LMFDB - Embedded newform 756.2.bb.a.611.2

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			611.2
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41013 + 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 - 0.575136i) q^{5} +(-2.47311 - 0.940076i) q^{7} +(-2.75529 + 0.639023i) q^{8} +O(q^{10})$	\(q+(-1.41013 + 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 - 0.575136i) q^{5} +(-2.47311 - 0.940076i) q^{7} +(-2.75529 + 0.639023i) q^{8} +(-1.34300 + 0.917936i) q^{10} +(-0.0206317 + 0.0357351i) q^{11} +(-2.90716 + 5.03535i) q^{13} +(3.58831 + 1.06020i) q^{14} +(3.81675 - 1.19683i) q^{16} +(2.56376 - 1.48019i) q^{17} +(6.29815 + 3.63624i) q^{19} +(1.79529 - 1.43855i) q^{20} +(0.0252580 - 0.0526056i) q^{22} +(3.04704 + 5.27762i) q^{23} +(-1.83844 + 3.18427i) q^{25} +(3.55906 - 7.41255i) q^{26} +(-5.17379 - 1.10990i) q^{28} +(6.45096 - 3.72446i) q^{29} -2.12782i q^{31} +(-5.25368 + 2.09734i) q^{32} +(-3.45639 + 2.36243i) q^{34} +(-3.00429 + 0.485903i) q^{35} +(3.94417 - 6.83150i) q^{37} +(-9.27151 - 4.45162i) q^{38} +(-2.37720 + 2.22124i) q^{40} +(2.02586 + 1.16963i) q^{41} +(4.07080 - 2.35028i) q^{43} +(-0.0299712 + 0.0768920i) q^{44} +(-4.86317 - 7.11513i) q^{46} +0.400516 q^{47} +(5.23252 + 4.64982i) q^{49} +(2.25068 - 4.68756i) q^{50} +(-4.22318 + 10.8347i) q^{52} +(-5.08527 + 2.93598i) q^{53} +0.0474640i q^{55} +(7.41487 + 1.00981i) q^{56} +(-8.69698 + 5.94436i) q^{58} +10.4137 q^{59} -1.36773 q^{61} +(0.228375 + 3.00052i) q^{62} +(7.18330 - 3.52139i) q^{64} +6.68806i q^{65} -0.957074i q^{67} +(4.62042 - 3.70231i) q^{68} +(4.18431 - 1.00763i) q^{70} -1.28212 q^{71} +(1.36920 + 2.37152i) q^{73} +(-4.82860 + 10.0567i) q^{74} +(13.5519 + 5.28229i) q^{76} +(0.0846180 - 0.0689814i) q^{77} +6.78467i q^{79} +(3.11378 - 3.38739i) q^{80} +(-2.98227 - 1.43190i) q^{82} +(6.87088 + 11.9007i) q^{83} +(1.70262 - 2.94902i) q^{85} +(-5.48812 + 3.75112i) q^{86} +(0.0340108 - 0.111645i) q^{88} +(0.578834 + 0.334190i) q^{89} +(11.9233 - 9.72001i) q^{91} +(7.62138 + 9.51134i) q^{92} +(-0.564782 + 0.0429866i) q^{94} +8.36533 q^{95} +(-2.04166 - 3.53626i) q^{97} +(-7.87761 - 5.99527i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−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	−0.260429	−	0.965493i	$-0.583864\pi$
$5$	0.996165	−	0.575136i	0.445498	−	0.257209i	0.705927	+	0.708284i	$0.250531\pi$
$6$		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
$10$	−1.34300	+	0.917936i	−0.424693	+	0.290277i
$11$	−0.0206317	+	0.0357351i	−0.00622068	+	0.0107745i	−0.869119	−	0.494603i	$-0.835313\pi$
$11$	−0.0206317	+	0.0357351i	−0.00622068	+	0.0107745i	0.862898	+	0.505378i	$0.168647\pi$
$12$		0			0
$13$	−2.90716	+	5.03535i	−0.806302	+	1.39656i	0.109107	+	0.994030i	$0.465201\pi$
$13$	−2.90716	+	5.03535i	−0.806302	+	1.39656i	−0.915409	+	0.402526i	$0.868132\pi$
$14$	3.58831	+	1.06020i	0.959016	+	0.283350i
$15$		0			0
$16$	3.81675	−	1.19683i	0.954188	−	0.299207i
$17$	2.56376	−	1.48019i	0.621804	−	0.358999i	−0.155767	−	0.987794i	$-0.549785\pi$
$17$	2.56376	−	1.48019i	0.621804	−	0.358999i	0.777571	+	0.628795i	$0.216452\pi$
$18$		0			0
$19$	6.29815	+	3.63624i	1.44489	+	0.834210i	0.998171	−	0.0604613i	$-0.0192572\pi$
$19$	6.29815	+	3.63624i	1.44489	+	0.834210i	0.446724	+	0.894672i	$0.352591\pi$
$20$	1.79529	−	1.43855i	0.401439	−	0.321671i
$21$		0			0
$22$	0.0252580	−	0.0526056i	0.00538503	−	0.0112156i
$23$	3.04704	+	5.27762i	0.635351	+	1.10046i	0.986441	+	0.164118i	$0.0524779\pi$
$23$	3.04704	+	5.27762i	0.635351	+	1.10046i	−0.351090	+	0.936342i	$0.614189\pi$
$24$		0			0
$25$	−1.83844	+	3.18427i	−0.367687	+	0.636853i
$26$	3.55906	−	7.41255i	0.697988	−	1.45372i
$27$		0			0
$28$	−5.17379	−	1.10990i	−0.977755	−	0.209751i
$29$	6.45096	−	3.72446i	1.19791	−	0.691615i	0.237823	−	0.971308i	$-0.423566\pi$
$29$	6.45096	−	3.72446i	1.19791	−	0.691615i	0.960089	+	0.279693i	$0.0902327\pi$
$30$		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
$34$	−3.45639	+	2.36243i	−0.592765	+	0.405153i
$35$	−3.00429	+	0.485903i	−0.507818	+	0.0821325i
$36$		0			0
$37$	3.94417	−	6.83150i	0.648417	−	1.12309i	−0.335084	−	0.942188i	$-0.608765\pi$
$37$	3.94417	−	6.83150i	0.648417	−	1.12309i	0.983501	−	0.180903i	$-0.0579021\pi$
$38$	−9.27151	−	4.45162i	−1.50404	−	0.722148i
$39$		0			0
$40$	−2.37720	+	2.22124i	−0.375869	+	0.351209i
$41$	2.02586	+	1.16963i	0.316386	+	0.182665i	0.649780	−	0.760122i	$-0.274861\pi$
$41$	2.02586	+	1.16963i	0.316386	+	0.182665i	−0.333395	+	0.942787i	$0.608194\pi$
$42$		0			0
$43$	4.07080	−	2.35028i	0.620791	−	0.358414i	−0.156386	−	0.987696i	$-0.549984\pi$
$43$	4.07080	−	2.35028i	0.620791	−	0.358414i	0.777177	+	0.629282i	$0.216651\pi$
$44$	−0.0299712	+	0.0768920i	−0.00451833	+	0.0115919i
$45$		0			0
$46$	−4.86317	−	7.11513i	−0.717035	−	1.04907i
$47$	0.400516			0.0584213			0.0292106	−	0.999573i	$-0.490701\pi$
$47$	0.400516			0.0584213			0.0292106	+	0.999573i	$0.490701\pi$
$48$		0			0
$49$	5.23252	+	4.64982i	0.747502	+	0.664259i
$50$	2.25068	−	4.68756i	0.318295	−	0.662921i
$51$		0			0
$52$	−4.22318	+	10.8347i	−0.585649	+	1.50250i
$53$	−5.08527	+	2.93598i	−0.698516	+	0.403288i	−0.806795	−	0.590832i	$-0.798800\pi$
$53$	−5.08527	+	2.93598i	−0.698516	+	0.403288i	0.108278	+	0.994121i	$0.465466\pi$
$54$		0			0
$55$			0.0474640i			0.00640005i
$56$	7.41487	+	1.00981i	0.990853	+	0.134942i
$57$		0			0
$58$	−8.69698	+	5.94436i	−1.14197	+	0.780533i
$59$	10.4137			1.35575			0.677875	−	0.735177i	$-0.262901\pi$
$59$	10.4137			1.35575			0.677875	+	0.735177i	$0.262901\pi$
$60$		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	$-0.0186198\pi$
$68$	4.62042	−	3.70231i	0.560308	−	0.448971i
$69$		0			0
$70$	4.18431	−	1.00763i	0.500121	−	0.120435i
$71$	−1.28212			−0.152159			−0.0760796	−	0.997102i	$-0.524240\pi$
$71$	−1.28212			−0.152159			−0.0760796	+	0.997102i	$0.524240\pi$
$72$		0			0
$73$	1.36920	+	2.37152i	0.160252	+	0.277565i	0.934959	−	0.354756i	$-0.115436\pi$
$73$	1.36920	+	2.37152i	0.160252	+	0.277565i	−0.774707	+	0.632321i	$0.782103\pi$
$74$	−4.82860	+	10.0567i	−0.561313	+	1.16906i
$75$		0			0
$76$	13.5519	+	5.28229i	1.55451	+	0.605920i
$77$	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	$0.875350\pi$
$80$	3.11378	−	3.38739i	0.348131	−	0.378722i
$81$		0			0
$82$	−2.98227	−	1.43190i	−0.329336	−	0.158127i
$83$	6.87088	+	11.9007i	0.754177	+	1.30627i	0.945782	+	0.324801i	$0.105297\pi$
