LMFDB - Embedded newform 756.2.bb.a.611.13

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			611.13
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.803010 - 1.16412i) q^{2} +(-0.710349 + 1.86960i) q^{4} +(1.33842 - 0.772734i) q^{5} +(2.59837 + 0.498458i) q^{7} +(2.74686 - 0.674378i) q^{8} +O(q^{10})$	\(q+(-0.803010 - 1.16412i) q^{2} +(-0.710349 + 1.86960i) q^{4} +(1.33842 - 0.772734i) q^{5} +(2.59837 + 0.498458i) q^{7} +(2.74686 - 0.674378i) q^{8} +(-1.97432 - 0.937562i) q^{10} +(-1.94050 + 3.36104i) q^{11} +(-0.0856046 + 0.148271i) q^{13} +(-1.50626 - 3.42508i) q^{14} +(-2.99081 - 2.65614i) q^{16} +(2.75692 - 1.59171i) q^{17} +(5.49591 + 3.17307i) q^{19} +(0.493963 + 3.05121i) q^{20} +(5.47090 - 0.439980i) q^{22} +(-0.309781 - 0.536557i) q^{23} +(-1.30576 + 2.26165i) q^{25} +(0.241347 - 0.0194096i) q^{26} +(-2.77767 + 4.50384i) q^{28} +(-4.83069 + 2.78900i) q^{29} +7.87554i q^{31} +(-0.690408 + 5.61456i) q^{32} +(-4.06678 - 1.93123i) q^{34} +(3.86288 - 1.34071i) q^{35} +(3.84283 - 6.65597i) q^{37} +(-0.719446 - 8.94590i) q^{38} +(3.15532 - 3.02519i) q^{40} +(1.61960 + 0.935076i) q^{41} +(3.04216 - 1.75639i) q^{43} +(-4.90538 - 6.01547i) q^{44} +(-0.375859 + 0.791484i) q^{46} -3.43990 q^{47} +(6.50308 + 2.59036i) q^{49} +(3.68137 - 0.296063i) q^{50} +(-0.216399 - 0.265371i) q^{52} +(8.97048 - 5.17911i) q^{53} +5.99797i q^{55} +(7.47350 - 0.383092i) q^{56} +(7.12582 + 3.38390i) q^{58} +5.63284 q^{59} +9.33853 q^{61} +(9.16807 - 6.32414i) q^{62} +(7.09043 - 3.70484i) q^{64} +0.264598i q^{65} -15.5382i q^{67} +(1.01749 + 6.28501i) q^{68} +(-4.66268 - 3.42025i) q^{70} -5.07956 q^{71} +(-5.51255 - 9.54801i) q^{73} +(-10.8342 + 0.871304i) q^{74} +(-9.83638 + 8.02117i) q^{76} +(-6.71748 + 7.76599i) q^{77} +0.975881i q^{79} +(-6.05543 - 1.24391i) q^{80} +(-0.212015 - 2.63628i) q^{82} +(-2.25453 - 3.90496i) q^{83} +(2.45994 - 4.26074i) q^{85} +(-4.48754 - 2.13104i) q^{86} +(-3.06366 + 10.5409i) q^{88} +(8.14910 + 4.70488i) q^{89} +(-0.296340 + 0.342594i) q^{91} +(1.22320 - 0.198025i) q^{92} +(2.76227 + 4.00445i) q^{94} +9.80775 q^{95} +(-5.12539 - 8.87743i) q^{97} +(-2.20655 - 9.65045i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.803010	−	1.16412i	−0.567814	−	0.823157i
$2$	−0.803010	−	1.16412i	−0.567814	−	0.823157i
$3$		0			0
$3$		0			0
$4$	−0.710349	+	1.86960i	−0.355174	+	0.934800i
$5$	1.33842	−	0.772734i	0.598558	−	0.345577i	−0.169916	−	0.985458i	$-0.554350\pi$
$5$	1.33842	−	0.772734i	0.598558	−	0.345577i	0.768474	+	0.639881i	$0.221016\pi$
$6$		0			0
$7$	2.59837	+	0.498458i	0.982092	+	0.188399i
$7$	2.59837	+	0.498458i	0.982092	+	0.188399i
$8$	2.74686	−	0.674378i	0.971160	−	0.238429i
$9$		0			0
$10$	−1.97432	−	0.937562i	−0.624334	−	0.296483i
$11$	−1.94050	+	3.36104i	−0.585083	+	1.01339i	0.409782	+	0.912183i	$0.365605\pi$
$11$	−1.94050	+	3.36104i	−0.585083	+	1.01339i	−0.994865	+	0.101210i	$0.967729\pi$
$12$		0			0
$13$	−0.0856046	+	0.148271i	−0.0237424	+	0.0411231i	−0.877652	−	0.479297i	$-0.840891\pi$
$13$	−0.0856046	+	0.148271i	−0.0237424	+	0.0411231i	0.853910	+	0.520421i	$0.174225\pi$
$14$	−1.50626	−	3.42508i	−0.402564	−	0.915392i
$15$		0			0
$16$	−2.99081	−	2.65614i	−0.747702	−	0.664034i
$17$	2.75692	−	1.59171i	0.668652	−	0.386047i	−0.126914	−	0.991914i	$-0.540507\pi$
$17$	2.75692	−	1.59171i	0.668652	−	0.386047i	0.795566	+	0.605867i	$0.207174\pi$
$18$		0			0
$19$	5.49591	+	3.17307i	1.26085	+	0.727951i	0.973239	−	0.229797i	$-0.0738061\pi$
$19$	5.49591	+	3.17307i	1.26085	+	0.727951i	0.287610	+	0.957748i	$0.407139\pi$
$20$	0.493963	+	3.05121i	0.110453	+	0.682272i
$21$		0			0
$22$	5.47090	−	0.439980i	1.16640	−	0.0938040i
$23$	−0.309781	−	0.536557i	−0.0645939	−	0.111880i	0.831920	−	0.554896i	$-0.187242\pi$
$23$	−0.309781	−	0.536557i	−0.0645939	−	0.111880i	−0.896514	+	0.443016i	$0.853909\pi$
$24$		0			0
$25$	−1.30576	+	2.26165i	−0.261153	+	0.452330i
$26$	0.241347	−	0.0194096i	0.0473321	−	0.00380653i
$27$		0			0
$28$	−2.77767	+	4.50384i	−0.524930	+	0.851146i
$29$	−4.83069	+	2.78900i	−0.897036	+	0.517904i	−0.876237	−	0.481880i	$-0.839954\pi$
$29$	−4.83069	+	2.78900i	−0.897036	+	0.517904i	−0.0207986	+	0.999784i	$0.506621\pi$
$30$		0			0
$31$			7.87554i			1.41449i	0.706969	+	0.707245i	$0.250062\pi$
$31$			7.87554i			1.41449i	−0.706969	+	0.707245i	$0.749938\pi$
$32$	−0.690408	+	5.61456i	−0.122048	+	0.992524i
$33$		0			0
$34$	−4.06678	−	1.93123i	−0.697447	−	0.331203i
$35$	3.86288	−	1.34071i	0.652945	−	0.226621i
$36$		0			0
$37$	3.84283	−	6.65597i	0.631757	−	1.09423i	−0.355436	−	0.934701i	$-0.615667\pi$
$37$	3.84283	−	6.65597i	0.631757	−	1.09423i	0.987192	−	0.159534i	$-0.0509992\pi$
$38$	−0.719446	−	8.94590i	−0.116710	−	1.45122i
$39$		0			0
$40$	3.15532	−	3.02519i	0.498900	−	0.478324i
$41$	1.61960	+	0.935076i	0.252939	+	0.146034i	0.621109	−	0.783724i	$-0.286682\pi$
$41$	1.61960	+	0.935076i	0.252939	+	0.146034i	−0.368170	+	0.929758i	$0.620016\pi$
$42$		0			0
$43$	3.04216	−	1.75639i	0.463925	−	0.267847i	−0.249768	−	0.968306i	$-0.580354\pi$
$43$	3.04216	−	1.75639i	0.463925	−	0.267847i	0.713693	+	0.700458i	$0.247021\pi$
$44$	−4.90538	−	6.01547i	−0.739514	−	0.906867i
$45$		0			0
$46$	−0.375859	+	0.791484i	−0.0554174	+	0.116698i
$47$	−3.43990			−0.501761			−0.250880	−	0.968018i	$-0.580720\pi$
$47$	−3.43990			−0.501761			−0.250880	+	0.968018i	$0.580720\pi$
$48$		0			0
$49$	6.50308	+	2.59036i	0.929011	+	0.370051i
$50$	3.68137	−	0.296063i	0.520624	−	0.0418696i
$51$		0			0
$52$	−0.216399	−	0.265371i	−0.0300092	−	0.0368003i
$53$	8.97048	−	5.17911i	1.23219	−	0.711406i	0.264704	−	0.964330i	$-0.414726\pi$
$53$	8.97048	−	5.17911i	1.23219	−	0.711406i	0.967486	+	0.252924i	$0.0813923\pi$
$54$		0			0
$55$			5.99797i			0.808766i
$56$	7.47350	−	0.383092i	0.998689	−	0.0511929i
$57$		0			0
$58$	7.12582	+	3.38390i	0.935666	+	0.444328i
$59$	5.63284			0.733334			0.366667	−	0.930352i	$-0.380499\pi$
$59$	5.63284			0.733334			0.366667	+	0.930352i	$0.380499\pi$
$60$		0			0
$61$	9.33853			1.19568			0.597838	−	0.801617i	$-0.296026\pi$
$61$	9.33853			1.19568			0.597838	+	0.801617i	$0.296026\pi$
$62$	9.16807	−	6.32414i	1.16435	−	0.803167i
$63$		0			0
$64$	7.09043	−	3.70484i	0.886304	−	0.463105i
$65$			0.264598i			0.0328194i
$66$		0			0
$67$		−	15.5382i		−	1.89829i	−0.314843	−	0.949144i	$-0.601952\pi$
$67$		−	15.5382i		−	1.89829i	0.314843	−	0.949144i	$-0.398048\pi$
$68$	1.01749	+	6.28501i	0.123388	+	0.762170i
$69$		0			0
$70$	−4.66268	−	3.42025i	−0.557296	−	0.408798i
$71$	−5.07956			−0.602833			−0.301417	−	0.953493i	$-0.597459\pi$
$71$	−5.07956			−0.602833			−0.301417	+	0.953493i	$0.597459\pi$
$72$		0			0
$73$	−5.51255	−	9.54801i	−0.645195	−	1.11751i	−0.984257	−	0.176746i	$-0.943443\pi$
$73$	−5.51255	−	9.54801i	−0.645195	−	1.11751i	0.339062	−	0.940764i	$-0.389890\pi$
$74$	−10.8342	+	0.871304i	−1.25945	+	0.101287i
$75$		0			0
$76$	−9.83638	+	8.02117i	−1.12831	+	0.920092i
$77$	−6.71748	+	7.76599i	−0.765528	+	0.885017i
$78$		0			0
$79$			0.975881i			0.109795i	0.998492	+	0.0548976i	$0.0174832\pi$
$79$			0.975881i			0.109795i	−0.998492	+	0.0548976i	$0.982517\pi$
$80$	−6.05543	−	1.24391i	−0.677018	−	0.139073i
$81$		0			0
$82$	−0.212015	−	2.63628i	−0.0234131	−	0.291129i
$83$	−2.25453	−	3.90496i	−0.247467	−	0.428625i	0.715355	−	0.698761i	$-0.246265\pi$
$83$	−2.25453	−	3.90496i	−0.247467	−	0.428625i	−0.962822	+	0.270136i	$0.912931\pi$
$84$		0			0
$85$	2.45994	−	4.26074i	0.266818	−	0.462142i
