LMFDB - Embedded newform 756.2.bb.a.611.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (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:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.19
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.298214 - 1.38241i) q^{2} +(-1.82214 + 0.824510i) q^{4} +(-2.82413 + 1.63051i) q^{5} +(-2.14986 - 1.54211i) q^{7} +(1.68320 + 2.27307i) q^{8} +O(q^{10})$	\(q+(-0.298214 - 1.38241i) q^{2} +(-1.82214 + 0.824510i) q^{4} +(-2.82413 + 1.63051i) q^{5} +(-2.14986 - 1.54211i) q^{7} +(1.68320 + 2.27307i) q^{8} +(3.09624 + 3.41787i) q^{10} +(-1.74511 + 3.02263i) q^{11} +(2.49315 - 4.31827i) q^{13} +(-1.49071 + 3.43188i) q^{14} +(2.64037 - 3.00474i) q^{16} +(1.85883 - 1.07319i) q^{17} +(4.57306 + 2.64026i) q^{19} +(3.80158 - 5.29954i) q^{20} +(4.69894 + 1.51108i) q^{22} +(-0.347811 - 0.602427i) q^{23} +(2.81714 - 4.87942i) q^{25} +(-6.71312 - 2.15880i) q^{26} +(5.18882 + 1.03735i) q^{28} +(6.28645 - 3.62948i) q^{29} +3.81153i q^{31} +(-4.94119 - 2.75402i) q^{32} +(-2.03793 - 2.24963i) q^{34} +(8.58591 + 0.849742i) q^{35} +(3.22871 - 5.59229i) q^{37} +(2.28618 - 7.10922i) q^{38} +(-8.45984 - 3.67496i) q^{40} +(0.0132552 + 0.00765288i) q^{41} +(-1.45919 + 0.842461i) q^{43} +(0.687651 - 6.94650i) q^{44} +(-0.729081 + 0.660471i) q^{46} +5.51987 q^{47} +(2.24380 + 6.63064i) q^{49} +(-7.58549 - 2.43934i) q^{50} +(-0.982411 + 9.92410i) q^{52} +(2.31470 - 1.33639i) q^{53} -11.3817i q^{55} +(-0.113328 - 7.48246i) q^{56} +(-6.89215 - 7.60811i) q^{58} +6.67359 q^{59} +8.82482 q^{61} +(5.26911 - 1.13665i) q^{62} +(-2.33367 + 7.65206i) q^{64} +16.2605i q^{65} +0.864985i q^{67} +(-2.50218 + 3.48813i) q^{68} +(-1.38574 - 12.1227i) q^{70} -11.9340 q^{71} +(0.923127 + 1.59890i) q^{73} +(-8.69371 - 2.79572i) q^{74} +(-10.5097 - 1.04038i) q^{76} +(8.41297 - 3.80707i) q^{77} +13.9307i q^{79} +(-2.55747 + 12.7909i) q^{80} +(0.00662657 - 0.0206063i) q^{82} +(-5.24458 - 9.08388i) q^{83} +(-3.49971 + 6.06168i) q^{85} +(1.59978 + 1.76596i) q^{86} +(-9.80801 + 1.12092i) q^{88} +(3.53619 + 2.04162i) q^{89} +(-12.0192 + 5.43896i) q^{91} +(1.13047 + 0.810931i) q^{92} +(-1.64610 - 7.63075i) q^{94} -17.2199 q^{95} +(3.33413 + 5.77488i) q^{97} +(8.49716 - 5.07921i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.298214	−	1.38241i	−0.210869	−	0.977514i
$2$	−0.298214	−	1.38241i	−0.210869	−	0.977514i
$3$		0			0
$3$		0			0
$4$	−1.82214	+	0.824510i	−0.911069	+	0.412255i
$5$	−2.82413	+	1.63051i	−1.26299	+	0.729187i	−0.973652	−	0.228040i	$-0.926768\pi$
$5$	−2.82413	+	1.63051i	−1.26299	+	0.729187i	−0.289337	+	0.957227i	$0.593435\pi$
$6$		0			0
$7$	−2.14986	−	1.54211i	−0.812571	−	0.582862i
$7$	−2.14986	−	1.54211i	−0.812571	−	0.582862i
$8$	1.68320	+	2.27307i	0.595101	+	0.803651i
$9$		0			0
$10$	3.09624	+	3.41787i	0.979116	+	1.08083i
$11$	−1.74511	+	3.02263i	−0.526172	+	0.911356i	0.473363	+	0.880867i	$0.343040\pi$
$11$	−1.74511	+	3.02263i	−0.526172	+	0.911356i	−0.999535	+	0.0304888i	$0.990294\pi$
$12$		0			0
$13$	2.49315	−	4.31827i	0.691476	−	1.19767i	−0.279878	−	0.960035i	$-0.590294\pi$
$13$	2.49315	−	4.31827i	0.691476	−	1.19767i	0.971354	−	0.237636i	$-0.0763725\pi$
$14$	−1.49071	+	3.43188i	−0.398410	+	0.917207i
$15$		0			0
$16$	2.64037	−	3.00474i	0.660092	−	0.751185i
$17$	1.85883	−	1.07319i	0.450832	−	0.260288i	−0.257350	−	0.966318i	$-0.582849\pi$
$17$	1.85883	−	1.07319i	0.450832	−	0.260288i	0.708181	+	0.706031i	$0.249516\pi$
$18$		0			0
$19$	4.57306	+	2.64026i	1.04913	+	0.605716i	0.922406	−	0.386222i	$-0.126220\pi$
$19$	4.57306	+	2.64026i	1.04913	+	0.605716i	0.126725	+	0.991938i	$0.459553\pi$
$20$	3.80158	−	5.29954i	0.850058	−	1.18501i
$21$		0			0
$22$	4.69894	+	1.51108i	1.00182	+	0.322164i
$23$	−0.347811	−	0.602427i	−0.0725237	−	0.125615i	0.827483	−	0.561491i	$-0.189772\pi$
$23$	−0.347811	−	0.602427i	−0.0725237	−	0.125615i	−0.900007	+	0.435876i	$0.856439\pi$
$24$		0			0
$25$	2.81714	−	4.87942i	0.563427	−	0.975885i
$26$	−6.71312	−	2.15880i	−1.31655	−	0.423376i
$27$		0			0
$28$	5.18882	+	1.03735i	0.980596	+	0.196041i
$29$	6.28645	−	3.62948i	1.16736	−	0.673978i	0.214306	−	0.976767i	$-0.431251\pi$
$29$	6.28645	−	3.62948i	1.16736	−	0.673978i	0.953058	+	0.302789i	$0.0979177\pi$
$30$		0			0
$31$			3.81153i			0.684570i	0.939596	+	0.342285i	$0.111201\pi$
$31$			3.81153i			0.684570i	−0.939596	+	0.342285i	$0.888799\pi$
$32$	−4.94119	−	2.75402i	−0.873487	−	0.486847i
$33$		0			0
$34$	−2.03793	−	2.24963i	−0.349502	−	0.385808i
$35$	8.58591	+	0.849742i	1.45128	+	0.143633i
$36$		0			0
$37$	3.22871	−	5.59229i	0.530797	−	0.919368i	−0.468557	−	0.883433i	$-0.655226\pi$
$37$	3.22871	−	5.59229i	0.530797	−	0.919368i	0.999354	−	0.0359344i	$-0.0114407\pi$
$38$	2.28618	−	7.10922i	0.370867	−	1.15327i
$39$		0			0
$40$	−8.45984	−	3.67496i	−1.33762	−	0.581062i
$41$	0.0132552	+	0.00765288i	0.00207011	+	0.00119518i	0.501035	−	0.865427i	$-0.332953\pi$
$41$	0.0132552	+	0.00765288i	0.00207011	+	0.00119518i	−0.498965	+	0.866622i	$0.666286\pi$
$42$		0			0
$43$	−1.45919	+	0.842461i	−0.222524	+	0.128474i	−0.607118	−	0.794611i	$-0.707675\pi$
$43$	−1.45919	+	0.842461i	−0.222524	+	0.128474i	0.384595	+	0.923086i	$0.374341\pi$
$44$	0.687651	−	6.94650i	0.103667	−	1.04722i
$45$		0			0
$46$	−0.729081	+	0.660471i	−0.107497	+	0.0973812i
$47$	5.51987			0.805156			0.402578	−	0.915386i	$-0.368114\pi$
$47$	5.51987			0.805156			0.402578	+	0.915386i	$0.368114\pi$
$48$		0			0
$49$	2.24380	+	6.63064i	0.320543	+	0.947234i
$50$	−7.58549	−	2.43934i	−1.07275	−	0.344974i
$51$		0			0
$52$	−0.982411	+	9.92410i	−0.136236	+	1.37623i
$53$	2.31470	−	1.33639i	0.317949	−	0.183568i	−0.332529	−	0.943093i	$-0.607902\pi$
$53$	2.31470	−	1.33639i	0.317949	−	0.183568i	0.650478	+	0.759525i	$0.274569\pi$
$54$		0			0
$55$		−	11.3817i		−	1.53471i
$56$	−0.113328	−	7.48246i	−0.0151442	−	0.999885i
$57$		0			0
$58$	−6.89215	−	7.60811i	−0.904984	−	0.998994i
$59$	6.67359			0.868828			0.434414	−	0.900713i	$-0.356956\pi$
$59$	6.67359			0.868828			0.434414	+	0.900713i	$0.356956\pi$
$60$		0			0
$61$	8.82482			1.12990			0.564951	−	0.825124i	$-0.308895\pi$
$61$	8.82482			1.12990			0.564951	+	0.825124i	$0.308895\pi$
$62$	5.26911	−	1.13665i	0.669177	−	0.144355i
$63$		0			0
$64$	−2.33367	+	7.65206i	−0.291709	+	0.956507i
$65$			16.2605i			2.01686i
$66$		0			0
$67$			0.864985i			0.105675i	0.998603	+	0.0528374i	$0.0168265\pi$
$67$			0.864985i			0.105675i	−0.998603	+	0.0528374i	$0.983174\pi$
$68$	−2.50218	+	3.48813i	−0.303434	+	0.422998i
$69$		0			0
$70$	−1.38574	−	12.1227i	−0.165628	−	1.44894i
$71$	−11.9340			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$71$	−11.9340			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$72$		0			0
$73$	0.923127	+	1.59890i	0.108044	+	0.187137i	0.914978	−	0.403504i	$-0.132208\pi$
$73$	0.923127	+	1.59890i	0.108044	+	0.187137i	−0.806934	+	0.590642i	$0.798875\pi$
$74$	−8.69371	−	2.79572i	−1.01062	−	0.324996i
$75$		0			0
$76$	−10.5097	−	1.04038i	−1.20554	−	0.119339i
$77$	8.41297	−	3.80707i	0.958747	−	0.433856i
$78$		0			0
$79$			13.9307i			1.56732i	0.621188	+	0.783662i	$0.286650\pi$
$79$			13.9307i			1.56732i	−0.621188	+	0.783662i	$0.713350\pi$
$80$	−2.55747	+	12.7909i	−0.285934	+	1.43007i
$81$		0			0
$82$	0.00662657	−	0.0206063i	0.000731783	−	0.00227559i
$83$	−5.24458	−	9.08388i	−0.575667	−	0.997085i	−0.995969	−	0.0897007i	$-0.971409\pi$
$83$	−5.24458	−	9.08388i	−0.575667	−	0.997085i	0.420301	−	0.907385i	$-0.361924\pi$