$83$	6.87088	+	11.9007i	0.754177	+	1.30627i	−0.191605	+	0.981472i	$0.561369\pi$
$84$		0			0
$85$	1.70262	−	2.94902i	0.184675	−	0.319867i
$86$	−5.48812	+	3.75112i	−0.591799	+	0.404493i
$87$		0			0
$88$	0.0340108	−	0.111645i	0.00362556	−	0.0119014i
$89$	0.578834	+	0.334190i	0.0613562	+	0.0354240i	0.530364	−	0.847770i	$-0.322055\pi$
$89$	0.578834	+	0.334190i	0.0613562	+	0.0354240i	−0.469008	+	0.883194i	$0.655388\pi$
$90$		0			0
$91$	11.9233	−	9.72001i	1.24991	−	1.01893i
$92$	7.62138	+	9.51134i	0.794584	+	0.991625i
$93$		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	0.743563	−	0.668665i	$-0.233134\pi$
$97$	−2.04166	−	3.53626i	−0.207299	−	0.359053i	−0.950863	+	0.309612i	$0.899801\pi$
$98$	−7.87761	−	5.99527i	−0.795759	−	0.605614i
$99$		0			0
$100$	−2.67066	+	6.85166i	−0.267066	+	0.685166i
$101$	−11.6375	−	6.71893i	−1.15798	−	0.668558i	−0.207158	−	0.978307i	$-0.566422\pi$
$101$	−11.6375	−	6.71893i	−1.15798	−	0.668558i	−0.950818	+	0.309749i	$0.899755\pi$
$102$		0			0
$103$	9.67731	−	5.58720i	0.953534	−	0.550523i	0.0593570	−	0.998237i	$-0.481095\pi$
$103$	9.67731	−	5.58720i	0.953534	−	0.550523i	0.894177	+	0.447714i	$0.147762\pi$
$104$	4.79238	−	15.7316i	0.469932	−	1.54261i
$105$		0			0
$106$	6.85581	−	4.68593i	0.665895	−	0.455137i
$107$	−5.65631	+	9.79702i	−0.546816	+	0.947114i	0.451674	+	0.892183i	$0.350827\pi$
$107$	−5.65631	+	9.79702i	−0.546816	+	0.947114i	−0.998490	+	0.0549307i	$0.982506\pi$
$108$		0			0
$109$	2.33792	+	4.04939i	0.223932	+	0.387861i	0.955998	−	0.293372i	$-0.0947774\pi$
$109$	2.33792	+	4.04939i	0.223932	+	0.387861i	−0.732067	+	0.681233i	$0.761444\pi$
$110$	−0.00509422	−	0.0669307i	−0.000485715	−	0.00638159i
$111$		0			0
$112$	−10.5643	−	0.628150i	−0.998237	−	0.0593546i
$113$	−0.248562	−	0.143507i	−0.0233827	−	0.0135000i	0.488263	−	0.872696i	$-0.337631\pi$
$113$	−0.248562	−	0.143507i	−0.0233827	−	0.0135000i	−0.511646	+	0.859196i	$0.670964\pi$
$114$		0			0
$115$	6.07070	+	3.50492i	0.566096	+	0.326836i
$116$	11.6259	−	9.31579i	1.07944	−	0.864949i
$117$		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	$-0.171014\pi$
$131$	−0.156314	−	0.270744i	−0.0136572	−	0.0236550i	−0.872773	+	0.488126i	$0.837681\pi$
$132$		0			0
$133$	−12.1577	−	14.9135i	−1.05420	−	1.29317i
$134$	0.102721	+	1.34960i	0.00887373	+	0.116588i
$135$		0			0
$136$	−6.11805	+	5.71666i	−0.524618	+	0.490200i
$137$	−7.85803	−	4.53684i	−0.671357	−	0.387608i	0.125234	−	0.992127i	$-0.460032\pi$
$137$	−7.85803	−	4.53684i	−0.671357	−	0.387608i	−0.796591	+	0.604519i	$0.793365\pi$
$138$		0			0
$139$	0.645404	+	0.372624i	0.0547424	+	0.0316056i	0.527121	−	0.849790i	$-0.323271\pi$
$139$	0.645404	+	0.372624i	0.0547424	+	0.0316056i	−0.472379	+	0.881396i	$0.656605\pi$
$140$	−5.79229	+	1.86999i	−0.489538	+	0.158043i
$141$		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
$146$	−2.18528	−	3.19721i	−0.180855	−	0.264603i
$147$		0			0
$148$	5.72961	−	14.6995i	0.470971	−	1.20829i
$149$	−13.0161	+	7.51484i	−1.06632	+	0.615640i	−0.927174	−	0.374632i	$-0.877769\pi$
$149$	−13.0161	+	7.51484i	−1.06632	+	0.615640i	−0.139146	+	0.990272i	$0.544436\pi$
$150$		0			0
$151$	−9.22723	−	5.32734i	−0.750901	−	0.433533i	0.0751182	−	0.997175i	$-0.476067\pi$
$151$	−9.22723	−	5.32734i	−0.750901	−	0.433533i	−0.826019	+	0.563642i	$0.809400\pi$
$152$	−19.6769	−	5.99425i	−1.59601	−	0.486198i
$153$		0			0
$154$	−0.111919	+	0.106355i	−0.00901870	+	0.00857032i
$155$	−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
$160$	−4.02728	+	5.11087i	−0.318385	+	0.404050i
$161$	−2.57428	−	15.9166i	−0.202882	−	1.25440i
$162$		0			0
$163$	−10.5970	−	6.11821i	−0.830025	−	0.479215i	0.0238365	−	0.999716i	$-0.492412\pi$
$163$	−10.5970	−	6.11821i	−0.830025	−	0.479215i	−0.853861	+	0.520501i	$0.825745\pi$
$164$	4.35908	+	1.69910i	0.340387	+	0.132677i
$165$		0			0
$166$	−10.9662	−	16.0442i	−0.851138	−	1.24527i
$167$	4.78444	−	8.28690i	0.370231	−	0.641259i	−0.619370	−	0.785100i	$-0.712612\pi$
$167$	4.78444	−	8.28690i	0.370231	−	0.641259i	0.989601	+	0.143840i	$0.0459451\pi$
$168$		0			0
$169$	−10.4032	−	18.0188i	−0.800245	−	1.38607i
$170$	−2.08441	+	4.34126i	−0.159867	+	0.332960i
$171$		0			0
$172$	7.33639	−	5.87861i	0.559395	−	0.448240i
$173$			20.3532i			1.54742i	0.633538	+	0.773711i	$0.281602\pi$
$173$			20.3532i			1.54742i	−0.633538	+	0.773711i	$0.718398\pi$
$174$		0			0
$175$	7.54010	−	6.14676i	0.569978	−	0.464651i
$176$	−0.0359772	+	0.161085i	−0.00271188	+	0.0121422i
$177$		0			0
$178$	−0.852102	−	0.409128i	−0.0638677	−	0.0306654i
$179$	−11.8952	−	20.6031i	−0.889089	−	1.53995i	−0.840954	−	0.541106i	$-0.818006\pi$
$179$	−11.8952	−	20.6031i	−0.889089	−	1.53995i	−0.0481342	−	0.998841i	$-0.515328\pi$
$180$		0			0
$181$	15.3783			1.14306			0.571530	−	0.820581i	$-0.306350\pi$
$181$	15.3783			1.14306			0.571530	+	0.820581i	$0.306350\pi$
$182$	−15.7703	+	14.9862i	−1.16897	+	1.11085i
$183$		0			0
$184$	−11.7680	−	12.5943i	−0.867549	−	0.928463i
$185$		−	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	$-0.422657\pi$
$191$	6.65024			0.481194			0.240597	+	0.970625i	$0.422657\pi$
$192$		0			0
$193$	−6.14756			−0.442511			−0.221255	−	0.975216i	$-0.571015\pi$
$193$	−6.14756			−0.442511			−0.221255	+	0.975216i	$0.571015\pi$
$194$	3.25856	+	4.76748i	0.233951	+	0.342285i
$195$		0			0
$196$	11.7520	+	7.60865i	0.839425	+	0.543475i
$197$		−	13.2243i		−	0.942196i	−0.882081	−	0.471098i	$-0.843858\pi$
$197$		−	13.2243i		−	0.942196i	0.882081	−	0.471098i	$-0.156142\pi$
$198$		0			0
$199$	−14.4456	+	8.34019i	−1.02402	+	0.591221i	−0.915267	−	0.402848i	$-0.868020\pi$
$199$	−14.4456	+	8.34019i	−1.02402	+	0.591221i	−0.108757	+	0.994068i	$0.534687\pi$
$200$	3.03062	−	9.94840i	0.214297	−	0.703458i
$201$		0			0
$202$	17.1316	+	8.22556i	1.20538	+	0.578748i
$203$	−19.4552	+	3.14660i	−1.36549	+	0.220848i
$204$		0			0
$205$	2.69078			0.187933
$206$	−13.0467	+	8.91735i	−0.909003	+	0.621301i
$207$		0			0
$208$	−5.06946	+	22.6981i	−0.351504	+	1.57383i
$209$	−0.259883	+	0.150043i	−0.0179765	+	0.0103787i
$210$		0			0
$211$	−1.95991	−	1.13155i	−0.134926	−	0.0778994i	0.431018	−	0.902343i	$-0.358155\pi$
$211$	−1.95991	−	1.13155i	−0.134926	−	0.0778994i	−0.565943	+	0.824444i	$0.691488\pi$
$212$	−9.16469	+	7.34361i	−0.629433	+	0.504361i
$213$		0			0
$214$	6.92467	−	14.4222i	0.473361	−	0.985882i
$215$	2.70346	−	4.68252i	0.184374	−	0.319345i
$216$		0			0
$217$	−2.00031	+	5.26233i	−0.135790	+	0.357230i
