LMFDB - Embedded newform 756.2.bb.a.683.43

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			683.43
Character	$\chi$	$=$	756.683
Dual form			756.2.bb.a.611.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41013 - 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 + 0.575136i) q^{5} +(2.47311 - 0.940076i) q^{7} +(2.75529 - 0.639023i) q^{8} +O(q^{10})$	\(q+(1.41013 - 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 + 0.575136i) q^{5} +(2.47311 - 0.940076i) q^{7} +(2.75529 - 0.639023i) q^{8} +(1.46646 + 0.704103i) q^{10} +(0.0206317 + 0.0357351i) q^{11} +(-2.90716 - 5.03535i) q^{13} +(3.38652 - 1.59107i) q^{14} +(3.81675 - 1.19683i) q^{16} +(2.56376 + 1.48019i) q^{17} +(-6.29815 + 3.63624i) q^{19} +(2.14347 + 0.835489i) q^{20} +(0.0329288 + 0.0481769i) q^{22} +(-3.04704 + 5.27762i) q^{23} +(-1.83844 - 3.18427i) q^{25} +(-4.63993 - 6.78851i) q^{26} +(4.60468 - 2.60709i) q^{28} +(6.45096 + 3.72446i) q^{29} -2.12782i q^{31} +(5.25368 - 2.09734i) q^{32} +(3.77412 + 1.81210i) q^{34} +(3.00429 + 0.485903i) q^{35} +(3.94417 + 6.83150i) q^{37} +(-8.49097 + 5.80356i) q^{38} +(3.11225 + 0.948097i) q^{40} +(2.02586 - 1.16963i) q^{41} +(-4.07080 - 2.35028i) q^{43} +(0.0516048 + 0.0644018i) q^{44} +(-3.73030 + 7.76919i) q^{46} -0.400516 q^{47} +(5.23252 - 4.64982i) q^{49} +(-2.93421 - 4.29293i) q^{50} +(-7.27152 - 9.07472i) q^{52} +(-5.08527 - 2.93598i) q^{53} +0.0474640i q^{55} +(6.21341 - 4.17056i) q^{56} +(9.49646 + 4.55963i) q^{58} -10.4137 q^{59} -1.36773 q^{61} +(-0.228375 - 3.00052i) q^{62} +(7.18330 - 3.52139i) q^{64} -6.68806i q^{65} -0.957074i q^{67} +(5.51650 + 2.15024i) q^{68} +(4.28861 + 0.362743i) q^{70} +1.28212 q^{71} +(1.36920 - 2.37152i) q^{73} +(6.29502 + 9.21002i) q^{74} +(-11.3505 + 9.09512i) q^{76} +(0.0846180 + 0.0689814i) q^{77} +6.78467i q^{79} +(4.49045 + 1.00291i) q^{80} +(2.73120 - 1.86677i) q^{82} +(-6.87088 + 11.9007i) q^{83} +(1.70262 + 2.94902i) q^{85} +(-5.99262 - 2.87730i) q^{86} +(0.0796818 + 0.0852766i) q^{88} +(0.578834 - 0.334190i) q^{89} +(-11.9233 - 9.72001i) q^{91} +(-4.42637 + 11.3560i) q^{92} +(-0.564782 + 0.0429866i) q^{94} -8.36533 q^{95} +(-2.04166 + 3.53626i) q^{97} +(6.87950 - 7.11846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.41013	−	0.107328i	0.997116	−	0.0758924i
$2$	1.41013	−	0.107328i	0.997116	−	0.0758924i
$3$		0			0
$3$		0			0
$4$	1.97696	−	0.302694i	0.988481	−	0.151347i
$5$	0.996165	+	0.575136i	0.445498	+	0.257209i	0.705927	−	0.708284i	$-0.250531\pi$
$5$	0.996165	+	0.575136i	0.445498	+	0.257209i	−0.260429	+	0.965493i	$0.583864\pi$
$6$		0			0
$7$	2.47311	−	0.940076i	0.934747	−	0.355315i
$7$	2.47311	−	0.940076i	0.934747	−	0.355315i
$8$	2.75529	−	0.639023i	0.974144	−	0.225929i
$9$		0			0
$10$	1.46646	+	0.704103i	0.463734	+	0.222657i
$11$	0.0206317	+	0.0357351i	0.00622068	+	0.0107745i	0.869119	−	0.494603i	$-0.164687\pi$
$11$	0.0206317	+	0.0357351i	0.00622068	+	0.0107745i	−0.862898	+	0.505378i	$0.831353\pi$
$12$		0			0
$13$	−2.90716	−	5.03535i	−0.806302	−	1.39656i	−0.915409	−	0.402526i	$-0.868132\pi$
$13$	−2.90716	−	5.03535i	−0.806302	−	1.39656i	0.109107	−	0.994030i	$-0.465201\pi$
$14$	3.38652	−	1.59107i	0.905085	−	0.425231i
$15$		0			0
$16$	3.81675	−	1.19683i	0.954188	−	0.299207i
$17$	2.56376	+	1.48019i	0.621804	+	0.358999i	0.777571	−	0.628795i	$-0.216452\pi$
$17$	2.56376	+	1.48019i	0.621804	+	0.358999i	−0.155767	+	0.987794i	$0.549785\pi$
$18$		0			0
$19$	−6.29815	+	3.63624i	−1.44489	+	0.834210i	−0.998171	−	0.0604613i	$-0.980743\pi$
$19$	−6.29815	+	3.63624i	−1.44489	+	0.834210i	−0.446724	+	0.894672i	$0.647409\pi$
$20$	2.14347	+	0.835489i	0.479294	+	0.186821i
$21$		0			0
$22$	0.0329288	+	0.0481769i	0.00702044	+	0.0102714i
$23$	−3.04704	+	5.27762i	−0.635351	+	1.10046i	0.351090	+	0.936342i	$0.385811\pi$
$23$	−3.04704	+	5.27762i	−0.635351	+	1.10046i	−0.986441	+	0.164118i	$0.947522\pi$
$24$		0			0
$25$	−1.83844	−	3.18427i	−0.367687	−	0.636853i
$26$	−4.63993	−	6.78851i	−0.909964	−	1.33134i
$27$		0			0
$28$	4.60468	−	2.60709i	0.870203	−	0.492693i
$29$	6.45096	+	3.72446i	1.19791	+	0.691615i	0.960089	−	0.279693i	$-0.0902327\pi$
$29$	6.45096	+	3.72446i	1.19791	+	0.691615i	0.237823	+	0.971308i	$0.423566\pi$
$30$		0			0
$31$		−	2.12782i		−	0.382168i	−0.981574	−	0.191084i	$-0.938800\pi$
$31$		−	2.12782i		−	0.382168i	0.981574	−	0.191084i	$-0.0612003\pi$
$32$	5.25368	−	2.09734i	0.928729	−	0.370760i
$33$		0			0
$34$	3.77412	+	1.81210i	0.647256	+	0.310773i
$35$	3.00429	+	0.485903i	0.507818	+	0.0821325i
$36$		0			0
$37$	3.94417	+	6.83150i	0.648417	+	1.12309i	0.983501	+	0.180903i	$0.0579021\pi$
$37$	3.94417	+	6.83150i	0.648417	+	1.12309i	−0.335084	+	0.942188i	$0.608765\pi$
$38$	−8.49097	+	5.80356i	−1.37742	+	0.941461i
$39$		0			0
$40$	3.11225	+	0.948097i	0.492090	+	0.149907i
$41$	2.02586	−	1.16963i	0.316386	−	0.182665i	−0.333395	−	0.942787i	$-0.608194\pi$
$41$	2.02586	−	1.16963i	0.316386	−	0.182665i	0.649780	+	0.760122i	$0.274861\pi$
$42$		0			0
$43$	−4.07080	−	2.35028i	−0.620791	−	0.358414i	0.156386	−	0.987696i	$-0.450016\pi$
$43$	−4.07080	−	2.35028i	−0.620791	−	0.358414i	−0.777177	+	0.629282i	$0.783349\pi$
$44$	0.0516048	+	0.0644018i	0.00777972	+	0.00970894i
$45$		0			0
$46$	−3.73030	+	7.76919i	−0.550002	+	1.14550i
$47$	−0.400516			−0.0584213			−0.0292106	−	0.999573i	$-0.509299\pi$
$47$	−0.400516			−0.0584213			−0.0292106	+	0.999573i	$0.509299\pi$
$48$		0			0
$49$	5.23252	−	4.64982i	0.747502	−	0.664259i
$50$	−2.93421	−	4.29293i	−0.414959	−	0.607112i
$51$		0			0
$52$	−7.27152	−	9.07472i	−1.00838	−	1.25844i
$53$	−5.08527	−	2.93598i	−0.698516	−	0.403288i	0.108278	−	0.994121i	$-0.465466\pi$
$53$	−5.08527	−	2.93598i	−0.698516	−	0.403288i	−0.806795	+	0.590832i	$0.798800\pi$
$54$		0			0
$55$			0.0474640i			0.00640005i
$56$	6.21341	−	4.17056i	0.830302	−	0.557314i
$57$		0			0
$58$	9.49646	+	4.55963i	1.24695	+	0.598708i
$59$	−10.4137			−1.35575			−0.677875	−	0.735177i	$-0.737099\pi$
$59$	−10.4137			−1.35575			−0.677875	+	0.735177i	$0.737099\pi$
$60$		0			0
$61$	−1.36773			−0.175120			−0.0875598	−	0.996159i	$-0.527907\pi$
$61$	−1.36773			−0.175120			−0.0875598	+	0.996159i	$0.527907\pi$
$62$	−0.228375	−	3.00052i	−0.0290037	−	0.381066i
$63$		0			0
$64$	7.18330	−	3.52139i	0.897912	−	0.440174i
$65$		−	6.68806i		−	0.829551i
$66$		0			0
$67$		−	0.957074i		−	0.116925i	−0.998290	−	0.0584626i	$-0.981380\pi$
$67$		−	0.957074i		−	0.116925i	0.998290	−	0.0584626i	$-0.0186198\pi$
$68$	5.51650	+	2.15024i	0.668974	+	0.260755i
$69$		0			0
$70$	4.28861	+	0.362743i	0.512587	+	0.0433561i
$71$	1.28212			0.152159			0.0760796	−	0.997102i	$-0.475760\pi$
$71$	1.28212			0.152159			0.0760796	+	0.997102i	$0.475760\pi$
$72$		0			0
$73$	1.36920	−	2.37152i	0.160252	−	0.277565i	−0.774707	−	0.632321i	$-0.782103\pi$
$73$	1.36920	−	2.37152i	0.160252	−	0.277565i	0.934959	+	0.354756i	$0.115436\pi$
$74$	6.29502	+	9.21002i	0.731781	+	1.07064i
$75$		0			0
$76$	−11.3505	+	9.09512i	−1.30200	+	1.04328i
$77$	0.0846180	+	0.0689814i	0.00964311	+	0.00786116i
$78$		0			0
$79$			6.78467i			0.763335i	0.924300	+	0.381668i	$0.124650\pi$
$79$			6.78467i			0.763335i	−0.924300	+	0.381668i	$0.875350\pi$
$80$	4.49045	+	1.00291i	0.502048	+	0.112129i
$81$		0			0
$82$	2.73120	−	1.86677i	0.301610	−	0.206150i
$83$	−6.87088	+	11.9007i	−0.754177	+	1.30627i	0.191605	+	0.981472i	$0.438631\pi$
$83$	−6.87088	+	11.9007i	−0.754177	+	1.30627i	−0.945782	+	0.324801i	$0.894703\pi$
$84$		0			0