$84$		0			0
$85$	−3.49971	+	6.06168i	−0.379597	+	0.657481i
$86$	1.59978	+	1.76596i	0.172509	+	0.190429i
$87$		0			0
$88$	−9.80801	+	1.12092i	−1.04554	+	0.119491i
$89$	3.53619	+	2.04162i	0.374836	+	0.216412i	0.675569	−	0.737297i	$-0.263898\pi$
$89$	3.53619	+	2.04162i	0.374836	+	0.216412i	−0.300733	+	0.953708i	$0.597231\pi$
$90$		0			0
$91$	−12.0192	+	5.43896i	−1.25995	+	0.570158i
$92$	1.13047	+	0.810931i	0.117859	+	0.0845454i
$93$		0			0
$94$	−1.64610	−	7.63075i	−0.169782	−	0.787052i
$95$	−17.2199			−1.76672
$96$		0			0
$97$	3.33413	+	5.77488i	0.338529	+	0.586350i	0.984156	−	0.177303i	$-0.0567372\pi$
$97$	3.33413	+	5.77488i	0.338529	+	0.586350i	−0.645627	+	0.763653i	$0.723404\pi$
$98$	8.49716	−	5.07921i	0.858342	−	0.513078i
$99$		0			0
$100$	−1.11008	+	11.2137i	−0.111008	+	1.12137i
$101$	−2.53905	−	1.46592i	−0.252645	−	0.145865i	0.368330	−	0.929695i	$-0.379930\pi$
$101$	−2.53905	−	1.46592i	−0.252645	−	0.145865i	−0.620975	+	0.783831i	$0.713263\pi$
$102$		0			0
$103$	14.6169	−	8.43905i	1.44024	−	0.831524i	0.442377	−	0.896829i	$-0.354135\pi$
$103$	14.6169	−	8.43905i	1.44024	−	0.831524i	0.997865	+	0.0653052i	$0.0208021\pi$
$104$	14.0122	−	1.60140i	1.37401	−	0.157031i
$105$		0			0
$106$	−2.53773	−	2.80134i	−0.246486	−	0.272091i
$107$	1.63897	−	2.83878i	0.158445	−	0.274435i	−0.775863	−	0.630902i	$-0.782685\pi$
$107$	1.63897	−	2.83878i	0.158445	−	0.274435i	0.934308	+	0.356466i	$0.116018\pi$
$108$		0			0
$109$	−5.12322	−	8.87368i	−0.490716	−	0.849944i	0.509227	−	0.860632i	$-0.329931\pi$
$109$	−5.12322	−	8.87368i	−0.490716	−	0.849944i	−0.999943	+	0.0106878i	$0.996598\pi$
$110$	−15.7342	+	3.39418i	−1.50020	+	0.323623i
$111$		0			0
$112$	−10.3101	+	2.38804i	−0.974209	+	0.225648i
$113$	−12.0033	−	6.93010i	−1.12917	−	0.651929i	−0.185447	−	0.982654i	$-0.559373\pi$
$113$	−12.0033	−	6.93010i	−1.12917	−	0.651929i	−0.943727	+	0.330725i	$0.892707\pi$
$114$		0			0
$115$	1.96453	+	1.13422i	0.183193	+	0.105767i
$116$	−8.46222	+	11.7966i	−0.785698	+	1.09529i
$117$		0			0
$118$	−1.99016	−	9.22567i	−0.183209	−	0.849292i
$119$	−5.65120	−	0.559296i	−0.518045	−	0.0512706i
$120$		0			0
$121$	−0.590845	−	1.02337i	−0.0537132	−	0.0930340i
$122$	−2.63168	−	12.1996i	−0.238261	−	1.10450i
$123$		0			0
$124$	−3.14264	−	6.94512i	−0.282218	−	0.623691i
$125$			2.06838i			0.185002i
$126$		0			0
$127$		−	9.18473i		−	0.815013i	−0.913202	−	0.407506i	$-0.866398\pi$
$127$		−	9.18473i		−	0.815013i	0.913202	−	0.407506i	$-0.133602\pi$
$128$	11.2742	+	0.944151i	0.996512	+	0.0834520i
$129$		0			0
$130$	22.4787	−	4.84909i	1.97151	−	0.425294i
$131$	3.91405	+	6.77933i	0.341972	+	0.592313i	0.984799	−	0.173699i	$-0.0555719\pi$
$131$	3.91405	+	6.77933i	0.341972	+	0.592313i	−0.642827	+	0.766011i	$0.722239\pi$
$132$		0			0
$133$	−5.75987	−	12.7283i	−0.499444	−	1.10369i
$134$	1.19577	−	0.257951i	0.103299	−	0.0222835i
$135$		0			0
$136$	5.56822	+	2.41884i	0.477471	+	0.207414i
$137$	14.0462	+	8.10958i	1.20005	+	0.692848i	0.960566	−	0.278053i	$-0.0896889\pi$
$137$	14.0462	+	8.10958i	1.20005	+	0.692848i	0.239482	+	0.970901i	$0.423022\pi$
$138$		0			0
$139$	14.9152	+	8.61130i	1.26509	+	0.730401i	0.974055	−	0.226311i	$-0.0726664\pi$
$139$	14.9152	+	8.61130i	1.26509	+	0.730401i	0.291037	+	0.956712i	$0.406000\pi$
$140$	−16.3453	+	5.53082i	−1.38143	+	0.467440i
$141$		0			0
$142$	3.55890	+	16.4978i	0.298656	+	1.38446i
$143$	8.70167	+	15.0717i	0.727670	+	1.26036i
$144$		0			0
$145$	−11.8358	+	20.5002i	−0.982912	+	1.70245i
$146$	1.93506	−	1.75296i	0.160146	−	0.145076i
$147$		0			0
$148$	−1.27225	+	12.8520i	−0.104579	+	1.05643i
$149$	2.55393	−	1.47451i	0.209226	−	0.120797i	−0.391726	−	0.920082i	$-0.628122\pi$
$149$	2.55393	−	1.47451i	0.209226	−	0.120797i	0.600952	+	0.799285i	$0.294788\pi$
$150$		0			0
$151$	−1.66272	−	0.959970i	−0.135310	−	0.0781212i	0.430817	−	0.902439i	$-0.358225\pi$
$151$	−1.66272	−	0.959970i	−0.135310	−	0.0781212i	−0.566127	+	0.824318i	$0.691559\pi$
$152$	1.69589	+	14.8389i	0.137555	+	1.20360i
$153$		0			0
$154$	−7.77181	−	10.4949i	−0.626270	−	0.845702i
$155$	−6.21474	−	10.7642i	−0.499180	−	0.864605i
$156$		0			0
$157$	12.0539			0.962004			0.481002	−	0.876719i	$-0.340273\pi$
$157$	12.0539			0.962004			0.481002	+	0.876719i	$0.340273\pi$
$158$	19.2580	−	4.15432i	1.53208	−	0.330500i
$159$		0			0
$160$	18.4450	−	0.278945i	1.45821	−	0.0220525i
$161$	−0.181262	+	1.83150i	−0.0142855	+	0.144342i
$162$		0			0
$163$	−8.62872	−	4.98179i	−0.675854	−	0.390204i	0.122437	−	0.992476i	$-0.460929\pi$
$163$	−8.62872	−	4.98179i	−0.675854	−	0.390204i	−0.798291	+	0.602272i	$0.794262\pi$
$164$	−0.0304626	−	0.00301557i	−0.00237873	−	0.000235477i
$165$		0			0
$166$	−10.9937	+	9.95912i	−0.853275	+	0.772978i
$167$	−5.09079	+	8.81751i	−0.393937	+	0.682319i	−0.992965	−	0.118409i	$-0.962221\pi$
$167$	−5.09079	+	8.81751i	−0.393937	+	0.682319i	0.599028	+	0.800728i	$0.295554\pi$
$168$		0			0
$169$	−5.93161	−	10.2739i	−0.456278	−	0.790297i
$170$	9.42341	+	3.03037i	0.722743	+	0.232419i
$171$		0			0
$172$	1.96422	−	2.73819i	0.149770	−	0.208785i
$173$		−	11.5975i		−	0.881742i	−0.897570	−	0.440871i	$-0.854670\pi$
$173$		−	11.5975i		−	0.881742i	0.897570	−	0.440871i	$-0.145330\pi$
$174$		0			0
$175$	−13.5811	+	6.14575i	−1.02663	+	0.464575i
$176$	4.47447	+	13.2245i	0.337276	+	0.996831i
$177$		0			0
$178$	1.76783	−	5.49733i	0.132504	−	0.412042i
$179$	2.14749	+	3.71956i	0.160511	+	0.278013i	0.935052	−	0.354511i	$-0.115352\pi$
$179$	2.14749	+	3.71956i	0.160511	+	0.278013i	−0.774541	+	0.632524i	$0.782019\pi$
$180$		0			0
$181$	13.1272			0.975735			0.487867	−	0.872918i	$-0.337775\pi$
$181$	13.1272			0.975735			0.487867	+	0.872918i	$0.337775\pi$
$182$	11.1032	+	14.9935i	0.823022	+	1.11139i
$183$		0			0
$184$	0.783921	−	1.80460i	0.0577914	−	0.133037i
$185$			21.0578i			1.54820i
$186$		0			0
$187$			7.49138i			0.547824i
$188$	−10.0580	+	4.55119i	−0.733552	+	0.331930i
$189$		0			0
$190$	5.13520	+	23.8050i	0.372547	+	1.72700i
$191$	17.5277			1.26826			0.634131	−	0.773225i	$-0.281358\pi$
$191$	17.5277			1.26826			0.634131	+	0.773225i	$0.281358\pi$
$192$		0			0
$193$	−12.5667			−0.904570			−0.452285	−	0.891873i	$-0.649391\pi$
$193$	−12.5667			−0.904570			−0.452285	+	0.891873i	$0.649391\pi$
$194$	6.98899	−	6.33129i	0.501780	−	0.454560i
$195$		0			0
$196$	−9.55554	−	10.2319i	−0.682538	−	0.730850i
$197$			15.0221i			1.07028i	0.844763	+	0.535141i	$0.179741\pi$
$197$			15.0221i			1.07028i	−0.844763	+	0.535141i	$0.820259\pi$
$198$		0			0
$199$	17.6652	−	10.1990i	1.25225	−	0.722987i	0.280695	−	0.959797i	$-0.409435\pi$
$199$	17.6652	−	10.1990i	1.25225	−	0.722987i	0.971556	+	0.236810i	$0.0761019\pi$
$200$	15.8331	−	1.80951i	1.11957	−	0.127951i
$201$		0			0
$202$	−1.26933	+	3.94717i	−0.0893097	+	0.277722i
$203$	−19.1120	−	1.89151i	−1.34140	−	0.132758i
$204$		0			0
$205$	−0.0499124			−0.00348604
$206$	−16.0252	−	17.6899i	−1.11653	−	1.23251i
$207$		0			0
$208$	−6.39243	−	18.8931i	−0.443235	−	1.31000i
$209$	−15.9610	+	9.21509i	−1.10405	+	0.637421i
$210$		0			0
$211$	−11.9369	−	6.89180i	−0.821773	−	0.474451i	0.0292543	−	0.999572i	$-0.490687\pi$
$211$	−11.9369	−	6.89180i	−0.821773	−	0.474451i	−0.851028	+	0.525121i	$0.824020\pi$
$212$	−3.11583	+	4.34359i	−0.213996	+	0.298319i
$213$		0			0
$214$	−4.41314	−	1.41917i	−0.301676	−	0.0970127i
$215$	2.74728	−	4.75844i	0.187363	−	0.324523i
$216$		0			0
$217$	5.87779	−	8.19425i	0.399010	−	0.556262i