$218$	−3.73139	−	5.45926i	−0.252722	−	0.369748i
$219$		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	$-0.556306\pi$
$223$	8.78900	−	5.07433i	0.588555	−	0.339802i	0.764526	+	0.644593i	$0.222973\pi$
$224$	14.9646	−	0.248075i	0.999863	−	0.0165752i
$225$		0			0
$226$	0.365908	+	0.175687i	0.0243398	+	0.0116865i
$227$	−1.46754	+	2.54186i	−0.0974044	+	0.168709i	−0.910610	−	0.413268i	$-0.864387\pi$
$227$	−1.46754	+	2.54186i	−0.0974044	+	0.168709i	0.813205	+	0.581977i	$0.197721\pi$
$228$		0			0
$229$	−0.221879	−	0.384305i	−0.0146622	−	0.0253956i	0.858601	−	0.512644i	$-0.171334\pi$
$229$	−0.221879	−	0.384305i	−0.0146622	−	0.0253956i	−0.873263	+	0.487248i	$0.838001\pi$
$230$	−8.93669	−	4.29086i	−0.589268	−	0.282931i
$231$		0			0
$232$	−15.3943	+	14.3843i	−1.01068	+	0.944376i
$233$	13.3304	+	7.69631i	0.873304	+	0.504202i	0.868445	−	0.495786i	$-0.165120\pi$
$233$	13.3304	+	7.69631i	0.873304	+	0.504202i	0.00485893	+	0.999988i	$0.498453\pi$
$234$		0			0
$235$	0.398980	−	0.230351i	0.0260266	−	0.0150265i
$236$	20.5875	−	3.15217i	1.34013	−	0.205189i
$237$		0			0
$238$	10.7689	−	2.59328i	0.698042	−	0.168097i
$239$	4.34671	−	7.52872i	0.281165	−	0.486992i	−0.690507	−	0.723326i	$-0.742612\pi$
$239$	4.34671	−	7.52872i	0.281165	−	0.486992i	0.971672	+	0.236334i	$0.0759458\pi$
$240$		0			0
$241$	1.78759	−	3.09620i	0.115149	−	0.199444i	−0.802690	−	0.596396i	$-0.796599\pi$
$241$	1.78759	−	3.09620i	0.115149	−	0.199444i	0.917839	+	0.396952i	$0.129932\pi$
$242$	−8.77682	−	12.8410i	−0.564195	−	0.825454i
$243$		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	$-0.326227\pi$
$251$	16.4516			1.03842			0.519209	+	0.854647i	$0.326227\pi$
$252$		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	0.390983	−	0.920398i	$-0.372135\pi$
$257$	22.1802	−	12.8057i	1.38356	−	0.798800i	0.992579	+	0.121598i	$0.0388019\pi$
$258$		0			0
$259$	−16.1765	+	13.1872i	−1.00516	+	0.819413i
$260$	2.02443	+	13.2220i	0.125550	+	0.819995i
$261$		0			0
$262$	0.249482	+	0.365009i	0.0154131	+	0.0225503i
$263$	6.45004	−	11.1718i	0.397727	−	0.688883i	−0.595718	−	0.803193i	$-0.703133\pi$
$263$	6.45004	−	11.1718i	0.397727	−	0.688883i	0.993445	+	0.114311i	$0.0364659\pi$
$264$		0			0
$265$	−3.37718	+	5.84945i	−0.207459	+	0.359329i
$266$	18.7446	+	19.7253i	1.14930	+	1.20943i
$267$		0			0
$268$	−0.289701	−	1.89210i	−0.0176963	−	0.115578i
$269$	6.13886	−	3.54427i	0.374293	−	0.216098i	−0.301039	−	0.953612i	$-0.597334\pi$
$269$	6.13886	−	3.54427i	0.374293	−	0.216098i	0.675332	+	0.737514i	$0.264000\pi$
$270$		0			0
$271$	−6.46932	−	3.73506i	−0.392983	−	0.226889i	0.290469	−	0.956884i	$-0.406189\pi$
$271$	−6.46932	−	3.73506i	−0.392983	−	0.226889i	−0.683452	+	0.729996i	$0.739522\pi$
$272$	8.01371	−	8.71790i	0.485903	−	0.528600i
$273$		0			0
$274$	11.5678	+	5.55416i	0.698837	+	0.335539i
$275$	−0.0758600	−	0.131393i	−0.00457453	−	0.00792332i
$276$		0			0
$277$	−10.7618	+	18.6400i	−0.646614	+	1.11997i	0.337312	+	0.941393i	$0.390482\pi$
$277$	−10.7618	+	18.6400i	−0.646614	+	1.11997i	−0.983926	+	0.178576i	$0.942851\pi$
$278$	−0.950100	−	0.456180i	−0.0569832	−	0.0273599i
$279$		0			0
$280$	7.96721	−	3.25862i	0.476132	−	0.194740i
$281$	5.67950	−	3.27906i	0.338810	−	0.195612i	−0.320935	−	0.947101i	$-0.603997\pi$
$281$	5.67950	−	3.27906i	0.338810	−	0.195612i	0.659746	+	0.751489i	$0.270664\pi$
$282$		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
$286$	0.191459	+	0.280116i	0.0113212	+	0.0165636i
$287$	−3.91062	−	4.79708i	−0.230837	−	0.283163i
$288$		0			0
$289$	−4.11808	+	7.13272i	−0.242240	+	0.419572i
$290$	−5.24481	+	10.9235i	−0.307986	+	0.641451i
$291$		0			0
$292$	3.42469	+	4.27395i	0.200415	+	0.250114i
$293$	−21.7642	−	12.5656i	−1.27148	−	0.734089i	−0.296213	−	0.955122i	$-0.595724\pi$
$293$	−21.7642	−	12.5656i	−1.27148	−	0.734089i	−0.975266	+	0.221033i	$0.929057\pi$
$294$		0			0
$295$	10.3738	−	5.98931i	0.603985	−	0.348711i
$296$	−6.50186	+	21.3432i	−0.377913	+	1.24055i
$297$		0			0
$298$	17.5479	−	11.9939i	1.01652	−	0.694790i
$299$	−35.4329			−2.04914
$300$		0			0
$301$	−12.2770	+	1.98563i	−0.707632	+	0.114450i
$302$	13.5834	+	6.52193i	0.781638	+	0.375295i
$303$		0			0
$304$	28.3904	+	6.34081i	1.62830	+	0.363671i
$305$	−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	$-0.112921\pi$
$308$	0.146406	−	0.161987i	0.00834227	−	0.00923006i
$309$		0			0
$310$	1.95320	+	2.85766i	0.110935	+	0.162304i
$311$	−11.8754			−0.673394			−0.336697	−	0.941613i	$-0.609310\pi$
$311$	−11.8754			−0.673394			−0.336697	+	0.941613i	$0.609310\pi$
$312$		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	$-0.674523\pi$
$317$		−	30.3895i		−	1.70684i	0.521220	−	0.853422i	$-0.325477\pi$
$318$		0			0
$319$			0.307367i			0.0172093i
$320$	5.13047	−	7.63926i	0.286802	−	0.427048i
$321$		0			0
$322$	5.33838	+	22.1682i	0.297496	+	1.23539i
$323$	21.5293			1.19792
$324$		0			0
$325$	−10.6893	−	18.5144i	−0.592934	−	1.02699i
$326$	15.5999	+	7.49014i	0.864000	+	0.414840i
$327$		0			0
$328$	−6.32926	−	1.92810i	−0.349475	−	0.106462i
$329$	−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	$-0.311716\pi$
$332$	17.1857	+	21.4475i	0.943190	+	1.17708i
$333$		0			0
$334$	−5.85729	+	12.1992i	−0.320497	+	0.667508i
$335$	−0.550448	−	0.953404i	−0.0300742	−	0.0520900i
$336$		0			0
$337$	−10.9483	+	18.9630i	−0.596392	+	1.03298i	0.396957	+	0.917837i	$0.370066\pi$
$337$	−10.9483	+	18.9630i	−0.596392	+	1.03298i	−0.993349	+	0.115144i	$0.963267\pi$
$338$	16.6038	+	24.2925i	0.903129	+	1.32134i
$339$		0			0
$340$	2.47336	−	6.34548i	0.134137	−	0.344132i
$341$	0.0760379	+	0.0439005i	0.00411768	+	0.00237735i
$342$		0			0
$343$	−8.56939	−	16.4185i	−0.462704	−	0.886513i
$344$	−9.71437	+	9.07703i	−0.523763	+	0.489401i
$345$		0			0
$346$	−2.18447	−	28.7007i	−0.117438	−	1.54296i
$347$	−29.4348			−1.58014			−0.790071	−	0.613015i	$-0.789956\pi$
$347$	−29.4348			−1.58014			−0.790071	+	0.613015i	$0.789956\pi$
$348$		0			0
$349$	10.4396	+	18.0819i	0.558817	+	0.967900i	0.997596	+	0.0693043i	$0.0220780\pi$
$349$	10.4396	+	18.0819i	0.558817	+	0.967900i	−0.438778	+	0.898595i	$0.644589\pi$
$350$	−9.97284	+	9.47703i	−0.533071	+	0.506568i
$351$		0			0
$352$	0.0334438	−	0.231012i	0.00178256	−	0.0123130i
$353$	24.8005	+	14.3186i	1.32000	+	0.762101i	0.983728	−	0.179665i	$-0.0575014\pi$
$353$	24.8005	+	14.3186i	1.32000	+	0.762101i	0.336269	+	0.941766i	$0.390835\pi$
$354$		0			0
$355$	−1.27720	+	0.737391i	−0.0677867	+	0.0391367i