$86$	−4.48754	−	2.13104i	−0.483904	−	0.229796i
$87$		0			0
$88$	−3.06366	+	10.5409i	−0.326587	+	1.12367i
$89$	8.14910	+	4.70488i	0.863803	+	0.498717i	0.865284	−	0.501282i	$-0.167138\pi$
$89$	8.14910	+	4.70488i	0.863803	+	0.498717i	−0.00148118	+	0.999999i	$0.500471\pi$
$90$		0			0
$91$	−0.296340	+	0.342594i	−0.0310648	+	0.0359136i
$92$	1.22320	−	0.198025i	0.127527	−	0.0206455i
$93$		0			0
$94$	2.76227	+	4.00445i	0.284907	+	0.413028i
$95$	9.80775			1.00625
$96$		0			0
$97$	−5.12539	−	8.87743i	−0.520404	−	0.901367i	−0.999719	−	0.0237232i	$-0.992448\pi$
$97$	−5.12539	−	8.87743i	−0.520404	−	0.901367i	0.479314	−	0.877643i	$-0.340885\pi$
$98$	−2.20655	−	9.65045i	−0.222895	−	0.974842i
$99$		0			0
$100$	−3.30083	−	4.04781i	−0.330083	−	0.404781i
$101$	−9.27628	−	5.35566i	−0.923024	−	0.532908i	−0.0384256	−	0.999261i	$-0.512234\pi$
$101$	−9.27628	−	5.35566i	−0.923024	−	0.532908i	−0.884599	+	0.466353i	$0.845568\pi$
$102$		0			0
$103$	−7.20504	+	4.15983i	−0.709934	+	0.409880i	−0.811036	−	0.584996i	$-0.801096\pi$
$103$	−7.20504	+	4.15983i	−0.709934	+	0.409880i	0.101103	+	0.994876i	$0.467763\pi$
$104$	−0.135152	+	0.465010i	−0.0132528	+	0.0455980i
$105$		0			0
$106$	−13.2325	−	6.28383i	−1.28525	−	0.610340i
$107$	−8.31500	+	14.4020i	−0.803842	+	1.39229i	0.113229	+	0.993569i	$0.463881\pi$
$107$	−8.31500	+	14.4020i	−0.803842	+	1.39229i	−0.917070	+	0.398725i	$0.869453\pi$
$108$		0			0
$109$	1.36179	+	2.35870i	0.130436	+	0.225922i	0.923845	−	0.382767i	$-0.125029\pi$
$109$	1.36179	+	2.35870i	0.130436	+	0.225922i	−0.793409	+	0.608689i	$0.791696\pi$
$110$	6.98235	−	4.81643i	0.665741	−	0.459228i
$111$		0			0
$112$	−6.44727	−	8.39242i	−0.609209	−	0.793009i
$113$	11.1248	+	6.42289i	1.04653	+	0.604215i	0.921676	−	0.387960i	$-0.126820\pi$
$113$	11.1248	+	6.42289i	1.04653	+	0.604215i	0.124855	+	0.992175i	$0.460153\pi$
$114$		0			0
$115$	−0.829232	−	0.478758i	−0.0773263	−	0.0446444i
$116$	−1.78284	−	11.0126i	−0.165533	−	1.02250i
$117$		0			0
$118$	−4.52323	−	6.55730i	−0.416397	−	0.603649i
$119$	7.95692	−	2.76165i	0.729409	−	0.253160i
$120$		0			0
$121$	−2.03108	−	3.51794i	−0.184644	−	0.319812i
$122$	−7.49894	−	10.8712i	−0.678922	−	0.984229i
$123$		0			0
$124$	−14.7241	−	5.59438i	−1.32226	−	0.502390i
$125$			11.7634i			1.05215i
$126$		0			0
$127$			8.84529i			0.784892i	0.919775	+	0.392446i	$0.128371\pi$
$127$			8.84529i			0.784892i	−0.919775	+	0.392446i	$0.871629\pi$
$128$	−10.0066	−	5.27909i	−0.884463	−	0.466610i
$129$		0			0
$130$	0.308024	−	0.212475i	0.0270155	−	0.0186353i
$131$	−2.16873	−	3.75636i	−0.189483	−	0.328194i	0.755595	−	0.655039i	$-0.227348\pi$
$131$	−2.16873	−	3.75636i	−0.189483	−	0.328194i	−0.945078	+	0.326845i	$0.894015\pi$
$132$		0			0
$133$	12.6988	+	10.9843i	1.10112	+	0.952458i
$134$	−18.0883	+	12.4773i	−1.56259	+	1.07787i
$135$		0			0
$136$	6.49946	−	6.23141i	0.557324	−	0.534339i
$137$	16.7291	+	9.65854i	1.42926	+	0.825185i	0.997062	−	0.0765930i	$-0.0244042\pi$
$137$	16.7291	+	9.65854i	1.42926	+	0.825185i	0.432200	+	0.901778i	$0.357738\pi$
$138$		0			0
$139$	−12.8588	−	7.42403i	−1.09067	−	0.629698i	−0.156915	−	0.987612i	$-0.550155\pi$
$139$	−12.8588	−	7.42403i	−1.09067	−	0.629698i	−0.933755	+	0.357914i	$0.883488\pi$
$140$	−0.237401	+	8.17441i	−0.0200641	+	0.690863i
$141$		0			0
$142$	4.07894	+	5.91322i	0.342297	+	0.496226i
$143$	−0.332231	−	0.575442i	−0.0277826	−	0.0481209i
$144$		0			0
$145$	−4.31031	+	7.46568i	−0.357952	+	0.619991i
$146$	−6.68839	+	14.0844i	−0.553535	+	1.16563i
$147$		0			0
$148$	9.71426	+	11.9126i	0.798507	+	0.979210i
$149$	−0.0595198	+	0.0343637i	−0.00487605	+	0.00281519i	−0.502436	−	0.864614i	$-0.667563\pi$
$149$	−0.0595198	+	0.0343637i	−0.00487605	+	0.00281519i	0.497560	+	0.867430i	$0.334229\pi$
$150$		0			0
$151$	−3.36778	−	1.94439i	−0.274066	−	0.158232i	0.356668	−	0.934231i	$-0.383913\pi$
$151$	−3.36778	−	1.94439i	−0.274066	−	0.158232i	−0.630734	+	0.775999i	$0.717246\pi$
$152$	17.2363	+	5.00963i	1.39805	+	0.406335i
$153$		0			0
$154$	14.4347	+	1.58378i	1.16319	+	0.127625i
$155$	6.08570	+	10.5407i	0.488815	+	0.846653i
$156$		0			0
$157$	−9.93807			−0.793144			−0.396572	−	0.918004i	$-0.629800\pi$
$157$	−9.93807			−0.793144			−0.396572	+	0.918004i	$0.629800\pi$
$158$	1.13604	−	0.783642i	0.0903786	−	0.0623432i
$159$		0			0
$160$	3.41451	+	8.04812i	0.269941	+	0.636260i
$161$	−0.537476	−	1.54859i	−0.0423591	−	0.122046i
$162$		0			0
$163$	−5.33006	−	3.07731i	−0.417482	−	0.241033i	0.276517	−	0.961009i	$-0.410820\pi$
$163$	−5.33006	−	3.07731i	−0.417482	−	0.241033i	−0.694000	+	0.719975i	$0.744153\pi$
$164$	−2.89870	+	2.36377i	−0.226350	+	0.184580i
$165$		0			0
$166$	−2.73543	+	5.76027i	−0.212311	+	0.447083i
$167$	−5.63100	+	9.75317i	−0.435740	+	0.754723i	−0.997356	−	0.0726749i	$-0.976846\pi$
$167$	−5.63100	+	9.75317i	−0.435740	+	0.754723i	0.561616	+	0.827398i	$0.310180\pi$
$168$		0			0
$169$	6.48534	+	11.2329i	0.498873	+	0.864073i
$170$	−6.93537	+	0.557755i	−0.531918	+	0.0427779i
$171$		0			0
$172$	1.12276	+	6.93528i	0.0856094	+	0.528810i
$173$		−	16.7291i		−	1.27189i	−0.771736	−	0.635944i	$-0.780611\pi$
$173$		−	16.7291i		−	1.27189i	0.771736	−	0.635944i	$-0.219389\pi$
$174$		0			0
$175$	−4.52019	+	5.22573i	−0.341695	+	0.395028i
$176$	14.7311	−	4.89801i	1.11040	−	0.369202i
$177$		0			0
$178$	−1.06676	−	13.2646i	−0.0799573	−	0.994223i
$179$	−7.05045	−	12.2117i	−0.526975	−	0.912748i	−0.999506	−	0.0314336i	$-0.989993\pi$
$179$	−7.05045	−	12.2117i	−0.526975	−	0.912748i	0.472531	−	0.881314i	$-0.343341\pi$
$180$		0			0
$181$	−18.0238			−1.33970			−0.669850	−	0.742496i	$-0.733642\pi$
$181$	−18.0238			−1.33970			−0.669850	+	0.742496i	$0.733642\pi$
$182$	0.636785	+	0.0698681i	0.0472016	+	0.00517897i
$183$		0			0
$184$	−1.21277	−	1.26494i	−0.0894064	−	0.0932523i
$185$		−	11.8779i		−	0.873283i
$186$		0			0
$187$			12.3549i			0.903477i
$188$	2.44353	−	6.43123i	0.178212	−	0.469046i
$189$		0			0
$190$	−7.87572	−	11.4174i	−0.571365	−	0.828305i
$191$	−12.1216			−0.877085			−0.438543	−	0.898710i	$-0.644505\pi$
$191$	−12.1216			−0.877085			−0.438543	+	0.898710i	$0.644505\pi$
$192$		0			0
$193$	6.01719			0.433127			0.216563	−	0.976269i	$-0.430515\pi$
$193$	6.01719			0.433127			0.216563	+	0.976269i	$0.430515\pi$
$194$	−6.21865	+	13.0952i	−0.446473	+	0.940183i
$195$		0			0
$196$	−9.46239	+	10.3181i	−0.675885	+	0.737007i
$197$		−	11.7089i		−	0.834225i	−0.908855	−	0.417113i	$-0.863042\pi$
$197$		−	11.7089i		−	0.834225i	0.908855	−	0.417113i	$-0.136958\pi$
$198$		0			0
$199$	8.68006	−	5.01144i	0.615313	−	0.355251i	−0.159729	−	0.987161i	$-0.551062\pi$
$199$	8.68006	−	5.01144i	0.615313	−	0.355251i	0.775042	+	0.631910i	$0.217729\pi$
$200$	−2.06154	+	7.09300i	−0.145773	+	0.501551i
$201$		0			0
$202$	1.21432	+	15.0993i	0.0854391	+	1.06239i
$203$	−13.9421	+	4.83896i	−0.978545	+	0.339629i
$204$		0			0
$205$	2.89026			0.201865
$206$	10.6283	+	5.04714i	0.740506	+	0.351651i
$207$		0			0
$208$	0.649856	−	0.216074i	0.0450594	−	0.0149821i
$209$	−21.3296	+	12.3147i	−1.47540	+	0.851823i
$210$		0			0
$211$	−1.05043	−	0.606467i	−0.0723147	−	0.0417509i	0.463407	−	0.886146i	$-0.346627\pi$
$211$	−1.05043	−	0.606467i	−0.0723147	−	0.0417509i	−0.535721	+	0.844395i	$0.679960\pi$
$212$	3.31070	+	20.4502i	0.227380	+	1.40452i
$213$		0			0
$214$	23.4427	−	1.88530i	1.60251	−	0.128877i
$215$	2.71445	−	4.70157i	0.185124	−	0.320644i
$216$		0			0
$217$	−3.92563	+	20.4636i	−0.266489	+	1.38916i