$218$	−10.7393	+	9.72867i	−0.727356	+	0.658908i
$219$		0			0
$220$	9.38434	+	20.7390i	0.632692	+	1.39823i
$221$		−	10.7025i		−	0.719931i
$222$		0			0
$223$	5.43463	−	3.13768i	0.363929	−	0.210115i	−0.306874	−	0.951750i	$-0.599283\pi$
$223$	5.43463	−	3.13768i	0.363929	−	0.210115i	0.670803	+	0.741636i	$0.265950\pi$
$224$	6.37586	+	13.5406i	0.426005	+	0.904721i
$225$		0			0
$226$	−6.00072	+	18.6602i	−0.399162	+	1.24126i
$227$	8.76790	−	15.1864i	0.581946	−	1.00796i	−0.413303	−	0.910594i	$-0.635625\pi$
$227$	8.76790	−	15.1864i	0.581946	−	1.00796i	0.995249	−	0.0973659i	$-0.0310417\pi$
$228$		0			0
$229$	0.575209	+	0.996291i	0.0380109	+	0.0658367i	0.884405	−	0.466720i	$-0.154565\pi$
$229$	0.575209	+	0.996291i	0.0380109	+	0.0658367i	−0.846394	+	0.532557i	$0.821231\pi$
$230$	0.982113	−	3.05403i	0.0647586	−	0.201377i
$231$		0			0
$232$	18.8314	+	8.18037i	1.23634	+	0.537068i
$233$	−3.68989	−	2.13036i	−0.241733	−	0.139565i	0.374240	−	0.927332i	$-0.377904\pi$
$233$	−3.68989	−	2.13036i	−0.241733	−	0.139565i	−0.615973	+	0.787767i	$0.711237\pi$
$234$		0			0
$235$	−15.5888	+	9.00022i	−1.01690	+	0.587109i
$236$	−12.1602	+	5.50244i	−0.791562	+	0.358179i
$237$		0			0
$238$	0.912088	+	7.97909i	0.0591219	+	0.517207i
$239$	9.49186	−	16.4404i	0.613977	−	1.06344i	−0.376586	−	0.926382i	$-0.622902\pi$
$239$	9.49186	−	16.4404i	0.613977	−	1.06344i	0.990563	−	0.137058i	$-0.0437647\pi$
$240$		0			0
$241$	−14.6843	+	25.4340i	−0.945901	+	1.63835i	−0.191965	+	0.981402i	$0.561486\pi$
$241$	−14.6843	+	25.4340i	−0.945901	+	1.63835i	−0.753936	+	0.656948i	$0.771847\pi$
$242$	−1.23853	+	1.12198i	−0.0796156	+	0.0721234i
$243$		0			0
$244$	−16.0800	+	7.27615i	−1.02942	+	0.465808i
$245$	−17.1481	−	15.0672i	−1.09555	−	0.962610i
$246$		0			0
$247$	22.8026	−	13.1651i	1.45090	−	0.837676i
$248$	−8.66386	+	6.41556i	−0.550155	+	0.407389i
$249$		0			0
$250$	2.85936	−	0.616820i	0.180842	−	0.0390111i
$251$	8.41058			0.530871			0.265436	−	0.964129i	$-0.414484\pi$
$251$	8.41058			0.530871			0.265436	+	0.964129i	$0.414484\pi$
$252$		0			0
$253$	2.42788			0.152640
$254$	−12.6971	+	2.73901i	−0.796686	+	0.171861i
$255$		0			0
$256$	−2.05693	−	15.8672i	−0.128558	−	0.991702i
$257$	6.90235	−	3.98507i	0.430557	−	0.248582i	−0.269027	−	0.963133i	$-0.586702\pi$
$257$	6.90235	−	3.98507i	0.430557	−	0.248582i	0.699584	+	0.714551i	$0.253369\pi$
$258$		0			0
$259$	−15.5652	+	7.04363i	−0.967175	+	0.437670i
$260$	−13.4069	−	29.6288i	−0.831461	−	1.83750i
$261$		0			0
$262$	8.20461	−	7.43252i	0.506883	−	0.459183i
$263$	−13.1762	+	22.8218i	−0.812477	+	1.40725i	0.0986479	+	0.995122i	$0.468548\pi$
$263$	−13.1762	+	22.8218i	−0.812477	+	1.40725i	−0.911125	+	0.412130i	$0.864785\pi$
$264$		0			0
$265$	−4.35801	+	7.54830i	−0.267710	+	0.463688i
$266$	−15.8781	+	11.7583i	−0.973552	+	0.720947i
$267$		0			0
$268$	−0.713189	−	1.57612i	−0.0435649	−	0.0962770i
$269$	7.75731	−	4.47868i	0.472972	−	0.273070i	−0.244511	−	0.969646i	$-0.578628\pi$
$269$	7.75731	−	4.47868i	0.472972	−	0.273070i	0.717483	+	0.696576i	$0.245294\pi$
$270$		0			0
$271$	−23.7070	−	13.6873i	−1.44010	−	0.831442i	−0.442245	−	0.896895i	$-0.645818\pi$
$271$	−23.7070	−	13.6873i	−1.44010	−	0.831442i	−0.997856	+	0.0654523i	$0.979151\pi$
$272$	1.68331	−	8.41892i	0.102066	−	0.510472i
$273$		0			0
$274$	7.02202	−	21.8361i	0.424216	−	1.31916i
$275$	9.83245	+	17.0303i	0.592919	+	1.02697i
$276$		0			0
$277$	−6.48409	+	11.2308i	−0.389591	+	0.674791i	−0.992394	−	0.123098i	$-0.960717\pi$
$277$	−6.48409	+	11.2308i	−0.389591	+	0.674791i	0.602803	+	0.797890i	$0.294050\pi$
$278$	7.45646	−	23.1870i	0.447209	−	1.39066i
$279$		0			0
$280$	12.5203	+	20.9466i	0.748230	+	1.25180i
$281$	24.4075	−	14.0917i	1.45603	−	0.840640i	0.457218	−	0.889354i	$-0.348846\pi$
$281$	24.4075	−	14.0917i	1.45603	−	0.840640i	0.998813	+	0.0487144i	$0.0155124\pi$
$282$		0			0
$283$		−	15.4405i		−	0.917841i	−0.888477	−	0.458921i	$-0.848236\pi$
$283$		−	15.4405i		−	0.917841i	0.888477	−	0.458921i	$-0.151764\pi$
$284$	21.7455	−	9.83974i	1.29036	−	0.583881i
$285$		0			0
$286$	18.2404	−	16.5239i	1.07858	−	0.977079i
$287$	−0.0166952	−	0.0368936i	−0.000985487	−	0.00217776i
$288$		0			0
$289$	−6.19651	+	10.7327i	−0.364501	+	0.631333i
$290$	31.8694	+	10.2485i	1.87144	+	0.601816i
$291$		0			0
$292$	−3.00037	−	2.15229i	−0.175584	−	0.125953i
$293$	9.34168	+	5.39342i	0.545747	+	0.315087i	0.747405	−	0.664369i	$-0.231300\pi$
$293$	9.34168	+	5.39342i	0.545747	+	0.315087i	−0.201658	+	0.979456i	$0.564633\pi$
$294$		0			0
$295$	−18.8471	+	10.8814i	−1.09732	+	0.633538i
$296$	18.1462	−	2.07387i	1.05473	−	0.120541i
$297$		0			0
$298$	−2.80001	−	3.09087i	−0.162200	−	0.179049i
$299$	−3.46859			−0.200594
$300$		0			0
$301$	4.43621	+	0.439049i	0.255699	+	0.0253064i
$302$	−0.831231	+	2.58484i	−0.0478319	+	0.148741i
$303$		0			0
$304$	20.0078	−	6.76960i	1.14753	−	0.388263i
$305$	−24.9224	+	14.3890i	−1.42705	+	0.823910i
$306$		0			0
$307$			16.4926i			0.941280i	0.882325	+	0.470640i	$0.155977\pi$
$307$			16.4926i			0.941280i	−0.882325	+	0.470640i	$0.844023\pi$
$308$	−12.1906	+	13.8736i	−0.694625	+	0.790520i
$309$		0			0
$310$	−13.0273	+	11.8014i	−0.739902	+	0.670274i
$311$	5.69224			0.322777			0.161389	−	0.986891i	$-0.448403\pi$
$311$	5.69224			0.322777			0.161389	+	0.986891i	$0.448403\pi$
$312$		0			0
$313$	−4.40253			−0.248846			−0.124423	−	0.992229i	$-0.539708\pi$
$313$	−4.40253			−0.248846			−0.124423	+	0.992229i	$0.539708\pi$
$314$	−3.59463	−	16.6634i	−0.202857	−	0.940373i
$315$		0			0
$316$	−11.4860	−	25.3836i	−0.646137	−	1.42794i
$317$		−	6.48205i		−	0.364068i	−0.983292	−	0.182034i	$-0.941732\pi$
$317$		−	6.48205i		−	0.364068i	0.983292	−	0.182034i	$-0.0582681\pi$
$318$		0			0
$319$			25.3354i			1.41851i
$320$	−5.88618	−	25.4155i	−0.329047	−	1.42077i
$321$		0			0
$322$	2.58594	−	0.295598i	0.144109	−	0.0164731i
$323$	11.3340			0.630642
$324$		0			0
$325$	−14.0471	−	24.3303i	−0.779193	−	1.34960i
$326$	−4.31370	+	13.4141i	−0.238914	+	0.742938i
$327$		0			0
$328$	0.00491561	+	0.0430113i	0.000271419	+	0.00237490i
$329$	−11.8670	−	8.51224i	−0.654246	−	0.469295i
$330$		0			0
$331$			6.99023i			0.384218i	0.981374	+	0.192109i	$0.0615327\pi$
$331$			6.99023i			0.384218i	−0.981374	+	0.192109i	$0.938467\pi$
$332$	17.0461	+	12.2279i	0.935526	+	0.671091i
$333$		0			0
$334$	13.7076	+	4.40808i	0.750046	+	0.241199i
$335$	−1.41037	−	2.44283i	−0.0770567	−	0.133466i
$336$		0			0
$337$	3.05189	−	5.28603i	0.166247	−	0.287948i	−0.770850	−	0.637016i	$-0.780168\pi$
$337$	3.05189	−	5.28603i	0.166247	−	0.287948i	0.937097	+	0.349068i	$0.113502\pi$
$338$	−12.4338	+	11.2638i	−0.676311	+	0.612667i
$339$		0			0
$340$	1.37904	−	13.9308i	0.0747889	−	0.755501i
$341$	−11.5208	−	6.65155i	−0.623887	−	0.360202i
$342$		0			0
$343$	5.40131	−	17.7151i	0.291643	−	0.956527i
$344$	−4.37107	−	1.89880i	−0.235672	−	0.102376i
$345$		0			0
$346$	−16.0326	+	3.45854i	−0.861915	+	0.185932i
$347$	1.71127			0.0918658			0.0459329	−	0.998945i	$-0.485374\pi$
$347$	1.71127			0.0918658			0.0459329	+	0.998945i	$0.485374\pi$
$348$		0			0
$349$	−5.06959	−	8.78079i	−0.271369	−	0.470025i	0.697844	−	0.716250i	$-0.254143\pi$
$349$	−5.06959	−	8.78079i	−0.271369	−	0.470025i	−0.969213	+	0.246225i	$0.920810\pi$
$350$	12.5460	+	16.9419i	0.670613	+	0.905582i
$351$		0			0
$352$	16.9473	−	10.1293i	0.903295	−	0.539892i
$353$	−6.56007	−	3.78746i	−0.349157	−	0.201586i	0.315157	−	0.949040i	$-0.397943\pi$
