			7.00103i			0.244041i	0.992528	+	0.122020i	$0.0389373\pi$
$823$			7.00103i			0.244041i	−0.992528	+	0.122020i	$0.961063\pi$
$824$	32.9519	−	22.2353i	1.14793	−	0.774603i
$825$		0			0
$826$	0.0306849	−	0.257782i	0.00106766	−	0.00896938i
$827$			25.4507i			0.885008i	0.896766	+	0.442504i	$0.145910\pi$
$827$			25.4507i			0.885008i	−0.896766	+	0.442504i	$0.854090\pi$
$828$		0			0
$829$	5.05603	+	2.91910i	0.175603	+	0.101385i	0.585225	−	0.810871i	$-0.301006\pi$
$829$	5.05603	+	2.91910i	0.175603	+	0.101385i	−0.409622	+	0.912255i	$0.634339\pi$
$830$	18.7836	+	15.0287i	0.651989	+	0.521652i
$831$		0			0
$832$	4.18408	+	1.68866i	0.145057	+	0.0585438i
$833$	−0.174945	−	2.66933i	−0.00606148	−	0.0924868i
$834$		0			0
$835$			10.3751i			0.359047i
$836$	31.0229	−	6.97640i	1.07295	−	0.241284i
$837$		0			0
$838$	−5.76217	+	7.20187i	−0.199051	+	0.248784i
$839$	−11.3989	+	19.7435i	−0.393534	+	0.681621i	−0.992913	−	0.118845i	$-0.962081\pi$
$839$	−11.3989	+	19.7435i	−0.393534	+	0.681621i	0.599379	+	0.800465i	$0.295414\pi$
$840$		0			0
$841$	7.85583	+	13.6067i	0.270891	+	0.469196i
$842$	9.82131	+	1.49640i	0.338465	+	0.0515693i
$843$		0			0
$844$	11.5235	−	36.9383i	0.396656	−	1.27147i
$845$	32.2063	−	18.5943i	1.10793	−	0.639663i
$846$		0			0
$847$	−17.1840	+	10.6856i	−0.590448	+	0.367162i
$848$	−24.0261	−	16.6070i	−0.825061	−	0.570285i
$849$		0			0
$850$	−1.81176	+	0.707720i	−0.0621428	+	0.0242746i
$851$		−	34.9724i		−	1.19884i
$852$		0			0
$853$	14.0823	+	8.13042i	0.482169	+	0.278380i	0.721320	−	0.692602i	$-0.243536\pi$
$853$	14.0823	+	8.13042i	0.482169	+	0.278380i	−0.239151	+	0.970982i	$0.576869\pi$
$854$	−36.5291	−	4.34822i	−1.25000	−	0.148793i
$855$		0			0
$856$	−25.3539	+	1.77768i	−0.866577	+	0.0607597i
$857$	−6.51196	+	3.75968i	−0.222444	+	0.128428i	−0.607082	−	0.794639i	$-0.707660\pi$
$857$	−6.51196	+	3.75968i	−0.222444	+	0.128428i	0.384637	+	0.923068i	$0.374327\pi$
$858$		0			0
$859$	14.1859	−	24.5706i	0.484016	−	0.838340i	−0.515816	−	0.856699i	$-0.672511\pi$
$859$	14.1859	−	24.5706i	0.484016	−	0.838340i	0.999831	+	0.0183599i	$0.00584447\pi$
$860$	−36.0374	−	11.2425i	−1.22886	−	0.383365i
$861$		0			0
$862$	4.13231	−	27.1216i	0.140747	−	0.923765i
$863$	3.94874	−	2.27980i	0.134417	−	0.0776054i	−0.431284	−	0.902216i	$-0.641939\pi$
$863$	3.94874	−	2.27980i	0.134417	−	0.0776054i	0.565700	+	0.824611i	$0.308606\pi$
$864$		0			0
$865$	14.5997	−	25.2874i	0.496405	−	0.859799i
$866$	−27.0355	+	10.5608i	−0.918704	+	0.358870i
$867$		0			0
$868$	−3.35069	+	0.869585i	−0.113730	+	0.0295156i
$869$	−5.78409	−	10.0183i	−0.196212	−	0.339849i
$870$		0			0
$871$	−0.511748	−	0.886373i	−0.0173399	−	0.0300336i
$872$	7.02236	−	4.73855i	0.237807	−	0.160468i
$873$		0			0
$874$	54.9591	−	21.4685i	1.85902	−	0.726181i