$218$	1.65227	−	3.47935i	0.111906	−	0.235651i
$219$		0			0
$220$	−11.2138	−	4.26065i	−0.756034	−	0.287253i
$221$			0.545031i			0.0366627i
$222$		0			0
$223$	18.1428	−	10.4748i	1.21493	−	0.701441i	0.251103	−	0.967960i	$-0.419207\pi$
$223$	18.1428	−	10.4748i	1.21493	−	0.701441i	0.963830	+	0.266519i	$0.0858735\pi$
$224$	−4.59256	+	14.2446i	−0.306853	+	0.951757i
$225$		0			0
$226$	−1.45630	−	18.1082i	−0.0968714	−	1.20454i
$227$	−10.3049	+	17.8486i	−0.683959	+	1.18465i	0.289803	+	0.957086i	$0.406410\pi$
$227$	−10.3049	+	17.8486i	−0.683959	+	1.18465i	−0.973763	+	0.227566i	$0.926923\pi$
$228$		0			0
$229$	−9.04093	−	15.6594i	−0.597441	−	1.03480i	−0.993197	−	0.116443i	$-0.962851\pi$
$229$	−9.04093	−	15.6594i	−0.597441	−	1.03480i	0.395756	−	0.918356i	$-0.370483\pi$
$230$	0.108551	+	1.34977i	0.00715766	+	0.0890014i
$231$		0			0
$232$	−11.3884	+	10.9187i	−0.747682	+	0.716847i
$233$	−14.3021	−	8.25735i	−0.936965	−	0.540957i	−0.0479572	−	0.998849i	$-0.515271\pi$
$233$	−14.3021	−	8.25735i	−0.936965	−	0.540957i	−0.889008	+	0.457893i	$0.848604\pi$
$234$		0			0
$235$	−4.60401	+	2.65813i	−0.300333	+	0.173397i
$236$	−4.00128	+	10.5312i	−0.260461	+	0.685521i
$237$		0			0
$238$	−9.60437	−	7.04517i	−0.622559	−	0.456671i
$239$	−3.21212	+	5.56356i	−0.207775	+	0.359877i	−0.951013	−	0.309150i	$-0.899956\pi$
$239$	−3.21212	+	5.56356i	−0.207775	+	0.359877i	0.743238	+	0.669027i	$0.233289\pi$
$240$		0			0
$241$	−2.18160	+	3.77864i	−0.140529	+	0.243403i	−0.927696	−	0.373337i	$-0.878214\pi$
$241$	−2.18160	+	3.77864i	−0.140529	+	0.243403i	0.787167	+	0.616740i	$0.211547\pi$
$242$	−2.46432	+	5.18936i	−0.158412	+	0.333585i
$243$		0			0
$244$	−6.63361	+	17.4593i	−0.424674	+	1.11772i
$245$	10.7055	−	1.55818i	0.683948	−	0.0995483i
$246$		0			0
$247$	−0.940950	+	0.543258i	−0.0598712	+	0.0345667i
$248$	5.31109	+	21.6330i	0.337255	+	1.37370i
$249$		0			0
$250$	13.6940	−	9.44611i	0.866083	−	0.597425i
$251$	4.63056			0.292278			0.146139	−	0.989264i	$-0.453315\pi$
$251$	4.63056			0.292278			0.146139	+	0.989264i	$0.453315\pi$
$252$		0			0
$253$	2.40452			0.151171
$254$	10.2970	−	7.10286i	0.646090	−	0.445673i
$255$		0			0
$256$	1.88989	+	15.8880i	0.118118	+	0.993000i
$257$	−6.46860	+	3.73465i	−0.403500	+	0.232961i	−0.687993	−	0.725717i	$-0.741508\pi$
$257$	−6.46860	+	3.73465i	−0.403500	+	0.232961i	0.284493	+	0.958678i	$0.408175\pi$
$258$		0			0
$259$	13.3028	−	15.3792i	0.826597	−	0.955617i
$260$	−0.494693	−	0.187957i	−0.0306796	−	0.0116566i
$261$		0			0
$262$	−2.63133	+	5.54106i	−0.162564	+	0.342328i
$263$	15.1179	−	26.1850i	0.932211	−	1.61464i	0.152678	−	0.988276i	$-0.451210\pi$
$263$	15.1179	−	26.1850i	0.932211	−	1.61464i	0.779533	−	0.626361i	$-0.215456\pi$
$264$		0			0
$265$	8.00415	−	13.8636i	0.491691	−	0.851634i
$266$	2.58977	−	23.6034i	0.158789	−	1.44722i
$267$		0			0
$268$	29.0501	+	11.0375i	1.77452	+	0.674223i
$269$	−19.7088	+	11.3789i	−1.20167	+	0.693782i	−0.960925	−	0.276808i	$-0.910723\pi$
$269$	−19.7088	+	11.3789i	−1.20167	+	0.693782i	−0.240740	+	0.970590i	$0.577390\pi$
$270$		0			0
$271$	−13.3326	−	7.69759i	−0.809899	−	0.467595i	0.0370221	−	0.999314i	$-0.488213\pi$
$271$	−13.3326	−	7.69759i	−0.809899	−	0.467595i	−0.846921	+	0.531719i	$0.821546\pi$
$272$	−12.4732	−	2.56226i	−0.756301	−	0.155360i
$273$		0			0
$274$	−2.18993	−	27.2306i	−0.132299	−	1.64506i
$275$	−5.06767	−	8.77745i	−0.305592	−	0.529300i
$276$		0			0
$277$	1.69907	−	2.94288i	0.102087	−	0.176820i	−0.810457	−	0.585798i	$-0.800781\pi$
$277$	1.69907	−	2.94288i	0.102087	−	0.176820i	0.912544	+	0.408978i	$0.134115\pi$
$278$	1.68329	+	20.9308i	0.100957	+	1.25534i
$279$		0			0
$280$	9.70662	−	6.28777i	0.580082	−	0.375766i
$281$	−10.5295	+	6.07918i	−0.628134	+	0.362654i	−0.780029	−	0.625743i	$-0.784796\pi$
$281$	−10.5295	+	6.07918i	−0.628134	+	0.362654i	0.151895	+	0.988397i	$0.451462\pi$
$282$		0			0
$283$			0.591173i			0.0351416i	0.999846	+	0.0175708i	$0.00559324\pi$
$283$			0.591173i			0.0351416i	−0.999846	+	0.0175708i	$0.994407\pi$
$284$	3.60826	−	9.49675i	0.214111	−	0.563529i
$285$		0			0
$286$	−0.403098	+	0.848843i	−0.0238357	+	0.0501931i
$287$	3.74223	+	3.23698i	0.220897	+	0.191073i
$288$		0			0
$289$	−3.43291	+	5.94598i	−0.201936	+	0.349764i
$290$	12.1522	−	0.977299i	0.713600	−	0.0573890i
$291$		0			0
$292$	21.7668	−	3.52384i	1.27381	−	0.206217i
$293$	3.94136	+	2.27554i	0.230257	+	0.132939i	0.610690	−	0.791869i	$-0.290892\pi$
$293$	3.94136	+	2.27554i	0.230257	+	0.132939i	−0.380434	+	0.924808i	$0.624225\pi$
$294$		0			0
$295$	7.53909	−	4.35269i	0.438943	−	0.253424i
$296$	6.06705	−	20.8745i	0.352640	−	1.21331i
$297$		0			0
$298$	0.0877985	+	0.0416937i	0.00508603	+	0.00241525i
$299$	0.106075			0.00613447
$300$		0			0
$301$	8.78016	−	3.04737i	0.506080	−	0.175648i
$302$	0.440862	+	5.48186i	0.0253687	+	0.315446i
$303$		0			0
$304$	−8.00913	−	24.0879i	−0.459355	−	1.38154i
$305$	12.4988	−	7.21621i	0.715681	−	0.413199i
$306$		0			0
$307$			21.3991i			1.22131i	0.791896	+	0.610655i	$0.209094\pi$
$307$			21.3991i			1.22131i	−0.791896	+	0.610655i	$0.790906\pi$
$308$	−9.74754	−	18.0756i	−0.555418	−	1.02995i
$309$		0			0
$310$	7.38381	−	15.5488i	0.419372	−	0.883113i
$311$	−7.71251			−0.437336			−0.218668	−	0.975799i	$-0.570171\pi$
$311$	−7.71251			−0.437336			−0.218668	+	0.975799i	$0.570171\pi$
$312$		0			0
$313$	−27.8319			−1.57315			−0.786576	−	0.617493i	$-0.788148\pi$
$313$	−27.8319			−1.57315			−0.786576	+	0.617493i	$0.788148\pi$
$314$	7.98037	+	11.5691i	0.450359	+	0.652882i
$315$		0			0
$316$	−1.82451	−	0.693215i	−0.102637	−	0.0389964i
$317$		−	31.8405i		−	1.78834i	−0.447729	−	0.894169i	$-0.647767\pi$
$317$		−	31.8405i		−	1.78834i	0.447729	−	0.894169i	$-0.352233\pi$
$318$		0			0
$319$		−	21.6482i		−	1.21207i
$320$	6.62708	−	10.4376i	0.370465	−	0.583481i
$321$		0			0
$322$	−1.37114	+	1.86922i	−0.0764108	+	0.104168i
$323$	20.2024			1.12409
$324$		0			0
$325$	−0.223559	−	0.387215i	−0.0124008	−	0.0214788i
$326$	0.697735	+	8.67593i	0.0386439	+	0.480516i
$327$		0			0
$328$	5.07940	+	1.47630i	0.280463	+	0.0815149i
$329$	−8.93814	−	1.71464i	−0.492775	−	0.0945314i
$330$		0			0
$331$		−	16.3826i		−	0.900468i	−0.892911	−	0.450234i	$-0.851341\pi$
$331$		−	16.3826i		−	0.900468i	0.892911	−	0.450234i	$-0.148659\pi$
$332$	8.90222	−	1.44119i	0.488573	−	0.0790954i
$333$		0			0
$334$	15.8756	−	1.27675i	0.868674	−	0.0698604i
$335$	−12.0069	−	20.7965i	−0.656005	−	1.13623i
$336$		0			0
$337$	−12.2748	+	21.2605i	−0.668649	+	1.15813i	0.309634	+	0.950856i	$0.399794\pi$
$337$	−12.2748	+	21.2605i	−0.668649	+	1.15813i	−0.978282	+	0.207277i	$0.933540\pi$
$338$	7.86869	−	16.5699i	0.428000	−	0.901283i
$339$		0			0
$340$	6.21847	+	7.62571i	0.337244	+	0.413562i
$341$	−26.4701	−	15.2825i	−1.43343	−	0.827593i
$342$		0			0
$343$	15.6062	+	9.97223i	0.842658	+	0.538450i
$344$	7.17191	−	6.87612i	0.386683	−	0.370736i
$345$		0			0
$346$	−19.4746	+	13.4336i	−1.04696	+	0.722195i
$347$	26.9330			1.44584			0.722919	−	0.690933i	$-0.242800\pi$
$347$	26.9330			1.44584			0.722919	+	0.690933i	$0.242800\pi$
$348$		0			0
$349$	−2.85095	−	4.93799i	−0.152608	−	0.264325i	0.779578	−	0.626306i	$-0.215434\pi$
$349$	−2.85095	−	4.93799i	−0.152608	−	0.264325i	−0.932185	+	0.361981i	$0.882100\pi$
$350$	9.71314	+	1.06573i	0.519189	+	0.0569655i
$351$		0			0
$352$	−17.5311	−	13.2156i	−0.934409	−	0.704392i
$353$	14.9321	+	8.62106i	0.794756	+	0.458853i	0.841634	−	0.540048i	$-0.181594\pi$