$356$	1.24549	+	0.485471i	0.0660108	+	0.0257299i
$357$		0			0
$358$	18.9851	+	27.7764i	1.00339	+	1.46803i
$359$	−5.54691	+	9.60753i	−0.292755	+	0.507066i	−0.974460	−	0.224561i	$-0.927905\pi$
$359$	−5.54691	+	9.60753i	−0.292755	+	0.507066i	0.681705	+	0.731627i	$0.261239\pi$
$360$		0			0
$361$	16.9445	+	29.3487i	0.891814	+	1.54467i
$362$	−21.6855	+	1.65052i	−1.13976	+	0.0867495i
$363$		0			0
$364$	20.6298	−	22.8252i	1.08129	−	1.19637i
$365$	2.72789	+	1.57495i	0.142784	+	0.0824365i
$366$		0			0
$367$	0.671527	+	0.387706i	0.0350534	+	0.0202381i	0.517424	−	0.855729i	$-0.326891\pi$
$367$	0.671527	+	0.387706i	0.0350534	+	0.0202381i	−0.482371	+	0.875967i	$0.660224\pi$
$368$	17.9462	+	16.4966i	0.935510	+	0.859945i
$369$		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	−0.999956	−	0.00940290i	$-0.997007\pi$
$373$	−9.81345	−	16.9974i	−0.508121	−	0.880091i	0.491835	−	0.870689i	$-0.336326\pi$
$374$	−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	$-0.252136\pi$
$383$	−5.19194	−	8.99271i	−0.265296	−	0.459506i	−0.967641	+	0.252330i	$0.918803\pi$
$384$		0			0
$385$	0.0446198	−	0.117384i	0.00227404	−	0.00598243i
$386$	8.66888	−	0.659805i	0.441235	−	0.0335832i
$387$		0			0
$388$	−5.10670	−	6.37306i	−0.259253	−	0.323543i
$389$	−23.9732	−	13.8409i	−1.21549	−	0.701762i	−0.251538	−	0.967847i	$-0.580936\pi$
$389$	−23.9732	−	13.8409i	−1.21549	−	0.701762i	−0.963950	+	0.266085i	$0.914270\pi$
$390$		0			0
$391$	15.6238	+	9.02038i	0.790127	+	0.456180i
$392$	−17.3885	−	9.46791i	−0.878250	−	0.478202i
$393$		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	−0.153126	−	0.988207i	$-0.548934\pi$
$397$	15.5264	−	26.8926i	0.779249	−	1.34970i	0.932375	−	0.361492i	$-0.117733\pi$
$398$	19.4752	−	13.3112i	0.976202	−	0.667231i
$399$		0			0
$400$	−3.20584	+	14.3539i	−0.160292	+	0.717693i
$401$	25.3125	−	14.6142i	1.26404	−	0.729796i	0.290190	−	0.956969i	$-0.406282\pi$
$401$	25.3125	−	14.6142i	1.26404	−	0.729796i	0.973854	+	0.227173i	$0.0729483\pi$
$402$		0			0
$403$	10.7143	+	6.18592i	0.533719	+	0.308143i
$404$	−25.0407	−	9.76045i	−1.24582	−	0.485601i
$405$		0			0
$406$	27.0967	−	6.52522i	1.34479	−	0.323841i
$407$	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
$412$	17.4405	−	13.9749i	0.859230	−	0.688496i
$413$	−25.7542	−	9.78968i	−1.26728	−	0.481719i
$414$		0			0
$415$	13.6891	+	7.90338i	0.671970	+	0.387962i
$416$	4.71249	−	32.5514i	0.231049	−	1.59597i
$417$		0			0
$418$	0.350366	−	0.239474i	0.0171369	−	0.0117131i
$419$	−0.375709	+	0.650747i	−0.0183546	+	0.0317911i	−0.875057	−	0.484020i	$-0.839176\pi$
$419$	−0.375709	+	0.650747i	−0.0183546	+	0.0317911i	0.856702	+	0.515811i	$0.172509\pi$
$420$		0			0
$421$	−12.5491	−	21.7357i	−0.611605	−	1.05933i	−0.990970	−	0.134084i	$-0.957191\pi$
$421$	−12.5491	−	21.7357i	−0.611605	−	1.05933i	0.379365	−	0.925247i	$-0.376142\pi$
$422$	2.88518	+	1.38529i	0.140449	+	0.0674349i
$423$		0			0
$424$	12.1353	−	11.3391i	0.589341	−	0.550676i
$425$			10.8849i			0.527997i
$426$		0			0
$427$	3.38254	+	1.28577i	0.163692	+	0.0622226i
$428$	−8.21681	+	21.0805i	−0.397175	+	1.01896i
$429$		0			0
$430$	−3.30967	+	6.89315i	−0.159607	+	0.332417i
$431$	6.13030	+	10.6180i	0.295286	+	0.511451i	0.975051	−	0.221979i	$-0.0712517\pi$
$431$	6.13030	+	10.6180i	0.295286	+	0.511451i	−0.679765	+	0.733430i	$0.737918\pi$
$432$		0			0
$433$	12.9845			0.623996			0.311998	−	0.950083i	$-0.399002\pi$
$433$	12.9845			0.623996			0.311998	+	0.950083i	$0.399002\pi$
$434$	2.25592	−	7.63529i	0.108287	−	0.366506i
$435$		0			0
$436$	5.84769	+	7.29781i	0.280054	+	0.349502i
$437$			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	$-0.539702\pi$
$443$	−5.23677			−0.248806			−0.124403	+	0.992232i	$0.539702\pi$
$444$		0			0
$445$	0.768818			0.0364455
$446$	−11.8491	+	8.09880i	−0.561069	+	0.383489i
$447$		0			0
$448$	−21.0754	+	1.95594i	−0.995721	+	0.0924094i
$449$		−	15.8939i		−	0.750082i	−0.927008	−	0.375041i	$-0.877629\pi$
$449$		−	15.8939i		−	0.750082i	0.927008	−	0.375041i	$-0.122371\pi$
$450$		0			0
$451$	−0.0835936	+	0.0482628i	−0.00393627	+	0.00227261i
$452$	−0.534836	−	0.208470i	−0.0251566	−	0.00980561i
$453$		0			0
$454$	1.79662	−	3.74188i	0.0843197	−	0.175615i
$455$	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	$0.526820\pi$
$458$	0.354126	+	0.518108i	0.0165472	+	0.0242096i
$459$		0			0
$460$	13.0625	+	5.09153i	0.609040	+	0.237394i
$461$	13.1236	−	7.57692i	0.611228	−	0.352892i	−0.162218	−	0.986755i	$-0.551865\pi$
$461$	13.1236	−	7.57692i	0.611228	−	0.352892i	0.773446	+	0.633862i	$0.218531\pi$
$462$		0			0
$463$	−22.8810	−	13.2104i	−1.06337	−	0.613938i	−0.137009	−	0.990570i	$-0.543749\pi$
$463$	−22.8810	−	13.2104i	−1.06337	−	0.613938i	−0.926363	+	0.376632i	$0.877082\pi$
$464$	20.1642	−	21.9360i	0.936098	−	1.01836i
$465$		0			0
$466$	−19.6237	−	9.42211i	−0.909050	−	0.436471i
$467$	11.6787	−	20.2281i	0.540426	−	0.936045i	−0.458454	−	0.888718i	$-0.651597\pi$
$467$	11.6787	−	20.2281i	0.540426	−	0.936045i	0.998879	−	0.0473266i	$-0.0150702\pi$
$468$		0			0
$469$	−0.899722	+	2.36695i	−0.0415453	+	0.109295i
$470$	−0.537893	+	0.367648i	−0.0248111	+	0.0169583i
$471$		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
$476$	−14.9072	+	4.81267i	−0.683272	+	0.220589i
$477$		0			0
$478$	−5.32140	+	11.0830i	−0.243395	+	0.506926i
$479$	−3.49034	+	6.04545i	−0.159478	+	0.276224i	−0.934680	−	0.355489i	$-0.884314\pi$
$479$	−3.49034	+	6.04545i	−0.159478	+	0.276224i	0.775203	+	0.631713i	$0.217648\pi$
$480$		0			0
$481$	22.9327	+	39.7206i	1.04564	+	1.81110i
$482$	−2.18844	+	4.55792i	−0.0996805	+	0.207607i
$483$		0			0
$484$	13.7547	+	17.1656i	0.625214	+	0.780255i
$485$	−4.06767	−	2.34847i	−0.184703	−	0.106638i
$486$		0			0
$487$	−7.56727	+	4.36896i	−0.342906	+	0.197977i	−0.661556	−	0.749896i	$-0.730104\pi$
$487$	−7.56727	+	4.36896i	−0.342906	+	0.197977i	0.318651	+	0.947872i	$0.396770\pi$
$488$	3.76849	−	0.874009i	0.170592	−	0.0395645i
$489$		0			0
$490$	−11.2955	−	1.44158i	−0.510278	−	0.0651240i
$491$	−14.3700	+	24.8895i	−0.648508	+	1.12325i	0.334972	+	0.942228i	$0.391273\pi$
$491$	−14.3700	+	24.8895i	−0.648508	+	1.12325i	−0.983479	+	0.181020i	$0.942060\pi$
$492$		0			0
$493$	11.0258	−	19.0973i	0.496578	−	0.860098i
$494$	49.3693	−	33.7438i	2.22123	−	1.51820i
$495$		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	$-0.757285\pi$
$499$	−10.8666	+	6.27382i	−0.486454	+	0.280855i	0.236648	+	0.971595i	$0.423951\pi$