$875$	−5.12372	+	9.58576i	−0.173213	+	0.324058i
$876$		0			0
$877$	13.8064	−	23.9134i	0.466210	−	0.807499i	−0.533046	−	0.846087i	$-0.678953\pi$
$877$	13.8064	−	23.9134i	0.466210	−	0.807499i	0.999255	+	0.0385877i	$0.0122859\pi$
$878$	3.59883	+	9.21299i	0.121455	+	0.310923i
$879$		0			0
$880$	−1.74179	+	21.4036i	−0.0587158	+	0.721516i
$881$			10.3088i			0.347313i	0.984806	+	0.173657i	$0.0555583\pi$
$881$			10.3088i			0.347313i	−0.984806	+	0.173657i	$0.944442\pi$
$882$		0			0
$883$		−	33.0806i		−	1.11325i	−0.830764	−	0.556625i	$-0.812096\pi$
$883$		−	33.0806i		−	1.11325i	0.830764	−	0.556625i	$-0.187904\pi$
$884$	0.316930	−	0.292187i	0.0106595	−	0.00982730i
$885$		0			0
$886$	−4.26170	+	1.66473i	−0.143175	+	0.0559277i
$887$	−3.58902	+	6.21637i	−0.120508	+	0.208725i	−0.919968	−	0.391994i	$-0.871786\pi$
$887$	−3.58902	+	6.21637i	−0.120508	+	0.208725i	0.799460	+	0.600719i	$0.205119\pi$
$888$		0			0
$889$	7.08462	−	13.2543i	0.237610	−	0.444535i
$890$	3.34206	+	8.55566i	0.112026	+	0.286787i
$891$		0			0
$892$	8.65496	+	38.4871i	0.289789	+	1.28864i
$893$	34.6381	+	59.9949i	1.15912	+	2.00765i
$894$		0			0
$895$	0.249809	+	0.432682i	0.00835019	+	0.0144630i
$896$	25.5949	−	15.5211i	0.855064	−	0.518522i
$897$		0			0
$898$	7.75777	+	19.8599i	0.258880	+	0.662732i
$899$	1.19238	−	2.06526i	0.0397681	−	0.0688803i
$900$		0			0
$901$	−2.41653	+	1.39518i	−0.0805062	+	0.0464803i
$902$	26.4263	+	4.02638i	0.879901	+	0.134064i
$903$		0			0
$904$	1.60370	+	22.8726i	0.0533383	+	0.760731i
$905$	−22.6083	+	39.1587i	−0.751525	+	1.30168i
$906$		0			0
$907$	−15.3581	+	8.86699i	−0.509956	+	0.294423i	−0.732816	−	0.680427i	$-0.761794\pi$
$907$	−15.3581	+	8.86699i	−0.509956	+	0.294423i	0.222859	+	0.974851i	$0.428461\pi$
$908$	−2.47755	−	0.772914i	−0.0822204	−	0.0256501i
$909$		0			0
$910$	−0.731451	+	6.14487i	−0.0242474	+	0.203701i
$911$	29.3352	+	16.9367i	0.971918	+	0.561137i	0.899820	−	0.436261i	$-0.143697\pi$
$911$	29.3352	+	16.9367i	0.971918	+	0.561137i	0.0720973	+	0.997398i	$0.477031\pi$
$912$		0			0
$913$		−	10.6198i		−	0.351464i
$914$	−13.8448	−	35.4427i	−0.457946	−	1.17234i
$915$		0			0
$916$	−25.4396	+	5.72083i	−0.840547	+	0.189022i
$917$	17.4420	−	10.8461i	0.575985	−	0.358169i
$918$		0			0
$919$	−45.7550	+	26.4167i	−1.50932	+	0.871406i	−0.509378	+	0.860543i	$0.670124\pi$
$919$	−45.7550	+	26.4167i	−1.50932	+	0.871406i	−0.999941	+	0.0108626i	$0.996542\pi$
$920$	2.78706	+	39.7500i	0.0918866	+	1.31052i
$921$		0			0
$922$	3.29582	−	21.6314i	0.108542	−	0.712393i
$923$	−2.71867	−	4.70887i	−0.0894861	−	0.154994i
$924$		0			0
$925$	−13.0994	+	22.6888i	−0.430705	+	0.746004i
$926$	−6.60659	−	5.28590i	−0.217106	−	0.173705i
$927$		0			0
$928$	−4.74929	+	20.0667i	−0.155903	+	0.658721i