$353$	14.9321	+	8.62106i	0.794756	+	0.458853i	−0.0468782	+	0.998901i	$0.514927\pi$
$354$		0			0
$355$	−6.79856	+	3.92515i	−0.360830	+	0.208326i
$356$	−14.5850	+	11.8934i	−0.773001	+	0.630351i
$357$		0			0
$358$	−8.55434	+	18.0137i	−0.452111	+	0.952054i
$359$	15.0739	−	26.1087i	0.795568	−	1.37796i	−0.126910	−	0.991914i	$-0.540506\pi$
$359$	15.0739	−	26.1087i	0.795568	−	1.37796i	0.922478	−	0.386050i	$-0.126161\pi$
$360$		0			0
$361$	10.6367	+	18.4233i	0.559826	+	0.969646i
$362$	14.4733	+	20.9819i	0.760701	+	1.10278i
$363$		0			0
$364$	−0.430010	−	0.797398i	−0.0225386	−	0.0417950i
$365$	−14.7562	−	8.51947i	−0.772372	−	0.445929i
$366$		0			0
$367$	−18.3981	−	10.6222i	−0.960375	−	0.554473i	−0.0640866	−	0.997944i	$-0.520413\pi$
$367$	−18.3981	−	10.6222i	−0.960375	−	0.554473i	−0.896288	+	0.443472i	$0.853747\pi$
$368$	−0.498671	+	2.42756i	−0.0259950	+	0.126545i
$369$		0			0
$370$	−13.8273	+	9.53811i	−0.718849	+	0.495863i
$371$	25.8902	−	8.98585i	1.34415	−	0.466522i
$372$		0			0
$373$	−5.02868	−	8.70992i	−0.260375	−	0.450983i	0.705967	−	0.708245i	$-0.250513\pi$
$373$	−5.02868	−	8.70992i	−0.260375	−	0.450983i	−0.966342	+	0.257262i	$0.917180\pi$
$374$	14.3825	−	9.92108i	0.743703	−	0.513007i
$375$		0			0
$376$	−9.44890	+	2.31979i	−0.487290	+	0.119634i
$377$		−	0.955004i		−	0.0491852i
$378$		0			0
$379$		−	1.19201i		−	0.0612292i	−0.999531	−	0.0306146i	$-0.990254\pi$
$379$		−	1.19201i		−	0.0612292i	0.999531	−	0.0306146i	$-0.00974646\pi$
$380$	−6.96692	+	18.3366i	−0.357395	+	0.940646i
$381$		0			0
$382$	9.73374	+	14.1109i	0.498021	+	0.721979i
$383$	−12.9339	−	22.4022i	−0.660892	−	1.14470i	−0.980382	−	0.197109i	$-0.936845\pi$
$383$	−12.9339	−	22.4022i	−0.660892	−	1.14470i	0.319490	−	0.947590i	$-0.396489\pi$
$384$		0			0
$385$	−2.98973	+	15.5849i	−0.152371	+	0.794283i
$386$	−4.83187	−	7.00473i	−0.245936	−	0.356531i
$387$		0			0
$388$	20.2381	−	3.27635i	1.02743	−	0.166332i
$389$	7.09766	+	4.09784i	0.359866	+	0.207769i	0.669022	−	0.743243i	$-0.266713\pi$
$389$	7.09766	+	4.09784i	0.359866	+	0.207769i	−0.309156	+	0.951011i	$0.600047\pi$
$390$		0			0
$391$	−1.70809	−	0.986165i	−0.0863817	−	0.0498725i
$392$	19.6099	+	2.72981i	0.990449	+	0.137876i
$393$		0			0
$394$	−13.6306	+	9.40238i	−0.686698	+	0.473685i
$395$	0.754097	+	1.30613i	0.0379427	+	0.0657187i
$396$		0			0
$397$	−5.78210	+	10.0149i	−0.290195	+	0.502633i	−0.973856	−	0.227167i	$-0.927054\pi$
$397$	−5.78210	+	10.0149i	−0.290195	+	0.502633i	0.683660	+	0.729800i	$0.260387\pi$
$398$	−12.8041	−	6.08040i	−0.641811	−	0.304783i
$399$		0			0
$400$	9.91253	−	3.29587i	0.495627	−	0.164794i
$401$	3.76137	−	2.17163i	0.187834	−	0.108446i	−0.403134	−	0.915141i	$-0.632079\pi$
$401$	3.76137	−	2.17163i	0.187834	−	0.108446i	0.590968	+	0.806695i	$0.298746\pi$
$402$		0			0
$403$	−1.16772	−	0.674183i	−0.0581682	−	0.0335834i
$404$	16.6023	−	13.5385i	0.825997	−	0.673568i
$405$		0			0
$406$	16.8288	+	12.3446i	0.835199	+	0.612650i
$407$	14.9140	+	25.8318i	0.739260	+	1.28044i
$408$		0			0
$409$	7.61225			0.376402			0.188201	−	0.982131i	$-0.439734\pi$
$409$	7.61225			0.376402			0.188201	+	0.982131i	$0.439734\pi$
$410$	−2.32091	−	3.36461i	−0.114622	−	0.166166i
$411$		0			0
$412$	−2.65913	−	16.4255i	−0.131006	−	0.809225i
$413$	14.6362	+	2.80774i	0.720202	+	0.138160i
$414$		0			0
$415$	−6.03500	−	3.48431i	−0.296246	−	0.171038i
$416$	−0.773378	−	0.583000i	−0.0379180	−	0.0285839i
$417$		0			0
$418$	31.4637	+	14.9414i	1.53894	+	0.730809i
$419$	8.94987	−	15.5016i	0.437230	−	0.757304i	−0.560245	−	0.828327i	$-0.689293\pi$
$419$	8.94987	−	15.5016i	0.437230	−	0.757304i	0.997475	+	0.0710229i	$0.0226263\pi$
$420$		0			0
$421$	−9.72803	−	16.8494i	−0.474115	−	0.821191i	0.525446	−	0.850827i	$-0.323899\pi$
$421$	−9.72803	−	16.8494i	−0.474115	−	0.821191i	−0.999561	+	0.0296358i	$0.990565\pi$
$422$	0.137507	+	1.70983i	0.00669376	+	0.0832331i
$423$		0			0
$424$	21.1479	−	20.2758i	1.02703	−	0.984678i
$425$			8.31359i			0.403268i
$426$		0			0
$427$	24.2650	+	4.65487i	1.17427	+	0.225265i
$428$	−21.0194	−	25.7762i	−1.01601	−	1.24594i
$429$		0			0
$430$	−7.65292	+	0.615462i	−0.369056	+	0.0296802i
$431$	−5.20757	−	9.01978i	−0.250840	−	0.434467i	0.712917	−	0.701248i	$-0.247373\pi$
$431$	−5.20757	−	9.01978i	−0.250840	−	0.434467i	−0.963757	+	0.266781i	$0.914040\pi$
$432$		0			0
$433$	−9.88442			−0.475015			−0.237507	−	0.971386i	$-0.576330\pi$
$433$	−9.88442			−0.475015			−0.237507	+	0.971386i	$0.576330\pi$
$434$	26.9744	−	11.8626i	1.29481	−	0.569422i
$435$		0			0
$436$	−5.37717	+	0.870513i	−0.257520	+	0.0416900i
$437$		−	3.93183i		−	0.188085i
$438$		0			0
$439$			15.3828i			0.734182i	0.930185	+	0.367091i	$0.119646\pi$
$439$			15.3828i			0.734182i	−0.930185	+	0.367091i	$0.880354\pi$
$440$	4.04489	+	16.4755i	0.192833	+	0.785441i
$441$		0			0
$442$	0.634481	−	0.437666i	0.0301792	−	0.0208176i
$443$	7.02818			0.333919			0.166959	−	0.985964i	$-0.446605\pi$
$443$	7.02818			0.333919			0.166959	+	0.985964i	$0.446605\pi$
$444$		0			0
$445$	14.5425			0.689381
$446$	−26.7627	−	12.7091i	−1.26725	−	0.601791i
$447$		0			0
$448$	20.2703	−	6.09226i	0.957681	−	0.287832i
$449$			23.0647i			1.08849i	0.838926	+	0.544246i	$0.183184\pi$
$449$			23.0647i			1.08849i	−0.838926	+	0.544246i	$0.816816\pi$
$450$		0			0
$451$	−6.28567	+	3.62903i	−0.295981	+	0.170884i
$452$	−19.9107	+	16.2364i	−0.936521	+	0.763696i
$453$		0			0
$454$	29.0528	−	2.33648i	1.36352	−	0.109656i
$455$	−0.131891	+	0.687525i	−0.00618316	+	0.0322317i
$456$		0			0
$457$	−4.96764			−0.232376			−0.116188	−	0.993227i	$-0.537068\pi$
$457$	−4.96764			−0.232376			−0.116188	+	0.993227i	$0.537068\pi$
$458$	−10.9694	+	23.0993i	−0.512566	+	1.07936i
$459$		0			0
$460$	1.48413	−	1.21025i	0.0691979	−	0.0564281i
$461$	26.7954	−	15.4703i	1.24799	−	0.720525i	0.277279	−	0.960789i	$-0.410567\pi$
$461$	26.7954	−	15.4703i	1.24799	−	0.720525i	0.970708	+	0.240264i	$0.0772341\pi$
$462$		0			0
$463$	18.3355	+	10.5860i	0.852123	+	0.491973i	0.861366	−	0.507984i	$-0.169609\pi$
$463$	18.3355	+	10.5860i	0.852123	+	0.491973i	−0.00924383	+	0.999957i	$0.502942\pi$
$464$	21.8556	+	4.48960i	1.01462	+	0.208424i
$465$		0			0
$466$	1.87223	+	23.2801i	0.0867295	+	1.07843i
$467$	−12.4027	+	21.4821i	−0.573928	+	0.994073i	0.422229	+	0.906489i	$0.361248\pi$
$467$	−12.4027	+	21.4821i	−0.573928	+	0.994073i	−0.996157	+	0.0875838i	$0.972085\pi$
$468$		0			0
$469$	7.74512	−	40.3739i	0.357636	−	1.86429i
$470$	6.79145	+	3.22512i	0.313266	+	0.148764i
$471$		0			0
$472$	15.4726	−	3.79866i	0.712185	−	0.174848i
$473$			13.6331i			0.626852i
$474$		0			0
$475$	−14.3527	+	8.28654i	−0.658547	+	0.380213i
$476$	−0.489009	+	16.8380i	−0.0224137	+	0.771768i
$477$		0			0
$478$	9.05602	−	0.728302i	0.414213	−	0.0333118i
$479$	−0.817964	+	1.41676i	−0.0373737	+	0.0647332i	−0.884107	−	0.467284i	$-0.845233\pi$
$479$	−0.817964	+	1.41676i	−0.0373737	+	0.0647332i	0.846733	+	0.532017i	$0.178566\pi$
$480$		0			0
$481$	0.657927	+	1.13956i	0.0299989	+	0.0519596i
$482$	6.15063	−	0.494645i	0.280154	−	0.0225305i
$483$		0			0
$484$	8.01991	−	1.29835i	0.364541	−	0.0590159i
$485$	−13.7198	−	7.92113i	−0.622984	−	0.359680i
$486$		0			0
$487$	−12.4864	+	7.20905i	−0.565815	+	0.326673i	−0.755476	−	0.655176i	$-0.772594\pi$
$487$	−12.4864	+	7.20905i	−0.565815	+	0.326673i	0.189661	+	0.981850i	$0.439261\pi$
$488$	25.6516	−	6.29770i	1.16119	−	0.285083i
$489$		0			0
$490$	−10.4105	−	11.2112i	−0.470299	−	0.506472i