$353$	−6.56007	−	3.78746i	−0.349157	−	0.201586i	−0.664314	+	0.747454i	$0.731276\pi$
$354$		0			0
$355$	33.7033	−	19.4586i	1.78878	−	1.03276i
$356$	−8.12677	−	0.804489i	−0.430718	−	0.0426378i
$357$		0			0
$358$	4.50156	−	4.07794i	0.237915	−	0.215526i
$359$	−0.961950	+	1.66615i	−0.0507698	+	0.0879359i	−0.890293	−	0.455387i	$-0.849501\pi$
$359$	−0.961950	+	1.66615i	−0.0507698	+	0.0879359i	0.839524	+	0.543323i	$0.182834\pi$
$360$		0			0
$361$	4.44189	+	7.69359i	0.233784	+	0.404926i
$362$	−3.91470	−	18.1472i	−0.205752	−	0.953795i
$363$		0			0
$364$	17.4161	−	19.8204i	0.912851	−	1.03887i
$365$	−5.21406	−	3.01034i	−0.272916	−	0.157568i
$366$		0			0
$367$	−8.89652	−	5.13641i	−0.464395	−	0.268118i	0.249496	−	0.968376i	$-0.419735\pi$
$367$	−8.89652	−	5.13641i	−0.464395	−	0.268118i	−0.713890	+	0.700258i	$0.753068\pi$
$368$	−2.72849	−	0.545545i	−0.142232	−	0.0284385i
$369$		0			0
$370$	29.1106	−	6.27973i	1.51339	−	0.326468i
$371$	−7.03715	−	0.696462i	−0.365351	−	0.0361585i
$372$		0			0
$373$	−6.90095	−	11.9528i	−0.357318	−	0.618893i	0.630194	−	0.776438i	$-0.282975\pi$
$373$	−6.90095	−	11.9528i	−0.357318	−	0.618893i	−0.987512	+	0.157545i	$0.949642\pi$
$374$	10.3562	−	2.23403i	0.535506	−	0.115519i
$375$		0			0
$376$	9.29105	+	12.5470i	0.479149	+	0.647064i
$377$		−	36.1954i		−	1.86416i
$378$		0			0
$379$		−	21.8668i		−	1.12322i	−0.827401	−	0.561612i	$-0.810182\pi$
$379$		−	21.8668i		−	1.12322i	0.827401	−	0.561612i	$-0.189818\pi$
$380$	31.3770	−	14.1980i	1.60960	−	0.728340i
$381$		0			0
$382$	−5.22701	−	24.2306i	−0.267437	−	1.23975i
$383$	4.40236	+	7.62511i	0.224950	+	0.389625i	0.956304	−	0.292373i	$-0.0944448\pi$
$383$	4.40236	+	7.62511i	0.224950	+	0.389625i	−0.731354	+	0.681998i	$0.761111\pi$
$384$		0			0
$385$	−17.5518	+	24.4691i	−0.894525	+	1.24706i
$386$	3.74756	+	17.3724i	0.190746	+	0.884230i
$387$		0			0
$388$	−10.8367	−	7.77360i	−0.550149	−	0.394645i
$389$	−30.1209	−	17.3903i	−1.52719	−	0.881723i	−0.999478	−	0.0322999i	$-0.989717\pi$
$389$	−30.1209	−	17.3903i	−1.52719	−	0.881723i	−0.527712	−	0.849424i	$-0.676950\pi$
$390$		0			0
$391$	−1.29304	−	0.746538i	−0.0653920	−	0.0377541i
$392$	−11.2951	+	16.2610i	−0.570490	+	0.821305i
$393$		0			0
$394$	20.7668	−	4.47980i	1.04622	−	0.225689i
$395$	−22.7141	−	39.3420i	−1.14287	−	1.97951i
$396$		0			0
$397$	7.78381	−	13.4820i	0.390658	−	0.676640i	−0.601878	−	0.798588i	$-0.705581\pi$
$397$	7.78381	−	13.4820i	0.390658	−	0.676640i	0.992537	+	0.121948i	$0.0389141\pi$
$398$	−19.3672	−	21.3791i	−0.970791	−	1.07164i
$399$		0			0
$400$	−7.22313	−	21.3482i	−0.361156	−	1.06741i
$401$	1.43231	−	0.826946i	0.0715263	−	0.0412957i	−0.463810	−	0.885935i	$-0.653518\pi$
$401$	1.43231	−	0.826946i	0.0715263	−	0.0412957i	0.535337	+	0.844639i	$0.320185\pi$
$402$		0			0
$403$	16.4592	+	9.50272i	0.819890	+	0.473364i
$404$	5.83516	+	0.577637i	0.290310	+	0.0287385i
$405$		0			0
$406$	3.08463	+	26.9848i	0.153088	+	1.33923i
$407$	11.2689	+	19.5184i	0.558581	+	0.967490i
$408$		0			0
$409$	3.93601			0.194623			0.0973116	−	0.995254i	$-0.468976\pi$
$409$	3.93601			0.194623			0.0973116	+	0.995254i	$0.468976\pi$
$410$	0.0148846	+	0.0689997i	0.000735097	+	0.00340765i
$411$		0			0
$412$	−19.6758	+	27.4288i	−0.969359	+	1.35132i
$413$	−14.3473	−	10.2914i	−0.705984	−	0.506407i
$414$		0			0
$415$	29.6227	+	17.1027i	1.45412	+	0.839538i
$416$	−24.2117	+	14.4712i	−1.18708	+	0.709507i
$417$		0			0
$418$	17.4989	+	19.3167i	0.855897	+	0.944808i
$419$	6.94927	−	12.0365i	0.339494	−	0.588021i	−0.644844	−	0.764314i	$-0.723078\pi$
$419$	6.94927	−	12.0365i	0.339494	−	0.588021i	0.984338	+	0.176294i	$0.0564109\pi$
$420$		0			0
$421$	1.45053	+	2.51239i	0.0706944	+	0.122446i	0.899206	−	0.437526i	$-0.144145\pi$
$421$	1.45053	+	2.51239i	0.0706944	+	0.122446i	−0.828511	+	0.559972i	$0.810812\pi$
$422$	−5.96756	+	18.5570i	−0.290496	+	0.903342i
$423$		0			0
$424$	6.93382	+	3.01205i	0.336736	+	0.146278i
$425$		−	12.0933i		−	0.586613i
$426$		0			0
$427$	−18.9721	−	13.6088i	−0.918126	−	0.658578i
$428$	−0.645827	+	6.52400i	−0.0312172	+	0.315349i
$429$		0			0
$430$	−7.39741	−	2.37885i	−0.356735	−	0.114718i
$431$	−14.3469	−	24.8496i	−0.691068	−	1.19697i	−0.971488	−	0.237088i	$-0.923807\pi$
$431$	−14.3469	−	24.8496i	−0.691068	−	1.19697i	0.280420	−	0.959877i	$-0.409526\pi$
$432$		0			0
$433$	30.0796			1.44553			0.722767	−	0.691092i	$-0.242870\pi$
$433$	30.0796			1.44553			0.722767	+	0.691092i	$0.242870\pi$
$434$	−13.0807	−	5.68190i	−0.627893	−	0.272740i
$435$		0			0
$436$	16.6516	+	11.9449i	0.797469	+	0.572058i
$437$		−	3.67324i		−	0.175715i
$438$		0			0
$439$		−	7.08303i		−	0.338054i	−0.985611	−	0.169027i	$-0.945937\pi$
$439$		−	7.08303i		−	0.338054i	0.985611	−	0.169027i	$-0.0540626\pi$
$440$	25.8714	−	19.1577i	1.23337	−	0.913308i
$441$		0			0
$442$	−14.7953	+	3.19165i	−0.703743	+	0.151811i
$443$	18.4047			0.874432			0.437216	−	0.899357i	$-0.355965\pi$
$443$	18.4047			0.874432			0.437216	+	0.899357i	$0.355965\pi$
$444$		0			0
$445$	−13.3156			−0.631218
$446$	−5.95826	−	6.57720i	−0.282132	−	0.311440i
$447$		0			0
$448$	16.8174	−	12.8521i	0.794546	−	0.607204i
$449$			8.67618i			0.409454i	0.978819	+	0.204727i	$0.0656307\pi$
$449$			8.67618i			0.409454i	−0.978819	+	0.204727i	$0.934369\pi$
$450$		0			0
$451$	−0.0462636	+	0.0267103i	−0.00217847	+	0.00125774i
$452$	27.5856	+	2.73076i	1.29752	+	0.128444i
$453$		0			0
$454$	−23.6087	−	7.59206i	−1.10801	−	0.356313i
$455$	25.0754	−	34.9577i	1.17555	−	1.63884i
$456$		0			0
$457$	−24.1589			−1.13011			−0.565054	−	0.825054i	$-0.691145\pi$
$457$	−24.1589			−1.13011			−0.565054	+	0.825054i	$0.691145\pi$
$458$	1.20575	−	1.09228i	0.0563410	−	0.0510391i
$459$		0			0
$460$	−4.51482	−	0.446933i	−0.210504	−	0.0208384i
$461$	−16.8170	+	9.70928i	−0.783244	+	0.452206i	−0.837579	−	0.546317i	$-0.816030\pi$
$461$	−16.8170	+	9.70928i	−0.783244	+	0.452206i	0.0543348	+	0.998523i	$0.482696\pi$
$462$		0			0
$463$	23.8215	+	13.7533i	1.10708	+	0.639172i	0.938071	−	0.346443i	$-0.112611\pi$
$463$	23.8215	+	13.7533i	1.10708	+	0.639172i	0.169007	+	0.985615i	$0.445944\pi$
$464$	5.69287	−	28.4723i	0.264285	−	1.32179i
$465$		0			0
$466$	−1.84466	+	5.73626i	−0.0854524	+	0.265727i
$467$	−17.8013	+	30.8327i	−0.823744	+	1.42677i	0.0791317	+	0.996864i	$0.474785\pi$
$467$	−17.8013	+	30.8327i	−0.823744	+	1.42677i	−0.902876	+	0.429902i	$0.858548\pi$
$468$		0			0
$469$	1.33390	−	1.85960i	0.0615939	−	0.0858682i
$470$	17.0908	+	18.8662i	0.788341	+	0.870234i
$471$		0			0
$472$	11.2330	+	15.1695i	0.517041	+	0.698234i
$473$		−	5.88076i		−	0.270398i
$474$		0			0
$475$	25.7658	−	14.8759i	1.18222	−	0.682554i
$476$	10.7584	−	3.64036i	0.493111	−	0.166856i
$477$		0			0
$478$	−25.5580	−	8.21893i	−1.16900	−	0.375925i
$479$	1.79541	−	3.10975i	0.0820345	−	0.142088i	−0.822089	−	0.569359i	$-0.807192\pi$
$479$	1.79541	−	3.10975i	0.0820345	−	0.142088i	0.904124	+	0.427271i	$0.140525\pi$
$480$		0			0
$481$	−16.0993	−	27.8849i	−0.734067	−	1.27144i
$482$	39.5394	+	12.7151i	1.80097	+	0.579155i
$483$		0			0
$484$	1.92038	+	1.37757i	0.0872901	+	0.0626168i
$485$	−18.8320	−	10.8727i	−0.855118	−	0.493702i
$486$		0			0
$487$	−37.1502	+	21.4487i	−1.68344	+	0.971932i	−0.724088	+	0.689707i	$0.757739\pi$
$487$	−37.1502	+	21.4487i	−1.68344	+	0.971932i	−0.959348	+	0.282225i	$0.908928\pi$
$488$	14.8539	+	20.0594i	0.672406	+	0.908047i
$489$		0			0
$490$	−15.7154	+	28.1990i	−0.709947	+	1.27390i