$85$	1.70262	+	2.94902i	0.184675	+	0.319867i
$86$	−5.99262	−	2.87730i	−0.646201	−	0.310267i
$87$		0			0
$88$	0.0796818	+	0.0852766i	0.00849411	+	0.00909051i
$89$	0.578834	−	0.334190i	0.0613562	−	0.0354240i	−0.469008	−	0.883194i	$-0.655388\pi$
$89$	0.578834	−	0.334190i	0.0613562	−	0.0354240i	0.530364	+	0.847770i	$0.322055\pi$
$90$		0			0
$91$	−11.9233	−	9.72001i	−1.24991	−	1.01893i
$92$	−4.42637	+	11.3560i	−0.461481	+	1.18394i
$93$		0			0
$94$	−0.564782	+	0.0429866i	−0.0582528	+	0.00443373i
$95$	−8.36533			−0.858265
$96$		0			0
$97$	−2.04166	+	3.53626i	−0.207299	+	0.359053i	−0.950863	−	0.309612i	$-0.899801\pi$
$97$	−2.04166	+	3.53626i	−0.207299	+	0.359053i	0.743563	+	0.668665i	$0.233134\pi$
$98$	6.87950	−	7.11846i	0.694934	−	0.719073i
$99$		0			0
$100$	−4.59838	−	5.73869i	−0.459838	−	0.573869i
$101$	−11.6375	+	6.71893i	−1.15798	+	0.668558i	−0.950818	−	0.309749i	$-0.899755\pi$
$101$	−11.6375	+	6.71893i	−1.15798	+	0.668558i	−0.207158	+	0.978307i	$0.566422\pi$
$102$		0			0
$103$	−9.67731	−	5.58720i	−0.953534	−	0.550523i	−0.0593570	−	0.998237i	$-0.518905\pi$
$103$	−9.67731	−	5.58720i	−0.953534	−	0.550523i	−0.894177	+	0.447714i	$0.852238\pi$
$104$	−11.2278	−	12.0161i	−1.10098	−	1.17828i
$105$		0			0
$106$	−7.48604	−	3.59434i	−0.727108	−	0.349113i
$107$	5.65631	+	9.79702i	0.546816	+	0.947114i	0.998490	+	0.0549307i	$0.0174938\pi$
$107$	5.65631	+	9.79702i	0.546816	+	0.947114i	−0.451674	+	0.892183i	$0.649173\pi$
$108$		0			0
$109$	2.33792	−	4.04939i	0.223932	−	0.387861i	−0.732067	−	0.681233i	$-0.761444\pi$
$109$	2.33792	−	4.04939i	0.223932	−	0.387861i	0.955998	+	0.293372i	$0.0947774\pi$
$110$	0.00509422	+	0.0669307i	0.000485715	+	0.00638159i
$111$		0			0
$112$	8.31413	−	6.54792i	0.785611	−	0.618721i
$113$	−0.248562	+	0.143507i	−0.0233827	+	0.0135000i	−0.511646	−	0.859196i	$-0.670964\pi$
$113$	−0.248562	+	0.143507i	−0.0233827	+	0.0135000i	0.488263	+	0.872696i	$0.337631\pi$
$114$		0			0
$115$	−6.07070	+	3.50492i	−0.566096	+	0.326836i
$116$	13.8807	+	5.41045i	1.28879	+	0.502348i
$117$		0			0
$118$	−14.6848	+	1.11768i	−1.35184	+	0.102891i
$119$	7.73195	+	1.25053i	0.708787	+	0.114636i
$120$		0			0
$121$	5.49915	−	9.52480i	0.499923	−	0.865891i
$122$	−1.92868	+	0.146796i	−0.174615	+	0.0132902i
$123$		0			0
$124$	−0.644079	−	4.20662i	−0.0578400	−	0.377766i
$125$		−	9.98077i		−	0.892707i
$126$		0			0
$127$			13.0105i			1.15449i	0.816570	+	0.577246i	$0.195873\pi$
$127$			13.0105i			1.15449i	−0.816570	+	0.577246i	$0.804127\pi$
$128$	9.75148	−	5.73661i	0.861917	−	0.507049i
$129$		0			0
$130$	−0.717816	−	9.43106i	−0.0629566	−	0.827159i
$131$	0.156314	−	0.270744i	0.0136572	−	0.0236550i	−0.859116	−	0.511781i	$-0.828986\pi$
$131$	0.156314	−	0.270744i	0.0136572	−	0.0236550i	0.872773	+	0.488126i	$0.162319\pi$
$132$		0			0
$133$	−12.1577	+	14.9135i	−1.05420	+	1.29317i
$134$	−0.102721	−	1.34960i	−0.00887373	−	0.116588i
$135$		0			0
$136$	8.00980	+	2.44005i	0.686834	+	0.209233i
$137$	−7.85803	+	4.53684i	−0.671357	+	0.387608i	−0.796591	−	0.604519i	$-0.793365\pi$
$137$	−7.85803	+	4.53684i	−0.671357	+	0.387608i	0.125234	+	0.992127i	$0.460032\pi$
$138$		0			0
$139$	−0.645404	+	0.372624i	−0.0547424	+	0.0316056i	−0.527121	−	0.849790i	$-0.676729\pi$
$139$	−0.645404	+	0.372624i	−0.0547424	+	0.0316056i	0.472379	+	0.881396i	$0.343395\pi$
$140$	6.08645	+	0.0512287i	0.514399	+	0.00432961i
$141$		0			0
$142$	1.80796	−	0.137607i	0.151720	−	0.0115477i
$143$	0.119959	−	0.207775i	0.0100315	−	0.0173751i
$144$		0			0
$145$	4.28415	+	7.42036i	0.355779	+	0.616227i
$146$	1.67622	−	3.49111i	0.138725	−	0.288926i
$147$		0			0
$148$	9.86532	+	12.3117i	0.810925	+	1.01202i
$149$	−13.0161	−	7.51484i	−1.06632	−	0.615640i	−0.139146	−	0.990272i	$-0.544436\pi$
$149$	−13.0161	−	7.51484i	−1.06632	−	0.615640i	−0.927174	+	0.374632i	$0.877769\pi$
$150$		0			0
$151$	9.22723	−	5.32734i	0.750901	−	0.433533i	−0.0751182	−	0.997175i	$-0.523933\pi$
$151$	9.22723	−	5.32734i	0.750901	−	0.433533i	0.826019	+	0.563642i	$0.190600\pi$
$152$	−15.0296	+	14.0436i	−1.21906	+	1.13908i
$153$		0			0
$154$	0.126726	+	0.0881911i	0.0102119	+	0.00710665i
$155$	1.22379	−	2.11966i	0.0982970	−	0.170255i
$156$		0			0
$157$	−10.7456			−0.857589			−0.428795	−	0.903402i	$-0.641062\pi$
$157$	−10.7456			−0.857589			−0.428795	+	0.903402i	$0.641062\pi$
$158$	0.728186	+	9.56730i	0.0579313	+	0.761134i
$159$		0			0
$160$	6.43979	+	0.932291i	0.509110	+	0.0737041i
$161$	−2.57428	+	15.9166i	−0.202882	+	1.25440i
$162$		0			0
$163$	10.5970	−	6.11821i	0.830025	−	0.479215i	−0.0238365	−	0.999716i	$-0.507588\pi$
$163$	10.5970	−	6.11821i	0.830025	−	0.479215i	0.853861	+	0.520501i	$0.174255\pi$
$164$	3.65100	−	2.92553i	0.285095	−	0.228445i
$165$		0			0
$166$	−8.41159	+	17.5191i	−0.652866	+	1.35974i
$167$	−4.78444	−	8.28690i	−0.370231	−	0.641259i	0.619370	−	0.785100i	$-0.287388\pi$
$167$	−4.78444	−	8.28690i	−0.370231	−	0.641259i	−0.989601	+	0.143840i	$0.954055\pi$
$168$		0			0
$169$	−10.4032	+	18.0188i	−0.800245	+	1.38607i
$170$	2.71744	+	3.97578i	0.208418	+	0.304929i
$171$		0			0
$172$	−8.75922	−	3.41420i	−0.667884	−	0.260330i
$173$		−	20.3532i		−	1.54742i	−0.633538	−	0.773711i	$-0.718398\pi$
$173$		−	20.3532i		−	1.54742i	0.633538	−	0.773711i	$-0.281602\pi$
$174$		0			0
$175$	−7.54010	−	6.14676i	−0.569978	−	0.464651i
$176$	0.121515	+	0.111699i	0.00915952	+	0.00841966i
$177$		0			0
$178$	0.780366	−	0.533378i	0.0584909	−	0.0399784i
$179$	11.8952	−	20.6031i	0.889089	−	1.53995i	0.0481342	−	0.998841i	$-0.484672\pi$
$179$	11.8952	−	20.6031i	0.889089	−	1.53995i	0.840954	−	0.541106i	$-0.181994\pi$
$180$		0			0
$181$	15.3783			1.14306			0.571530	−	0.820581i	$-0.306350\pi$
$181$	15.3783			1.14306			0.571530	+	0.820581i	$0.306350\pi$
$182$	−17.8567	−	12.4268i	−1.32363	−	0.921137i
$183$		0			0
$184$	−5.02296	+	16.4885i	−0.370298	+	1.21555i
$185$			9.07373i			0.667114i
$186$		0			0
$187$			0.122155i			0.00893286i
$188$	−0.791805	+	0.121234i	−0.0577483	+	0.00884189i
$189$		0			0
$190$	−11.7962	+	0.897834i	−0.855789	+	0.0651358i
$191$	−6.65024			−0.481194			−0.240597	−	0.970625i	$-0.577343\pi$
$191$	−6.65024			−0.481194			−0.240597	+	0.970625i	$0.577343\pi$
$192$		0			0
$193$	−6.14756			−0.442511			−0.221255	−	0.975216i	$-0.571015\pi$
$193$	−6.14756			−0.442511			−0.221255	+	0.975216i	$0.571015\pi$
$194$	−2.49948	+	5.20574i	−0.179452	+	0.373750i
$195$		0			0
$196$	8.93701	−	10.7764i	0.638358	−	0.769740i
$197$			13.2243i			0.942196i	0.882081	+	0.471098i	$0.156142\pi$
$197$			13.2243i			0.942196i	−0.882081	+	0.471098i	$0.843858\pi$
$198$		0			0
$199$	14.4456	+	8.34019i	1.02402	+	0.591221i	0.915267	−	0.402848i	$-0.131980\pi$
$199$	14.4456	+	8.34019i	1.02402	+	0.591221i	0.108757	+	0.994068i	$0.465313\pi$
$200$	−7.10026	−	7.59879i	−0.502064	−	0.537316i
$201$		0			0
$202$	−15.6893	+	10.7236i	−1.10390	+	0.754512i
$203$	19.4552	+	3.14660i	1.36549	+	0.220848i
$204$		0			0
$205$	2.69078			0.187933
$206$	−14.2460	−	6.84006i	−0.992565	−	0.476569i
$207$		0			0
$208$	−17.1224	−	15.7393i	−1.18722	−	1.09133i
$209$	−0.259883	−	0.150043i	−0.0179765	−	0.0103787i
$210$		0			0
$211$	1.95991	−	1.13155i	0.134926	−	0.0778994i	−0.431018	−	0.902343i	$-0.641845\pi$
$211$	1.95991	−	1.13155i	0.134926	−	0.0778994i	0.565943	+	0.824444i	$0.308512\pi$
$212$	−10.9421	−	4.26505i	−0.751506	−	0.292925i
$213$		0			0
$214$	9.02766	+	13.2080i	0.617118	+	0.902883i
$215$	−2.70346	−	4.68252i	−0.184374	−	0.319345i
$216$		0			0
$217$	−2.00031	−	5.26233i	−0.135790	−	0.357230i