$491$	5.41087	−	9.37190i	0.244189	−	0.422948i	−0.717714	−	0.696338i	$-0.754812\pi$
$491$	5.41087	−	9.37190i	0.244189	−	0.422948i	0.961903	+	0.273390i	$0.0881449\pi$
$492$		0			0
$493$	−8.87856	+	15.3781i	−0.399870	+	0.692595i
$494$	1.38801	+	0.659137i	0.0624495	+	0.0296560i
$495$		0			0
$496$	20.9185	−	23.5542i	0.939269	−	1.05762i
$497$	−13.1986	−	2.53195i	−0.592038	−	0.113573i
$498$		0			0
$499$	−14.6556	+	8.46143i	−0.656076	+	0.378786i	−0.790780	−	0.612100i	$-0.790325\pi$
$499$	−14.6556	+	8.46143i	−0.656076	+	0.378786i	0.134704	+	0.990886i	$0.456992\pi$
$500$	−21.9928	−	8.35610i	−0.983548	−	0.373696i
$501$		0			0
$502$	−3.71839	−	5.39052i	−0.165960	−	0.240591i
$503$	15.3914			0.686267			0.343134	−	0.939287i	$-0.388512\pi$
$503$	15.3914			0.686267			0.343134	+	0.939287i	$0.388512\pi$
$504$		0			0
$505$	−16.5540			−0.736644
$506$	−1.93086	−	2.79915i	−0.0858371	−	0.124438i
$507$		0			0
$508$	−16.5372	−	6.28324i	−0.733718	−	0.278774i
$509$	7.38951	−	4.26633i	0.327534	−	0.189102i	−0.327212	−	0.944951i	$-0.606109\pi$
$509$	7.38951	−	4.26633i	0.327534	−	0.189102i	0.654746	+	0.755849i	$0.272776\pi$
$510$		0			0
$511$	−9.56437	−	27.5571i	−0.423103	−	1.21905i
$512$	16.9779	−	14.9583i	0.750325	−	0.661069i
$513$		0			0
$514$	9.54193	+	4.53126i	0.420876	+	0.199865i
$515$	−6.42889	+	11.1352i	−0.283291	+	0.490674i
$516$		0			0
$517$	6.67512	−	11.5616i	0.293572	−	0.508481i
$518$	−28.5855	−	3.13641i	−1.25598	−	0.137806i
$519$		0			0
$520$	0.178439	+	0.726814i	0.00782508	+	0.0318729i
$521$	−6.78339	+	3.91639i	−0.297186	+	0.171580i	−0.641178	−	0.767392i	$-0.721554\pi$
$521$	−6.78339	+	3.91639i	−0.297186	+	0.171580i	0.343992	+	0.938972i	$0.388221\pi$
$522$		0			0
$523$	−9.19266	−	5.30738i	−0.401967	−	0.232076i	0.285365	−	0.958419i	$-0.407885\pi$
$523$	−9.19266	−	5.30738i	−0.401967	−	0.232076i	−0.687332	+	0.726343i	$0.741218\pi$
$524$	8.56344	−	1.38634i	0.374096	−	0.0605626i
$525$		0			0
$526$	−42.6223	+	3.42777i	−1.85842	+	0.149458i
$527$	12.5356	+	21.7123i	0.546059	+	0.945801i
$528$		0			0
$529$	11.3081	−	19.5862i	0.491655	−	0.851572i
$530$	−22.5663	+	1.81482i	−0.980218	+	0.0788309i
$531$		0			0
$532$	−29.5568	+	15.9390i	−1.28145	+	0.691042i
$533$	−0.277290	+	0.160094i	−0.0120108	+	0.00693443i
$534$		0			0
$535$			25.7012i			1.11116i
$536$	−10.4786	−	42.6811i	−0.452606	−	1.84354i
$537$		0			0
$538$	29.0727	+	13.8060i	1.25341	+	0.595220i
$539$	−21.3255	+	16.8305i	−0.918556	+	0.724943i
$540$		0			0
$541$	21.3452	−	36.9709i	0.917701	−	1.58950i	0.114803	−	0.993388i	$-0.463376\pi$
$541$	21.3452	−	36.9709i	0.917701	−	1.58950i	0.802898	−	0.596116i	$-0.203290\pi$
$542$	1.74531	+	21.7020i	0.0749677	+	0.932181i
$543$		0			0
$544$	7.03336	+	16.5779i	0.301553	+	0.710770i
$545$	3.64529	+	2.10461i	0.156147	+	0.0901516i
$546$		0			0
$547$	23.1435	−	13.3619i	0.989546	−	0.571315i	0.0844076	−	0.996431i	$-0.473100\pi$
$547$	23.1435	−	13.3619i	0.989546	−	0.571315i	0.905139	+	0.425117i	$0.139767\pi$
$548$	−29.9411	+	24.4158i	−1.27902	+	1.04299i
$549$		0			0
$550$	−6.14862	+	12.9478i	−0.262178	+	0.552094i
$551$	−35.3987			−1.50803
$552$		0			0
$553$	−0.486436	+	2.53570i	−0.0206853	+	0.107829i
$554$	−4.79023	+	0.385239i	−0.203518	+	0.0163673i
$555$		0			0
$556$	23.0142	−	18.7672i	0.976020	−	0.795905i
$557$	−35.8496	+	20.6977i	−1.51899	+	0.876992i	−0.519244	+	0.854626i	$0.673787\pi$
$557$	−35.8496	+	20.6977i	−1.51899	+	0.876992i	−0.999750	+	0.0223660i	$0.992880\pi$
$558$		0			0
$559$			0.601421i			0.0254374i
$560$	−15.1142	−	6.25052i	−0.638693	−	0.264133i
$561$		0			0
$562$	15.5322	+	7.37589i	0.655184	+	0.311133i
$563$	−9.47419			−0.399289			−0.199645	−	0.979868i	$-0.563979\pi$
$563$	−9.47419			−0.399289			−0.199645	+	0.979868i	$0.563979\pi$
$564$		0			0
$565$	19.8528			0.835212
$566$	0.688196	−	0.474718i	0.0289270	−	0.0199539i
$567$		0			0
$568$	−13.9528	+	3.42554i	−0.585448	+	0.143733i
$569$			17.6227i			0.738783i	0.929274	+	0.369391i	$0.120434\pi$
$569$			17.6227i			0.738783i	−0.929274	+	0.369391i	$0.879566\pi$
$570$		0			0
$571$		−	13.3121i		−	0.557093i	−0.960423	−	0.278546i	$-0.910147\pi$
$571$		−	13.3121i		−	0.557093i	0.960423	−	0.278546i	$-0.0898526\pi$
$572$	1.31185	−	0.212376i	0.0548510	−	0.00887988i
$573$		0			0
$574$	0.763183	−	6.95573i	0.0318547	−	0.290326i
$575$	1.61800			0.0674754
$576$		0			0
$577$	4.73291	+	8.19764i	0.197034	+	0.341272i	0.947565	−	0.319562i	$-0.103536\pi$
$577$	4.73291	+	8.19764i	0.197034	+	0.341272i	−0.750532	+	0.660835i	$0.770202\pi$
$578$	9.67850	−	0.778363i	0.402573	−	0.0323756i
$579$		0			0
$580$	−10.8960	−	13.3618i	−0.452432	−	0.554818i
$581$	−3.91165	−	11.2703i	−0.162283	−	0.467572i
$582$		0			0
$583$			40.2003i			1.66492i
$584$	−21.5811	−	22.5095i	−0.893034	−	0.931448i
$585$		0			0
$586$	−0.515946	−	6.41550i	−0.0213135	−	0.265022i
$587$	2.72485	+	4.71959i	0.112467	+	0.194798i	0.916764	−	0.399429i	$-0.130791\pi$
$587$	2.72485	+	4.71959i	0.112467	+	0.194798i	−0.804297	+	0.594227i	$0.797458\pi$
$588$		0			0
$589$	−24.9896	+	43.2833i	−1.02968	+	1.78346i
$590$	−11.1210	−	5.28114i	−0.457845	−	0.217421i
$591$		0			0
$592$	−29.1723	+	9.69967i	−1.19898	+	0.398654i
$593$	13.8445	+	7.99315i	0.568527	+	0.328239i	0.756561	−	0.653923i	$-0.226878\pi$
$593$	13.8445	+	7.99315i	0.568527	+	0.328239i	−0.188034	+	0.982163i	$0.560211\pi$
$594$		0			0
$595$	8.51564	−	9.84481i	0.349107	−	0.403598i
$596$	−0.0219667	−	0.135688i	−0.000899791	−	0.00555801i
$597$		0			0
$598$	−0.0851792	−	0.123484i	−0.00348324	−	0.00504963i
$599$	4.64512			0.189795			0.0948973	−	0.995487i	$-0.469748\pi$
$599$	4.64512			0.189795			0.0948973	+	0.995487i	$0.469748\pi$
$600$		0			0
$601$	9.45270	+	16.3726i	0.385584	+	0.667851i	0.991850	−	0.127411i	$-0.0406667\pi$
$601$	9.45270	+	16.3726i	0.385584	+	0.667851i	−0.606266	+	0.795262i	$0.707333\pi$
$602$	−10.5981	−	7.77408i	−0.431945	−	0.316848i
$603$		0			0
$604$	6.02753	−	4.91521i	0.245257	−	0.199997i
$605$	−5.43686	−	3.13897i	−0.221040	−	0.127617i
$606$		0			0
$607$	2.14914	−	1.24081i	0.0872308	−	0.0503627i	−0.455750	−	0.890108i	$-0.650629\pi$
$607$	2.14914	−	1.24081i	0.0872308	−	0.0503627i	0.542981	+	0.839745i	$0.317296\pi$
$608$	−21.6098	+	28.6664i	−0.876393	+	1.16258i
$609$		0			0
$610$	−18.4372	−	8.75545i	−0.746501	−	0.354498i
$611$	0.294471	−	0.510039i	0.0119130	−	0.0206340i
$612$		0			0
$613$	1.20503	+	2.08717i	0.0486706	+	0.0842999i	0.889334	−	0.457257i	$-0.151168\pi$
$613$	1.20503	+	2.08717i	0.0486706	+	0.0842999i	−0.840664	+	0.541557i	$0.817835\pi$
$614$	24.9111	−	17.1837i	1.00533	−	0.693478i
$615$		0			0
$616$	−13.2147	+	25.8622i	−0.532437	+	1.04202i
$617$	−28.2269	−	16.2968i	−1.13637	−	0.656084i	−0.190842	−	0.981621i	$-0.561122\pi$
$617$	−28.2269	−	16.2968i	−1.13637	−	0.656084i	−0.945530	+	0.325536i	$0.894455\pi$
$618$		0			0
$619$	6.37568	+	3.68100i	0.256260	+	0.147952i	0.622627	−	0.782518i	$-0.286065\pi$
$619$	6.37568	+	3.68100i	0.256260	+	0.147952i	−0.366367	+	0.930470i	$0.619399\pi$
$620$	−24.0300	+	3.89023i	−0.965066	+	0.156235i
$621$		0			0
$622$	6.19323	+	8.97829i	0.248326	+	0.359996i
$623$	18.8292	+	16.2870i	0.754376	+	0.652526i
$624$		0			0
$625$	2.56115	+	4.43605i	0.102446	+	0.177442i
$626$	22.3493	+	32.3997i	0.893258	+	1.29495i
$627$		0			0
$628$	7.05949	−	18.5802i	0.281704	−	0.741431i
$629$		−	24.4667i		−	0.975550i
$630$		0			0
$631$		−	8.28274i		−	0.329731i	−0.986316	−	0.164865i	$-0.947281\pi$
$631$		−	8.28274i		−	0.329731i	0.986316	−	0.164865i	$-0.0527190\pi$