$500$	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	$-0.551910\pi$
$503$	−7.28257			−0.324714			−0.162357	+	0.986732i	$0.551910\pi$
$504$		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	−0.0982986	−	0.995157i	$-0.531340\pi$
$509$	16.1172	−	9.30528i	0.714383	−	0.412449i	0.812682	+	0.582708i	$0.198007\pi$
$510$		0			0
$511$	−1.15676	−	7.15216i	−0.0511721	−	0.316393i
$512$	−17.5419	+	14.2928i	−0.775248	+	0.631657i
$513$		0			0
$514$	−29.9026	+	20.4384i	−1.31895	+	0.901498i
$515$	6.42680	−	11.1315i	0.283199	−	0.490514i
$516$		0			0
$517$	−0.00826331	+	0.0143125i	−0.000363420	+	0.000629462i
$518$	21.3957	−	20.3319i	0.940071	−	0.893334i
$519$		0			0
$520$	−4.27382	−	18.4276i	−0.187419	−	0.808102i
$521$	13.4091	−	7.74176i	0.587464	−	0.339172i	−0.176630	−	0.984277i	$-0.556520\pi$
$521$	13.4091	−	7.74176i	0.587464	−	0.339172i	0.764094	+	0.645105i	$0.223186\pi$
$522$		0			0
$523$	−30.4929	−	17.6051i	−1.33336	−	0.769818i	−0.347550	−	0.937662i	$-0.612986\pi$
$523$	−30.4929	−	17.6051i	−1.33336	−	0.769818i	−0.985814	+	0.167844i	$0.946320\pi$
$524$	−0.390980	−	0.487935i	−0.0170800	−	0.0213155i
$525$		0			0
$526$	−7.89638	+	16.4460i	−0.344299	+	0.717081i
$527$	−3.14958	−	5.45523i	−0.137198	−	0.237634i
$528$		0			0
$529$	−7.06887	+	12.2436i	−0.307342	+	0.532332i
$530$	4.13447	−	8.61098i	0.179590	−	0.374037i
$531$		0			0
$532$	−28.5495	−	25.8035i	−1.23778	−	1.11872i
$533$	−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
$538$	−8.27622	+	5.65677i	−0.356813	+	0.243881i
$539$	−0.274117	+	0.0910510i	−0.0118071	+	0.00392184i
$540$		0			0
$541$	3.06242	−	5.30426i	0.131664	−	0.228048i	−0.792654	−	0.609671i	$-0.791301\pi$
$541$	3.06242	−	5.30426i	0.131664	−	0.228048i	0.924318	+	0.381623i	$0.124635\pi$
$542$	9.52349	+	4.57260i	0.409069	+	0.196410i
$543$		0			0
$544$	−10.3647	+	13.1535i	−0.444385	+	0.563952i
$545$	4.65790	+	2.68924i	0.199522	+	0.115194i
$546$		0			0
$547$	16.2992	−	9.41033i	0.696902	−	0.402357i	−0.109290	−	0.994010i	$-0.534858\pi$
$547$	16.2992	−	9.41033i	0.696902	−	0.402357i	0.806193	+	0.591653i	$0.201525\pi$
$548$	−16.9083	−	6.59057i	−0.722287	−	0.281535i
$549$		0			0
$550$	0.121075	+	0.177141i	0.00516266	+	0.00755330i
$551$	54.1721			2.30781
$552$		0			0
$553$	6.37810	−	16.7792i	0.271225	−	0.713525i
$554$	13.1750	−	27.4399i	0.559752	−	1.16581i
$555$		0			0
$556$	1.38873	+	0.541304i	0.0588953	+	0.0229564i
$557$	−33.9310	+	19.5901i	−1.43770	+	0.830057i	−0.997690	−	0.0679349i	$-0.978359\pi$
$557$	−33.9310	+	19.5901i	−1.43770	+	0.830057i	−0.440012	+	0.897992i	$0.645026\pi$
$558$		0			0
$559$			27.3305i			1.15596i
$560$	−10.8851	+	5.45020i	−0.459980	+	0.230313i
$561$		0			0
$562$	−7.65692	+	5.23348i	−0.322988	+	0.220761i
$563$	10.8051			0.455380			0.227690	−	0.973734i	$-0.426883\pi$
$563$	10.8051			0.455380			0.227690	+	0.973734i	$0.426883\pi$
$564$		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	$0.134877\pi$
$569$			19.6155i			0.822326i	−0.911562	+	0.411163i	$0.865123\pi$
$570$		0			0
$571$		−	25.1755i		−	1.05356i	−0.850001	−	0.526781i	$-0.823399\pi$
$571$		−	25.1755i		−	1.05356i	0.850001	−	0.526781i	$-0.176601\pi$
$572$	−0.300047	−	0.374453i	−0.0125456	−	0.0156567i
$573$		0			0
$574$	6.02937	+	6.34481i	0.251661	+	0.264827i
$575$	−22.4071			−0.934442
$576$		0			0
$577$	−6.37775	−	11.0466i	−0.265509	−	0.459876i	0.702188	−	0.711992i	$-0.252207\pi$
$577$	−6.37775	−	11.0466i	−0.265509	−	0.459876i	−0.967697	+	0.252116i	$0.918873\pi$
$578$	5.04151	−	10.5001i	0.209699	−	0.436746i
$579$		0			0
$580$	6.22349	−	15.9665i	0.258416	−	0.662975i
$581$	−5.80485	−	35.8909i	−0.240826	−	1.48901i
$582$		0			0
$583$		−	0.242297i		−	0.0100349i
$584$	−5.28799	−	5.65928i	−0.218819	−	0.234183i
$585$		0			0
$586$	32.0391	+	15.3833i	1.32352	+	0.635476i
$587$	−17.1705	−	29.7401i	−0.708702	−	1.22751i	−0.965339	−	0.260999i	$-0.915948\pi$
$587$	−17.1705	−	29.7401i	−0.708702	−	1.22751i	0.256637	−	0.966508i	$-0.417385\pi$
$588$		0			0
$589$	7.73727	−	13.4013i	0.318809	−	0.552193i
$590$	−13.9856	+	9.55913i	−0.575779	+	0.393543i
$591$		0			0
$592$	6.87778	−	30.7946i	0.282675	−	1.26565i
$593$	40.1331	+	23.1709i	1.64807	+	0.951514i	0.977838	+	0.209363i	$0.0671391\pi$
$593$	40.1331	+	23.1709i	1.64807	+	0.951514i	0.670233	+	0.742151i	$0.266194\pi$
$594$		0			0
$595$	−6.98307	+	5.69266i	−0.286278	+	0.233376i
$596$	−23.4576	+	18.7964i	−0.960861	+	0.769932i
$597$		0			0
$598$	49.9652	−	3.80295i	2.04323	−	0.155514i
$599$	−14.1024			−0.576208			−0.288104	−	0.957599i	$-0.593025\pi$
$599$	−14.1024			−0.576208			−0.288104	+	0.957599i	$0.593025\pi$
$600$		0			0
$601$	−6.34404	−	10.9882i	−0.258779	−	0.448218i	0.707136	−	0.707077i	$-0.249987\pi$
$601$	−6.34404	−	10.9882i	−0.258779	−	0.448218i	−0.965915	+	0.258859i	$0.916653\pi$
$602$	17.0990	−	4.11766i	0.696905	−	0.167823i
$603$		0			0
$604$	−19.8544	−	7.73892i	−0.807865	−	0.314892i
$605$	10.9561	+	6.32552i	0.445429	+	0.257169i
$606$		0			0
$607$	29.6669	−	17.1282i	1.20414	−	0.695211i	0.242668	−	0.970109i	$-0.421978\pi$
$607$	29.6669	−	17.1282i	1.20414	−	0.695211i	0.961473	+	0.274898i	$0.0886442\pi$
$608$	−40.7149	−	5.89431i	−1.65121	−	0.239046i
$609$		0			0
$610$	1.83686	−	1.25549i	0.0743721	−	0.0508331i
$611$	−1.16437	+	2.01674i	−0.0471052	+	0.0815886i
$612$		0			0
$613$	−1.88844	−	3.27087i	−0.0762734	−	0.132109i	0.825366	−	0.564598i	$-0.190969\pi$
$613$	−1.88844	−	3.27087i	−0.0762734	−	0.132109i	−0.901639	+	0.432489i	$0.857636\pi$
$614$	1.30644	+	17.1647i	0.0527235	+	0.692710i
$615$		0			0
$616$	−0.189067	+	0.244137i	−0.00761772	+	0.00983655i
$617$	−22.7647	−	13.1432i	−0.916470	−	0.529124i	−0.0339631	−	0.999423i	$-0.510813\pi$
$617$	−22.7647	−	13.1432i	−0.916470	−	0.529124i	−0.882507	+	0.470299i	$0.844146\pi$
$618$		0			0
$619$	−15.1141	−	8.72611i	−0.607485	−	0.350732i	0.164495	−	0.986378i	$-0.447400\pi$
$619$	−15.1141	−	8.72611i	−0.607485	−	0.350732i	−0.771981	+	0.635646i	$0.780734\pi$
$620$	−3.06099	−	3.82006i	−0.122932	−	0.153417i
$621$		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
$640$	−6.41475	+	11.3230i	−0.253565	+	0.447582i
$641$	−29.2098	−	16.8643i	−1.15372	−	0.666098i	−0.203926	−	0.978986i	$-0.565370\pi$
$641$	−29.2098	−	16.8643i	−1.15372	−	0.666098i	−0.949790	+	0.312888i	$0.898703\pi$
$642$		0			0
$643$	14.4308	+	8.33160i	0.569093	+	0.328566i	0.756787	−	0.653661i	$-0.226768\pi$