$491$	14.5393	−	25.1829i	0.656151	−	1.13649i	−0.325453	−	0.945558i	$-0.605517\pi$
$491$	14.5393	−	25.1829i	0.656151	−	1.13649i	0.981604	−	0.190929i	$-0.0611499\pi$
$492$		0			0
$493$	7.79028	−	13.4932i	0.350856	−	0.607701i
$494$	−24.9997	−	27.5967i	−1.12479	−	1.24163i
$495$		0			0
$496$	11.4526	+	10.0638i	0.514239	+	0.451879i
$497$	25.6565	+	18.4036i	1.15085	+	0.825514i
$498$		0			0
$499$	−15.7297	+	9.08155i	−0.704158	+	0.406546i	−0.808894	−	0.587954i	$-0.799934\pi$
$499$	−15.7297	+	9.08155i	−0.704158	+	0.406546i	0.104736	+	0.994500i	$0.466600\pi$
$500$	−1.70540	−	3.76887i	−0.0762678	−	0.168549i
$501$		0			0
$502$	−2.50815	−	11.6269i	−0.111944	−	0.518934i
$503$	−18.7339			−0.835304			−0.417652	−	0.908607i	$-0.637147\pi$
$503$	−18.7339			−0.835304			−0.417652	+	0.908607i	$0.637147\pi$
$504$		0			0
$505$	9.56080			0.425450
$506$	−0.724028	−	3.35634i	−0.0321870	−	0.149207i
$507$		0			0
$508$	7.57290	+	16.7358i	0.335993	+	0.742532i
$509$	−29.7613	+	17.1827i	−1.31915	+	0.761609i	−0.983591	−	0.180412i	$-0.942257\pi$
$509$	−29.7613	+	17.1827i	−1.31915	+	0.761609i	−0.335554	+	0.942021i	$0.608924\pi$
$510$		0			0
$511$	0.481088	−	4.86098i	0.0212821	−	0.215037i
$512$	−21.3217	+	7.57535i	−0.942294	+	0.334786i
$513$		0			0
$514$	−7.56740	−	8.35350i	−0.333784	−	0.368457i
$515$	−27.5199	+	47.6659i	−1.21267	+	2.10041i
$516$		0			0
$517$	−9.63281	+	16.6845i	−0.423650	+	0.733784i
$518$	14.3790	+	19.4171i	0.631776	+	0.853137i
$519$		0			0
$520$	−36.9611	+	27.3696i	−1.62085	+	1.20024i
$521$	8.26183	−	4.76997i	0.361957	−	0.208976i	−0.307982	−	0.951392i	$-0.599654\pi$
$521$	8.26183	−	4.76997i	0.361957	−	0.208976i	0.669939	+	0.742416i	$0.266320\pi$
$522$		0			0
$523$	14.5568	+	8.40435i	0.636523	+	0.367497i	0.783274	−	0.621677i	$-0.213548\pi$
$523$	14.5568	+	8.40435i	0.636523	+	0.367497i	−0.146751	+	0.989173i	$0.546882\pi$
$524$	−12.7216	−	9.12569i	−0.555744	−	0.398658i
$525$		0			0
$526$	35.4785	+	11.4091i	1.54694	+	0.497462i
$527$	4.09051	+	7.08497i	0.178185	+	0.308626i
$528$		0			0
$529$	11.2581	−	19.4995i	0.489481	−	0.847805i
$530$	11.7345	+	3.77357i	0.509714	+	0.163913i
$531$		0			0
$532$	20.9899	+	18.4437i	0.910028	+	0.799635i
$533$	0.0660944	−	0.0381596i	0.00286286	−	0.00165288i
$534$		0			0
$535$			10.6894i			0.462145i
$536$	−1.96617	+	1.45594i	−0.0849256	+	0.0628872i
$537$		0			0
$538$	−8.50473	−	9.38821i	−0.366665	−	0.404754i
$539$	−23.9576	−	4.78905i	−1.03193	−	0.206279i
$540$		0			0
$541$	−20.2946	+	35.1513i	−0.872534	+	1.51127i	−0.0131677	+	0.999913i	$0.504192\pi$
$541$	−20.2946	+	35.1513i	−0.872534	+	1.51127i	−0.859366	+	0.511360i	$0.829142\pi$
$542$	−11.8517	+	36.8547i	−0.509074	+	1.58304i
$543$		0			0
$544$	−12.1404	+	0.183600i	−0.520516	+	0.00787178i
$545$	28.9373	+	16.7069i	1.23954	+	0.715647i
$546$		0			0
$547$	14.3844	−	8.30484i	0.615033	−	0.355089i	−0.159900	−	0.987133i	$-0.551117\pi$
$547$	14.3844	−	8.30484i	0.615033	−	0.355089i	0.774932	+	0.632044i	$0.217784\pi$
$548$	−32.2805	−	3.19553i	−1.37896	−	0.136506i
$549$		0			0
$550$	20.6108	−	18.6712i	0.878846	−	0.796142i
$551$	38.3310			1.63296
$552$		0			0
$553$	21.4826	−	29.9490i	0.913534	−	1.27356i
$554$	17.4592	+	5.61452i	0.741771	+	0.238538i
$555$		0			0
$556$	−34.2777	−	3.39323i	−1.45370	−	0.143905i
$557$	22.9319	−	13.2397i	0.971655	−	0.560985i	0.0719143	−	0.997411i	$-0.477089\pi$
$557$	22.9319	−	13.2397i	0.971655	−	0.560985i	0.899740	+	0.436426i	$0.143756\pi$
$558$		0			0
$559$			8.40153i			0.355347i
$560$	25.2232	−	23.5548i	1.06587	−	0.995372i
$561$		0			0
$562$	−26.7592	−	29.5390i	−1.12877	−	1.24603i
$563$	−15.0217			−0.633090			−0.316545	−	0.948577i	$-0.602523\pi$
$563$	−15.0217			−0.633090			−0.316545	+	0.948577i	$0.602523\pi$
$564$		0			0
$565$	45.1985			1.90151
$566$	−21.3451	+	4.60456i	−0.897203	+	0.193544i
$567$		0			0
$568$	−20.0874	−	27.1269i	−0.842848	−	1.13822i
$569$			20.4369i			0.856761i	0.903599	+	0.428380i	$0.140916\pi$
$569$			20.4369i			0.856761i	−0.903599	+	0.428380i	$0.859084\pi$
$570$		0			0
$571$			31.1726i			1.30453i	0.757989	+	0.652267i	$0.226182\pi$
$571$			31.1726i			1.30453i	−0.757989	+	0.652267i	$0.773818\pi$
$572$	−28.2824	−	20.2881i	−1.18255	−	0.848290i
$573$		0			0
$574$	−0.0460234	+	0.0340819i	−0.00192098	+	0.00142255i
$575$	−3.91933			−0.163447
$576$		0			0
$577$	0.131518	+	0.227796i	0.00547518	+	0.00948329i	0.868750	−	0.495251i	$-0.164924\pi$
$577$	0.131518	+	0.227796i	0.00547518	+	0.00948329i	−0.863275	+	0.504734i	$0.831591\pi$
$578$	16.6849	+	5.36551i	0.693999	+	0.223176i
$579$		0			0
$580$	4.66383	−	47.1130i	0.193655	−	1.95626i
$581$	−2.73322	+	27.6168i	−0.113393	+	1.14574i
$582$		0			0
$583$			9.32864i			0.386353i
$584$	−2.08061	+	4.78960i	−0.0860961	+	0.198195i
$585$		0			0
$586$	4.67012	−	14.5225i	0.192921	−	0.599917i
$587$	7.09191	+	12.2835i	0.292714	+	0.506996i	0.974451	−	0.224602i	$-0.0721082\pi$
$587$	7.09191	+	12.2835i	0.292714	+	0.506996i	−0.681736	+	0.731598i	$0.738775\pi$
$588$		0			0
$589$	−10.0634	+	17.4303i	−0.414655	+	0.718204i
$590$	20.6630	+	22.8095i	0.850683	+	0.939052i
$591$		0			0
$592$	−8.27841	−	24.4672i	−0.340240	−	1.00559i
$593$	36.8695	+	21.2866i	1.51405	+	0.874137i	0.999865	+	0.0164569i	$0.00523863\pi$
$593$	36.8695	+	21.2866i	1.51405	+	0.874137i	0.514184	+	0.857680i	$0.328095\pi$
$594$		0			0
$595$	16.8717	−	7.63482i	0.691671	−	0.312997i
$596$	−3.43786	+	4.79251i	−0.140820	+	0.196309i
$597$		0			0
$598$	1.03438	+	4.79502i	0.0422990	+	0.196083i
$599$	−25.8366			−1.05566			−0.527828	−	0.849352i	$-0.676993\pi$
$599$	−25.8366			−1.05566			−0.527828	+	0.849352i	$0.676993\pi$
$600$		0			0
$601$	−10.3571	−	17.9390i	−0.422474	−	0.731746i	0.573707	−	0.819060i	$-0.305505\pi$
$601$	−10.3571	−	17.9390i	−0.422474	−	0.731746i	−0.996181	+	0.0873147i	$0.972171\pi$
$602$	−0.715992	−	6.26361i	−0.0291816	−	0.255286i
$603$		0			0
$604$	3.82120	+	0.378270i	0.155482	+	0.0153916i
$605$	3.33725	+	1.92676i	0.135678	+	0.0783339i
$606$		0			0
$607$	−33.3745	+	19.2688i	−1.35463	+	0.782097i	−0.988894	−	0.148622i	$-0.952516\pi$
$607$	−33.3745	+	19.2688i	−1.35463	+	0.782097i	−0.365737	+	0.930718i	$0.619183\pi$
$608$	−15.3250	−	25.6403i	−0.621511	−	1.03985i
$609$		0			0
$610$	27.3237	+	30.1621i	1.10631	+	1.22123i
$611$	13.7619	−	23.8363i	0.556746	−	0.964313i
$612$		0			0
$613$	4.81689	+	8.34309i	0.194552	+	0.336974i	0.946754	−	0.321959i	$-0.104341\pi$
$613$	4.81689	+	8.34309i	0.194552	+	0.336974i	−0.752201	+	0.658933i	$0.771008\pi$
$614$	22.7996	−	4.91831i	0.920115	−	0.198487i
$615$		0			0
$616$	22.8144	+	12.7152i	0.919220	+	0.512310i
$617$	27.4232	+	15.8328i	1.10402	+	0.637405i	0.937273	−	0.348595i	$-0.113341\pi$
$617$	27.4232	+	15.8328i	1.10402	+	0.637405i	0.166744	+	0.986000i	$0.446675\pi$
$618$		0			0
$619$	−13.5966	−	7.85001i	−0.546494	−	0.315519i	0.201213	−	0.979548i	$-0.435512\pi$
$619$	−13.5966	−	7.85001i	−0.546494	−	0.315519i	−0.747707	+	0.664029i	$0.768845\pi$
$620$	20.1993	+	14.4898i	0.811225	+	0.581925i
$621$		0			0
$622$	−1.69751	−	7.86904i	−0.0680638	−	0.315520i
$623$	−4.45392	−	9.84240i	−0.178443	−	0.394328i
$624$		0			0
$625$	10.7132	+	18.5557i	0.428527	+	0.742230i
$626$	1.31289	+	6.08612i	0.0524738	+	0.243250i
$627$		0			0
$628$	−21.9638	+	9.93854i	−0.876452	+	0.396591i
$629$		−	13.8601i		−	0.552640i
$630$		0			0
$631$			9.84589i			0.391959i	0.980608	+	0.195979i	$0.0627885\pi$
$631$			9.84589i			0.391959i	−0.980608	+	0.195979i	$0.937211\pi$
$632$	−31.6654	+	23.4481i	−1.25958	+	0.932716i