$929$			41.4000i			1.35829i	0.734005	+	0.679144i	$0.237649\pi$
$929$			41.4000i			1.35829i	−0.734005	+	0.679144i	$0.762351\pi$
$930$		0			0
$931$	26.8867	−	54.5202i	0.881176	−	1.78683i
$932$	−31.2085	−	9.73601i	−1.02227	−	0.318914i
$933$		0			0
$934$	28.2877	−	35.3555i	0.925603	−	1.15687i
$935$	1.77675	+	1.02581i	0.0581059	+	0.0335474i
$936$		0			0
$937$			34.0441i			1.11217i	0.831125	+	0.556086i	$0.187697\pi$
$937$			34.0441i			1.11217i	−0.831125	+	0.556086i	$0.812303\pi$
$938$	−6.74242	−	0.802580i	−0.220148	−	0.0262052i
$939$		0			0
$940$	−45.6454	+	10.2647i	−1.48879	+	0.334798i
$941$		−	45.4739i		−	1.48241i	−0.671281	−	0.741203i	$-0.734256\pi$
$941$		−	45.4739i		−	1.48241i	0.671281	−	0.741203i	$-0.265744\pi$
$942$		0			0
$943$	49.6024			1.61528
$944$	0.0225102	−	0.276612i	0.000732645	−	0.00900294i
$945$		0			0
$946$	6.06372	+	15.5231i	0.197149	+	0.504699i
$947$		−	37.1017i		−	1.20564i	−0.797876	−	0.602822i	$-0.794043\pi$
$947$		−	37.1017i		−	1.20564i	0.797876	−	0.602822i	$-0.205957\pi$
$948$		0			0
$949$	−8.55726			−0.277780
$950$	−43.6967	−	6.65774i	−1.41771	−	0.216006i
$951$		0			0
$952$	−0.293245	−	2.84468i	−0.00950414	−	0.0921966i
$953$	−28.7039			−0.929812			−0.464906	−	0.885360i	$-0.653912\pi$
$953$	−28.7039			−0.929812			−0.464906	+	0.885360i	$0.653912\pi$
$954$		0			0
$955$	21.2136	−	36.7431i	0.686457	−	1.18898i
$956$	4.87141	−	15.6151i	0.157553	−	0.505030i
$957$		0			0
$958$	21.0952	−	26.3659i	0.681554	−	0.851843i
$959$	1.63505	+	49.9489i	0.0527984	+	1.61294i
$960$		0			0
$961$	−30.5720			−0.986194
$962$	0.874544	−	5.73989i	0.0281964	−	0.185062i
$963$		0			0
$964$	−5.02690	+	16.1136i	−0.161906	+	0.518983i
$965$	−50.4665	−	29.1368i	−1.62457	−	0.937948i
$966$		0			0
$967$	15.4417	−	8.91526i	0.496571	−	0.286695i	−0.230725	−	0.973019i	$-0.574110\pi$
$967$	15.4417	−	8.91526i	0.496571	−	0.286695i	0.727296	+	0.686324i	$0.240777\pi$
$968$	−17.9319	+	12.1001i	−0.576354	+	0.388912i
$969$		0			0
$970$	−4.76102	+	5.95057i	−0.152867	+	0.191061i
$971$	−11.4504	−	19.8326i	−0.367460	−	0.636459i	0.621708	−	0.783249i	$-0.286439\pi$
$971$	−11.4504	−	19.8326i	−0.367460	−	0.636459i	−0.989168	+	0.146790i	$0.953106\pi$
$972$		0			0
$973$	0.618549	+	18.8960i	0.0198298	+	0.605778i
$974$	−0.912507	+	5.98905i	−0.0292386	+	0.191902i
$975$		0			0
$976$	−39.1974	−	3.18982i	−1.25468	−	0.102104i
$977$	38.1927			1.22189			0.610947	−	0.791671i	$-0.290789\pi$
$977$	38.1927			1.22189			0.610947	+	0.791671i	$0.290789\pi$
$978$		0			0
$979$	2.02748	−	3.51169i	0.0647984	−	0.112234i
$980$	29.7416	+	28.2993i	0.950062	+	0.903987i
$981$		0			0
$982$	8.42041	+	6.73712i	0.268706	+	0.214990i
$983$	2.20510	+	3.81934i	0.0703316	+	0.121818i	0.899047	−	0.437853i	$-0.144261\pi$
