LMFDB - Embedded newform 756.2.bf.c.271.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.7
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.c.703.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.428236 + 1.34782i) q^{2} +(-1.63323 - 1.15437i) q^{4} +(0.703801 + 0.406340i) q^{5} +(2.60258 - 0.476010i) q^{7} +(2.25528 - 1.70695i) q^{8} +O(q^{10})$	\(q+(-0.428236 + 1.34782i) q^{2} +(-1.63323 - 1.15437i) q^{4} +(0.703801 + 0.406340i) q^{5} +(2.60258 - 0.476010i) q^{7} +(2.25528 - 1.70695i) q^{8} +(-0.849065 + 0.774587i) q^{10} +(-1.86129 + 1.07462i) q^{11} -5.14045i q^{13} +(-0.472941 + 3.71165i) q^{14} +(1.33487 + 3.77069i) q^{16} +(1.78009 - 1.02773i) q^{17} +(1.57359 - 2.72553i) q^{19} +(-0.680403 - 1.47609i) q^{20} +(-0.651317 - 2.96887i) q^{22} +(1.64186 + 0.947931i) q^{23} +(-2.16978 - 3.75816i) q^{25} +(6.92839 + 2.20132i) q^{26} +(-4.80010 - 2.22690i) q^{28} +7.65207 q^{29} +(-0.513811 - 0.889946i) q^{31} +(-5.65385 + 0.184421i) q^{32} +(0.622902 + 2.83935i) q^{34} +(2.02512 + 0.722515i) q^{35} +(2.94725 - 5.10478i) q^{37} +(2.99966 + 3.28808i) q^{38} +(2.28088 - 0.284945i) q^{40} -2.55145i q^{41} +10.2817i q^{43} +(4.28041 + 0.393518i) q^{44} +(-1.98074 + 1.80700i) q^{46} +(-1.06224 + 1.83986i) q^{47} +(6.54683 - 2.47771i) q^{49} +(5.99450 - 1.31509i) q^{50} +(-5.93396 + 8.39552i) q^{52} +(3.32185 + 5.75361i) q^{53} -1.74664 q^{55} +(5.05703 - 5.51602i) q^{56} +(-3.27689 + 10.3136i) q^{58} +(6.32614 + 10.9572i) q^{59} +(5.15384 + 2.97557i) q^{61} +(1.41952 - 0.311417i) q^{62} +(2.17261 - 7.69933i) q^{64} +(2.08877 - 3.61785i) q^{65} +(-6.91842 + 3.99435i) q^{67} +(-4.09368 - 0.376351i) q^{68} +(-1.84105 + 2.42009i) q^{70} -11.0579i q^{71} +(8.64340 - 4.99027i) q^{73} +(5.61820 + 6.15840i) q^{74} +(-5.71629 + 2.63492i) q^{76} +(-4.33262 + 3.68277i) q^{77} +(6.82469 + 3.94024i) q^{79} +(-0.592698 + 3.19623i) q^{80} +(3.43889 + 1.09262i) q^{82} -17.5056 q^{83} +1.67044 q^{85} +(-13.8579 - 4.40300i) q^{86} +(-2.36342 + 5.60070i) q^{88} +(0.484920 + 0.279969i) q^{89} +(-2.44690 - 13.3784i) q^{91} +(-1.58728 - 3.44350i) q^{92} +(-2.02491 - 2.21961i) q^{94} +(2.21498 - 1.27882i) q^{95} -1.84737i q^{97} +(0.535915 + 9.88498i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) $ 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.428236	+	1.34782i	−0.302808	+	0.953052i
$2$	−0.428236	+	1.34782i	−0.302808	+	0.953052i
$3$		0			0
$3$		0			0
$4$	−1.63323	−	1.15437i	−0.816614	−	0.577184i
$5$	0.703801	+	0.406340i	0.314749	+	0.181721i	0.649050	−	0.760746i	$-0.275167\pi$