$633$		0			0
$634$	−8.96088	+	1.93304i	−0.355882	+	0.0767707i
$635$	14.9758	+	25.9389i	0.594297	+	1.02935i
$636$		0			0
$637$	34.2270	+	6.84187i	1.35612	+	0.271085i
$638$	35.0241	−	7.55538i	1.38662	−	0.299120i
$639$		0			0
$640$	−33.3794	+	15.7164i	−1.31944	+	0.621245i
$641$	12.7539	+	7.36348i	0.503750	+	0.290840i	0.730261	−	0.683169i	$-0.239399\pi$
$641$	12.7539	+	7.36348i	0.503750	+	0.290840i	−0.226511	+	0.974009i	$0.572732\pi$
$642$		0			0
$643$	−6.92914	−	4.00054i	−0.273259	−	0.157766i	0.357109	−	0.934063i	$-0.383763\pi$
$643$	−6.92914	−	4.00054i	−0.273259	−	0.157766i	−0.630368	+	0.776297i	$0.717096\pi$
$644$	−1.17980	−	3.48669i	−0.0464908	−	0.137395i
$645$		0			0
$646$	−3.37996	−	15.6683i	−0.132983	−	0.616462i
$647$	7.58887	+	13.1443i	0.298349	+	0.516756i	0.975758	−	0.218850i	$-0.0702306\pi$
$647$	7.58887	+	13.1443i	0.298349	+	0.516756i	−0.677409	+	0.735606i	$0.736897\pi$
$648$		0			0
$649$	−11.6462	+	20.1718i	−0.457153	+	0.791811i
$650$	−29.4455	+	26.6745i	−1.15495	+	1.04626i
$651$		0			0
$652$	19.8302	+	1.96305i	0.776613	+	0.0768788i
$653$	34.4753	−	19.9043i	1.34912	−	0.778916i	0.360996	−	0.932567i	$-0.382437\pi$
$653$	34.4753	−	19.9043i	1.34912	−	0.778916i	0.988125	+	0.153652i	$0.0491034\pi$
$654$		0			0
$655$	−22.1075	−	12.7638i	−0.863813	−	0.498723i
$656$	0.0579935	−	0.0196220i	0.00226426	−	0.000766109i
$657$		0			0
$658$	−8.22856	+	18.9435i	−0.320783	+	0.738495i
$659$	−8.89552	−	15.4075i	−0.346520	−	0.600191i	0.639109	−	0.769117i	$-0.279303\pi$
$659$	−8.89552	−	15.4075i	−0.346520	−	0.600191i	−0.985629	+	0.168926i	$0.945970\pi$
$660$		0			0
$661$	19.4193			0.755323			0.377661	−	0.925944i	$-0.376728\pi$
$661$	19.4193			0.755323			0.377661	+	0.925944i	$0.376728\pi$
$662$	9.66339	−	2.08458i	0.375578	−	0.0810196i
$663$		0			0
$664$	11.8206	−	27.2113i	0.458728	−	1.05600i
$665$	37.0203	+	26.5549i	1.43559	+	1.02976i
$666$		0			0
$667$	−4.37299	−	2.52475i	−0.169323	−	0.0977587i
$668$	2.00599	−	20.2641i	0.0776143	−	0.784042i
$669$		0			0
$670$	−2.95641	+	2.67820i	−0.114216	+	0.103468i
$671$	−15.4003	+	26.6741i	−0.594523	+	1.02974i
$672$		0			0
$673$	2.49434	+	4.32033i	0.0961499	+	0.166537i	0.910088	−	0.414415i	$-0.136014\pi$
$673$	2.49434	+	4.32033i	0.0961499	+	0.166537i	−0.813938	+	0.580952i	$0.802681\pi$
$674$	−8.21759	−	2.64261i	−0.316530	−	0.101789i
$675$		0			0
$676$	19.2791	+	13.8297i	0.741504	+	0.531912i
$677$		−	3.17347i		−	0.121966i	−0.998139	−	0.0609831i	$-0.980576\pi$
$677$		−	3.17347i		−	0.121966i	0.998139	−	0.0609831i	$-0.0194236\pi$
$678$		0			0
$679$	1.73758	−	17.5568i	0.0666823	−	0.673767i
$680$	−19.6693	+	2.24794i	−0.754284	+	0.0862045i
$681$		0			0
$682$	−5.75953	+	17.9101i	−0.220544	+	0.685814i
$683$	9.71480	+	16.8265i	0.371727	+	0.643849i	0.989831	−	0.142246i	$-0.0454325\pi$
$683$	9.71480	+	16.8265i	0.371727	+	0.643849i	−0.618105	+	0.786096i	$0.712099\pi$
$684$		0			0
$685$	−52.8911			−2.02086
$686$	−26.1004	−	2.18395i	−0.996518	−	0.0833836i
$687$		0			0
$688$	−1.32141	+	6.60888i	−0.0503782	+	0.251961i
$689$		−	13.3273i		−	0.507731i
$690$		0			0
$691$		−	34.9549i		−	1.32975i	−0.746955	−	0.664874i	$-0.768485\pi$
$691$		−	34.9549i		−	1.32975i	0.746955	−	0.664874i	$-0.231515\pi$
$692$	9.56226	+	21.1322i	0.363503	+	0.803327i
$693$		0			0
$694$	−0.510324	−	2.36568i	−0.0193716	−	0.0898001i
$695$	−56.1633			−2.13040
$696$		0			0
$697$	0.0328521			0.00124436
$698$	−10.6269	+	9.62683i	−0.402233	+	0.364381i
$699$		0			0
$700$	19.6793	−	22.3961i	0.743808	−	0.846493i
$701$			30.8557i			1.16540i	0.812686	+	0.582701i	$0.198004\pi$
$701$			30.8557i			1.16540i	−0.812686	+	0.582701i	$0.801996\pi$
$702$		0			0
$703$	29.5302	−	17.0493i	1.11375	−	0.643025i
$704$	−19.0568	−	20.4075i	−0.718230	−	0.769138i
$705$		0			0
$706$	−3.27953	+	10.1982i	−0.123427	+	0.383814i
$707$	3.19799	+	7.06701i	0.120273	+	0.265782i
$708$		0			0
$709$	36.6341			1.37582			0.687910	−	0.725796i	$-0.258528\pi$
$709$	36.6341			1.37582			0.687910	+	0.725796i	$0.258528\pi$
$710$	−36.9506	−	40.7891i	−1.38673	−	1.53079i
$711$		0			0
$712$	1.31138	+	11.4745i	0.0491460	+	0.430024i
$713$	2.29617	−	1.32569i	0.0859921	−	0.0496476i
$714$		0			0
$715$	−49.1493	−	28.3763i	−1.83808	−	1.06122i
$716$	−6.97983	−	5.00692i	−0.260849	−	0.187117i
$717$		0			0
$718$	2.59017	+	0.832946i	0.0966644	+	0.0310853i
$719$	−7.22758	+	12.5185i	−0.269543	+	0.466863i	−0.968744	−	0.248063i	$-0.920206\pi$
$719$	−7.22758	+	12.5185i	−0.269543	+	0.466863i	0.699201	+	0.714925i	$0.253539\pi$
$720$		0			0
$721$	−44.4381	−	4.39802i	−1.65496	−	0.163791i
$722$	9.31109	−	8.43487i	0.346523	−	0.313913i
$723$		0			0
$724$	−23.9195	+	10.8235i	−0.888961	+	0.402251i
$725$		−	40.8990i		−	1.51895i
$726$		0			0
$727$	−14.5736	+	8.41407i	−0.540505	+	0.312060i	−0.745283	−	0.666748i	$-0.767686\pi$
$727$	−14.5736	+	8.41407i	−0.540505	+	0.312060i	0.204779	+	0.978808i	$0.434352\pi$
$728$	−32.5938	−	18.1655i	−1.20801	−	0.673259i
$729$		0			0
$730$	−2.60663	+	8.10571i	−0.0964757	+	0.300006i
$731$	−1.80825	+	3.13198i	−0.0668805	+	0.115840i
$732$		0			0
$733$	10.5372	+	18.2509i	0.389199	+	0.674113i	0.992342	−	0.123521i	$-0.0394185\pi$
$733$	10.5372	+	18.2509i	0.389199	+	0.674113i	−0.603143	+	0.797633i	$0.706085\pi$
$734$	−4.44758	+	13.8304i	−0.164163	+	0.510490i
$735$		0			0
$736$	0.0595029	+	3.93459i	0.00219330	+	0.145031i
$737$	−2.61453	−	1.50950i	−0.0963073	−	0.0556031i
$738$		0			0
$739$	14.9950	−	8.65737i	0.551600	−	0.318467i	−0.198167	−	0.980168i	$-0.563499\pi$
$739$	14.9950	−	8.65737i	0.551600	−	0.318467i	0.749767	+	0.661702i	$0.230165\pi$
$740$	−17.3624	−	38.3702i	−0.638254	−	1.41052i
$741$		0			0
$742$	1.13578	+	9.93595i	0.0416956	+	0.364760i
$743$	13.0581	−	22.6172i	0.479054	−	0.829745i	−0.520658	−	0.853765i	$-0.674313\pi$
$743$	13.0581	−	22.6172i	0.479054	−	0.829745i	0.999711	+	0.0240202i	$0.00764661\pi$
$744$		0			0
$745$	−4.80842	+	8.32843i	−0.176167	+	0.305130i
$746$	−14.4658	+	13.1045i	−0.529629	+	0.479789i
$747$		0			0
$748$	−6.17672	−	13.6503i	−0.225843	−	0.499105i
$749$	−7.90127	+	3.57551i	−0.288706	+	0.130646i
$750$		0			0
$751$	−1.47903	+	0.853918i	−0.0539706	+	0.0311599i	−0.526742	−	0.850025i	$-0.676587\pi$
$751$	−1.47903	+	0.853918i	−0.0539706	+	0.0311599i	0.472772	+	0.881185i	$0.343253\pi$
$752$	14.5745	−	16.5858i	0.531477	−	0.604821i
$753$		0			0
$754$	−50.0370	+	10.7940i	−1.82224	+	0.393093i
$755$	6.26097			0.227860
$756$		0			0
$757$	50.5016			1.83551			0.917757	−	0.397143i	$-0.129998\pi$
$757$	50.5016			1.83551			0.917757	+	0.397143i	$0.129998\pi$
$758$	−30.2290	+	6.52099i	−1.09797	+	0.236853i
$759$		0			0
$760$	−28.9845	−	39.1419i	−1.05138	−	1.41983i
$761$	−43.4046	+	25.0596i	−1.57341	+	0.908411i	−0.577668	+	0.816272i	$0.696037\pi$
$761$	−43.4046	+	25.0596i	−1.57341	+	0.908411i	−0.995746	+	0.0921394i	$0.970629\pi$
$762$		0			0
$763$	−2.66997	+	26.9777i	−0.0966594	+	0.976660i
$764$	−31.9379	+	14.4518i	−1.15547	+	0.522848i
$765$		0			0
$766$	9.22822	−	8.35980i	0.333429	−	0.302052i
$767$	16.6383	−	28.8184i	0.600774	−	1.04057i
$768$		0			0
$769$	−26.5257	+	45.9439i	−0.956542	+	1.65678i	−0.225743	+	0.974187i	$0.572481\pi$
$769$	−26.5257	+	45.9439i	−0.956542	+	1.65678i	−0.730799	+	0.682592i	$0.760852\pi$
$770$	39.0606	+	16.9669i	1.40765	+	0.611444i
$771$		0			0
$772$	22.8982	−	10.3614i	0.824126	−	0.372914i
$773$	−17.0231	+	9.82827i	−0.612277	+	0.353498i	−0.773856	−	0.633361i	$-0.781675\pi$