$643$	14.4308	+	8.33160i	0.569093	+	0.328566i	−0.187694	+	0.982228i	$0.560101\pi$
$644$	−9.90711	−	30.6872i	−0.390395	−	1.20925i
$645$		0			0
$646$	−30.3592	+	2.31070i	−1.19447	+	0.0909131i
$647$	3.12081	+	5.40539i	0.122692	+	0.212508i	0.920828	−	0.389968i	$-0.127514\pi$
$647$	3.12081	+	5.40539i	0.122692	+	0.212508i	−0.798137	+	0.602476i	$0.794181\pi$
$648$		0			0
$649$	−0.214852	+	0.372135i	−0.00843369	+	0.0146076i
$650$	17.0604	+	24.9605i	0.669165	+	0.979031i
$651$		0			0
$652$	−22.8019	−	8.88780i	−0.892991	−	0.348073i
$653$	−33.2340	+	19.1877i	−1.30055	+	0.750871i	−0.980498	−	0.196530i	$-0.937033\pi$
$653$	−33.2340	+	19.1877i	−1.30055	+	0.750871i	−0.320049	+	0.947401i	$0.603699\pi$
$654$		0			0
$655$	−0.311429	−	0.179804i	−0.0121685	−	0.00702552i
$656$	9.13204	+	2.03958i	0.356546	+	0.0796323i
$657$		0			0
$658$	1.43718	+	0.424627i	0.0560270	+	0.0165537i
$659$	−12.4132	−	21.5003i	−0.483551	−	0.837535i	0.516271	−	0.856425i	$-0.327320\pi$
$659$	−12.4132	−	21.5003i	−0.483551	−	0.837535i	−0.999822	+	0.0188909i	$0.993986\pi$
$660$		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
$664$	−26.5361	−	28.3993i	−1.02980	−	1.10211i
$665$	−20.6883	−	7.86404i	−0.802260	−	0.304954i
$666$		0			0
$667$	39.3126	+	22.6971i	1.52219	+	0.878837i
$668$	6.95026	−	17.8311i	0.268914	−	0.689906i
$669$		0			0
$670$	0.878533	+	1.28535i	0.0339407	+	0.0496574i
$671$	0.0282185	−	0.0488759i	0.00108936	−	0.00188683i
$672$		0			0
$673$	18.6887	+	32.3698i	0.720396	+	1.24776i	0.960841	+	0.277100i	$0.0893734\pi$
$673$	18.6887	+	32.3698i	0.720396	+	1.24776i	−0.240445	+	0.970663i	$0.577293\pi$
$674$	13.4033	−	27.9155i	0.516276	−	1.07526i
$675$		0			0
$676$	−26.0209	−	32.4736i	−1.00080	−	1.24898i
$677$			17.1093i			0.657565i	0.944406	+	0.328783i	$0.106638\pi$
$677$			17.1093i			0.657565i	−0.944406	+	0.328783i	$0.893362\pi$
$678$		0			0
$679$	1.72490	+	10.6649i	0.0661954	+	0.409280i
$680$	−2.80673	+	9.21345i	−0.107633	+	0.353320i
$681$		0			0
$682$	−0.111935	−	0.0537446i	−0.00428623	−	0.00205799i
$683$	20.8154	+	36.0533i	0.796480	+	1.37954i	0.921895	+	0.387439i	$0.126640\pi$
$683$	20.8154	+	36.0533i	0.796480	+	1.37954i	−0.125416	+	0.992104i	$0.540027\pi$
$684$		0			0
$685$	−10.4372			−0.398785
$686$	13.8462	+	22.2325i	0.528649	+	0.848841i
$687$		0			0
$688$	12.7243	−	13.8425i	0.485111	−	0.527739i
$689$		−	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
$698$	−16.6619	−	24.3774i	−0.630662	−	0.922698i
$699$		0			0
$700$	13.0459	−	14.4343i	0.493089	−	0.545564i
$701$		−	5.38772i		−	0.203491i	−0.994810	−	0.101746i	$-0.967557\pi$
$701$		−	5.38772i		−	0.203491i	0.994810	−	0.101746i	$-0.0324428\pi$
$702$		0			0
$703$	49.6819	−	28.6839i	1.87379	−	1.08183i
$704$	−0.0223661	+	0.329348i	−0.000842954	+	0.0124128i
$705$		0			0
$706$	−36.5088	−	17.5293i	−1.37403	−	0.659725i
$707$	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	$0.506132\pi$
$710$	1.72188	−	1.17690i	0.0646210	−	0.0441683i
$711$		0			0
$712$	−1.80841	−	0.550903i	−0.0677731	−	0.0206460i
$713$	11.2298	−	6.48355i	0.420561	−	0.242811i
$714$		0			0
$715$	−0.238998	−	0.137986i	−0.00893803	−	0.00516037i
$716$	−29.7528	−	37.1309i	−1.11191	−	1.38765i
$717$		0			0
$718$	6.79074	−	14.1433i	0.253428	−	0.527822i
$719$	−21.4410	+	37.1370i	−0.799616	+	1.38498i	0.120250	+	0.992744i	$0.461630\pi$
$719$	−21.4410	+	37.1370i	−0.799616	+	1.38498i	−0.919866	+	0.392232i	$0.871703\pi$
$720$		0			0
$721$	−29.1854	+	4.72033i	−1.08692	+	0.175794i
$722$	−27.0439	−	39.5670i	−1.00647	−	1.47253i
$723$		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	$-0.604164\pi$
$727$	9.11133	−	5.26043i	0.337921	−	0.195098i	0.659352	+	0.751834i	$0.270831\pi$
$728$	−26.6410	+	34.4008i	−0.987381	+	1.27498i
$729$		0			0
$730$	−4.01573	−	1.92811i	−0.148629	−	0.0713625i
$731$	6.95771	−	12.0511i	0.257340	−	0.445726i
$732$		0			0
$733$	−17.8701	−	30.9520i	−0.660048	−	1.14324i	−0.980602	−	0.196007i	$-0.937202\pi$
$733$	−17.8701	−	30.9520i	−0.660048	−	1.14324i	0.320554	−	0.947230i	$-0.396131\pi$
$734$	−0.988555	−	0.474644i	−0.0364882	−	0.0175194i
$735$		0			0
$736$	−27.0771	−	21.3363i	−0.998075	−	0.786466i
$737$	0.0342011	+	0.0197460i	0.00125981	+	0.000727354i
$738$		0			0
$739$	11.4786	−	6.62717i	0.422247	−	0.243784i	−0.273791	−	0.961789i	$-0.588278\pi$
$739$	11.4786	−	6.62717i	0.422247	−	0.243784i	0.696038	+	0.718005i	$0.254944\pi$
$740$	−2.74657	−	17.9384i	−0.100966	−	0.659429i
$741$		0			0
$742$	−21.3603	+	5.14382i	−0.784160	+	0.188836i
$743$	8.67905	−	15.0326i	0.318404	−	0.551491i	−0.661752	−	0.749723i	$-0.730187\pi$
$743$	8.67905	−	15.0326i	0.318404	−	0.551491i	0.980155	+	0.198232i	$0.0635200\pi$
$744$		0			0
$745$	−8.64411	+	14.9720i	−0.316696	+	0.548533i
$746$	15.6626	+	22.9154i	0.573448	+	0.838991i
$747$		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	$-0.413928\pi$
$751$	33.8508	−	19.5438i	1.23524	−	0.713163i	0.968116	+	0.250500i	$0.0805951\pi$
$752$	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	−0.998122	−	0.0612515i	$-0.980491\pi$
$761$	−39.8383	+	23.0007i	−1.44414	+	0.833774i	−0.446016	+	0.895025i	$0.647158\pi$
$762$		0			0
$763$	−1.97518	−	12.2124i	−0.0715064	−	0.442118i
$764$	13.1473	−	2.01299i	0.475651	−	0.0728273i
$765$		0			0
$766$	8.28651	+	12.1237i	0.299404	+	0.438047i
$767$	−30.2744	+	52.4368i	−1.09314	+	1.89338i
$768$		0			0
$769$	9.35320	−	16.2002i	0.337285	−	0.584195i	−0.646636	−	0.762799i	$-0.723825\pi$
$769$	9.35320	−	16.2002i	0.337285	−	0.584195i	0.983921	+	0.178604i	$0.0571581\pi$
$770$	−0.0503214	+	0.170316i	−0.00181346	+	0.00613775i
$771$		0			0
$772$	−12.1535	+	1.86083i	−0.437413	+	0.0669727i
$773$	5.68811	−	3.28403i	0.204587	−	0.118118i	−0.394206	−	0.919022i	$-0.628980\pi$
$773$	5.68811	−	3.28403i	0.204587	−	0.118118i	0.598793	+	0.800904i	$0.295647\pi$
$774$		0			0
$775$	6.77555	+	3.91187i	0.243385	+	0.140518i
$776$	7.88514	+	8.43878i	0.283060	+	0.302935i
$777$		0			0
$778$	35.2909	+	16.9446i	1.26524	+	0.607492i
$779$	8.50610	+	14.7330i	0.304763	+	0.527865i
$780$		0			0
$781$	0.0264522	−	0.0458165i	0.000946534	−	0.00163944i
$782$	−22.9997	−	11.0431i	−0.822469	−	0.394900i
$783$		0			0
$784$	25.5363	+	11.4848i	0.912009	+	0.410170i
$785$	−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
$790$	−6.22789	−	9.11180i	−0.221579	−	0.324183i
$791$	0.479812	+	0.588576i	0.0170602	+	0.0209273i
$792$		0			0
$793$	3.97621	−	6.88699i	0.141199	−	0.244564i
$794$	−19.0080	+	39.5886i	−0.674570	+	1.40495i