$5$	0.703801	+	0.406340i	0.314749	+	0.181721i	−0.334300	+	0.942467i	$0.608500\pi$
$6$		0			0
$7$	2.60258	−	0.476010i	0.983682	−	0.179915i
$7$	2.60258	−	0.476010i	0.983682	−	0.179915i
$8$	2.25528	−	1.70695i	0.797363	−	0.603500i
$9$		0			0
$10$	−0.849065	+	0.774587i	−0.268498	+	0.244946i
$11$	−1.86129	+	1.07462i	−0.561200	+	0.324009i	−0.753627	−	0.657302i	$-0.771697\pi$
$11$	−1.86129	+	1.07462i	−0.561200	+	0.324009i	0.192427	+	0.981311i	$0.438364\pi$
$12$		0			0
$13$		−	5.14045i		−	1.42570i	−0.701315	−	0.712852i	$-0.747403\pi$
$13$		−	5.14045i		−	1.42570i	0.701315	−	0.712852i	$-0.252597\pi$
$14$	−0.472941	+	3.71165i	−0.126399	+	0.991979i
$15$		0			0
$16$	1.33487	+	3.77069i	0.333718	+	0.942673i
$17$	1.78009	−	1.02773i	0.431735	−	0.249262i	−0.268351	−	0.963321i	$-0.586479\pi$
$17$	1.78009	−	1.02773i	0.431735	−	0.249262i	0.700085	+	0.714059i	$0.253145\pi$
$18$		0			0
$19$	1.57359	−	2.72553i	0.361005	−	0.625280i	−0.627121	−	0.778922i	$-0.715767\pi$
$19$	1.57359	−	2.72553i	0.361005	−	0.625280i	0.988127	+	0.153642i	$0.0491003\pi$
$20$	−0.680403	−	1.47609i	−0.152143	−	0.330064i
$21$		0			0
$22$	−0.651317	−	2.96887i	−0.138861	−	0.632965i
$23$	1.64186	+	0.947931i	0.342352	+	0.197657i	0.661312	−	0.750111i	$-0.270000\pi$
$23$	1.64186	+	0.947931i	0.342352	+	0.197657i	−0.318959	+	0.947768i	$0.603333\pi$
$24$		0			0
$25$	−2.16978	−	3.75816i	−0.433955	−	0.751632i
$26$	6.92839	+	2.20132i	1.35877	+	0.431715i
$27$		0			0
$28$	−4.80010	−	2.22690i	−0.907133	−	0.420844i
$29$	7.65207			1.42095			0.710477	−	0.703721i	$-0.248479\pi$
$29$	7.65207			1.42095			0.710477	+	0.703721i	$0.248479\pi$
$30$		0			0
$31$	−0.513811	−	0.889946i	−0.0922831	−	0.159839i	0.816188	−	0.577786i	$-0.196083\pi$
$31$	−0.513811	−	0.889946i	−0.0922831	−	0.159839i	−0.908471	+	0.417947i	$0.862750\pi$
$32$	−5.65385	+	0.184421i	−0.999468	+	0.0326013i
$33$		0			0
$34$	0.622902	+	2.83935i	0.106827	+	0.486944i
$35$	2.02512	+	0.722515i	0.342308	+	0.122127i
$36$		0			0
$37$	2.94725	−	5.10478i	0.484524	−	0.839221i	−0.515318	−	0.856999i	$-0.672326\pi$
$37$	2.94725	−	5.10478i	0.484524	−	0.839221i	0.999842	+	0.0177786i	$0.00565939\pi$
$38$	2.99966	+	3.28808i	0.486608	+	0.533397i
$39$		0			0
$40$	2.28088	−	0.284945i	0.360638	−	0.0450537i
$41$		−	2.55145i		−	0.398469i	−0.979952	−	0.199235i	$-0.936154\pi$
$41$		−	2.55145i		−	0.398469i	0.979952	−	0.199235i	$-0.0638456\pi$
$42$		0			0
$43$			10.2817i			1.56795i	0.620793	+	0.783974i	$0.286811\pi$
$43$			10.2817i			1.56795i	−0.620793	+	0.783974i	$0.713189\pi$