$983$	2.20510	+	3.81934i	0.0703316	+	0.121818i	−0.828715	+	0.559671i	$0.810928\pi$
$984$		0			0
$985$	−47.5099	−	27.4299i	−1.51379	−	0.873989i
$986$	1.53831	+	1.23079i	0.0489897	+	0.0391964i
$987$		0			0
$988$	9.55709	−	2.14919i	0.304052	−	0.0683749i
$989$	15.4621	+	26.7811i	0.491665	+	0.851589i
$990$		0			0
$991$	46.5115	+	26.8534i	1.47749	+	0.853027i	0.999676	−	0.0254358i	$-0.00809734\pi$
$991$	46.5115	+	26.8534i	1.47749	+	0.853027i	0.477810	+	0.878463i	$0.341431\pi$
$992$	−3.54490	+	1.06248i	−0.112551	+	0.0337337i
$993$		0			0
$994$	−35.8192	−	4.26372i	−1.13612	−	0.135237i
$995$	7.32115	−	4.22687i	0.232096	−	0.134001i
$996$		0			0
$997$	35.7424	−	20.6359i	1.13197	−	0.653544i	0.187542	−	0.982257i	$-0.439948\pi$
$997$	35.7424	−	20.6359i	1.13197	−	0.653544i	0.944430	+	0.328713i	$0.106615\pi$
$998$	4.43746	−	29.1244i	0.140465	−	0.921917i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bj.b.451.17		84
3.2	odd	2		252.2.bj.b.115.26	yes	84
4.3	odd	2	inner	756.2.bj.b.451.18		84
7.5	odd	6		756.2.n.b.19.11		84
9.4	even	3		756.2.n.b.199.40		84
9.5	odd	6		252.2.n.b.31.3	✓	84
12.11	even	2		252.2.bj.b.115.25	yes	84
21.5	even	6		252.2.n.b.187.32	yes	84
28.19	even	6		756.2.n.b.19.40		84
36.23	even	6		252.2.n.b.31.32	yes	84
36.31	odd	6		756.2.n.b.199.11		84
63.5	even	6		252.2.bj.b.103.26	yes	84
63.40	odd	6	inner	756.2.bj.b.523.17		84
84.47	odd	6		252.2.n.b.187.3	yes	84
252.103	even	6	inner	756.2.bj.b.523.18		84
252.131	odd	6		252.2.bj.b.103.25	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.3	✓	84	9.5	odd	6
252.2.n.b.31.32	yes	84	36.23	even	6
252.2.n.b.187.3	yes	84	84.47	odd	6
252.2.n.b.187.32	yes	84	21.5	even	6
252.2.bj.b.103.25	yes	84	252.131	odd	6
252.2.bj.b.103.26	yes	84	63.5	even	6
252.2.bj.b.115.25	yes	84	12.11	even	2
252.2.bj.b.115.26	yes	84	3.2	odd	2
756.2.n.b.19.11		84	7.5	odd	6
756.2.n.b.19.40		84	28.19	even	6
756.2.n.b.199.11		84	36.31	odd	6
756.2.n.b.199.40		84	9.4	even	3
756.2.bj.b.451.17		84	1.1	even	1	trivial
756.2.bj.b.451.18		84	4.3	odd	2	inner
756.2.bj.b.523.17		84	63.40	odd	6	inner
756.2.bj.b.523.18		84	252.103	even	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bj (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.514563 - 1.31728i) q^{2} +(-1.47045 + 1.35565i) q^{4} +(-2.53954 - 1.46621i) q^{5} +(2.33334 + 1.24720i) q^{7} +(2.54241 + 1.23943i) q^{8} +O(q^{10})\)	\(q+(-0.514563 - 1.31728i) q^{2} +(-1.47045 + 1.35565i) q^{4} +(-2.53954 - 1.46621i) q^{5} +(2.33334 + 1.24720i) q^{7} +(2.54241 + 1.23943i) q^{8} +(-0.624647 + 4.09975i) q^{10} +(1.58550 - 0.915388i) q^{11} +(0.488438 - 0.282000i) q^{13} +(0.442264 - 3.71543i) q^{14} +(0.324441 - 3.98682i) q^{16} +(-0.330952 - 0.191075i) q^{17} +(-4.34210 - 7.52073i) q^{19} +(5.72193 - 1.28674i) q^{20} +(-2.02166 - 