$773$	−17.0231	+	9.82827i	−0.612277	+	0.353498i	0.161579	+	0.986860i	$0.448341\pi$
$774$		0			0
$775$	18.5981	+	10.7376i	0.668062	+	0.385706i
$776$	−7.51468	+	17.2990i	−0.269761	+	0.620997i
$777$		0			0
$778$	−15.0581	+	46.8256i	−0.539860	+	1.67878i
$779$	0.0404111	+	0.0699941i	0.00144788	+	0.00250780i
$780$		0			0
$781$	20.8263	−	36.0721i	0.745222	−	1.29076i
$782$	−0.646422	+	2.01015i	−0.0231160	+	0.0718827i
$783$		0			0
$784$	25.8478	+	10.7653i	0.923136	+	0.384474i
$785$	−34.0417	+	19.6540i	−1.21500	+	0.701481i
$786$		0			0
$787$			9.02326i			0.321644i	0.986983	+	0.160822i	$0.0514146\pi$
$787$			9.02326i			0.321644i	−0.986983	+	0.160822i	$0.948585\pi$
$788$	−12.3859	−	27.3724i	−0.441229	−	0.975100i
$789$		0			0
$790$	−47.6133	+	43.1327i	−1.69401	+	1.53459i
$791$	15.1184	+	33.4091i	0.537549	+	1.18789i
$792$		0			0
$793$	22.0016	−	38.1079i	0.781301	−	1.35325i
$794$	−20.9589	−	6.73994i	−0.743803	−	0.239192i
$795$		0			0
$796$	−23.7792	+	33.1491i	−0.842831	+	1.17494i
$797$	6.91765	+	3.99391i	0.245036	+	0.141472i	0.617489	−	0.786579i	$-0.288150\pi$
$797$	6.91765	+	3.99391i	0.245036	+	0.141472i	−0.372453	+	0.928051i	$0.621483\pi$
$798$		0			0
$799$	10.2605	−	5.92389i	0.362990	−	0.209572i
$800$	−27.3581	+	16.3517i	−0.967253	+	0.578120i
$801$		0			0
$802$	−1.57032	−	1.73344i	−0.0554498	−	0.0612100i
$803$	−6.44385			−0.227398
$804$		0			0
$805$	−2.47437	−	5.46793i	−0.0872101	−	0.192719i
$806$	8.22833	−	25.5872i	0.289831	−	0.901272i
$807$		0			0
$808$	−0.941592	−	8.23887i	−0.0331251	−	0.289842i
$809$	−3.62158	+	2.09092i	−0.127328	+	0.0735128i	−0.562311	−	0.826926i	$-0.690088\pi$
$809$	−3.62158	+	2.09092i	−0.127328	+	0.0735128i	0.434983	+	0.900439i	$0.356754\pi$
$810$		0			0
$811$			16.2233i			0.569676i	0.958576	+	0.284838i	$0.0919397\pi$
$811$			16.2233i			0.569676i	−0.958576	+	0.284838i	$0.908060\pi$
$812$	36.3843	−	12.3115i	1.27684	−	0.432048i
$813$		0			0
$814$	23.6219	−	21.3990i	0.827948	−	0.750034i
$815$	32.4915			1.13813
$816$		0			0
$817$	−8.89725			−0.311275
$818$	−1.17377	−	5.44120i	−0.0410400	−	0.190247i
$819$		0			0
$820$	0.0909473	−	0.0411533i	0.00317602	−	0.00143714i
$821$			14.3394i			0.500448i	0.968188	+	0.250224i	$0.0805043\pi$
$821$			14.3394i			0.500448i	−0.968188	+	0.250224i	$0.919496\pi$
$822$		0			0
$823$		−	20.9895i		−	0.731648i	−0.930684	−	0.365824i	$-0.880787\pi$
$823$		−	20.9895i		−	0.731648i	0.930684	−	0.365824i	$-0.119213\pi$
$824$	43.7856	+	19.0205i	1.52534	+	0.662610i
$825$		0			0
$826$	−9.94843	+	22.9029i	−0.346150	+	0.796895i
$827$	54.7693			1.90451			0.952257	−	0.305297i	$-0.0987557\pi$
$827$	54.7693			1.90451			0.952257	+	0.305297i	$0.0987557\pi$
$828$		0			0
$829$	−8.48567	−	14.6976i	−0.294719	−	0.510469i	0.680200	−	0.733026i	$-0.261893\pi$
$829$	−8.48567	−	14.6976i	−0.294719	−	0.510469i	−0.974920	+	0.222557i	$0.928560\pi$
$830$	14.8091	−	46.0512i	0.514031	−	1.59846i
$831$		0			0
$832$	27.2254	+	29.1552i	0.943872	+	1.01077i
$833$	11.2868	+	9.91718i	0.391064	+	0.343610i
$834$		0			0
$835$		−	33.2024i		−	1.14902i
$836$	21.4852	−	29.9512i	0.743081	−	1.03588i
$837$		0			0
$838$	−18.7118	−	6.01732i	−0.646387	−	0.207865i
$839$	15.1602	+	26.2582i	0.523387	+	0.906533i	0.999629	+	0.0272192i	$0.00866520\pi$
$839$	15.1602	+	26.2582i	0.523387	+	0.906533i	−0.476242	+	0.879314i	$0.658001\pi$
$840$		0			0
$841$	11.8463	−	20.5183i	0.408492	−	0.707529i
$842$	3.04059	−	2.75446i	0.104786	−	0.0949250i
$843$		0			0
$844$	27.4331	+	2.71567i	0.944287	+	0.0934773i
$845$	33.5033	+	19.3431i	1.15255	+	0.665424i
$846$		0			0
$847$	−0.307919	+	3.11126i	−0.0105802	+	0.106904i
$848$	2.09615	−	10.4836i	0.0719819	−	0.360010i
$849$		0			0
$850$	−16.7180	+	3.60640i	−0.573423	+	0.123699i
$851$	−4.49193			−0.153981
$852$		0			0
$853$	−11.3540	−	19.6657i	−0.388754	−	0.673342i	0.603528	−	0.797342i	$-0.293761\pi$
$853$	−11.3540	−	19.6657i	−0.388754	−	0.673342i	−0.992282	+	0.124000i	$0.960428\pi$
$854$	−13.1553	+	30.2857i	−0.450165	+	1.03635i
$855$		0			0
$856$	9.21146	−	1.05275i	0.314841	−	0.0359821i
$857$	31.3876	+	18.1217i	1.07218	+	0.619024i	0.928777	−	0.370640i	$-0.120862\pi$
$857$	31.3876	+	18.1217i	1.07218	+	0.619024i	0.143405	+	0.989664i	$0.454195\pi$
$858$		0			0
$859$	10.3376	−	5.96844i	0.352716	−	0.203641i	−0.313165	−	0.949699i	$-0.601389\pi$
$859$	10.3376	−	5.96844i	0.352716	−	0.203641i	0.665881	+	0.746058i	$0.268056\pi$
$860$	−1.08255	+	10.9357i	−0.0369147	+	0.372904i
$861$		0			0
$862$	−30.0740	+	27.2439i	−1.02433	+	0.927932i
$863$	−6.05378	+	10.4855i	−0.206073	+	0.356929i	−0.950474	−	0.310804i	$-0.899402\pi$
$863$	−6.05378	+	10.4855i	−0.206073	+	0.356929i	0.744401	+	0.667733i	$0.232735\pi$
$864$		0			0
$865$	18.9099	+	32.7528i	0.642955	+	1.11363i
$866$	−8.97016	−	41.5825i	−0.304818	−	1.41303i
$867$		0			0
$868$	−3.95390	+	19.7773i	−0.134204	+	0.671287i
$869$	−42.1072	−	24.3106i	−1.42839	−	0.824681i
$870$		0			0
$871$	3.73524	+	2.15654i	0.126564	+	0.0730716i
$872$	11.5471	−	26.5816i	0.391033	−	0.900167i
$873$		0			0
$874$	−5.07794	+	1.09541i	−0.171764	+	0.0370529i
$875$	3.18967	−	4.44673i	0.107830	−	0.150327i
$876$		0			0
$877$	5.07313	+	8.78692i	0.171308	+	0.296713i	0.938877	−	0.344252i	$-0.111867\pi$
$877$	5.07313	+	8.78692i	0.171308	+	0.296713i	−0.767570	+	0.640965i	$0.778534\pi$
$878$	−9.79168	+	2.11226i	−0.330453	+	0.0712852i
$879$		0			0
$880$	−34.1991	−	30.0519i	−1.15285	−	1.01305i
$881$		−	18.2971i		−	0.616447i	−0.951314	−	0.308223i	$-0.900266\pi$
$881$		−	18.2971i		−	0.616447i	0.951314	−	0.308223i	$-0.0997344\pi$
$882$		0			0
$883$		−	7.23069i		−	0.243332i	−0.992571	−	0.121666i	$-0.961176\pi$
$883$		−	7.23069i		−	0.243332i	0.992571	−	0.121666i	$-0.0388237\pi$
$884$	8.82435	+	19.5015i	0.296795	+	0.655907i
$885$		0			0
$886$	−5.48853	−	25.4429i	−0.184391	−	0.854770i
$887$	−22.0132	−	38.1280i	−0.739132	−	1.28021i	−0.952887	−	0.303326i	$-0.901903\pi$
$887$	−22.0132	−	38.1280i	−0.739132	−	1.28021i	0.213755	−	0.976887i	$-0.431431\pi$
$888$		0			0
$889$	−14.1638	+	19.7459i	−0.475040	+	0.662255i
$890$	3.97088	+	18.4076i	0.133104	+	0.617025i
$891$		0			0
$892$	−7.31558	+	10.1982i	−0.244944	+	0.341461i
$893$	25.2427	+	14.5739i	0.844714	+	0.487696i
$894$		0			0
$895$	−12.1296	−	7.00301i	−0.405447	−	0.234085i
$896$	−22.7821	−	19.4159i	−0.761095	−	0.648640i
$897$		0			0
$898$	11.9941	−	2.58736i	0.400247	−	0.0863412i
$899$	13.8339	+	23.9610i	0.461385	+	0.799143i
$900$		0			0
$901$	2.86842	−	4.96825i	0.0955609	−	0.165516i
$902$	0.0507211	+	0.0559901i	0.00168883	+	0.00186427i
$903$		0			0
$904$	−4.45135	−	38.9490i	−0.148050	−	1.29543i
$905$	−37.0728	+	21.4040i	−1.23234	+	0.711493i
$906$		0			0
$907$	44.0560	+	25.4357i	1.46285	+	0.844580i	0.999142	−	0.0414062i	$-0.0131838\pi$
$907$	44.0560	+	25.4357i	1.46285	+	0.844580i	0.463712	+	0.885986i	$0.346517\pi$
$908$	−3.45494	+	34.9010i	−0.114656	+	1.15823i
$909$		0			0
$910$	−55.8039	−	24.2397i	−1.84988	−	0.803538i
$911$	−20.5992	−	35.6788i	−0.682480	−	1.18209i	−0.974222	−	0.225594i	$-0.927568\pi$
$911$	−20.5992	−	35.6788i	−0.682480	−	1.18209i	0.291741	−	0.956497i	$-0.405765\pi$
$912$		0			0
$913$	36.6096			1.21160
$914$	7.20453	+	33.3977i	0.238305	+	1.10470i
$915$		0			0
$916$	−1.86956	−	1.34111i	−0.0617720	−	0.0443116i
$917$	2.03981	−	20.6105i	0.0673604	−	0.680618i
$918$		0			0
$919$	−28.8143	−	16.6359i	−0.950495	−	0.548769i	−0.0572603	−	0.998359i	$-0.518237\pi$
$919$	−28.8143	−	16.6359i	−0.950495	−	0.548769i	−0.893235	+	0.449591i	$0.851570\pi$