$44$	4.28041	+	0.393518i	0.645297	+	0.0593251i
$45$		0			0
$46$	−1.98074	+	1.80700i	−0.292045	+	0.266427i
$47$	−1.06224	+	1.83986i	−0.154944	+	0.268371i	−0.933039	−	0.359776i	$-0.882853\pi$
$47$	−1.06224	+	1.83986i	−0.154944	+	0.268371i	0.778095	+	0.628147i	$0.216186\pi$
$48$		0			0
$49$	6.54683	−	2.47771i	0.935261	−	0.353958i
$50$	5.99450	−	1.31509i	0.847750	−	0.185981i
$51$		0			0
$52$	−5.93396	+	8.39552i	−0.822893	+	1.16425i
$53$	3.32185	+	5.75361i	0.456291	+	0.790319i	0.998761	−	0.0497559i	$-0.0158443\pi$
$53$	3.32185	+	5.75361i	0.456291	+	0.790319i	−0.542471	+	0.840075i	$0.682511\pi$
$54$		0			0
$55$	−1.74664			−0.235516
$56$	5.05703	−	5.51602i	0.675774	−	0.737109i
$57$		0			0
$58$	−3.27689	+	10.3136i	−0.430276	+	1.35424i
$59$	6.32614	+	10.9572i	0.823593	+	1.42651i	0.902990	+	0.429662i	$0.141367\pi$
$59$	6.32614	+	10.9572i	0.823593	+	1.42651i	−0.0793963	+	0.996843i	$0.525299\pi$
$60$		0			0
$61$	5.15384	+	2.97557i	0.659882	+	0.380983i	0.792232	−	0.610220i	$-0.208919\pi$
$61$	5.15384	+	2.97557i	0.659882	+	0.380983i	−0.132350	+	0.991203i	$0.542252\pi$
$62$	1.41952	−	0.311417i	0.180279	−	0.0395500i
$63$		0			0
$64$	2.17261	−	7.69933i	0.271577	−	0.962417i
$65$	2.08877	−	3.61785i	0.259080	−	0.448739i
$66$		0			0
$67$	−6.91842	+	3.99435i	−0.845220	+	0.487988i	−0.859035	−	0.511917i	$-0.828936\pi$
$67$	−6.91842	+	3.99435i	−0.845220	+	0.487988i	0.0138151	+	0.999905i	$0.495602\pi$
$68$	−4.09368	−	0.376351i	−0.496431	−	0.0456392i
$69$		0			0
$70$	−1.84105	+	2.42009i	−0.220047	+	0.289256i
$71$		−	11.0579i		−	1.31234i	−0.754615	−	0.656168i	$-0.772176\pi$
$71$		−	11.0579i		−	1.31234i	0.754615	−	0.656168i	$-0.227824\pi$
$72$		0			0
$73$	8.64340	−	4.99027i	1.01163	−	0.584067i	0.0999643	−	0.994991i	$-0.468127\pi$
$73$	8.64340	−	4.99027i	1.01163	−	0.584067i	0.911670	+	0.410924i	$0.134794\pi$
$74$	5.61820	+	6.15840i	0.653103	+	0.715900i
$75$		0			0
$76$	−5.71629	+	2.63492i	−0.655703	+	0.302246i
$77$	−4.33262	+	3.68277i	−0.493748	+	0.419690i
$78$		0			0
$79$	6.82469	+	3.94024i	0.767837	+	0.443311i	0.832103	−	0.554622i	$-0.187137\pi$
$79$	6.82469	+	3.94024i	0.767837	+	0.443311i	−0.0642652	+	0.997933i	$0.520470\pi$
$80$	−0.592698	+	3.19623i	−0.0662656	+	0.357349i
$81$		0			0
$82$	3.43889	+	1.09262i	0.379762	+	0.120660i
$83$	−17.5056			−1.92148			−0.960742	−	0.277443i	$-0.910513\pi$
$83$	−17.5056			−1.92148			−0.960742	+	0.277443i	$0.910513\pi$
$84$		0			0
$85$	1.67044			0.181184
$86$	−13.8579	−	4.40300i	−1.49434	−	0.474788i
$87$		0			0