$632$	0.658112	+	2.68060i	0.0261783	+	0.106629i
$633$		0			0
$634$	−37.0661	+	25.5682i	−1.47208	+	1.01544i
$635$	6.83506	+	11.8387i	0.271241	+	0.469803i
$636$		0			0
$637$	−0.940770	+	0.742475i	−0.0372747	+	0.0294179i
$638$	−25.2011	+	17.3837i	−0.997721	+	0.688229i
$639$		0			0
$640$	−17.4723	+	0.666806i	−0.690652	+	0.0263578i
$641$	32.1249	+	18.5473i	1.26886	+	0.732575i	0.974772	−	0.223204i	$-0.0716515\pi$
$641$	32.1249	+	18.5473i	1.26886	+	0.732575i	0.294086	+	0.955779i	$0.404985\pi$
$642$		0			0
$643$	−16.1566	−	9.32802i	−0.637154	−	0.367861i	0.146363	−	0.989231i	$-0.453243\pi$
$643$	−16.1566	−	9.32802i	−0.637154	−	0.367861i	−0.783518	+	0.621370i	$0.786577\pi$
$644$	3.27704	+	0.0951718i	0.129133	+	0.00375029i
$645$		0			0
$646$	−16.2227	−	23.5180i	−0.638275	−	0.925304i
$647$	8.56124	+	14.8285i	0.336577	+	0.582969i	0.983786	−	0.179344i	$-0.0573974\pi$
$647$	8.56124	+	14.8285i	0.336577	+	0.582969i	−0.647209	+	0.762312i	$0.724064\pi$
$648$		0			0
$649$	−10.9305	+	18.9322i	−0.429061	+	0.743156i
$650$	−0.271244	+	0.571186i	−0.0106391	+	0.0224038i
$651$		0			0
$652$	9.53954	−	7.77911i	0.373597	−	0.304654i
$653$	18.1433	−	10.4750i	0.710001	−	0.409919i	−0.101061	−	0.994880i	$-0.532224\pi$
$653$	18.1433	−	10.4750i	0.710001	−	0.409919i	0.811061	+	0.584961i	$0.198890\pi$
$654$		0			0
$655$	−5.80533	−	3.35171i	−0.226833	−	0.130962i
$656$	−2.36023	−	7.09851i	−0.0921513	−	0.277150i
$657$		0			0
$658$	5.18136	+	11.7819i	0.201991	+	0.459308i
$659$	−17.2213	−	29.8281i	−0.670845	−	1.16194i	−0.977665	−	0.210170i	$-0.932598\pi$
$659$	−17.2213	−	29.8281i	−0.670845	−	1.16194i	0.306820	−	0.951768i	$-0.400735\pi$
$660$		0			0
$661$	23.3282			0.907361			0.453681	−	0.891164i	$-0.350111\pi$
$661$	23.3282			0.907361			0.453681	+	0.891164i	$0.350111\pi$
$662$	−19.0713	+	13.1554i	−0.741226	+	0.511298i
$663$		0			0
$664$	−8.82629	−	9.20596i	−0.342526	−	0.357260i
$665$	25.4842	+	4.88875i	0.988234	+	0.189578i
$666$		0			0
$667$	2.99291	+	1.72796i	0.115886	+	0.0669069i
$668$	−14.2346	−	17.4559i	−0.550752	−	0.675388i
$669$		0			0
$670$	−14.5680	+	30.6772i	−0.562810	+	1.18516i
$671$	−18.1214	+	31.3872i	−0.699570	+	1.21169i
$672$		0			0
$673$	−10.8472	−	18.7879i	−0.418129	−	0.724220i	0.577623	−	0.816304i	$-0.303981\pi$
$673$	−10.8472	−	18.7879i	−0.418129	−	0.724220i	−0.995751	+	0.0920839i	$0.970647\pi$
$674$	34.6065	−	2.78312i	1.33299	−	0.107202i
$675$		0			0
$676$	−25.6080	+	4.14569i	−0.984922	+	0.159450i
$677$			0.913354i			0.0351030i	0.999846	+	0.0175515i	$0.00558711\pi$
$677$			0.913354i			0.0351030i	−0.999846	+	0.0175515i	$0.994413\pi$
$678$		0			0
$679$	−8.89264	−	25.6217i	−0.341268	−	0.983269i
$680$	3.88375	−	13.3626i	0.148935	−	0.512431i
$681$		0			0
$682$	3.46508	+	43.0863i	0.132685	+	1.64986i
$683$	−20.9596	−	36.3031i	−0.801996	−	1.38910i	−0.918300	−	0.395884i	$-0.870438\pi$
$683$	−20.9596	−	36.3031i	−0.801996	−	1.38910i	0.116305	−	0.993214i	$-0.462895\pi$
$684$		0			0
$685$	29.8540			1.14066
$686$	−0.923102	−	26.1753i	−0.0352442	−	0.999379i
$687$		0			0
$688$	−13.7637	−	2.82736i	−0.524738	−	0.107792i
$689$			1.77342i			0.0675620i
$690$		0			0
$691$			44.8729i			1.70704i	0.521056	+	0.853522i	$0.325538\pi$
$691$			44.8729i			1.70704i	−0.521056	+	0.853522i	$0.674462\pi$
$692$	31.2767	+	11.8835i	1.18896	+	0.451742i
$693$		0			0
$694$	−21.6275	−	31.3532i	−0.820967	−	1.19015i
$695$	−22.9472			−0.870438
$696$		0			0
$697$	5.95348			0.225504
$698$	−3.45907	+	7.28410i	−0.130928	+	0.275707i
$699$		0			0
$700$	−6.55912	−	12.1630i	−0.247911	−	0.459720i
$701$			9.85201i			0.372105i	0.982540	+	0.186053i	$0.0595695\pi$
$701$			9.85201i			0.372105i	−0.982540	+	0.186053i	$0.940431\pi$
$702$		0			0
$703$	42.2397	−	24.3871i	1.59310	−	0.919776i
$704$	−1.30686	+	31.0205i	−0.0492541	+	1.16913i
$705$		0			0
$706$	−1.95470	−	24.3056i	−0.0735660	−	0.914752i
$707$	−21.4337	−	18.5398i	−0.806095	−	0.697262i
$708$		0			0
$709$	1.82140			0.0684039			0.0342020	−	0.999415i	$-0.489111\pi$
$709$	1.82140			0.0684039			0.0342020	+	0.999415i	$0.489111\pi$
$710$	10.0287	+	4.76240i	0.376369	+	0.178730i
$711$		0			0
$712$	25.5573	+	7.42807i	0.957799	+	0.278379i
$713$	4.22568	−	2.43970i	0.158253	−	0.0913674i
$714$		0			0
$715$	−0.889327	−	0.513453i	−0.0332590	−	0.0192021i
$716$	27.8393	−	4.50693i	1.04040	−	0.168432i
$717$		0			0
$718$	−42.4981	+	3.41778i	−1.58601	+	0.127550i
$719$	−18.5276	+	32.0907i	−0.690962	+	1.19678i	0.280561	+	0.959836i	$0.409479\pi$
$719$	−18.5276	+	32.0907i	−0.690962	+	1.19678i	−0.971523	+	0.236945i	$0.923854\pi$
$720$		0			0
$721$	−20.7949	+	7.21738i	−0.774442	+	0.268789i
$722$	12.9055	−	27.1765i	0.480294	−	1.01140i
$723$		0			0
$724$	12.8032	−	33.6974i	0.475827	−	1.25235i
$725$		−	14.5671i		−	0.541008i
$726$		0			0
$727$	−19.2090	+	11.0903i	−0.712422	+	0.411317i	−0.811957	−	0.583717i	$-0.801598\pi$
$727$	−19.2090	+	11.0903i	−0.712422	+	0.411317i	0.0995353	+	0.995034i	$0.468264\pi$
$728$	−0.582964	+	1.14090i	−0.0216061	+	0.0422846i
$729$		0			0
$730$	1.93166	+	24.0191i	0.0714941	+	0.888989i
$731$	5.59134	−	9.68448i	0.206803	−	0.358194i
$732$		0			0
$733$	−26.8554	−	46.5149i	−0.991926	−	1.71807i	−0.605791	−	0.795624i	$-0.707143\pi$
$733$	−26.8554	−	46.5149i	−0.991926	−	1.71807i	−0.386135	−	0.922442i	$-0.626190\pi$
$734$	2.40842	+	29.9473i	0.0888964	+	1.10538i
$735$		0			0
$736$	3.22641	−	1.36884i	0.118927	−	0.0504563i
$737$	52.2244	+	30.1518i	1.92371	+	1.11066i
$738$		0			0
$739$	22.4805	−	12.9791i	0.826959	−	0.477445i	−0.0258513	−	0.999666i	$-0.508230\pi$
$739$	22.4805	−	12.9791i	0.826959	−	0.477445i	0.852810	+	0.522221i	$0.174896\pi$
$740$	22.2070	+	8.43748i	0.816345	+	0.310168i
$741$		0			0
$742$	−31.2507	−	22.9236i	−1.14725	−	0.841551i
$743$	−14.1181	+	24.4532i	−0.517942	+	0.897102i	0.481841	+	0.876259i	$0.339968\pi$
$743$	−14.1181	+	24.4532i	−0.517942	+	0.897102i	−0.999783	+	0.0208431i	$0.993365\pi$
$744$		0			0
$745$	−0.0531081	+	0.0919859i	−0.00194573	+	0.00337010i
$746$	−6.10131	+	12.8481i	−0.223385	+	0.470404i
$747$		0			0
$748$	−23.0986	−	8.77626i	−0.844570	−	0.320892i
$749$	−28.7843	+	33.2771i	−1.05175	+	1.21592i
$750$		0			0
$751$	16.6206	−	9.59592i	0.606495	−	0.350160i	−0.165098	−	0.986277i	$-0.552794\pi$
$751$	16.6206	−	9.59592i	0.606495	−	0.350160i	0.771592	+	0.636117i	$0.219461\pi$
$752$	10.2881	+	9.13683i	0.375168	+	0.333186i
$753$		0			0
$754$	−1.11174	+	0.766878i	−0.0404871	+	0.0279281i
$755$	−6.00998			−0.218726
$756$		0			0
$757$	40.6959			1.47912			0.739558	−	0.673092i	$-0.235034\pi$
$757$	40.6959			1.47912			0.739558	+	0.673092i	$0.235034\pi$
$758$	−1.38764	+	0.957193i	−0.0504013	+	0.0347668i
$759$		0			0
$760$	26.9405	−	6.61413i	0.977233	−	0.239920i
$761$	29.7072	−	17.1515i	1.07689	−	0.621740i	0.146831	−	0.989162i	$-0.453093\pi$
$761$	29.7072	−	17.1515i	1.07689	−	0.621740i	0.930054	+	0.367422i	$0.119759\pi$
$762$		0			0
$763$	2.36274	+	6.80757i	0.0855368	+	0.246450i
$764$	8.61053	−	22.6625i	0.311518	−	0.819899i
$765$		0			0
$766$	−15.6928	+	33.0458i	−0.567003	+	1.19399i
$767$	−0.482197	+	0.835190i	−0.0174111	+	0.0301570i
$768$		0			0
$769$	−24.8681	+	43.0728i	−0.896766	+	1.55324i	−0.0651624	+	0.997875i	$0.520757\pi$
$769$	−24.8681	+	43.0728i	−0.896766	+	1.55324i	−0.831604	+	0.555370i	$0.812577\pi$
$770$	20.5435	−	9.03447i	0.740337	−	0.325580i
$771$		0			0
$772$	−4.27430	+	11.2497i	−0.153836	+	0.404887i
$773$	9.51823	−	5.49535i	0.342347	−	0.197654i	−0.318962	−	0.947767i	$-0.603334\pi$