$218$	2.86216	−	5.96111i	0.193850	−	0.403737i
$219$		0			0
$220$	0.0143671	+	0.0938346i	0.000968629	+	0.00632633i
$221$		−	17.2126i		−	1.15784i
$222$		0			0
$223$	−8.78900	−	5.07433i	−0.588555	−	0.339802i	0.175971	−	0.984395i	$-0.443694\pi$
$223$	−8.78900	−	5.07433i	−0.588555	−	0.339802i	−0.764526	+	0.644593i	$0.777027\pi$
$224$	11.0213	−	10.1258i	0.736389	−	0.676558i
$225$		0			0
$226$	−0.335103	+	0.229042i	−0.0222907	+	0.0152357i
$227$	1.46754	+	2.54186i	0.0974044	+	0.168709i	0.910610	−	0.413268i	$-0.135613\pi$
$227$	1.46754	+	2.54186i	0.0974044	+	0.168709i	−0.813205	+	0.581977i	$0.802279\pi$
$228$		0			0
$229$	−0.221879	+	0.384305i	−0.0146622	+	0.0253956i	−0.873263	−	0.487248i	$-0.838001\pi$
$229$	−0.221879	+	0.384305i	−0.0146622	+	0.0253956i	0.858601	+	0.512644i	$0.171334\pi$
$230$	−8.18433	+	5.59397i	−0.539659	+	0.368855i
$231$		0			0
$232$	20.1543	+	6.13968i	1.32320	+	0.403090i
$233$	13.3304	−	7.69631i	0.873304	−	0.504202i	0.00485893	−	0.999988i	$-0.498453\pi$
$233$	13.3304	−	7.69631i	0.873304	−	0.504202i	0.868445	+	0.495786i	$0.165120\pi$
$234$		0			0
$235$	−0.398980	−	0.230351i	−0.0260266	−	0.0150265i
$236$	−20.5875	+	3.15217i	−1.34013	+	0.205189i
$237$		0			0
$238$	11.0373	+	0.933568i	0.715443	+	0.0605142i
$239$	−4.34671	−	7.52872i	−0.281165	−	0.486992i	0.690507	−	0.723326i	$-0.257388\pi$
$239$	−4.34671	−	7.52872i	−0.281165	−	0.486992i	−0.971672	+	0.236334i	$0.924054\pi$
$240$		0			0
$241$	1.78759	+	3.09620i	0.115149	+	0.199444i	0.917839	−	0.396952i	$-0.129932\pi$
$241$	1.78759	+	3.09620i	0.115149	+	0.199444i	−0.802690	+	0.596396i	$0.796599\pi$
$242$	6.73226	−	14.0215i	0.432766	−	0.901334i
$243$		0			0
$244$	−2.70394	+	0.414003i	−0.173102	+	0.0265038i
$245$	7.88672	−	1.62257i	0.503864	−	0.103662i
$246$		0			0
$247$	36.6195	+	21.1423i	2.33004	+	1.34525i
$248$	−1.35973	−	5.86278i	−0.0863428	−	0.372287i
$249$		0			0
$250$	−1.07122	−	14.0742i	−0.0677497	−	0.890132i
$251$	−16.4516			−1.03842			−0.519209	−	0.854647i	$-0.673773\pi$
$251$	−16.4516			−1.03842			−0.519209	+	0.854647i	$0.673773\pi$
$252$		0			0
$253$	−0.251462			−0.0158093
$254$	1.39639	+	18.3465i	0.0876172	+	1.15116i
$255$		0			0
$256$	13.1352	−	9.13600i	0.820950	−	0.571000i
$257$	22.1802	+	12.8057i	1.38356	+	0.798800i	0.992579	−	0.121598i	$-0.0388019\pi$
$257$	22.1802	+	12.8057i	1.38356	+	0.798800i	0.390983	+	0.920398i	$0.372135\pi$
$258$		0			0
$259$	16.1765	+	13.1872i	1.00516	+	0.819413i
$260$	−2.02443	−	13.2220i	−0.125550	−	0.819995i
$261$		0			0
$262$	0.191366	−	0.398563i	0.0118226	−	0.0246233i
$263$	−6.45004	−	11.1718i	−0.397727	−	0.688883i	0.595718	−	0.803193i	$-0.296867\pi$
$263$	−6.45004	−	11.1718i	−0.397727	−	0.688883i	−0.993445	+	0.114311i	$0.963534\pi$
$264$		0			0
$265$	−3.37718	−	5.84945i	−0.207459	−	0.359329i
$266$	−15.5433	+	22.3350i	−0.953021	+	1.36944i
$267$		0			0
$268$	−0.289701	−	1.89210i	−0.0176963	−	0.115578i
$269$	6.13886	+	3.54427i	0.374293	+	0.216098i	0.675332	−	0.737514i	$-0.264000\pi$
$269$	6.13886	+	3.54427i	0.374293	+	0.216098i	−0.301039	+	0.953612i	$0.597334\pi$
$270$		0			0
$271$	6.46932	−	3.73506i	0.392983	−	0.226889i	−0.290469	−	0.956884i	$-0.593811\pi$
$271$	6.46932	−	3.73506i	0.392983	−	0.226889i	0.683452	+	0.729996i	$0.260478\pi$
$272$	11.5568	+	2.58113i	0.700733	+	0.156504i
$273$		0			0
$274$	−10.5940	+	7.24094i	−0.640004	+	0.437441i
$275$	0.0758600	−	0.131393i	0.00457453	−	0.00792332i
$276$		0			0
$277$	−10.7618	−	18.6400i	−0.646614	−	1.11997i	−0.983926	−	0.178576i	$-0.942851\pi$
$277$	−10.7618	−	18.6400i	−0.646614	−	1.11997i	0.337312	−	0.941393i	$-0.390482\pi$
$278$	−0.870114	+	0.594720i	−0.0521859	+	0.0356689i
$279$		0			0
$280$	8.58822	−	0.581008i	0.513244	−	0.0347219i
$281$	5.67950	+	3.27906i	0.338810	+	0.195612i	0.659746	−	0.751489i	$-0.270664\pi$
$281$	5.67950	+	3.27906i	0.338810	+	0.195612i	−0.320935	+	0.947101i	$0.603997\pi$
$282$		0			0
$283$			8.15834i			0.484963i	0.970156	+	0.242481i	$0.0779613\pi$
$283$			8.15834i			0.484963i	−0.970156	+	0.242481i	$0.922039\pi$
$284$	2.53469	−	0.388089i	0.150406	−	0.0230289i
$285$		0			0
$286$	0.146859	−	0.305866i	0.00868393	−	0.0180863i
$287$	3.91062	−	4.79708i	0.230837	−	0.283163i
$288$		0			0
$289$	−4.11808	−	7.13272i	−0.242240	−	0.419572i
$290$	6.83764	+	10.0039i	0.401520	+	0.587449i
$291$		0			0
$292$	1.98900	−	5.10284i	0.116398	−	0.298621i
$293$	−21.7642	+	12.5656i	−1.27148	+	0.734089i	−0.975266	−	0.221033i	$-0.929057\pi$
$293$	−21.7642	+	12.5656i	−1.27148	+	0.734089i	−0.296213	+	0.955122i	$0.595724\pi$
$294$		0			0
$295$	−10.3738	−	5.98931i	−0.603985	−	0.348711i
$296$	15.2328	+	16.3024i	0.885390	+	0.947557i
$297$		0			0
$298$	−19.1610	−	9.19995i	−1.10997	−	0.532939i
$299$	35.4329			2.04914
$300$		0			0
$301$	−12.2770	−	1.98563i	−0.707632	−	0.114450i
$302$	12.4399	−	8.50261i	0.715834	−	0.489270i
$303$		0			0
$304$	−19.6865	+	21.4164i	−1.12910	+	1.22832i
$305$	−1.36248	−	0.786629i	−0.0780155	−	0.0450423i
$306$		0			0
$307$		−	12.1724i		−	0.694713i	−0.937733	−	0.347357i	$-0.887079\pi$
$307$		−	12.1724i		−	0.694713i	0.937733	−	0.347357i	$-0.112921\pi$
$308$	0.188167	+	0.110760i	0.0107218	+	0.00631114i
$309$		0			0
$310$	1.49821	−	3.12036i	0.0850924	−	0.177224i
$311$	11.8754			0.673394			0.336697	−	0.941613i	$-0.390690\pi$
$311$	11.8754			0.673394			0.336697	+	0.941613i	$0.390690\pi$
$312$		0			0
$313$	23.4497			1.32546			0.662728	−	0.748861i	$-0.269399\pi$
$313$	23.4497			1.32546			0.662728	+	0.748861i	$0.269399\pi$
$314$	−15.1527	+	1.15330i	−0.855116	+	0.0650845i
$315$		0			0
$316$	2.05368	+	13.4130i	0.115529	+	0.754542i
$317$			30.3895i			1.70684i	0.521220	+	0.853422i	$0.325477\pi$
$317$			30.3895i			1.70684i	−0.521220	+	0.853422i	$0.674523\pi$
$318$		0			0
$319$			0.307367i			0.0172093i
$320$	9.18103	+	0.623486i	0.513235	+	0.0348539i
$321$		0			0
$322$	−1.92179	+	22.7208i	−0.107097	+	1.26618i
$323$	−21.5293			−1.19792
$324$		0			0
$325$	−10.6893	+	18.5144i	−0.592934	+	1.02699i
$326$	14.2866	−	9.76486i	0.791262	−	0.540825i
$327$		0			0
$328$	4.83442	−	4.51724i	0.266936	−	0.249423i
$329$	−0.990519	+	0.376515i	−0.0546091	+	0.0207580i
$330$		0			0
$331$		−	30.2047i		−	1.66020i	−0.557616	−	0.830099i	$-0.688284\pi$
$331$		−	30.2047i		−	1.66020i	0.557616	−	0.830099i	$-0.311716\pi$
$332$	−9.98119	+	25.6070i	−0.547789	+	1.40537i
$333$		0			0
$334$	−7.63613	−	11.1721i	−0.417830	−	0.611312i
$335$	0.550448	−	0.953404i	0.0300742	−	0.0520900i
$336$		0			0
$337$	−10.9483	−	18.9630i	−0.596392	−	1.03298i	−0.993349	−	0.115144i	$-0.963267\pi$
$337$	−10.9483	−	18.9630i	−0.596392	−	1.03298i	0.396957	−	0.917837i	$-0.370066\pi$
$338$	−12.7360	+	26.5256i	−0.692745	+	1.44280i
$339$		0			0
$340$	4.25867	+	5.31473i	0.230959	+	0.288232i
$341$	0.0760379	−	0.0439005i	0.00411768	−	0.00237735i
$342$		0			0
$343$	8.56939	−	16.4185i	0.462704	−	0.886513i
$344$	−12.7181	−	3.87437i	−0.685715	−	0.208892i
$345$		0			0
$346$	−2.18447	−	28.7007i	−0.117438	−	1.54296i
$347$	29.4348			1.58014			0.790071	−	0.613015i	$-0.210044\pi$
$347$	29.4348			1.58014			0.790071	+	0.613015i	$0.210044\pi$
$348$		0			0
$349$	10.4396	−	18.0819i	0.558817	−	0.967900i	−0.438778	−	0.898595i	$-0.644589\pi$
$349$	10.4396	−	18.0819i	0.558817	−	0.967900i	0.997596	−	0.0693043i	$-0.0220780\pi$
$350$	−11.2923	−	7.85850i	−0.603598	−	0.420054i
$351$		0			0
$352$	0.183341	+	0.144469i	0.00977209	+	0.00770024i
$353$	24.8005	−	14.3186i	1.32000	−	0.762101i	0.336269	−	0.941766i	$-0.390835\pi$