$88$	−2.36342	+	5.60070i	−0.251941	+	0.597037i
$89$	0.484920	+	0.279969i	0.0514014	+	0.0296766i	0.525480	−	0.850806i	$-0.323886\pi$
$89$	0.484920	+	0.279969i	0.0514014	+	0.0296766i	−0.474079	+	0.880482i	$0.657219\pi$
$90$		0			0
$91$	−2.44690	−	13.3784i	−0.256505	−	1.40244i
$92$	−1.58728	−	3.44350i	−0.165485	−	0.359010i
$93$		0			0
$94$	−2.02491	−	2.21961i	−0.208853	−	0.228935i
$95$	2.21498	−	1.27882i	0.227252	−	0.131204i
$96$		0			0
$97$		−	1.84737i		−	0.187572i	−0.995592	−	0.0937859i	$-0.970103\pi$
$97$		−	1.84737i		−	0.187572i	0.995592	−	0.0937859i	$-0.0298969\pi$
$98$	0.535915	+	9.88498i	0.0541356	+	0.998534i
$99$		0			0
$100$	−0.794560	+	8.64266i	−0.0794560	+	0.864266i
$101$	−14.1467	+	8.16763i	−1.40765	+	0.812709i	−0.995162	−	0.0982519i	$-0.968675\pi$
$101$	−14.1467	+	8.16763i	−1.40765	+	0.812709i	−0.412492	+	0.910961i	$0.635342\pi$
$102$		0			0
$103$	2.38508	−	4.13108i	0.235009	−	0.407048i	−0.724266	−	0.689520i	$-0.757821\pi$
$103$	2.38508	−	4.13108i	0.235009	−	0.407048i	0.959275	+	0.282473i	$0.0911547\pi$
$104$	−8.77451	−	11.5932i	−0.860411	−	1.13680i
$105$		0			0
$106$	−9.17735	+	2.01335i	−0.891383	+	0.195554i
$107$	−4.05383	−	2.34048i	−0.391898	−	0.226263i	0.291084	−	0.956697i	$-0.405984\pi$
$107$	−4.05383	−	2.34048i	−0.391898	−	0.226263i	−0.682982	+	0.730435i	$0.739317\pi$
$108$		0			0
$109$	−4.19616	−	7.26796i	−0.401919	−	0.696144i	0.592038	−	0.805910i	$-0.298323\pi$
$109$	−4.19616	−	7.26796i	−0.401919	−	0.696144i	−0.993958	+	0.109765i	$0.964990\pi$
$110$	0.747972	−	2.35415i	0.0713163	−	0.224459i
$111$		0			0
$112$	5.26900	+	9.17811i	0.497873	+	0.867250i
$113$	2.60313			0.244882			0.122441	−	0.992476i	$-0.460928\pi$
$113$	2.60313			0.244882			0.122441	+	0.992476i	$0.460928\pi$
$114$		0			0
$115$	0.770364	+	1.33431i	0.0718368	+	0.124425i
$116$	−12.4976	−	8.83330i	−1.16037	−	0.820151i
$117$		0			0
$118$	−17.4774	+	3.83423i	−1.60892	+	0.352969i
$119$	4.14361	−	3.52210i	0.379844	−	0.322870i
$120$		0			0
$121$	−3.19040	+	5.52594i	−0.290036	+	0.502358i
$122$	−6.21759	+	5.67220i	−0.562914	+	0.513537i
$123$		0			0
$124$	−0.188155	+	2.04661i	−0.0168968	+	0.183791i
$125$		−	7.59006i		−	0.678876i
$126$		0			0
$127$			6.70221i			0.594725i	0.954765	+	0.297363i	$0.0961070\pi$
$127$			6.70221i			0.594725i	−0.954765	+	0.297363i	$0.903893\pi$
$128$	9.44691	+	6.22542i	0.834997	+	0.550254i
$129$		0			0
$130$	3.98172	+	4.36457i	0.349220	+	0.382798i
$131$	7.37529	−	12.7744i	0.644382	−	1.11610i	−0.340062	−	0.940403i	$-0.610448\pi$