1.61752i) q^{22} +(-4.16067 - 2.40216i) q^{23} +(1.79952 + 3.11687i) q^{25} +(-0.622805 - 0.498302i) q^{26} +(-5.12183 + 1.32924i) q^{28} +(1.82266 - 3.15694i) q^{29} +0.654198 q^{31} +(-5.41870 + 1.62409i) q^{32} +(-0.0814037 + 0.534277i) q^{34} +(-4.09697 - 6.58849i) q^{35} +(3.63968 + 6.30411i) q^{37} +(-7.67262 + 9.58965i) q^{38} +(-4.63930 - 6.87527i) q^{40} +(-8.94130 + 5.16226i) q^{41} +(-5.57437 - 3.21836i) q^{43} +(-1.09045 + 3.49541i) q^{44} +(-1.02339 + 6.71682i) q^{46} -7.97727 q^{47} +(3.88897 + 5.82030i) q^{49} +(3.17982 - 3.97430i) q^{50} +(-0.335931 + 1.07682i) q^{52} +(3.65087 - 6.32349i) q^{53} -5.36859 q^{55} +(4.38648 + 6.06290i) q^{56} +(-5.09644 - 0.776506i) q^{58} +0.0693815 q^{59} -9.83174i q^{61} +(-0.336626 - 0.861761i) q^{62} +(4.92765 + 6.30224i) q^{64} -1.65388 q^{65} -1.81471i q^{67} +(0.745679 - 0.167688i) q^{68} +(-6.57073 + 8.78704i) q^{70} -9.64068i q^{71} +(-13.1397 - 7.58623i) q^{73} +(6.43143 - 8.03834i) q^{74} +(16.5803 + 5.17250i) q^{76} +(4.84118 - 0.158473i) q^{77} -6.31873i q^{79} +(-6.66944 + 9.64901i) q^{80} +(11.4010 + 9.12188i) q^{82} +(2.90035 - 5.02356i) q^{83} +(0.560312 + 0.970489i) q^{85} +(-1.37112 + 8.99905i) q^{86} +(5.16553 - 0.362179i) q^{88} +(1.91814 - 1.10744i) q^{89} +(1.49140 - 0.0488201i) q^{91} +(9.37453 - 2.10814i) q^{92} +(4.10481 + 10.5083i) q^{94} +25.4656i q^{95} +(1.59144 + 0.918820i) q^{97} +(5.66585 - 8.11777i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8}+O(q^{10}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8	\( 84 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 16 q^{8} - 18 q^{10} + 18 q^{13} - 14 q^{14} + 14 q^{16} - 6 q^{17} + 24 q^{20} + 6 q^{22} + 16 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} + 18 q^{32} - 24 q^{34} + 2 q^{37} - 33 q^{38} + 6 q^{40} - 6 q^{41} + 13 q^{44} + 10 q^{46} - 28 q^{49} + 17 q^{50} - 27 q^{52} + 2 q^{53} - 58 q^{56} - 13 q^{58} - 8 q^{64} + 100 q^{65} + 18 q^{68} - 19 q^{70} + 30 q^{73} + 23 q^{74} + 2 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} + 9 q^{86} + q^{88} + 102 q^{89} - 28 q^{92} + 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q - 2 * q^2 - 2 * q^4 - 6 * q^5 + 16 * q^8 - 18 * q^10 + 18 * q^13 - 14 * q^14 + 14 * q^16 - 6 * q^17 + 24 * q^20 + 6 * q^22 + 16 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 + 18 * q^32 - 24 * q^34 + 2 * q^37 - 33 * q^38 + 6 * q^40 - 6 * q^41 + 13 * q^44 + 10 * q^46 - 28 * q^49 + 17 * q^50 - 27 * q^52 + 2 * q^53 - 58 * q^56 - 13 * q^58 - 8 * q^64 + 100 * q^65 + 18 * q^68 - 19 * q^70 + 30 * q^73 + 23 * q^74 + 2 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 + 9 * q^86 + q^88 + 102 * q^89 - 28 * q^92 + 6 * q^97 - 21 * q^98

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