$353$	24.8005	−	14.3186i	1.32000	−	0.762101i	0.983728	+	0.179665i	$0.0575014\pi$
$354$		0			0
$355$	1.27720	+	0.737391i	0.0677867	+	0.0391367i
$356$	1.04317	−	0.835890i	0.0552881	−	0.0443021i
$357$		0			0
$358$	14.5625	−	30.3298i	0.769654	−	1.60298i
$359$	5.54691	+	9.60753i	0.292755	+	0.507066i	0.974460	−	0.224561i	$-0.0720947\pi$
$359$	5.54691	+	9.60753i	0.292755	+	0.507066i	−0.681705	+	0.731627i	$0.738761\pi$
$360$		0			0
$361$	16.9445	−	29.3487i	0.891814	−	1.54467i
$362$	21.6855	−	1.65052i	1.13976	−	0.0867495i
$363$		0			0
$364$	−26.5142	−	15.6070i	−1.38972	−	0.818027i
$365$	2.72789	−	1.57495i	0.142784	−	0.0824365i
$366$		0			0
$367$	−0.671527	+	0.387706i	−0.0350534	+	0.0202381i	−0.517424	−	0.855729i	$-0.673109\pi$
$367$	−0.671527	+	0.387706i	−0.0350534	+	0.0202381i	0.482371	+	0.875967i	$0.339776\pi$
$368$	−5.31337	+	23.7902i	−0.276979	+	1.24015i
$369$		0			0
$370$	0.973866	+	12.7952i	0.0506289	+	0.665190i
$371$	−15.3365	−	2.48046i	−0.796230	−	0.128779i
$372$		0			0
$373$	−9.81345	+	16.9974i	−0.508121	+	0.880091i	0.491835	+	0.870689i	$0.336326\pi$
$373$	−9.81345	+	16.9974i	−0.508121	+	0.880091i	−0.999956	+	0.00940290i	$0.997007\pi$
$374$	0.0131107	+	0.172255i	0.000677936	+	0.00890710i
$375$		0			0
$376$	−1.10354	+	0.255939i	−0.0569107	+	0.0131990i
$377$		−	43.3105i		−	2.23060i
$378$		0			0
$379$			15.7843i			0.810784i	0.914143	+	0.405392i	$0.132865\pi$
$379$			15.7843i			0.810784i	−0.914143	+	0.405392i	$0.867135\pi$
$380$	−16.5379	+	2.53214i	−0.848378	+	0.129896i
$381$		0			0
$382$	−9.37773	+	0.713757i	−0.479807	+	0.0365190i
$383$	5.19194	−	8.99271i	0.265296	−	0.459506i	−0.702345	−	0.711837i	$-0.747864\pi$
$383$	5.19194	−	8.99271i	0.265296	−	0.459506i	0.967641	+	0.252330i	$0.0811970\pi$
$384$		0			0
$385$	0.0446198	+	0.117384i	0.00227404	+	0.00598243i
$386$	−8.66888	+	0.659805i	−0.441235	+	0.0335832i
$387$		0			0
$388$	−2.96588	+	7.60906i	−0.150570	+	0.386291i
$389$	−23.9732	+	13.8409i	−1.21549	+	0.701762i	−0.963950	−	0.266085i	$-0.914270\pi$
$389$	−23.9732	+	13.8409i	−1.21549	+	0.701762i	−0.251538	+	0.967847i	$0.580936\pi$
$390$		0			0
$391$	−15.6238	+	9.02038i	−0.790127	+	0.456180i
$392$	11.4458	−	16.1553i	0.578099	−	0.815966i
$393$		0			0
$394$	1.41934	+	18.6481i	0.0715055	+	0.939478i
$395$	−3.90211	+	6.75865i	−0.196336	+	0.340065i
$396$		0			0
$397$	15.5264	+	26.8926i	0.779249	+	1.34970i	0.932375	+	0.361492i	$0.117733\pi$
$397$	15.5264	+	26.8926i	0.779249	+	1.34970i	−0.153126	+	0.988207i	$0.548934\pi$
$398$	21.2654	+	10.2104i	1.06594	+	0.511800i
$399$		0			0
$400$	−10.8279	−	9.95326i	−0.541394	−	0.497663i
$401$	25.3125	+	14.6142i	1.26404	+	0.729796i	0.973854	−	0.227173i	$-0.0729483\pi$
$401$	25.3125	+	14.6142i	1.26404	+	0.729796i	0.290190	+	0.956969i	$0.406282\pi$
$402$		0			0
$403$	−10.7143	+	6.18592i	−0.533719	+	0.308143i
$404$	−20.9732	+	16.8057i	−1.04345	+	0.836113i
$405$		0			0
$406$	27.7722	+	2.34905i	1.37831	+	0.116581i
$407$	−0.162749	+	0.281890i	−0.00806719	+	0.0139728i
$408$		0			0
$409$	27.5085			1.36021			0.680104	−	0.733115i	$-0.261935\pi$
$409$	27.5085			1.36021			0.680104	+	0.733115i	$0.261935\pi$
$410$	3.79437	−	0.288797i	0.187391	−	0.0142626i
$411$		0			0
$412$	−20.8229	−	8.11641i	−1.02587	−	0.399867i
$413$	−25.7542	+	9.78968i	−1.26728	+	0.481719i
$414$		0			0
$415$	−13.6891	+	7.90338i	−0.671970	+	0.387962i
$416$	−25.8341	−	20.3569i	−1.26662	−	0.998077i
$417$		0			0
$418$	−0.382573	−	0.183689i	−0.0187123	−	0.00898450i
$419$	0.375709	+	0.650747i	0.0183546	+	0.0317911i	0.875057	−	0.484020i	$-0.160824\pi$
$419$	0.375709	+	0.650747i	0.0183546	+	0.0317911i	−0.856702	+	0.515811i	$0.827491\pi$
$420$		0			0
$421$	−12.5491	+	21.7357i	−0.611605	+	1.05933i	0.379365	+	0.925247i	$0.376142\pi$
$421$	−12.5491	+	21.7357i	−0.611605	+	1.05933i	−0.990970	+	0.134084i	$0.957191\pi$
$422$	2.64229	−	1.80600i	0.128625	−	0.0879146i
$423$		0			0
$424$	−15.8876	−	4.83990i	−0.771570	−	0.235046i
$425$		−	10.8849i		−	0.527997i
$426$		0			0
$427$	−3.38254	+	1.28577i	−0.163692	+	0.0622226i
$428$	14.1478	+	17.6562i	0.683860	+	0.853445i
$429$		0			0
$430$	−4.31480	−	6.31283i	−0.208078	−	0.304432i
$431$	−6.13030	+	10.6180i	−0.295286	+	0.511451i	−0.975051	−	0.221979i	$-0.928748\pi$
$431$	−6.13030	+	10.6180i	−0.295286	+	0.511451i	0.679765	+	0.733430i	$0.262082\pi$
$432$		0			0
$433$	12.9845			0.623996			0.311998	−	0.950083i	$-0.399002\pi$
$433$	12.9845			0.623996			0.311998	+	0.950083i	$0.399002\pi$
$434$	−3.38551	−	7.20591i	−0.162510	−	0.345895i
$435$		0			0
$436$	3.39624	−	8.71316i	0.162651	−	0.417285i
$437$		−	44.3190i		−	2.12007i
$438$		0			0
$439$			19.3025i			0.921257i	0.887593	+	0.460629i	$0.152376\pi$
$439$			19.3025i			0.921257i	−0.887593	+	0.460629i	$0.847624\pi$
$440$	0.0303306	+	0.130777i	0.00144596	+	0.00623457i
$441$		0			0
$442$	−1.84740	−	24.2721i	−0.0878716	−	1.15451i
$443$	5.23677			0.248806			0.124403	−	0.992232i	$-0.460298\pi$
$443$	5.23677			0.248806			0.124403	+	0.992232i	$0.460298\pi$
$444$		0			0
$445$	0.768818			0.0364455
$446$	−12.9383	−	6.21219i	−0.612646	−	0.294156i
$447$		0			0
$448$	14.4547	−	15.4616i	0.682920	−	0.730493i
$449$			15.8939i			0.750082i	0.927008	+	0.375041i	$0.122371\pi$
$449$			15.8939i			0.750082i	−0.927008	+	0.375041i	$0.877629\pi$
$450$		0			0
$451$	0.0835936	+	0.0482628i	0.00393627	+	0.00227261i
$452$	−0.447958	+	0.358946i	−0.0210702	+	0.0168834i
$453$		0			0
$454$	2.34225	+	3.42686i	0.109927	+	0.160831i
$455$	−6.28728	−	16.5403i	−0.294752	−	0.775420i
$456$		0			0
$457$	−3.59823			−0.168318			−0.0841590	−	0.996452i	$-0.526820\pi$
$457$	−3.59823			−0.168318			−0.0841590	+	0.996452i	$0.526820\pi$
$458$	−0.271632	+	0.565736i	−0.0126925	+	0.0264351i
$459$		0			0
$460$	−10.9406	+	8.76666i	−0.510109	+	0.408748i
$461$	13.1236	+	7.57692i	0.611228	+	0.352892i	0.773446	−	0.633862i	$-0.218531\pi$
$461$	13.1236	+	7.57692i	0.611228	+	0.352892i	−0.162218	+	0.986755i	$0.551865\pi$
$462$		0			0
$463$	22.8810	−	13.2104i	1.06337	−	0.613938i	0.137009	−	0.990570i	$-0.456251\pi$
$463$	22.8810	−	13.2104i	1.06337	−	0.613938i	0.926363	+	0.376632i	$0.122918\pi$
$464$	29.0793	+	6.49466i	1.34997	+	0.301507i
$465$		0			0
$466$	17.9716	−	12.2836i	0.832520	−	0.569025i
$467$	−11.6787	−	20.2281i	−0.540426	−	0.936045i	−0.998879	−	0.0473266i	$-0.984930\pi$
$467$	−11.6787	−	20.2281i	−0.540426	−	0.936045i	0.458454	−	0.888718i	$-0.348403\pi$
$468$		0			0
$469$	−0.899722	−	2.36695i	−0.0415453	−	0.109295i
$470$	−0.587339	−	0.282005i	−0.0270919	−	0.0130079i
$471$		0			0
$472$	−28.6929	+	6.65461i	−1.32070	+	0.306303i
$473$		−	0.193960i		−	0.00891831i
$474$		0			0
$475$	23.1575	+	13.3700i	1.06254	+	0.613457i
$476$	15.6643	+	0.131844i	0.717972	+	0.00604305i
$477$		0			0
$478$	−6.93749	−	10.1500i	−0.317313	−	0.464249i
$479$	3.49034	+	6.04545i	0.159478	+	0.276224i	0.934680	−	0.355489i	$-0.115686\pi$
$479$	3.49034	+	6.04545i	0.159478	+	0.276224i	−0.775203	+	0.631713i	$0.782352\pi$
$480$		0			0
$481$	22.9327	−	39.7206i	1.04564	−	1.81110i
$482$	2.85305	+	4.17420i	0.129953	+	0.190130i
$483$		0			0
$484$	7.98850	−	20.4947i	0.363114	−	0.931579i
$485$	−4.06767	+	2.34847i	−0.184703	+	0.106638i
$486$		0			0
$487$	7.56727	+	4.36896i	0.342906	+	0.197977i	0.661556	−	0.749896i	$-0.269896\pi$
$487$	7.56727	+	4.36896i	0.342906	+	0.197977i	−0.318651	+	0.947872i	$0.603230\pi$
$488$	−3.76849	+	0.874009i	−0.170592	+	0.0395645i
$489$		0			0
$490$	10.9472	−	3.13452i	0.494544	−	0.141603i