$131$	7.37529	−	12.7744i	0.644382	−	1.11610i	0.984444	−	0.175699i	$-0.0562187\pi$
$132$		0			0
$133$	2.79800	−	7.84245i	0.242617	−	0.680027i
$134$	−2.42095	−	11.0353i	−0.209138	−	0.953305i
$135$		0			0
$136$	2.26031	−	5.35636i	0.193820	−	0.459304i
$137$	−10.0957	−	17.4863i	−0.862534	−	1.49395i	−0.869475	−	0.493977i	$-0.835543\pi$
$137$	−10.0957	−	17.4863i	−0.862534	−	1.49395i	0.00694033	−	0.999976i	$-0.497791\pi$
$138$		0			0
$139$	22.5005			1.90847			0.954235	−	0.299058i	$-0.0966725\pi$
$139$	22.5005			1.90847			0.954235	+	0.299058i	$0.0966725\pi$
$140$	−2.47344	−	3.51776i	−0.209043	−	0.297305i
$141$		0			0
$142$	14.9041	+	4.73540i	1.25072	+	0.397386i
$143$	5.52401	+	9.56786i	0.461941	+	0.800105i
$144$		0			0
$145$	5.38553	+	3.10934i	0.447244	+	0.258217i
$146$	3.02457	+	13.7868i	0.250315	+	1.14100i
$147$		0			0
$148$	−10.7063	+	4.93507i	−0.880054	+	0.405660i
$149$	−5.94705	+	10.3006i	−0.487201	+	0.843857i	−0.999892	−	0.0147163i	$-0.995315\pi$
$149$	−5.94705	+	10.3006i	−0.487201	+	0.843857i	0.512691	+	0.858573i	$0.328649\pi$
$150$		0			0
$151$	−8.34848	+	4.82000i	−0.679390	+	0.392246i	−0.799625	−	0.600499i	$-0.794968\pi$
$151$	−8.34848	+	4.82000i	−0.679390	+	0.392246i	0.120235	+	0.992745i	$0.461635\pi$
$152$	−1.10347	−	8.83289i	−0.0895035	−	0.716442i
$153$		0			0
$154$	−3.10832	−	7.41668i	−0.250475	−	0.597653i
$155$		−	0.835127i		−	0.0670790i
$156$		0			0
$157$	5.18117	−	2.99135i	0.413503	−	0.238736i	−0.278791	−	0.960352i	$-0.589934\pi$
$157$	5.18117	−	2.99135i	0.413503	−	0.238736i	0.692294	+	0.721616i	$0.256600\pi$
$158$	−8.23330	+	7.51109i	−0.655006	+	0.597550i
$159$		0			0
$160$	−4.05412	−	2.16759i	−0.320506	−	0.171363i
$161$	4.72430	+	1.68552i	0.372327	+	0.132838i
$162$		0			0
$163$	−8.53520	−	4.92780i	−0.668528	−	0.385975i	0.126990	−	0.991904i	$-0.459468\pi$
$163$	−8.53520	−	4.92780i	−0.668528	−	0.385975i	−0.795519	+	0.605929i	$0.792802\pi$
$164$	−2.94531	+	4.16710i	−0.229990	+	0.325396i
$165$		0			0
$166$	7.49650	−	23.5943i	0.581841	−	1.83127i
$167$	20.4794			1.58474			0.792371	−	0.610040i	$-0.208847\pi$
$167$	20.4794			1.58474			0.792371	+	0.610040i	$0.208847\pi$
$168$		0			0
$169$	−13.4242			−1.03263
$170$	−0.715341	+	2.25145i	−0.0548641	+	0.172678i
$171$		0			0
$172$	11.8689	−	16.7924i	0.904994	−	1.28041i
$173$	−3.46120	−	1.99833i	−0.263150	−	0.151930i	0.362620	−	0.931937i	$-0.381882\pi$
$173$	−3.46120	−	1.99833i	−0.263150	−	0.151930i	−0.625771	+	0.780007i	$0.715215\pi$
$174$		0			0
$175$	−7.43594	−	8.74808i	−0.562104	−	0.661292i
$176$	−6.53663	−	5.58388i	−0.492717	−	0.420900i