$795$		0			0
$796$	−26.0339	+	20.8609i	−0.922749	+	0.739393i
$797$	9.90432	+	5.71826i	0.350829	+	0.202551i	0.665050	−	0.746798i	$-0.268410\pi$
$797$	9.90432	+	5.71826i	0.350829	+	0.202551i	−0.314221	+	0.949350i	$0.601743\pi$
$798$		0			0
$799$	1.02683	−	0.592840i	0.0363266	−	0.0209732i
$800$	2.98009	−	20.5849i	0.105362	−	0.727788i
$801$		0			0
$802$	−34.1255	+	23.3247i	−1.20501	+	0.823623i
$803$	−0.112995			−0.00398751
$804$		0			0
$805$	−11.7186	−	14.3750i	−0.413026	−	0.506651i
$806$	−15.7726	−	7.57304i	−0.555566	−	0.266749i
$807$		0			0
$808$	36.3584	+	11.0760i	1.27908	+	0.389652i
$809$	46.6840	−	26.9530i	1.64132	−	0.947617i	0.660957	−	0.750424i	$-0.270151\pi$
$809$	46.6840	−	26.9530i	1.64132	−	0.947617i	0.980365	−	0.197193i	$-0.0631826\pi$
$810$		0			0
$811$			7.92248i			0.278196i	0.990279	+	0.139098i	$0.0444203\pi$
$811$			7.92248i			0.278196i	−0.990279	+	0.139098i	$0.955580\pi$
$812$	−37.5097	+	12.1097i	−1.31633	+	0.424967i
$813$		0			0
$814$	−0.259753	−	0.380036i	−0.00910435	−	0.0133203i
$815$	−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	$0.143240\pi$
$821$			24.9264i			0.869936i	−0.900446	+	0.434968i	$0.856760\pi$
$822$		0			0
$823$		−	19.3265i		−	0.673679i	−0.941562	−	0.336840i	$-0.890642\pi$
$823$		−	19.3265i		−	0.673679i	0.941562	−	0.336840i	$-0.109358\pi$
$824$	−23.0935	+	21.5784i	−0.804500	+	0.751719i
$825$		0			0
$826$	37.3677	+	11.0406i	1.30019	+	0.384152i
$827$	50.6751			1.76215			0.881074	−	0.472979i	$-0.156821\pi$
$827$	50.6751			1.76215			0.881074	+	0.472979i	$0.156821\pi$
$828$		0			0
$829$	18.8507	+	32.6504i	0.654713	+	1.13400i	0.981966	+	0.189059i	$0.0605436\pi$
$829$	18.8507	+	32.6504i	0.654713	+	1.13400i	−0.327253	+	0.944937i	$0.606123\pi$
$830$	−20.1517	−	9.67562i	−0.699475	−	0.335846i
$831$		0			0
$832$	−3.15156	+	46.4077i	−0.109261	+	1.60890i
$833$	20.2975	+	4.17591i	0.703268	+	0.144687i
$834$		0			0
$835$		−	11.0068i		−	0.380907i
$836$	−0.468361	+	0.375295i	−0.0161986	+	0.0129798i
$837$		0			0
$838$	0.459957	−	0.957965i	0.0158889	−	0.0330924i
$839$	13.8503	+	23.9895i	0.478166	+	0.828208i	0.999687	−	0.0250307i	$-0.00796835\pi$
$839$	13.8503	+	23.9895i	0.478166	+	0.828208i	−0.521521	+	0.853239i	$0.674635\pi$
$840$		0			0
$841$	13.2432	−	22.9380i	0.456663	−	0.790964i
$842$	20.0287	+	29.3033i	0.690236	+	1.00986i
$843$		0			0
$844$	−4.21718	−	1.64379i	−0.145161	−	0.0565814i
$845$	−20.7266	−	11.9665i	−0.713016	−	0.411660i
$846$		0			0
$847$	−4.64595	−	28.7255i	−0.159637	−	0.987019i
$848$	−15.8954	+	17.2921i	−0.545849	+	0.593814i
$849$		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	0.930943	−	0.365164i	$-0.118987\pi$
$853$	4.35844	+	7.54903i	0.149230	+	0.258474i	−0.781713	+	0.623638i	$0.785654\pi$
$854$	−4.90783	−	1.45006i	−0.167943	−	0.0496202i
$855$		0			0
$856$	9.32429	−	30.6082i	0.318698	−	1.04617i
$857$	−21.2925	−	12.2932i	−0.727338	−	0.419929i	0.0901098	−	0.995932i	$-0.471278\pi$
$857$	−21.2925	−	12.2932i	−0.727338	−	0.419929i	−0.817447	+	0.576003i	$0.804612\pi$
$858$		0			0
$859$	−2.32063	+	1.33982i	−0.0791790	+	0.0457140i	−0.539067	−	0.842263i	$-0.681223\pi$
$859$	−2.32063	+	1.33982i	−0.0791790	+	0.0457140i	0.459888	+	0.887977i	$0.347890\pi$
$860$	3.92726	−	10.0755i	0.133918	−	0.343571i
$861$		0			0
$862$	−9.78416	−	14.3149i	−0.333250	−	0.487566i
$863$	14.5911	−	25.2725i	0.496686	−	0.860285i	−0.503307	−	0.864108i	$-0.667884\pi$
$863$	14.5911	−	25.2725i	0.496686	−	0.860285i	0.999993	+	0.00382290i	$0.00121687\pi$
$864$		0			0
$865$	11.7058	+	20.2751i	0.398011	+	0.689375i
$866$	−18.3099	+	1.39360i	−0.622196	+	0.0473566i
$867$		0			0
$868$	−2.36167	+	11.0089i	−0.0801602	+	0.373667i
$869$	−0.242451	−	0.139979i	−0.00822458	−	0.00474846i
$870$		0			0
$871$	4.81921	+	2.78237i	0.163293	+	0.0942770i
$872$	−9.02930	−	9.66328i	−0.305771	−	0.327240i
$873$		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	0.947609	−	0.319432i	$-0.103492\pi$
$877$	5.83899	+	10.1134i	0.197169	+	0.341506i	−0.750441	+	0.660938i	$0.770159\pi$
$878$	−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	$0.209762\pi$
$881$			36.3492i			1.22463i	−0.790612	+	0.612317i	$0.790238\pi$
$882$		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	0.994854	+	0.101323i	$0.0323074\pi$
$887$	17.4280	+	30.1862i	0.585175	+	1.01355i	−0.409679	+	0.912230i	$0.634359\pi$
$888$		0			0
$889$	12.2308	−	32.1763i	0.410209	−	1.07916i
$890$	−1.08414	+	0.0825158i	−0.0363404	+	0.00276594i
$891$		0			0
$892$	15.8395	−	12.6921i	0.530347	−	0.424964i
$893$	2.52251	+	1.45637i	0.0844126	+	0.0487356i
$894$		0			0
$895$	−23.6992	−	13.6827i	−0.792175	−	0.457363i
$896$	29.5093	−	5.02012i	0.985836	−	0.167711i
$897$		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
$902$	0.112698	−	0.0770290i	0.00375244	−	0.00256479i
$903$		0			0
$904$	0.776565	+	0.236568i	0.0258282	+	0.00786813i
$905$	15.3193	−	8.84461i	0.509231	−	0.294005i
$906$		0			0
$907$	30.3505	+	17.5229i	1.00777	+	0.581838i	0.910539	−	0.413423i	$-0.135667\pi$
$907$	30.3505	+	17.5229i	1.00777	+	0.581838i	0.0972343	+	0.995262i	$0.469000\pi$
$908$	−2.13187	+	5.46938i	−0.0707487	+	0.181508i
$909$		0			0
$910$	−7.09068	+	23.9988i	−0.235054	+	0.795553i
$911$	11.5348	+	19.9789i	0.382166	+	0.661930i	0.991372	−	0.131082i	$-0.0418450\pi$
$911$	11.5348	+	19.9789i	0.382166	+	0.661930i	−0.609206	+	0.793012i	$0.708512\pi$
$912$		0			0
$913$	−0.567031			−0.0187660
$914$	5.07399	−	0.386191i	0.167833	−	0.0127741i
$915$		0			0
$916$	−0.554972	−	0.692595i	−0.0183368	−	0.0228840i
$917$	0.132062	+	0.816526i	0.00436106	+	0.0269641i
$918$		0			0
$919$	33.1126	+	19.1176i	1.09228	+	0.630630i	0.934184	−	0.356793i	$-0.116130\pi$
$919$	33.1126	+	19.1176i	1.09228	+	0.630630i	0.158100	+	0.987423i	$0.449463\pi$
$920$	−18.9663	−	5.77777i	−0.625300	−	0.190488i
$921$		0			0
$922$	−17.6929	+	12.0930i	−0.582683	+	0.398262i
$923$	3.72732	−	6.45591i	0.122686	−	0.212499i
$924$		0			0
$925$	14.5022	+	25.1186i	0.476830	+	0.825893i
$926$	33.6832	+	16.1726i	1.10690	+	0.531466i
$927$		0			0
$928$	−26.0798	+	33.0970i	−0.856113	+	1.08646i
$929$			11.7834i			0.386601i	0.981140	+	0.193301i	$0.0619193\pi$
$929$			11.7834i			0.386601i	−0.981140	+	0.193301i	$0.938081\pi$
$930$		0			0
$931$	16.0473	+	48.3119i	0.525930	+	1.58336i
$932$	28.6833	+	11.1803i	0.939553	+	0.366222i
$933$		0			0
$934$	−14.2975	+	29.7778i	−0.467829	+	0.974360i
$935$	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	$0.668148\pi$