$773$	9.51823	−	5.49535i	0.342347	−	0.197654i	0.661309	+	0.750113i	$0.270001\pi$
$774$		0			0
$775$	−17.8117	−	10.2836i	−0.639815	−	0.369397i
$776$	−20.0654	−	20.9286i	−0.720307	−	0.751292i
$777$		0			0
$778$	−0.929124	−	11.5531i	−0.0333107	−	0.414200i
$779$	5.93412	+	10.2782i	0.212612	+	0.368254i
$780$		0			0
$781$	9.85689	−	17.0726i	0.352707	−	0.610907i
$782$	0.223598	+	2.78032i	0.00799586	+	0.0994240i
$783$		0			0
$784$	−12.5691	−	25.0203i	−0.448897	−	0.893583i
$785$	−13.3013	+	7.67949i	−0.474743	+	0.274093i
$786$		0			0
$787$			33.9037i			1.20854i	0.796781	+	0.604269i	$0.206535\pi$
$787$			33.9037i			1.20854i	−0.796781	+	0.604269i	$0.793465\pi$
$788$	21.8910	+	8.31741i	0.779834	+	0.296295i
$789$		0			0
$790$	0.914948	−	1.92670i	0.0325524	−	0.0685488i
$791$	25.7048	+	22.2343i	0.913957	+	0.790561i
$792$		0			0
$793$	−0.799421	+	1.38464i	−0.0283883	+	0.0491700i
$794$	16.3016	−	1.31101i	0.578523	−	0.0465259i
$795$		0			0
$796$	3.20351	+	19.7881i	0.113546	+	0.701371i
$797$	28.2411	+	16.3050i	1.00035	+	0.577553i	0.908352	−	0.418206i	$-0.137341\pi$
$797$	28.2411	+	16.3050i	1.00035	+	0.577553i	0.0919989	+	0.995759i	$0.470674\pi$
$798$		0			0
$799$	−9.48353	+	5.47532i	−0.335503	+	0.193703i
$800$	−11.7967	−	8.89275i	−0.417075	−	0.314406i
$801$		0			0
$802$	−5.54845	−	2.63484i	−0.195923	−	0.0930395i
$803$	42.7884			1.50997
$804$		0			0
$805$	−1.91601	−	1.65733i	−0.0675306	−	0.0584131i
$806$	0.152861	+	1.90074i	0.00538430	+	0.0669507i
$807$		0			0
$808$	−29.0923	−	8.45551i	−1.02346	−	0.297464i
$809$	−7.22387	+	4.17070i	−0.253978	+	0.146634i	−0.621584	−	0.783347i	$-0.713511\pi$
$809$	−7.22387	+	4.17070i	−0.253978	+	0.146634i	0.367606	+	0.929981i	$0.380177\pi$
$810$		0			0
$811$		−	26.9277i		−	0.945560i	−0.881180	−	0.472780i	$-0.843250\pi$
$811$		−	26.9277i		−	0.945560i	0.881180	−	0.472780i	$-0.156750\pi$
$812$	0.856843	−	29.5035i	0.0300693	−	1.03537i
$813$		0			0
$814$	18.0952	−	38.1049i	0.634237	−	1.33558i
$815$	−9.51177			−0.333183
$816$		0			0
$817$	22.2926			0.779919
$818$	−6.11272	−	8.86157i	−0.213726	−	0.309838i
$819$		0			0
$820$	−2.05309	+	5.40364i	−0.0716972	+	0.188703i
$821$		−	0.101963i		−	0.00355855i	−0.999998	−	0.00177927i	$-0.999434\pi$
$821$		−	0.101963i		−	0.00355855i	0.999998	−	0.00177927i	$-0.000566361\pi$
$822$		0			0
$823$			9.81163i			0.342012i	0.985270	+	0.171006i	$0.0547017\pi$
$823$			9.81163i			0.342012i	−0.985270	+	0.171006i	$0.945298\pi$
$824$	−16.9859	+	16.2854i	−0.591732	+	0.567328i
$825$		0			0
$826$	−8.48450	−	19.2930i	−0.295214	−	0.671288i
$827$	−21.0637			−0.732456			−0.366228	−	0.930525i	$-0.619351\pi$
$827$	−21.0637			−0.732456			−0.366228	+	0.930525i	$0.619351\pi$
$828$		0			0
$829$	−12.1904	−	21.1143i	−0.423389	−	0.733330i	0.572880	−	0.819639i	$-0.305826\pi$
$829$	−12.1904	−	21.1143i	−0.423389	−	0.733330i	−0.996268	+	0.0863089i	$0.972493\pi$
$830$	0.790015	+	9.82339i	0.0274218	+	0.340975i
$831$		0			0
$832$	−0.0576517	+	1.36846i	−0.00199871	+	0.0474428i
$833$	22.0516	−	3.20960i	0.764042	−	0.111206i
$834$		0			0
$835$			17.4051i			0.602327i
$836$	−7.87203	−	48.6256i	−0.272260	−	1.68175i
$837$		0			0
$838$	−25.2326	+	2.02925i	−0.871645	+	0.0700993i
$839$	−28.4151	−	49.2164i	−0.980999	−	1.69914i	−0.658520	−	0.752563i	$-0.728817\pi$
$839$	−28.4151	−	49.2164i	−0.980999	−	1.69914i	−0.322478	−	0.946577i	$-0.604516\pi$
$840$		0			0
$841$	1.05702	−	1.83081i	0.0364490	−	0.0631314i
$842$	−11.8031	+	24.8549i	−0.406760	+	0.856555i
$843$		0			0
$844$	1.88002	−	1.53308i	0.0647131	−	0.0527709i
$845$	17.3602	+	10.0229i	0.597208	+	0.344798i
$846$		0			0
$847$	−3.52396	−	10.1533i	−0.121085	−	0.348872i
$848$	−40.5854	−	8.33708i	−1.39371	−	0.286297i
$849$		0			0
$850$	9.67801	−	6.67590i	0.331953	−	0.228981i
$851$	−4.76175			−0.163231
$852$		0			0
$853$	−5.98214	−	10.3614i	−0.204824	−	0.354766i	0.745252	−	0.666783i	$-0.232329\pi$
$853$	−5.98214	−	10.3614i	−0.204824	−	0.354766i	−0.950077	+	0.312016i	$0.898996\pi$
$854$	−14.0662	−	31.9853i	−0.481336	−	1.09451i
$855$		0			0
$856$	−13.1277	+	45.1677i	−0.448696	+	1.54380i
$857$	18.0557	+	10.4244i	0.616770	+	0.356092i	0.775610	−	0.631212i	$-0.217442\pi$
$857$	18.0557	+	10.4244i	0.616770	+	0.356092i	−0.158841	+	0.987304i	$0.550776\pi$
$858$		0			0
$859$	16.0873	−	9.28802i	0.548892	−	0.316903i	−0.199783	−	0.979840i	$-0.564024\pi$
$859$	16.0873	−	9.28802i	0.548892	−	0.316903i	0.748675	+	0.662937i	$0.230690\pi$
$860$	6.86184	+	8.41469i	0.233987	+	0.286939i
$861$		0			0
$862$	−6.31836	+	13.3052i	−0.215204	+	0.453177i
$863$	−9.14990	+	15.8481i	−0.311466	+	0.539475i	−0.978680	−	0.205391i	$-0.934153\pi$
$863$	−9.14990	+	15.8481i	−0.311466	+	0.539475i	0.667214	+	0.744866i	$0.267487\pi$
$864$		0			0
$865$	−12.9271	−	22.3904i	−0.439535	−	0.761298i
$866$	7.93729	+	11.5066i	0.269720	+	0.391012i
$867$		0			0
$868$	−35.4702	−	21.8756i	−1.20394	−	0.742508i
$869$	−3.27998	−	1.89370i	−0.111266	−	0.0642393i
$870$		0			0
$871$	2.30387	+	1.33014i	0.0780635	+	0.0450700i
$872$	5.33130	+	5.56063i	0.180541	+	0.188307i
$873$		0			0
$874$	−4.57712	+	3.15730i	−0.154823	+	0.106797i
$875$	−5.86355	+	30.5656i	−0.198224	+	1.03331i
$876$		0			0
$877$	24.3854	+	42.2367i	0.823436	+	1.42623i	0.903108	+	0.429412i	$0.141279\pi$
$877$	24.3854	+	42.2367i	0.823436	+	1.42623i	−0.0796722	+	0.996821i	$0.525387\pi$
$878$	17.9074	−	12.3526i	0.604347	−	0.416879i
$879$		0			0
$880$	15.9314	−	17.9388i	0.537048	−	0.604716i
$881$		−	25.9274i		−	0.873518i	−0.899579	−	0.436759i	$-0.856126\pi$
$881$		−	25.9274i		−	0.873518i	0.899579	−	0.436759i	$-0.143874\pi$
$882$		0			0
$883$			25.5672i			0.860405i	0.902732	+	0.430202i	$0.141558\pi$
$883$			25.5672i			0.860405i	−0.902732	+	0.430202i	$0.858442\pi$
$884$	−1.01899	−	0.387162i	−0.0342723	−	0.0130217i
$885$		0			0
$886$	−5.64370	−	8.18164i	−0.189604	−	0.274868i
$887$	−12.2190	−	21.1640i	−0.410275	−	0.710618i	0.584644	−	0.811290i	$-0.301234\pi$
$887$	−12.2190	−	21.1640i	−0.410275	−	0.710618i	−0.994920	+	0.100672i	$0.967901\pi$
$888$		0			0
$889$	−4.40901	+	22.9834i	−0.147873	+	0.770837i
$890$	−11.6778	−	16.9292i	−0.391440	−	0.567469i
$891$		0			0
$892$	6.69589	+	41.3605i	0.224195	+	1.38485i
$893$	−18.9054	−	10.9150i	−0.632644	−	0.365257i
$894$		0			0
$895$	−18.8729	−	10.8962i	−0.630850	−	0.364221i
$896$	−23.3694	−	18.7049i	−0.780716	−	0.624886i
$897$		0			0
$898$	26.8501	−	18.5212i	0.895999	−	0.618061i
$899$	−21.9649	−	38.0443i	−0.732570	−	1.26885i
$900$		0			0
$901$	16.4873	−	28.5568i	0.549271	−	0.951366i
$902$	9.27208	+	4.40312i	0.308727	+	0.146608i
$903$		0			0
$904$	34.8896	+	10.1405i	1.16041	+	0.337267i
$905$	−24.1234	+	13.9276i	−0.801888	+	0.462970i
$906$		0			0
$907$	−40.4658	−	23.3629i	−1.34364	−	0.775754i	−0.356304	−	0.934370i	$-0.615963\pi$
$907$	−40.4658	−	23.3629i	−1.34364	−	0.775754i	−0.987340	+	0.158616i	$0.949297\pi$
$908$	−26.0497	−	31.9447i	−0.864488	−	1.06012i
$909$		0			0
$910$	0.906272	−	0.398553i	0.0300426	−	0.0132119i
$911$	5.05516	+	8.75579i	0.167485	+	0.290092i	0.937535	−	0.347891i	$-0.113102\pi$
$911$	5.05516	+	8.75579i	0.167485	+	0.290092i	−0.770050	+	0.637983i	$0.779769\pi$
$912$		0			0
$913$	17.4997			0.579154
$914$	3.98906	+	5.78292i	0.131946	+	0.191282i
$915$		0			0
$916$	35.6989	−	5.77933i	1.17953	−	0.190954i
$917$	−3.76279	−	10.8414i	−0.124258	−	0.358016i
$918$		0			0
$919$	7.01321	+	4.04908i	0.231344	+	0.133567i	0.611192	−	0.791482i	$-0.290690\pi$