$491$	14.3700	+	24.8895i	0.648508	+	1.12325i	0.983479	+	0.181020i	$0.0579399\pi$
$491$	14.3700	+	24.8895i	0.648508	+	1.12325i	−0.334972	+	0.942228i	$0.608727\pi$
$492$		0			0
$493$	11.0258	+	19.0973i	0.496578	+	0.860098i
$494$	53.9076	+	25.8832i	2.42542	+	1.16454i
$495$		0			0
$496$	−2.54664	−	8.12137i	−0.114347	−	0.364660i
$497$	3.17081	−	1.20529i	0.142230	−	0.0540645i
$498$		0			0
$499$	10.8666	+	6.27382i	0.486454	+	0.280855i	0.723102	−	0.690741i	$-0.242715\pi$
$499$	10.8666	+	6.27382i	0.486454	+	0.280855i	−0.236648	+	0.971595i	$0.576049\pi$
$500$	−3.02112	−	19.7316i	−0.135109	−	0.882423i
$501$		0			0
$502$	−23.1990	+	1.76572i	−1.03542	+	0.0788081i
$503$	7.28257			0.324714			0.162357	−	0.986732i	$-0.448090\pi$
$503$	7.28257			0.324714			0.162357	+	0.986732i	$0.448090\pi$
$504$		0			0
$505$	−15.4572			−0.687836
$506$	−0.354595	+	0.0269889i	−0.0157637	+	0.00119980i
$507$		0			0
$508$	3.93819	+	25.7212i	0.174729	+	1.14119i
$509$	16.1172	+	9.30528i	0.714383	+	0.412449i	0.812682	−	0.582708i	$-0.198007\pi$
$509$	16.1172	+	9.30528i	0.714383	+	0.412449i	−0.0982986	+	0.995157i	$0.531340\pi$
$510$		0			0
$511$	1.15676	−	7.15216i	0.0511721	−	0.316393i
$512$	17.5419	−	14.2928i	0.775248	−	0.631657i
$513$		0			0
$514$	32.6515	+	15.6773i	1.44019	+	0.691494i
$515$	−6.42680	−	11.1315i	−0.283199	−	0.490514i
$516$		0			0
$517$	−0.00826331	−	0.0143125i	−0.000363420	−	0.000629462i
$518$	24.2264	+	16.8596i	1.06445	+	0.740766i
$519$		0			0
$520$	−4.27382	−	18.4276i	−0.187419	−	0.808102i
$521$	13.4091	+	7.74176i	0.587464	+	0.339172i	0.764094	−	0.645105i	$-0.223186\pi$
$521$	13.4091	+	7.74176i	0.587464	+	0.339172i	−0.176630	+	0.984277i	$0.556520\pi$
$522$		0			0
$523$	30.4929	−	17.6051i	1.33336	−	0.769818i	0.347550	−	0.937662i	$-0.387014\pi$
$523$	30.4929	−	17.6051i	1.33336	−	0.769818i	0.985814	+	0.167844i	$0.0536805\pi$
$524$	0.227074	−	0.582566i	0.00991979	−	0.0254495i
$525$		0			0
$526$	−10.2945	−	15.0615i	−0.448861	−	0.656712i
$527$	3.14958	−	5.45523i	0.137198	−	0.237634i
$528$		0			0
$529$	−7.06887	−	12.2436i	−0.307342	−	0.532332i
$530$	−5.39009	−	7.88605i	−0.234131	−	0.342548i
$531$		0			0
$532$	−19.5210	+	33.1636i	−0.846342	+	1.43782i
$533$	−11.7790	−	6.80061i	−0.510205	−	0.294567i
$534$		0			0
$535$			13.0126i			0.562584i
$536$	−0.611592	−	2.63702i	−0.0264168	−	0.113902i
$537$		0			0
$538$	9.03702	+	4.33903i	0.389614	+	0.187069i
$539$	0.274117	+	0.0910510i	0.0118071	+	0.00392184i
$540$		0			0
$541$	3.06242	+	5.30426i	0.131664	+	0.228048i	0.924318	−	0.381623i	$-0.124635\pi$
$541$	3.06242	+	5.30426i	0.131664	+	0.228048i	−0.792654	+	0.609671i	$0.791301\pi$
$542$	8.72174	−	5.96128i	0.374631	−	0.256059i
$543$		0			0
$544$	16.5737	+	2.39937i	0.710589	+	0.102872i
$545$	4.65790	−	2.68924i	0.199522	−	0.115194i
$546$		0			0
$547$	−16.2992	−	9.41033i	−0.696902	−	0.402357i	0.109290	−	0.994010i	$-0.465142\pi$
$547$	−16.2992	−	9.41033i	−0.696902	−	0.402357i	−0.806193	+	0.591653i	$0.798475\pi$
$548$	−14.1617	+	11.3477i	−0.604960	+	0.484751i
$549$		0			0
$550$	0.0928707	−	0.193424i	0.00396002	−	0.00824764i
$551$	−54.1721			−2.30781
$552$		0			0
$553$	6.37810	+	16.7792i	0.271225	+	0.713525i
$554$	−17.1762	−	25.1299i	−0.729746	−	1.06767i
$555$		0			0
$556$	−1.16315	+	0.932023i	−0.0493284	+	0.0395266i
$557$	−33.9310	−	19.5901i	−1.43770	−	0.830057i	−0.440012	−	0.897992i	$-0.645026\pi$
$557$	−33.9310	−	19.5901i	−1.43770	−	0.830057i	−0.997690	+	0.0679349i	$0.978359\pi$
$558$		0			0
$559$			27.3305i			1.15596i
$560$	12.0482	−	1.74106i	0.509129	−	0.0735730i
$561$		0			0
$562$	8.36079	+	4.01435i	0.352679	+	0.169335i
$563$	−10.8051			−0.455380			−0.227690	−	0.973734i	$-0.573117\pi$
$563$	−10.8051			−0.455380			−0.227690	+	0.973734i	$0.573117\pi$
$564$		0			0
$565$	−0.330145			−0.0138893
$566$	0.875619	+	11.5044i	0.0368050	+	0.483564i
$567$		0			0
$568$	3.53261	−	0.819302i	0.148225	−	0.0343771i
$569$		−	19.6155i		−	0.822326i	−0.911562	−	0.411163i	$-0.865123\pi$
$569$		−	19.6155i		−	0.822326i	0.911562	−	0.411163i	$-0.134877\pi$
$570$		0			0
$571$		−	25.1755i		−	1.05356i	−0.850001	−	0.526781i	$-0.823399\pi$
$571$		−	25.1755i		−	1.05356i	0.850001	−	0.526781i	$-0.176601\pi$
$572$	0.174262	−	0.447075i	0.00728627	−	0.0186931i
$573$		0			0
$574$	4.99964	−	7.18425i	0.208681	−	0.299865i
$575$	22.4071			0.934442
$576$		0			0
$577$	−6.37775	+	11.0466i	−0.265509	+	0.459876i	−0.967697	−	0.252116i	$-0.918873\pi$
$577$	−6.37775	+	11.0466i	−0.265509	+	0.459876i	0.702188	+	0.711992i	$0.252207\pi$
$578$	−6.57259	−	9.61612i	−0.273384	−	0.399978i
$579$		0			0
$580$	10.7157	+	13.3730i	0.444945	+	0.555283i
$581$	−5.80485	+	35.8909i	−0.240826	+	1.48901i
$582$		0			0
$583$		−	0.242297i		−	0.0100349i
$584$	2.25708	−	7.40917i	0.0933988	−	0.306594i
$585$		0			0
$586$	−29.3419	+	20.0551i	−1.21210	+	0.828468i
$587$	17.1705	−	29.7401i	0.708702	−	1.22751i	−0.256637	−	0.966508i	$-0.582615\pi$
$587$	17.1705	−	29.7401i	0.708702	−	1.22751i	0.965339	−	0.260999i	$-0.0840521\pi$
$588$		0			0
$589$	7.73727	+	13.4013i	0.318809	+	0.552193i
$590$	−15.2713	−	7.33233i	−0.628708	−	0.301867i
$591$		0			0
$592$	23.2301	+	21.3536i	0.954749	+	0.877630i
$593$	40.1331	−	23.1709i	1.64807	−	0.951514i	0.670233	−	0.742151i	$-0.266194\pi$
$593$	40.1331	−	23.1709i	1.64807	−	0.951514i	0.977838	−	0.209363i	$-0.0671391\pi$
$594$		0			0
$595$	6.98307	+	5.69266i	0.286278	+	0.233376i
$596$	−28.0070	−	10.9167i	−1.14721	−	0.447164i
$597$		0			0
$598$	49.9652	−	3.80295i	2.04323	−	0.155514i
$599$	14.1024			0.576208			0.288104	−	0.957599i	$-0.406975\pi$
$599$	14.1024			0.576208			0.288104	+	0.957599i	$0.406975\pi$
$600$		0			0
$601$	−6.34404	+	10.9882i	−0.258779	+	0.448218i	−0.965915	−	0.258859i	$-0.916653\pi$
$601$	−6.34404	+	10.9882i	−0.258779	+	0.448218i	0.707136	+	0.707077i	$0.249987\pi$
$602$	−17.5253	−	1.48234i	−0.714277	−	0.0604156i
$603$		0			0
$604$	16.6293	−	13.3250i	0.676638	−	0.542186i
$605$	10.9561	−	6.32552i	0.445429	−	0.257169i
$606$		0			0
$607$	−29.6669	−	17.1282i	−1.20414	−	0.695211i	−0.242668	−	0.970109i	$-0.578022\pi$
$607$	−29.6669	−	17.1282i	−1.20414	−	0.695211i	−0.961473	+	0.274898i	$0.911356\pi$
$608$	−25.4621	+	32.3130i	−1.03262	+	1.31046i
$609$		0			0
$610$	−2.00571	−	0.963021i	−0.0812089	−	0.0389916i
$611$	1.16437	+	2.01674i	0.0471052	+	0.0815886i
$612$		0			0
$613$	−1.88844	+	3.27087i	−0.0762734	+	0.132109i	−0.901639	−	0.432489i	$-0.857636\pi$
$613$	−1.88844	+	3.27087i	−0.0762734	+	0.132109i	0.825366	+	0.564598i	$0.190969\pi$
$614$	−1.30644	−	17.1647i	−0.0527235	−	0.692710i
$615$		0			0
$616$	0.277228	+	0.135991i	0.0111698	+	0.00547924i
$617$	−22.7647	+	13.1432i	−0.916470	+	0.529124i	−0.882507	−	0.470299i	$-0.844146\pi$
$617$	−22.7647	+	13.1432i	−0.916470	+	0.529124i	−0.0339631	+	0.999423i	$0.510813\pi$
$618$		0			0
$619$	15.1141	−	8.72611i	0.607485	−	0.350732i	−0.164495	−	0.986378i	$-0.552600\pi$
$619$	15.1141	−	8.72611i	0.607485	−	0.350732i	0.771981	+	0.635646i	$0.219266\pi$
$620$	1.77777	−	4.56092i	0.0713970	−	0.183171i
$621$		0			0
$622$	16.7460	−	1.27457i	0.671452	−	0.0511055i
$623$	1.11735	−	1.37063i	0.0447658	−	0.0549133i
$624$		0			0
$625$	−3.45189	+	5.97884i	−0.138075	+	0.239154i
$626$	33.0672	−	2.51681i	1.32163	−	0.100592i
$627$		0			0
$628$	−21.2436	+	3.25262i	−0.847711	+	0.129794i
$629$			23.3525i			0.931124i
$630$		0			0
$631$		−	24.9923i		−	0.994929i	−0.867484	−	0.497465i	$-0.834264\pi$
$631$		−	24.9923i		−	0.994929i	0.867484	−	0.497465i	$-0.165736\pi$