$938$	1.01469	−	3.43428i	0.0331308	−	0.112133i
$939$		0			0
$940$	0.719042	−	0.576164i	0.0234526	−	0.0187924i
$941$		−	27.2927i		−	0.889716i	−0.895601	−	0.444858i	$-0.853254\pi$
$941$		−	27.2927i		−	0.889716i	0.895601	−	0.444858i	$-0.146746\pi$
$942$		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	$-0.531732\pi$
$947$	−6.12529			−0.199045			−0.0995227	+	0.995035i	$0.531732\pi$
$948$		0			0
$949$	−15.9219			−0.516847
$950$	31.2202	−	21.3389i	1.01292	−	0.692327i
$951$		0			0
$952$	20.5047	−	8.38649i	0.664560	−	0.271808i
$953$		−	32.5362i		−	1.05395i	−0.849881	−	0.526975i	$-0.823326\pi$
$953$		−	32.5362i		−	1.05395i	0.849881	−	0.526975i	$-0.176674\pi$
$954$		0			0
$955$	6.62473	−	3.82479i	0.214371	−	0.123767i
$956$	6.31437	−	16.1997i	0.204221	−	0.523936i
$957$		0			0
$958$	4.27301	−	8.89951i	0.138055	−	0.287530i
$959$	15.1688	+	18.6072i	0.489825	+	0.600859i
$960$		0			0
$961$	26.4724			0.853948
$962$	−36.6013	−	53.5500i	−1.18007	−	1.72652i
$963$		0			0
$964$	2.59680	−	6.66216i	0.0836372	−	0.214574i
$965$	−6.12398	+	3.53568i	−0.197138	+	0.113818i
$966$		0			0
$967$	−29.4129	−	16.9816i	−0.945856	−	0.546090i	−0.0540646	−	0.998537i	$-0.517218\pi$
$967$	−29.4129	−	16.9816i	−0.945856	−	0.546090i	−0.891791	+	0.452447i	$0.850551\pi$
$968$	−21.2383	−	22.7296i	−0.682626	−	0.730556i
$969$		0			0
$970$	5.98802	+	2.87508i	0.192264	+	0.0923133i
$971$	−9.81717	+	17.0038i	−0.315048	+	0.545679i	−0.979448	−	0.201698i	$-0.935354\pi$
$971$	−9.81717	+	17.0038i	−0.315048	+	0.545679i	0.664400	+	0.747377i	$0.268687\pi$
$972$		0			0
$973$	−1.24586	−	1.52827i	−0.0399404	−	0.0489940i
$974$	10.2020	−	6.97301i	0.326892	−	0.223430i
$975$		0			0
$976$	−5.22028	+	1.63694i	−0.167097	+	0.0523970i
$977$			44.9748i			1.43887i	0.694559	+	0.719435i	$0.255599\pi$
$977$			44.9748i			1.43887i	−0.694559	+	0.719435i	$0.744401\pi$
$978$		0			0
$979$	−0.0238846	+	0.0137898i	−0.000763355	+	0.000440723i
$980$	16.0829	+	0.820502i	0.513749	+	0.0262100i
$981$		0			0
$982$	17.5923	−	36.6399i	0.561391	−	1.16923i
$983$	2.53298	−	4.38725i	0.0807895	−	0.139932i	−0.822800	−	0.568331i	$-0.807589\pi$
$983$	2.53298	−	4.38725i	0.0807895	−	0.139932i	0.903589	+	0.428400i	$0.140923\pi$
$984$		0			0
$985$	−7.60580	−	13.1736i	−0.242341	−	0.419747i
$986$	−13.4982	+	28.1131i	−0.429871	+	0.895304i
$987$		0			0
$988$	−65.9957	+	52.8820i	−2.09960	+	1.68240i
$989$	24.8077	+	14.3228i	0.788840	+	0.455437i
$990$		0			0
$991$	−26.7965	+	15.4710i	−0.851220	+	0.491452i	−0.861062	−	0.508500i	$-0.830200\pi$
$991$	−26.7965	+	15.4710i	−0.851220	+	0.491452i	0.00984253	+	0.999952i	$0.496867\pi$
$992$	4.46276	+	11.1789i	0.141693	+	0.354931i
$993$		0			0
$994$	−4.60063	−	1.35930i	−0.145923	−	0.0431144i
$995$	−9.59349	+	16.6164i	−0.304134	+	0.526776i
$996$		0			0
$997$	6.02219	−	10.4307i	0.190725	−	0.330345i	−0.754766	−	0.655994i	$-0.772250\pi$
$997$	6.02219	−	10.4307i	0.190725	−	0.330345i	0.945491	+	0.325649i	$0.105583\pi$
$998$	14.6500	−	10.0132i	0.463737	−	0.316963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.2		88
3.2	odd	2		252.2.bb.a.23.43	yes	88
4.3	odd	2	inner	756.2.bb.a.611.43		88
7.4	even	3		756.2.o.a.179.28		88
9.2	odd	6		756.2.o.a.359.12		88
9.7	even	3		252.2.o.a.191.33	yes	88
12.11	even	2		252.2.bb.a.23.2	yes	88
21.11	odd	6		252.2.o.a.95.17	✓	88
28.11	odd	6		756.2.o.a.179.12		88
36.7	odd	6		252.2.o.a.191.17	yes	88
36.11	even	6		756.2.o.a.359.28		88
63.11	odd	6	inner	756.2.bb.a.683.43		88
63.25	even	3		252.2.bb.a.11.2	yes	88
84.11	even	6		252.2.o.a.95.33	yes	88
252.11	even	6	inner	756.2.bb.a.683.2		88
252.151	odd	6		252.2.bb.a.11.43	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.17	✓	88	21.11	odd	6
252.2.o.a.95.33	yes	88	84.11	even	6
252.2.o.a.191.17	yes	88	36.7	odd	6
252.2.o.a.191.33	yes	88	9.7	even	3
252.2.bb.a.11.2	yes	88	63.25	even	3
252.2.bb.a.11.43	yes	88	252.151	odd	6
252.2.bb.a.23.2	yes	88	12.11	even	2
252.2.bb.a.23.43	yes	88	3.2	odd	2
756.2.o.a.179.12		88	28.11	odd	6
756.2.o.a.179.28		88	7.4	even	3
756.2.o.a.359.12		88	9.2	odd	6
756.2.o.a.359.28		88	36.11	even	6
756.2.bb.a.611.2		88	1.1	even	1	trivial
756.2.bb.a.611.43		88	4.3	odd	2	inner
756.2.bb.a.683.2		88	252.11	even	6	inner
756.2.bb.a.683.43		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)

\(f(q)\)	\(=\)	\(q+(-1.41013 + 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 - 0.575136i) q^{5} +(-2.47311 - 0.940076i) q^{7} +(-2.75529 + 0.639023i) q^{8} +O(q^{10})\)	\(q+(-1.41013 + 0.107328i) q^{2} +(1.97696 - 0.302694i) q^{4} +(0.996165 - 0.575136i) q^{5} +(-2.47311 - 0.940076i) q^{7} +(-2.75529 + 0.639023i) q^{8} +(-1.34300 + 0.917936i) q^{10} +(-0.0206317 + 0.0357351i) q^{11} +(-2.90716 + 5.03535i) q^{13} +(3.58831 + 1.06020i) q^{14} +(3.81675 - 1.19683i) q^{16} +(2.56376 - 1.48019i) q^{17} +(6.29815 + 3.63624i) q^{19} +(1.79529 - 1.43855i) q^{20} +(0.0252580 - 0.0526056i) q^{22} +(3.04704 + 5.27762i) q^{23} +(-1.83844 + 3.18427i) q^{25} +(3.55906 - 7.41255i) q^{26} +(-5.17379 - 1.10990i) q^{28} +(6.45096 - 3.72446i) q^{29} -2.12782i q^{31} +(-5.25368 + 2.09734i) q^{32} +(-3.45639 + 2.36243i) q^{34} +(-3.00429 + 0.485903i) q^{35} +(3.94417 - 6.83150i) q^{37} +(-9.27151 - 4.45162i) q^{38} +(-2.37720 + 2.22124i) q^{40} +(2.02586 + 1.16963i) q^{41} +(4.07080 - 2.35028i) q^{43} +(-0.0299712 + 0.0768920i) q^{44} +(-4.86317 - 7.11513i) q^{46} +0.400516 q^{47} +(5.23252 + 4.64982i) q^{49} +(2.25068 - 4.68756i) q^{50} +(-4.22318 + 10.8347i) q^{52} +(-5.08527 + 2.93598i) q^{53} +0.0474640i q^{55} +(7.41487 + 1.00981i) q^{56} +(-8.69698 + 5.94436i) q^{58} +10.4137 q^{59} -1.36773 q^{61} +(0.228375 + 3.00052i) q^{62} +(7.18330 - 3.52139i) q^{64} +6.68806i q^{65} -0.957074i q^{67} +(4.62042 - 3.70231i) q^{68} +(4.18431 - 1.00763i) q^{70} -1.28212 q^{71} +(1.36920 + 2.37152i) q^{73} +(-4.82860 + 10.0567i) q^{74} +(13.5519 + 5.28229i) q^{76} +(0.0846180 - 0.0689814i) q^{77} +6.78467i q^{79} +(3.11378 - 3.38739i) q^{80} +(-2.98227 - 1.43190i) q^{82} +(6.87088 + 11.9007i) q^{83} +(1.70262 - 2.94902i) q^{85} +(-5.48812 + 3.75112i) q^{86} +(0.0340108 - 0.111645i) q^{88} +(0.578834 + 0.334190i) q^{89} +(11.9233 - 9.72001i) q^{91} +(7.62138 + 9.51134i) q^{92} +(-0.564782 + 0.0429866i) q^{94} +8.36533 q^{95} +(-2.04166 - 3.53626i) q^{97} +(-7.87761 - 5.99527i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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