$920$	0.728534	+	6.37463i	0.0240191	+	0.210165i
$921$		0			0
$922$	18.4373	+	20.3526i	0.607200	+	0.670276i
$923$	−29.7534	+	51.5344i	−0.979345	+	1.69627i
$924$		0			0
$925$	−18.1915	−	31.5085i	−0.598131	−	1.03599i
$926$	11.9089	−	37.0326i	0.391351	−	1.21697i
$927$		0			0
$928$	−41.0582	+	0.620924i	−1.34780	+	0.0203828i
$929$			56.0876i			1.84017i	0.391715	+	0.920087i	$0.371882\pi$
$929$			56.0876i			1.84017i	−0.391715	+	0.920087i	$0.628118\pi$
$930$		0			0
$931$	−7.24555	+	36.2465i	−0.237463	+	1.18793i
$932$	8.47999	+	0.839456i	0.277771	+	0.0274973i
$933$		0			0
$934$	47.9321	+	15.4140i	1.56839	+	0.504361i
$935$	−12.2148	−	21.1566i	−0.399466	−	0.691896i
$936$		0			0
$937$	−5.66894			−0.185196			−0.0925982	−	0.995704i	$-0.529517\pi$
$937$	−5.66894			−0.185196			−0.0925982	+	0.995704i	$0.529517\pi$
$938$	−2.96852	−	1.28945i	−0.0969257	−	0.0421019i
$939$		0			0
$940$	20.9842	−	29.2528i	0.684430	−	0.954120i
$941$		−	33.4443i		−	1.09025i	−0.838353	−	0.545127i	$-0.816481\pi$
$941$		−	33.4443i		−	1.09025i	0.838353	−	0.545127i	$-0.183519\pi$
$942$		0			0
$943$		−	0.0106470i		−	0.000346715i
$944$	17.6207	−	20.0524i	0.573506	−	0.652650i
$945$		0			0
$946$	−8.12965	+	1.75372i	−0.264318	+	0.0570185i
$947$	−27.0212			−0.878071			−0.439035	−	0.898470i	$-0.644680\pi$
$947$	−27.0212			−0.878071			−0.439035	+	0.898470i	$0.644680\pi$
$948$		0			0
$949$	9.20598			0.298839
$950$	−28.2484	−	31.1829i	−0.916499	−	1.01171i
$951$		0			0
$952$	−8.24079	−	13.7870i	−0.267085	−	0.446838i
$953$		−	22.7071i		−	0.735554i	−0.929914	−	0.367777i	$-0.880119\pi$
$953$		−	22.7071i		−	0.735554i	0.929914	−	0.367777i	$-0.119881\pi$
$954$		0			0
$955$	−49.5006	+	28.5792i	−1.60180	+	0.924801i
$956$	−3.74021	+	37.7828i	−0.120967	+	1.22198i
$957$		0			0
$958$	−4.83438	−	1.55464i	−0.156192	−	0.0502280i
$959$	−17.6915	−	39.0952i	−0.571289	−	1.26245i
$960$		0			0
$961$	16.4723			0.531363
$962$	−33.7474	+	30.5716i	−1.08806	+	0.985669i
$963$		0			0
$964$	5.78627	−	58.4517i	0.186363	−	1.88260i
$965$	35.4900	−	20.4901i	1.14246	−	0.659601i
$966$		0			0
$967$	−30.4285	−	17.5679i	−0.978516	−	0.564946i	−0.0766939	−	0.997055i	$-0.524436\pi$
$967$	−30.4285	−	17.5679i	−0.978516	−	0.564946i	−0.901822	+	0.432108i	$0.857770\pi$
$968$	1.33169	−	3.06557i	0.0428020	−	0.0985313i
$969$		0			0
$970$	−9.41456	+	29.2760i	−0.302283	+	0.939996i
$971$	25.5778	−	44.3020i	0.820830	−	1.42172i	−0.0842357	−	0.996446i	$-0.526845\pi$
$971$	25.5778	−	44.3020i	0.820830	−	1.42172i	0.905065	−	0.425273i	$-0.139822\pi$
$972$		0			0
$973$	−18.7861	−	41.5140i	−0.602254	−	1.33088i
$974$	40.7297	+	44.9607i	1.30506	+	1.44063i
$975$		0			0
$976$	23.3008	−	26.5163i	0.745839	−	0.848766i
$977$			16.5112i			0.528241i	0.964490	+	0.264120i	$0.0850816\pi$
$977$			16.5112i			0.528241i	−0.964490	+	0.264120i	$0.914918\pi$
$978$		0			0
$979$	−12.3421	+	7.12573i	−0.394456	+	0.227739i
$980$	43.6693	+	13.3158i	1.39496	+	0.425357i
$981$		0			0
$982$	−39.1490	−	12.5895i	−1.24929	−	0.401747i
$983$	7.91463	−	13.7085i	0.252438	−	0.437235i	−0.711759	−	0.702424i	$-0.752101\pi$
$983$	7.91463	−	13.7085i	0.252438	−	0.437235i	0.964196	+	0.265189i	$0.0854344\pi$
$984$		0			0
$985$	−24.4937	−	42.4244i	−0.780435	−	1.35175i
$986$	−20.9763	−	6.74554i	−0.668021	−	0.214822i
$987$		0			0
$988$	−30.6948	+	42.7897i	−0.976531	+	1.36132i
$989$	1.01504	+	0.586035i	0.0322765	+	0.0186348i
$990$		0			0
$991$	0.0465290	−	0.0268636i	0.00147804	−	0.000853349i	−0.499261	−	0.866452i	$-0.666395\pi$
$991$	0.0465290	−	0.0268636i	0.00147804	−	0.000853349i	0.500739	+	0.865598i	$0.333062\pi$
$992$	10.4970	−	18.8335i	0.333281	−	0.597963i
$993$		0			0
$994$	17.7903	−	40.9561i	0.564273	−	1.29905i
$995$	−33.2591	+	57.6065i	−1.05439	+	1.82625i
$996$		0			0
$997$	−22.9416	+	39.7360i	−0.726567	+	1.25845i	0.231759	+	0.972773i	$0.425552\pi$
$997$	−22.9416	+	39.7360i	−0.726567	+	1.25845i	−0.958326	+	0.285678i	$0.907781\pi$
$998$	17.2453	+	19.0367i	0.545890	+	0.602597i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.19		88
3.2	odd	2		252.2.bb.a.23.26	yes	88
4.3	odd	2	inner	756.2.bb.a.611.26		88
7.4	even	3		756.2.o.a.179.42		88
9.2	odd	6		756.2.o.a.359.33		88
9.7	even	3		252.2.o.a.191.12	yes	88
12.11	even	2		252.2.bb.a.23.19	yes	88
21.11	odd	6		252.2.o.a.95.3	✓	88
28.11	odd	6		756.2.o.a.179.33		88
36.7	odd	6		252.2.o.a.191.3	yes	88
36.11	even	6		756.2.o.a.359.42		88
63.11	odd	6	inner	756.2.bb.a.683.26		88
63.25	even	3		252.2.bb.a.11.19	yes	88
84.11	even	6		252.2.o.a.95.12	yes	88
252.11	even	6	inner	756.2.bb.a.683.19		88
252.151	odd	6		252.2.bb.a.11.26	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.3	✓	88	21.11	odd	6
252.2.o.a.95.12	yes	88	84.11	even	6
252.2.o.a.191.3	yes	88	36.7	odd	6
252.2.o.a.191.12	yes	88	9.7	even	3
252.2.bb.a.11.19	yes	88	63.25	even	3
252.2.bb.a.11.26	yes	88	252.151	odd	6
252.2.bb.a.23.19	yes	88	12.11	even	2
252.2.bb.a.23.26	yes	88	3.2	odd	2
756.2.o.a.179.33		88	28.11	odd	6
756.2.o.a.179.42		88	7.4	even	3
756.2.o.a.359.33		88	9.2	odd	6
756.2.o.a.359.42		88	36.11	even	6
756.2.bb.a.611.19		88	1.1	even	1	trivial
756.2.bb.a.611.26		88	4.3	odd	2	inner
756.2.bb.a.683.19		88	252.11	even	6	inner
756.2.bb.a.683.26		88	63.11	odd	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.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.298214 - 1.38241i) q^{2} +(-1.82214 + 0.824510i) q^{4} +(-2.82413 + 1.63051i) q^{5} +(-2.14986 - 1.54211i) q^{7} +(1.68320 + 2.27307i) q^{8} +O(q^{10})\)	\(q+(-0.298214 - 1.38241i) q^{2} +(-1.82214 + 0.824510i) q^{4} +(-2.82413 + 1.63051i) q^{5} +(-2.14986 - 1.54211i) q^{7} +(1.68320 + 2.27307i) q^{8} +(3.09624 + 3.41787i) q^{10} +(-1.74511 + 3.02263i) q^{11} +(2.49315 - 4.31827i) q^{13} +(-1.49071 + 3.43188i) q^{14} +(2.64037 - 3.00474i) q^{16} +(1.85883 - 1.07319i) q^{17} +(4.57306 + 2.64026i) q^{19} +(3.80158 - 5.29954i) q^{20} +(4.69894 + 1.51108i) q^{22} +(-0.347811 - 0.602427i) q^{23} +(2.81714 - 4.87942i) q^{25} +(-6.71312 - 2.15880i) q^{26} +(5.18882 + 1.03735i) q^{28} +(6.28645 - 3.62948i) q^{29} +3.81153i q^{31} +(-4.94119 - 2.75402i) q^{32} +(-2.03793 - 2.24963i) q^{34} +(8.58591 + 0.849742i) q^{35} +(3.22871 - 5.59229i) q^{37} +(2.28618 - 7.10922i) q^{38} +(-8.45984 - 3.67496i) q^{40} +(0.0132552 + 0.00765288i) q^{41} +(-1.45919 + 0.842461i) q^{43} +(0.687651 - 6.94650i) q^{44} +(-0.729081 + 0.660471i) q^{46} +5.51987 q^{47} +(2.24380 + 6.63064i) q^{49} +(-7.58549 - 2.43934i) q^{50} +(-0.982411 + 9.92410i) q^{52} +(2.31470 - 1.33639i) q^{53} -11.3817i q^{55} +(-0.113328 - 7.48246i) q^{56} +(-6.89215 - 7.60811i) q^{58} +6.67359 q^{59} +8.82482 q^{61} +(5.26911 - 1.13665i) q^{62} +(-2.33367 + 7.65206i) q^{64} +16.2605i q^{65} +0.864985i q^{67} +(-2.50218 + 3.48813i) q^{68} +(-1.38574 - 12.1227i) q^{70} -11.9340 q^{71} +(0.923127 + 1.59890i) q^{73} +(-8.69371 - 2.79572i) q^{74} +(-10.5097 - 1.04038i) q^{76} +(8.41297 - 3.80707i) q^{77} +13.9307i q^{79} +(-2.55747 + 12.7909i) q^{80} +(0.00662657 - 0.0206063i) q^{82} +(-5.24458 - 9.08388i) q^{83} +(-3.49971 + 6.06168i) q^{85} +(1.59978 + 1.76596i) q^{86} +(-9.80801 + 1.12092i) q^{88} +(3.53619 + 2.04162i) q^{89} +(-12.0192 + 5.43896i) q^{91} +(1.13047 + 0.810931i) q^{92} +(-1.64610 - 7.63075i) q^{94} -17.2199 q^{95} +(3.33413 + 5.77488i) q^{97} +(8.49716 - 5.07921i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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