$632$	4.33556	+	18.6938i	0.172459	+	0.743598i
$633$		0			0
$634$	3.26165	+	42.8533i	0.129536	+	1.70192i
$635$	−7.48279	+	12.9606i	−0.296945	+	0.514324i
$636$		0			0
$637$	−38.6252	−	12.8298i	−1.53039	−	0.508335i
$638$	0.0329891	+	0.433429i	0.00130605	+	0.0171596i
$639$		0			0
$640$	13.0134	−	0.106183i	0.514400	−	0.00419724i
$641$	−29.2098	+	16.8643i	−1.15372	+	0.666098i	−0.949790	−	0.312888i	$-0.898703\pi$
$641$	−29.2098	+	16.8643i	−1.15372	+	0.666098i	−0.203926	+	0.978986i	$0.565370\pi$
$642$		0			0
$643$	−14.4308	+	8.33160i	−0.569093	+	0.328566i	−0.756787	−	0.653661i	$-0.773232\pi$
$643$	−14.4308	+	8.33160i	−0.569093	+	0.328566i	0.187694	+	0.982228i	$0.439899\pi$
$644$	−0.271406	+	32.2457i	−0.0106949	+	1.27066i
$645$		0			0
$646$	−30.3592	+	2.31070i	−1.19447	+	0.0909131i
$647$	−3.12081	+	5.40539i	−0.122692	+	0.212508i	−0.920828	−	0.389968i	$-0.872486\pi$
$647$	−3.12081	+	5.40539i	−0.122692	+	0.212508i	0.798137	+	0.602476i	$0.205819\pi$
$648$		0			0
$649$	−0.214852	−	0.372135i	−0.00843369	−	0.0146076i
$650$	−13.0862	+	27.2550i	−0.513283	+	1.06903i
$651$		0			0
$652$	19.0980	−	15.3031i	0.747936	−	0.599316i
$653$	−33.2340	−	19.1877i	−1.30055	−	0.750871i	−0.320049	−	0.947401i	$-0.603699\pi$
$653$	−33.2340	−	19.1877i	−1.30055	−	0.750871i	−0.980498	+	0.196530i	$0.937033\pi$
$654$		0			0
$655$	0.311429	−	0.179804i	0.0121685	−	0.00702552i
$656$	6.33235	−	6.88879i	0.247237	−	0.268962i
$657$		0			0
$658$	−1.35636	+	0.637248i	−0.0528762	+	0.0248425i
$659$	12.4132	−	21.5003i	0.483551	−	0.837535i	−0.516271	−	0.856425i	$-0.672680\pi$
$659$	12.4132	−	21.5003i	0.483551	−	0.837535i	0.999822	+	0.0188909i	$0.00601351\pi$
$660$		0			0
$661$	−8.72145			−0.339225			−0.169613	−	0.985511i	$-0.554252\pi$
$661$	−8.72145			−0.339225			−0.169613	+	0.985511i	$0.554252\pi$
$662$	−3.24181	−	42.5926i	−0.125996	−	1.65541i
$663$		0			0
$664$	−11.3265	+	37.1806i	−0.439552	+	1.44289i
$665$	−20.6883	+	7.86404i	−0.802260	+	0.304954i
$666$		0			0
$667$	−39.3126	+	22.6971i	−1.52219	+	0.878837i
$668$	−11.9671	−	14.9347i	−0.463019	−	0.577839i
$669$		0			0
$670$	0.673879	−	1.40351i	0.0260342	−	0.0542222i
$671$	−0.0282185	−	0.0488759i	−0.00108936	−	0.00188683i
$672$		0			0
$673$	18.6887	−	32.3698i	0.720396	−	1.24776i	−0.240445	−	0.970663i	$-0.577293\pi$
$673$	18.6887	−	32.3698i	0.720396	−	1.24776i	0.960841	−	0.277100i	$-0.0893734\pi$
$674$	−17.4738	−	25.5653i	−0.673067	−	0.984740i
$675$		0			0
$676$	−15.1125	+	38.7716i	−0.581250	+	1.49121i
$677$		−	17.1093i		−	0.657565i	−0.944406	−	0.328783i	$-0.893362\pi$
$677$		−	17.1093i		−	0.657565i	0.944406	−	0.328783i	$-0.106638\pi$
$678$		0			0
$679$	−1.72490	+	10.6649i	−0.0661954	+	0.409280i
$680$	6.57572	+	7.03742i	0.252167	+	0.269873i
$681$		0			0
$682$	0.102512	−	0.0700666i	0.00392539	−	0.00268299i
$683$	−20.8154	+	36.0533i	−0.796480	+	1.37954i	0.125416	+	0.992104i	$0.459973\pi$
$683$	−20.8154	+	36.0533i	−0.796480	+	1.37954i	−0.921895	+	0.387439i	$0.873360\pi$
$684$		0			0
$685$	−10.4372			−0.398785
$686$	10.3218	−	24.0720i	0.394090	−	0.919072i
$687$		0			0
$688$	−18.3501	−	4.09837i	−0.699591	−	0.156249i
$689$			34.1415i			1.30069i
$690$		0			0
$691$			29.7036i			1.12998i	0.825098	+	0.564989i	$0.191120\pi$
$691$			29.7036i			1.12998i	−0.825098	+	0.564989i	$0.808880\pi$
$692$	−6.16078	−	40.2374i	−0.234198	−	1.52960i
$693$		0			0
$694$	41.5070	−	3.15918i	1.57558	−	0.119921i
$695$	−0.857238			−0.0325169
$696$		0			0
$697$	6.92509			0.262307
$698$	12.7805	−	26.6183i	0.483749	−	1.00752i
$699$		0			0
$700$	−16.7671	−	9.86956i	−0.633736	−	0.373034i
$701$			5.38772i			0.203491i	0.994810	+	0.101746i	$0.0324428\pi$
$701$			5.38772i			0.203491i	−0.994810	+	0.101746i	$0.967557\pi$
$702$		0			0
$703$	−49.6819	−	28.6839i	−1.87379	−	1.08183i
$704$	0.274041	+	0.184044i	0.0103283	+	0.00693640i
$705$		0			0
$706$	33.4353	−	22.8529i	1.25835	−	0.860081i
$707$	−22.4645	+	27.5568i	−0.844866	+	1.03638i
$708$		0			0
$709$	−1.02587			−0.0385273			−0.0192637	−	0.999814i	$-0.506132\pi$
$709$	−1.02587			−0.0385273			−0.0192637	+	0.999814i	$0.506132\pi$
$710$	1.88017	+	0.902742i	0.0705614	+	0.0338793i
$711$		0			0
$712$	1.38130	−	1.29068i	0.0517665	−	0.0483703i
$713$	11.2298	+	6.48355i	0.420561	+	0.242811i
$714$		0			0
$715$	0.238998	−	0.137986i	0.00893803	−	0.00516037i
$716$	17.2799	−	44.3321i	0.645781	−	1.65677i
$717$		0			0
$718$	8.85305	+	12.9526i	0.330393	+	0.483386i
$719$	21.4410	+	37.1370i	0.799616	+	1.38498i	0.919866	+	0.392232i	$0.128297\pi$
$719$	21.4410	+	37.1370i	0.799616	+	1.38498i	−0.120250	+	0.992744i	$0.538370\pi$
$720$		0			0
$721$	−29.1854	−	4.72033i	−1.08692	−	0.175794i
$722$	20.7440	−	43.2042i	0.772013	−	1.60789i
$723$		0			0
$724$	30.4023	−	4.65492i	1.12989	−	0.172999i
$725$		−	27.3888i		−	1.01719i
$726$		0			0
$727$	−9.11133	−	5.26043i	−0.337921	−	0.195098i	0.321432	−	0.946933i	$-0.395836\pi$
$727$	−9.11133	−	5.26043i	−0.337921	−	0.195098i	−0.659352	+	0.751834i	$0.729169\pi$
$728$	−39.0636	−	19.1622i	−1.44779	−	0.710199i
$729$		0			0
$730$	3.67766	−	2.51367i	0.136116	−	0.0930350i
$731$	−6.95771	−	12.0511i	−0.257340	−	0.445726i
$732$		0			0
$733$	−17.8701	+	30.9520i	−0.660048	+	1.14324i	0.320554	+	0.947230i	$0.396131\pi$
$733$	−17.8701	+	30.9520i	−0.660048	+	1.14324i	−0.980602	+	0.196007i	$0.937202\pi$
$734$	−0.905331	+	0.618792i	−0.0334164	+	0.0228400i
$735$		0			0
$736$	−4.93922	+	34.1176i	−0.182062	+	1.25759i
$737$	0.0342011	−	0.0197460i	0.00125981	−	0.000727354i
$738$		0			0
$739$	−11.4786	−	6.62717i	−0.422247	−	0.243784i	0.273791	−	0.961789i	$-0.411722\pi$
$739$	−11.4786	−	6.62717i	−0.422247	−	0.243784i	−0.696038	+	0.718005i	$0.745056\pi$
$740$	2.74657	+	17.9384i	0.100966	+	0.659429i
$741$		0			0
$742$	−21.8927	−	1.85175i	−0.803707	−	0.0679799i
$743$	−8.67905	−	15.0326i	−0.318404	−	0.551491i	0.661752	−	0.749723i	$-0.269813\pi$
$743$	−8.67905	−	15.0326i	−0.318404	−	0.551491i	−0.980155	+	0.198232i	$0.936480\pi$
$744$		0			0
$745$	−8.64411	−	14.9720i	−0.316696	−	0.548533i
$746$	−12.0140	+	25.0219i	−0.439863	+	0.916116i
$747$		0			0
$748$	0.0369756	+	0.241496i	0.00135196	+	0.00882996i
$749$	23.1986	+	18.9117i	0.847659	+	0.691019i
$750$		0			0
$751$	−33.8508	−	19.5438i	−1.23524	−	0.713163i	−0.267119	−	0.963664i	$-0.586072\pi$
$751$	−33.8508	−	19.5438i	−1.23524	−	0.713163i	−0.968116	+	0.250500i	$0.919405\pi$
$752$	−1.52867	+	0.479349i	−0.0557449	+	0.0174801i
$753$		0			0
$754$	−4.64843	−	61.0736i	−0.169286	−	2.22417i
$755$	12.2558			0.446034
$756$		0			0
$757$	−50.4536			−1.83377			−0.916883	−	0.399156i	$-0.869303\pi$
$757$	−50.4536			−1.83377			−0.916883	+	0.399156i	$0.869303\pi$
$758$	1.69410	+	22.2580i	0.0615323	+	0.808445i
$759$		0			0
$760$	−23.0489	+	5.34564i	−0.836073	+	0.193907i
$761$	−39.8383	−	23.0007i	−1.44414	−	0.833774i	−0.446016	−	0.895025i	$-0.647158\pi$
$761$	−39.8383	−	23.0007i	−1.44414	−	0.833774i	−0.998122	+	0.0612515i	$0.980491\pi$
$762$		0			0
$763$	1.97518	−	12.2124i	0.0715064	−	0.442118i
$764$	−13.1473	+	2.01299i	−0.475651	+	0.0728273i
$765$		0			0
$766$	6.35617	−	13.2382i	0.229658	−	0.478315i
$767$	30.2744	+	52.4368i	1.09314	+	1.89338i
$768$		0			0
$769$	9.35320	+	16.2002i	0.337285	+	0.584195i	0.983921	−	0.178604i	$-0.0571581\pi$
$769$	9.35320	+	16.2002i	0.337285	+	0.584195i	−0.646636	+	0.762799i	$0.723825\pi$
$770$	0.0755185	+	0.160738i	0.00272150	+	0.00579259i
$771$		0			0
$772$	−12.1535	+	1.86083i	−0.437413	+	0.0669727i