$919$	7.01321	+	4.04908i	0.231344	+	0.133567i	−0.379848	+	0.925049i	$0.624024\pi$
$920$	−2.60065	−	0.755862i	−0.0857407	−	0.0249200i
$921$		0			0
$922$	−39.5263	−	18.7702i	−1.30173	−	0.618164i
$923$	0.434834	−	0.753154i	0.0143127	−	0.0247904i
$924$		0			0
$925$	10.0356	+	17.3822i	0.329970	+	0.571524i
$926$	−2.40022	−	29.8454i	−0.0788761	−	0.980780i
$927$		0			0
$928$	−12.3239	−	29.0477i	−0.404551	−	0.953539i
$929$		−	36.0204i		−	1.18179i	−0.806749	−	0.590895i	$-0.798775\pi$
$929$		−	36.0204i		−	1.18179i	0.806749	−	0.590895i	$-0.201225\pi$
$930$		0			0
$931$	27.5210	+	34.8711i	0.901963	+	1.14285i
$932$	25.5974	−	20.8737i	0.838472	−	0.683741i
$933$		0			0
$934$	34.9672	−	2.81213i	1.14416	−	0.0920157i
$935$	9.54703	+	16.5359i	0.312221	+	0.540783i
$936$		0			0
$937$	59.6868			1.94988			0.974942	−	0.222461i	$-0.0714090\pi$
$937$	59.6868			1.94988			0.974942	+	0.222461i	$0.0714090\pi$
$938$	−53.2195	+	23.4044i	−1.73768	+	0.764182i
$939$		0			0
$940$	−1.69918	−	10.4959i	−0.0554212	−	0.342337i
$941$			12.1922i			0.397453i	0.980055	+	0.198726i	$0.0636805\pi$
$941$			12.1922i			0.397453i	−0.980055	+	0.198726i	$0.936319\pi$
$942$		0			0
$943$		−	1.15868i		−	0.0377317i
$944$	−16.8468	−	14.9616i	−0.548316	−	0.486959i
$945$		0			0
$946$	15.8706	−	10.9475i	0.515997	−	0.355935i
$947$	−12.8677			−0.418145			−0.209073	−	0.977900i	$-0.567045\pi$
$947$	−12.8677			−0.418145			−0.209073	+	0.977900i	$0.567045\pi$
$948$		0			0
$949$	1.88760			0.0612740
$950$	21.1719	+	10.0541i	0.686907	+	0.326198i
$951$		0			0
$952$	19.9941	−	12.9518i	0.648013	−	0.419771i
$953$		−	3.31336i		−	0.107330i	−0.998559	−	0.0536651i	$-0.982910\pi$
$953$		−	3.31336i		−	0.107330i	0.998559	−	0.0536651i	$-0.0170903\pi$
$954$		0			0
$955$	−16.2237	+	9.36675i	−0.524986	+	0.303101i
$956$	−8.11991	−	9.95746i	−0.262617	−	0.322047i
$957$		0			0
$958$	2.30611	−	0.185461i	0.0745069	−	0.00599199i
$959$	38.6540	+	33.4352i	1.24820	+	1.07968i
$960$		0			0
$961$	−31.0242			−1.00078
$962$	0.798266	−	1.68099i	0.0257371	−	0.0541972i
$963$		0			0
$964$	−5.51485	−	6.76286i	−0.177621	−	0.217817i
$965$	8.05350	−	4.64969i	0.259251	−	0.149679i
$966$		0			0
$967$	−2.59128	−	1.49608i	−0.0833300	−	0.0481106i	0.457756	−	0.889078i	$-0.348653\pi$
$967$	−2.59128	−	1.49608i	−0.0833300	−	0.0481106i	−0.541086	+	0.840967i	$0.681987\pi$
$968$	−7.95151	−	8.29355i	−0.255571	−	0.266565i
$969$		0			0
$970$	1.79600	+	22.3322i	0.0576660	+	0.717045i
$971$	−12.6023	+	21.8277i	−0.404425	+	0.700485i	−0.994254	−	0.107043i	$-0.965862\pi$
$971$	−12.6023	+	21.8277i	−0.404425	+	0.700485i	0.589829	+	0.807528i	$0.299195\pi$
$972$		0			0
$973$	−29.7114	−	25.7000i	−0.952504	−	0.823904i
$974$	18.4189	+	8.74677i	0.590181	+	0.280265i
$975$		0			0
$976$	−27.9298	−	24.8044i	−0.894010	−	0.793970i
$977$			20.3215i			0.650142i	0.945690	+	0.325071i	$0.105388\pi$
$977$			20.3215i			0.650142i	−0.945690	+	0.325071i	$0.894612\pi$
$978$		0			0
$979$	−31.6267	+	18.2597i	−1.01079	+	0.583581i
$980$	−4.69146	+	21.1218i	−0.149863	+	0.674712i
$981$		0			0
$982$	−15.2550	+	1.22684i	−0.486807	+	0.0391499i
$983$	−0.880237	+	1.52462i	−0.0280752	+	0.0486277i	−0.879722	−	0.475489i	$-0.842271\pi$
$983$	−0.880237	+	1.52462i	−0.0280752	+	0.0486277i	0.851646	+	0.524117i	$0.175604\pi$
$984$		0			0
$985$	−9.04788	−	15.6714i	−0.288289	−	0.499332i
$986$	25.0315	−	2.01308i	0.797166	−	0.0641096i
$987$		0			0
$988$	−0.347272	−	2.14510i	−0.0110482	−	0.0682448i
$989$	−1.88481	−	1.08820i	−0.0599335	−	0.0346026i
$990$		0			0
$991$	10.4024	−	6.00585i	0.330444	−	0.190782i	−0.325594	−	0.945510i	$-0.605564\pi$
$991$	10.4024	−	6.00585i	0.330444	−	0.190782i	0.656038	+	0.754728i	$0.272231\pi$
$992$	−44.2177	−	5.43734i	−1.40391	−	0.172636i
$993$		0			0
$994$	7.65112	+	17.3979i	0.242679	+	0.551829i
$995$	7.74502	−	13.4148i	0.245534	−	0.425277i
$996$		0			0
$997$	9.62654	−	16.6737i	0.304876	−	0.528060i	−0.672358	−	0.740226i	$-0.734718\pi$
$997$	9.62654	−	16.6737i	0.304876	−	0.528060i	0.977234	+	0.212166i	$0.0680517\pi$
$998$	21.6187	+	10.2663i	0.684329	+	0.324973i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.13		88
3.2	odd	2		252.2.bb.a.23.32	yes	88
4.3	odd	2	inner	756.2.bb.a.611.32		88
7.4	even	3		756.2.o.a.179.43		88
9.2	odd	6		756.2.o.a.359.27		88
9.7	even	3		252.2.o.a.191.18	yes	88
12.11	even	2		252.2.bb.a.23.13	yes	88
21.11	odd	6		252.2.o.a.95.2	✓	88
28.11	odd	6		756.2.o.a.179.27		88
36.7	odd	6		252.2.o.a.191.2	yes	88
36.11	even	6		756.2.o.a.359.43		88
63.11	odd	6	inner	756.2.bb.a.683.32		88
63.25	even	3		252.2.bb.a.11.13	yes	88
84.11	even	6		252.2.o.a.95.18	yes	88
252.11	even	6	inner	756.2.bb.a.683.13		88
252.151	odd	6		252.2.bb.a.11.32	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.2	✓	88	21.11	odd	6
252.2.o.a.95.18	yes	88	84.11	even	6
252.2.o.a.191.2	yes	88	36.7	odd	6
252.2.o.a.191.18	yes	88	9.7	even	3
252.2.bb.a.11.13	yes	88	63.25	even	3
252.2.bb.a.11.32	yes	88	252.151	odd	6
252.2.bb.a.23.13	yes	88	12.11	even	2
252.2.bb.a.23.32	yes	88	3.2	odd	2
756.2.o.a.179.27		88	28.11	odd	6
756.2.o.a.179.43		88	7.4	even	3
756.2.o.a.359.27		88	9.2	odd	6
756.2.o.a.359.43		88	36.11	even	6
756.2.bb.a.611.13		88	1.1	even	1	trivial
756.2.bb.a.611.32		88	4.3	odd	2	inner
756.2.bb.a.683.13		88	252.11	even	6	inner
756.2.bb.a.683.32		88	63.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.803010 - 1.16412i) q^{2} +(-0.710349 + 1.86960i) q^{4} +(1.33842 - 0.772734i) q^{5} +(2.59837 + 0.498458i) q^{7} +(2.74686 - 0.674378i) q^{8} +O(q^{10})\)	\(q+(-0.803010 - 1.16412i) q^{2} +(-0.710349 + 1.86960i) q^{4} +(1.33842 - 0.772734i) q^{5} +(2.59837 + 0.498458i) q^{7} +(2.74686 - 0.674378i) q^{8} +(-1.97432 - 0.937562i) q^{10} +(-1.94050 + 3.36104i) q^{11} +(-0.0856046 + 0.148271i) q^{13} +(-1.50626 - 3.42508i) q^{14} +(-2.99081 - 2.65614i) q^{16} +(2.75692 - 1.59171i) q^{17} +(5.49591 + 3.17307i) q^{19} +(0.493963 + 3.05121i) q^{20} +(5.47090 - 0.439980i) q^{22} +(-0.309781 - 0.536557i) q^{23} +(-1.30576 + 2.26165i) q^{25} +(0.241347 - 0.0194096i) q^{26} +(-2.77767 + 4.50384i) q^{28} +(-4.83069 + 2.78900i) q^{29} +7.87554i q^{31} +(-0.690408 + 5.61456i) q^{32} +(-4.06678 - 1.93123i) q^{34} +(3.86288 - 1.34071i) q^{35} +(3.84283 - 6.65597i) q^{37} +(-0.719446 - 8.94590i) q^{38} +(3.15532 - 3.02519i) q^{40} +(1.61960 + 0.935076i) q^{41} +(3.04216 - 1.75639i) q^{43} +(-4.90538 - 6.01547i) q^{44} +(-0.375859 + 0.791484i) q^{46} -3.43990 q^{47} +(6.50308 + 2.59036i) q^{49} +(3.68137 - 0.296063i) q^{50} +(-0.216399 - 0.265371i) q^{52} +(8.97048 - 5.17911i) q^{53} +5.99797i q^{55} +(7.47350 - 0.383092i) q^{56} +(7.12582 + 3.38390i) q^{58} +5.63284 q^{59} +9.33853 q^{61} +(9.16807 - 6.32414i) q^{62} +(7.09043 - 3.70484i) q^{64} +0.264598i q^{65} -15.5382i q^{67} +(1.01749 + 6.28501i) q^{68} +(-4.66268 - 3.42025i) q^{70} -5.07956 q^{71} +(-5.51255 - 9.54801i) q^{73} +(-10.8342 + 0.871304i) q^{74} +(-9.83638 + 8.02117i) q^{76} +(-6.71748 + 7.76599i) q^{77} +0.975881i q^{79} +(-6.05543 - 1.24391i) q^{80} +(-0.212015 - 2.63628i) q^{82} +(-2.25453 - 3.90496i) q^{83} +(2.45994 - 4.26074i) q^{85} +(-4.48754 - 2.13104i) q^{86} +(-3.06366 + 10.5409i) q^{88} +(8.14910 + 4.70488i) q^{89} +(-0.296340 + 0.342594i) q^{91} +(1.22320 - 0.198025i) q^{92} +(2.76227 + 4.00445i) q^{94} +9.80775 q^{95} +(-5.12539 - 8.87743i) q^{97} +(-2.20655 - 9.65045i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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