$773$	5.68811	+	3.28403i	0.204587	+	0.118118i	0.598793	−	0.800904i	$-0.295647\pi$
$773$	5.68811	+	3.28403i	0.204587	+	0.118118i	−0.394206	+	0.919022i	$0.628980\pi$
$774$		0			0
$775$	−6.77555	+	3.91187i	−0.243385	+	0.140518i
$776$	−3.36563	+	11.0481i	−0.120819	+	0.396604i
$777$		0			0
$778$	−32.3199	+	22.0906i	−1.15872	+	0.791985i
$779$	−8.50610	+	14.7330i	−0.304763	+	0.527865i
$780$		0			0
$781$	0.0264522	+	0.0458165i	0.000946534	+	0.00163944i
$782$	−21.0635	+	14.3968i	−0.753228	+	0.514829i
$783$		0			0
$784$	14.4062	−	24.0096i	0.514507	−	0.857486i
$785$	−10.7044	−	6.18016i	−0.382055	−	0.220579i
$786$		0			0
$787$		−	10.4640i		−	0.373002i	−0.982455	−	0.186501i	$-0.940285\pi$
$787$		−	10.4640i		−	0.373002i	0.982455	−	0.186501i	$-0.0597147\pi$
$788$	4.00293	+	26.1440i	0.142599	+	0.931342i
$789$		0			0
$790$	−4.77711	+	9.94942i	−0.169962	+	0.353984i
$791$	−0.479812	+	0.588576i	−0.0170602	+	0.0209273i
$792$		0			0
$793$	3.97621	+	6.88699i	0.141199	+	0.244564i
$794$	24.7807	+	36.2557i	0.879434	+	1.28667i
$795$		0			0
$796$	31.0830	+	12.1156i	1.10171	+	0.429427i
$797$	9.90432	−	5.71826i	0.350829	−	0.202551i	−0.314221	−	0.949350i	$-0.601743\pi$
$797$	9.90432	−	5.71826i	0.350829	−	0.202551i	0.665050	+	0.746798i	$0.268410\pi$
$798$		0			0
$799$	−1.02683	−	0.592840i	−0.0363266	−	0.0209732i
$800$	−16.3370	−	12.8733i	−0.577602	−	0.455140i
$801$		0			0
$802$	37.2625	+	17.8912i	1.31578	+	0.631760i
$803$	0.112995			0.00398751
$804$		0			0
$805$	−11.7186	+	14.3750i	−0.413026	+	0.506651i
$806$	−14.4447	+	9.87294i	−0.508794	+	0.347759i
$807$		0			0
$808$	−27.7713	+	25.9493i	−0.976989	+	0.912892i
$809$	46.6840	+	26.9530i	1.64132	+	0.947617i	0.980365	+	0.197193i	$0.0631826\pi$
$809$	46.6840	+	26.9530i	1.64132	+	0.947617i	0.660957	+	0.750424i	$0.270151\pi$
$810$		0			0
$811$			7.92248i			0.278196i	0.990279	+	0.139098i	$0.0444203\pi$
$811$			7.92248i			0.278196i	−0.990279	+	0.139098i	$0.955580\pi$
$812$	39.4146	+	0.331746i	1.38318	+	0.0116420i
$813$		0			0
$814$	−0.199244	+	0.414971i	−0.00698350	+	0.0145447i
$815$	14.0752			0.493033
$816$		0			0
$817$	34.1847			1.19597
$818$	38.7907	−	2.95244i	1.35629	−	0.103229i
$819$		0			0
$820$	5.31958	−	0.814485i	0.185768	−	0.0284430i
$821$		−	24.9264i		−	0.869936i	−0.900446	−	0.434968i	$-0.856760\pi$
$821$		−	24.9264i		−	0.869936i	0.900446	−	0.434968i	$-0.143240\pi$
$822$		0			0
$823$		−	19.3265i		−	0.673679i	−0.941562	−	0.336840i	$-0.890642\pi$
$823$		−	19.3265i		−	0.673679i	0.941562	−	0.336840i	$-0.109358\pi$
$824$	−30.2342	−	9.21036i	−1.05326	−	0.320858i
$825$		0			0
$826$	−35.2663	+	16.5689i	−1.22707	+	0.576507i
$827$	−50.6751			−1.76215			−0.881074	−	0.472979i	$-0.843179\pi$
$827$	−50.6751			−1.76215			−0.881074	+	0.472979i	$0.843179\pi$
$828$		0			0
$829$	18.8507	−	32.6504i	0.654713	−	1.13400i	−0.327253	−	0.944937i	$-0.606123\pi$
$829$	18.8507	−	32.6504i	0.654713	−	1.13400i	0.981966	−	0.189059i	$-0.0605436\pi$
$830$	−18.4552	+	12.6141i	−0.640588	+	0.437840i
$831$		0			0
$832$	−38.6145	−	25.9332i	−1.33872	−	0.899071i
$833$	20.2975	−	4.17591i	0.703268	−	0.144687i
$834$		0			0
$835$		−	11.0068i		−	0.380907i
$836$	−0.559195	−	0.217965i	−0.0193402	−	0.00753847i
$837$		0			0
$838$	0.599644	+	0.877317i	0.0207143	+	0.0303064i
$839$	−13.8503	+	23.9895i	−0.478166	+	0.828208i	−0.999687	−	0.0250307i	$-0.992032\pi$
$839$	−13.8503	+	23.9895i	−0.478166	+	0.828208i	0.521521	+	0.853239i	$0.325365\pi$
$840$		0			0
$841$	13.2432	+	22.9380i	0.456663	+	0.790964i
$842$	−15.3631	+	31.9971i	−0.529446	+	1.10269i
$843$		0			0
$844$	3.53215	−	2.83029i	0.121582	−	0.0974227i
$845$	−20.7266	+	11.9665i	−0.713016	+	0.411660i
$846$		0			0
$847$	4.64595	−	28.7255i	0.159637	−	0.987019i
$848$	−22.9231	−	5.11972i	−0.787183	−	0.175812i
$849$		0			0
$850$	−1.16826	−	15.3492i	−0.0400710	−	0.526474i
$851$	−48.0721			−1.64789
$852$		0			0
$853$	4.35844	−	7.54903i	0.149230	−	0.258474i	−0.781713	−	0.623638i	$-0.785654\pi$
$853$	4.35844	−	7.54903i	0.149230	−	0.258474i	0.930943	+	0.365164i	$0.118987\pi$
$854$	−4.63183	+	2.17615i	−0.158498	+	0.0744662i
$855$		0			0
$856$	21.8453	+	23.3792i	0.746658	+	0.799084i
$857$	−21.2925	+	12.2932i	−0.727338	+	0.419929i	−0.817447	−	0.576003i	$-0.804612\pi$
$857$	−21.2925	+	12.2932i	−0.727338	+	0.419929i	0.0901098	+	0.995932i	$0.471278\pi$
$858$		0			0
$859$	2.32063	+	1.33982i	0.0791790	+	0.0457140i	0.539067	−	0.842263i	$-0.318777\pi$
$859$	2.32063	+	1.33982i	0.0791790	+	0.0457140i	−0.459888	+	0.887977i	$0.652110\pi$
$860$	−6.76200	−	8.43885i	−0.230582	−	0.287762i
$861$		0			0
$862$	−7.50494	+	15.6308i	−0.255619	+	0.532386i
$863$	−14.5911	−	25.2725i	−0.496686	−	0.860285i	0.503307	−	0.864108i	$-0.332116\pi$
$863$	−14.5911	−	25.2725i	−0.496686	−	0.860285i	−0.999993	+	0.00382290i	$0.998783\pi$
$864$		0			0
$865$	11.7058	−	20.2751i	0.398011	−	0.689375i
$866$	18.3099	−	1.39360i	0.622196	−	0.0473566i
$867$		0			0
$868$	−5.54742	−	9.79794i	−0.188292	−	0.332564i
$869$	−0.242451	+	0.139979i	−0.00822458	+	0.00474846i
$870$		0			0
$871$	−4.81921	+	2.78237i	−0.163293	+	0.0942770i
$872$	3.85399	−	12.6512i	0.130513	−	0.428425i
$873$		0			0
$874$	−4.75667	−	62.4958i	−0.160897	−	2.11395i
$875$	−9.38268	−	24.6835i	−0.317192	−	0.834455i
$876$		0			0
$877$	5.83899	−	10.1134i	0.197169	−	0.341506i	−0.750441	−	0.660938i	$-0.770159\pi$
$877$	5.83899	−	10.1134i	0.197169	−	0.341506i	0.947609	+	0.319432i	$0.103492\pi$
$878$	2.07170	+	27.2191i	0.0699164	+	0.918600i
$879$		0			0
$880$	0.0568064	+	0.181159i	0.00191494	+	0.00610685i
$881$		−	36.3492i		−	1.22463i	−0.790612	−	0.612317i	$-0.790238\pi$
$881$		−	36.3492i		−	1.22463i	0.790612	−	0.612317i	$-0.209762\pi$
$882$		0			0
$883$			44.6127i			1.50134i	0.660680	+	0.750668i	$0.270268\pi$
$883$			44.6127i			1.50134i	−0.660680	+	0.750668i	$0.729732\pi$
$884$	−5.21015	−	34.0286i	−0.175236	−	1.14451i
$885$		0			0
$886$	7.38455	−	0.562052i	0.248089	−	0.0188825i
$887$	−17.4280	+	30.1862i	−0.585175	+	1.01355i	0.409679	+	0.912230i	$0.365641\pi$
$887$	−17.4280	+	30.1862i	−0.585175	+	1.01355i	−0.994854	+	0.101323i	$0.967693\pi$
$888$		0			0
$889$	12.2308	+	32.1763i	0.410209	+	1.07916i
$890$	1.08414	−	0.0825158i	0.0363404	−	0.00276594i
$891$		0			0
$892$	−18.9115	−	7.37138i	−0.633203	−	0.246812i
$893$	2.52251	−	1.45637i	0.0844126	−	0.0487356i
$894$		0			0
$895$	23.6992	−	13.6827i	0.792175	−	0.457363i
$896$	18.7236	−	23.3544i	0.625512	−	0.780215i
$897$		0			0
$898$	1.70587	+	22.4126i	0.0569255	+	0.747919i
$899$	7.92499	−	13.7265i	0.264313	−	0.457804i
$900$		0			0
$901$	−8.69162	−	15.0543i	−0.289560	−	0.501533i
$902$	0.123058	+	0.0590851i	0.00409739	+	0.00196732i
$903$		0			0
$904$	−0.593157	+	0.554241i	−0.0197281	+	0.0184338i
$905$	15.3193	+	8.84461i	0.509231	+	0.294005i
$906$		0			0
$907$	−30.3505	+	17.5229i	−1.00777	+	0.581838i	−0.910539	−	0.413423i	$-0.864333\pi$
$907$	−30.3505	+	17.5229i	−1.00777	+	0.581838i	−0.0972343	+	0.995262i	$0.531000\pi$
$908$	3.67069	+	4.58095i	0.121816	+	0.152024i
$909$		0			0
$910$	−10.6411	−	22.6492i	−0.352751	−	0.750814i
$911$	−11.5348	+	19.9789i	−0.382166	+	0.661930i	−0.991372	−	0.131082i	$-0.958155\pi$
$911$	−11.5348	+	19.9789i	−0.382166	+	0.661930i	0.609206	+	0.793012i	$0.291488\pi$
$912$		0			0
$913$	−0.567031			−0.0187660
$914$	−5.07399	+	0.386191i	−0.167833	+	0.0127741i
$915$		0			0
$916$	−0.322319	+	0.826918i	−0.0106497	+	0.0273221i
$917$	0.132062	−	0.816526i	0.00436106	−	0.0269641i
$918$		0			0
$919$	−33.1126	+	19.1176i	−1.09228	+	0.630630i	−0.934184	−	0.356793i	$-0.883870\pi$
$919$	−33.1126	+	19.1176i	−1.09228	+	0.630630i	−0.158100	+	0.987423i	$0.550537\pi$
$920$	−14.4868	+	13.5364i	−0.477617	+	0.446282i
$921$		0			0
$922$	19.3193	+	9.27595i	0.636247	+	0.305487i
$923$	−3.72732	−	6.45591i	−0.122686	−	0.212499i
$924$		0			0
$925$	14.5022	−	25.1186i	0.476830	−	0.825893i
$926$	30.8475	−	21.0842i	1.01371	−	0.692869i
$927$		0			0
$928$	41.7027	+	6.03732i	1.36896	+	0.198185i
$929$		−	11.7834i		−	0.386601i	−0.981140	−	0.193301i	$-0.938081\pi$
$929$		−	11.7834i		−	0.386601i	0.981140	−	0.193301i	$-0.0619193\pi$
$930$		0			0
$931$	−16.0473	+	48.3119i	−0.525930	+	1.58336i
$932$	24.0241	−	19.2503i	0.786934	−	0.630566i
$933$		0			0
$934$	−18.6396	−	27.2709i	−0.609906	−	0.892331i
$935$	−0.0702558	+	0.121687i	−0.00229761	+	0.00397958i
$936$		0			0
$937$	−30.8568			−1.00805			−0.504024	−	0.863690i	$-0.668148\pi$
$937$	−30.8568			−1.00805			−0.504024	+	0.863690i	$0.668148\pi$
$938$	−1.52277	−	3.24115i	−0.0497202	−	0.105827i
$939$		0			0
$940$	−0.858494	−	0.334627i	−0.0280010	−	0.0109143i
$941$			27.2927i			0.889716i	0.895601	+	0.444858i	$0.146746\pi$
$941$			27.2927i			0.889716i	−0.895601	+	0.444858i	$0.853254\pi$
$942$		0			0
$943$			14.2556i			0.464227i
$944$	−39.7466	+	12.4634i	−1.29364	+	0.405651i
$945$		0			0
$946$	−0.0208174	−	0.273510i	−0.000676832	−	0.00889259i
$947$	6.12529			0.199045			0.0995227	−	0.995035i	$-0.468268\pi$
$947$	6.12529			0.199045			0.0995227	+	0.995035i	$0.468268\pi$
$948$		0			0
$949$	−15.9219			−0.516847
$950$	34.0902	+	16.3680i	1.10603	+	0.531049i
$951$		0			0
$952$	22.1029	−	1.49530i	0.716360	−	0.0484630i
$953$			32.5362i			1.05395i	0.849881	+	0.526975i	$0.176674\pi$
$953$			32.5362i			1.05395i	−0.849881	+	0.526975i	$0.823326\pi$
$954$		0			0
$955$	−6.62473	−	3.82479i	−0.214371	−	0.123767i
$956$	−10.8722	−	13.5683i	−0.351631	−	0.438829i
$957$		0			0
$958$	5.57070	+	8.15029i	0.179981	+	0.263324i
$959$	−15.1688	+	18.6072i	−0.489825	+	0.600859i
$960$		0			0
$961$	26.4724			0.853948
$962$	28.0750	−	58.4727i	0.905176	−	1.88523i
$963$		0			0
$964$	4.47120	+	5.57997i	0.144008	+	0.179719i
$965$	−6.12398	−	3.53568i	−0.197138	−	0.113818i
$966$		0			0
$967$	29.4129	−	16.9816i	0.945856	−	0.546090i	0.0540646	−	0.998537i	$-0.482782\pi$
$967$	29.4129	−	16.9816i	0.945856	−	0.546090i	0.891791	+	0.452447i	$0.149449\pi$
$968$	9.06521	−	29.7577i	0.291367	−	0.956450i
$969$		0			0
$970$	−5.48390	+	3.74823i	−0.176077	+	0.120348i
$971$	9.81717	+	17.0038i	0.315048	+	0.545679i	0.979448	−	0.201698i	$-0.0646461\pi$
$971$	9.81717	+	17.0038i	0.315048	+	0.545679i	−0.664400	+	0.747377i	$0.731313\pi$
$972$		0			0
$973$	−1.24586	+	1.52827i	−0.0399404	+	0.0489940i
$974$	11.1398	+	5.34865i	0.356942	+	0.171382i
$975$		0			0
$976$	−5.22028	+	1.63694i	−0.167097	+	0.0523970i
$977$		−	44.9748i		−	1.43887i	−0.694559	−	0.719435i	$-0.744401\pi$
$977$		−	44.9748i		−	1.43887i	0.694559	−	0.719435i	$-0.255599\pi$
$978$		0			0
$979$	0.0238846	+	0.0137898i	0.000763355	+	0.000440723i
$980$	15.1006	−	5.59503i	0.482371	−	0.178727i
$981$		0			0
$982$	22.9349	+	33.5553i	0.731883	+	1.07079i
$983$	−2.53298	−	4.38725i	−0.0807895	−	0.139932i	0.822800	−	0.568331i	$-0.192411\pi$
$983$	−2.53298	−	4.38725i	−0.0807895	−	0.139932i	−0.903589	+	0.428400i	$0.859077\pi$
$984$		0			0
$985$	−7.60580	+	13.1736i	−0.242341	+	0.419747i
$986$	17.5976	+	25.7464i	0.560421	+	0.819931i
$987$		0			0
$988$	78.7950	+	30.7130i	2.50680	+	0.977109i
$989$	24.8077	−	14.3228i	0.788840	−	0.455437i
$990$		0			0
$991$	26.7965	+	15.4710i	0.851220	+	0.491452i	0.861062	−	0.508500i	$-0.169800\pi$
$991$	26.7965	+	15.4710i	0.851220	+	0.491452i	−0.00984253	+	0.999952i	$0.503133\pi$
$992$	−4.46276	−	11.1789i	−0.141693	−	0.354931i
$993$		0			0
$994$	4.34191	−	2.03993i	0.137717	−	0.0647028i
$995$	9.59349	+	16.6164i	0.304134	+	0.526776i
$996$		0			0
$997$	6.02219	+	10.4307i	0.190725	+	0.330345i	0.945491	−	0.325649i	$-0.105583\pi$
$997$	6.02219	+	10.4307i	0.190725	+	0.330345i	−0.754766	+	0.655994i	$0.772250\pi$
$998$	15.9967	+	7.68064i	0.506366	+	0.243126i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.683.43		88
3.2	odd	2		252.2.bb.a.11.2	yes	88
4.3	odd	2	inner	756.2.bb.a.683.2		88
7.2	even	3		756.2.o.a.359.12		88
9.4	even	3		252.2.o.a.95.17	✓	88
9.5	odd	6		756.2.o.a.179.28		88
12.11	even	2		252.2.bb.a.11.43	yes	88
21.2	odd	6		252.2.o.a.191.33	yes	88
28.23	odd	6		756.2.o.a.359.28		88
36.23	even	6		756.2.o.a.179.12		88
36.31	odd	6		252.2.o.a.95.33	yes	88
63.23	odd	6	inner	756.2.bb.a.611.2		88
63.58	even	3		252.2.bb.a.23.43	yes	88
84.23	even	6		252.2.o.a.191.17	yes	88
252.23	even	6	inner	756.2.bb.a.611.43		88
252.247	odd	6		252.2.bb.a.23.2	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.17	✓	88	9.4	even	3
252.2.o.a.95.33	yes	88	36.31	odd	6
252.2.o.a.191.17	yes	88	84.23	even	6
252.2.o.a.191.33	yes	88	21.2	odd	6
252.2.bb.a.11.2	yes	88	3.2	odd	2
252.2.bb.a.11.43	yes	88	12.11	even	2
252.2.bb.a.23.2	yes	88	252.247	odd	6
252.2.bb.a.23.43	yes	88	63.58	even	3
756.2.o.a.179.12		88	36.23	even	6
756.2.o.a.179.28		88	9.5	odd	6
756.2.o.a.359.12		88	7.2	even	3
756.2.o.a.359.28		88	28.23	odd	6
756.2.bb.a.611.2		88	63.23	odd	6	inner
756.2.bb.a.611.43		88	252.23	even	6	inner
756.2.bb.a.683.2		88	4.3	odd	2	inner
756.2.bb.a.683.43		88	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.41013 - 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 + 0.575136i) q^{5} +(2.47311 - 0.940076i) q^{7} +(2.75529 - 0.639023i) q^{8} +O(q^{10})\)	\(q+(1.41013 - 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 + 0.575136i) q^{5} +(2.47311 - 0.940076i) q^{7} +(2.75529 - 0.639023i) q^{8} +(1.46646 + 0.704103i) q^{10} +(0.0206317 + 0.0357351i) q^{11} +(-2.90716 - 5.03535i) q^{13} +(3.38652 - 1.59107i) q^{14} +(3.81675 - 1.19683i) q^{16} +(2.56376 + 1.48019i) q^{17} +(-6.29815 + 3.63624i) q^{19} +(2.14347 + 0.835489i) q^{20} +(0.0329288 + 0.0481769i) q^{22} +(-3.04704 + 5.27762i) q^{23} +(-1.83844 - 3.18427i) q^{25} +(-4.63993 - 6.78851i) q^{26} +(4.60468 - 2.60709i) q^{28} +(6.45096 + 3.72446i) q^{29} -2.12782i q^{31} +(5.25368 - 2.09734i) q^{32} +(3.77412 + 1.81210i) q^{34} +(3.00429 + 0.485903i) q^{35} +(3.94417 + 6.83150i) q^{37} +(-8.49097 + 5.80356i) q^{38} +(3.11225 + 0.948097i) q^{40} +(2.02586 - 1.16963i) q^{41} +(-4.07080 - 2.35028i) q^{43} +(0.0516048 + 0.0644018i) q^{44} +(-3.73030 + 7.76919i) q^{46} -0.400516 q^{47} +(5.23252 - 4.64982i) q^{49} +(-2.93421 - 4.29293i) q^{50} +(-7.27152 - 9.07472i) q^{52} +(-5.08527 - 2.93598i) q^{53} +0.0474640i q^{55} +(6.21341 - 4.17056i) q^{56} +(9.49646 + 4.55963i) q^{58} -10.4137 q^{59} -1.36773 q^{61} +(-0.228375 - 3.00052i) q^{62} +(7.18330 - 3.52139i) q^{64} -6.68806i q^{65} -0.957074i q^{67} +(5.51650 + 2.15024i) q^{68} +(4.28861 + 0.362743i) q^{70} +1.28212 q^{71} +(1.36920 - 2.37152i) q^{73} +(6.29502 + 9.21002i) q^{74} +(-11.3505 + 9.09512i) q^{76} +(0.0846180 + 0.0689814i) q^{77} +6.78467i q^{79} +(4.49045 + 1.00291i) q^{80} +(2.73120 - 1.86677i) q^{82} +(-6.87088 + 11.9007i) q^{83} +(1.70262 + 2.94902i) q^{85} +(-5.99262 - 2.87730i) q^{86} +(0.0796818 + 0.0852766i) q^{88} +(0.578834 - 0.334190i) q^{89} +(-11.9233 - 9.72001i) q^{91} +(-4.42637 + 11.3560i) q^{92} +(-0.564782 + 0.0429866i) q^{94} -8.36533 q^{95} +(-2.04166 + 3.53626i) q^{97} +(6.87950 - 7.11846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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