$177$		0			0
$178$	−0.585007	+	0.533691i	−0.0438481	+	0.0400019i
$179$	−15.9493	+	9.20832i	−1.19211	+	0.688262i	−0.958784	−	0.284137i	$-0.908293\pi$
$179$	−15.9493	+	9.20832i	−1.19211	+	0.688262i	−0.233322	+	0.972400i	$0.574959\pi$
$180$		0			0
$181$			8.77700i			0.652389i	0.945303	+	0.326195i	$0.105767\pi$
$181$			8.77700i			0.652389i	−0.945303	+	0.326195i	$0.894233\pi$
$182$	19.0795	+	2.43113i	1.41427	+	0.180207i
$183$		0			0
$184$	5.32094	−	0.664734i	0.392265	−	0.0490049i
$185$	4.14855	−	2.39517i	0.305007	−	0.176096i
$186$		0			0
$187$	−2.20884	+	3.82582i	−0.161526	+	0.279772i
$188$	3.85876	−	1.77869i	0.281429	−	0.129725i
$189$		0			0
$190$	0.775084	+	3.53303i	0.0562305	+	0.256313i
$191$	−19.0198	−	10.9811i	−1.37623	−	0.794565i	−0.384523	−	0.923115i	$-0.625634\pi$
$191$	−19.0198	−	10.9811i	−1.37623	−	0.794565i	−0.991703	+	0.128551i	$0.958968\pi$
$192$		0			0
$193$	−0.350671	−	0.607379i	−0.0252418	−	0.0437201i	0.853129	−	0.521701i	$-0.174702\pi$
$193$	−0.350671	−	0.607379i	−0.0252418	−	0.0437201i	−0.878370	+	0.477981i	$0.841369\pi$
$194$	2.48992	+	0.791109i	0.178766	+	0.0567983i
$195$		0			0
$196$	−13.5527	−	3.51078i	−0.968047	−	0.250770i
$197$	−23.9596			−1.70705			−0.853524	−	0.521053i	$-0.825539\pi$
$197$	−23.9596			−1.70705			−0.853524	+	0.521053i	$0.825539\pi$
$198$		0			0
$199$	−1.09676	−	1.89965i	−0.0777473	−	0.134662i	0.824530	−	0.565818i	$-0.191439\pi$
$199$	−1.09676	−	1.89965i	−0.0777473	−	0.134662i	−0.902278	+	0.431155i	$0.858106\pi$
$200$	−11.3085	−	4.77201i	−0.799630	−	0.337432i
$201$		0			0
$202$	−4.95034	−	22.5649i	−0.348305	−	1.58766i
$203$	19.9151	−	3.64246i	1.39777	−	0.255651i
$204$		0			0
$205$	1.03675	−	1.79571i	0.0724101	−	0.125418i
$206$	4.54657	+	4.98373i	0.316775	+	0.347233i
$207$		0			0
$208$	19.3830	−	6.86184i	1.34397	−	0.475783i
$209$			6.76400i			0.467876i
$210$		0			0
$211$			11.0443i			0.760320i	0.924921	+	0.380160i	$0.124131\pi$
$211$			11.0443i			0.760320i	−0.924921	+	0.380160i	$0.875869\pi$
$212$	1.21644	−	13.2316i	0.0835455	−	0.908749i
$213$		0			0
$214$	4.89053	−	4.46155i	0.334310	−	0.304985i
$215$	−4.17787	+	7.23629i	−0.284929	+	0.493511i
$216$		0			0
$217$	−1.76086	−	2.07158i	−0.119535	−	0.140628i
$218$	11.5928	−	2.54326i	0.785166	−	0.172251i
$219$		0			0
$220$	2.85266	+	2.01626i	0.192326	+	0.135936i
$221$	−5.28301	−	9.15045i	−0.355374	−	0.615526i
$222$		0			0
$223$	20.4097			1.36673			0.683367	−	0.730075i	$-0.260515\pi$
$223$	20.4097			1.36673			0.683367	+	0.730075i	$0.260515\pi$
$224$	−14.6268	+	3.17126i	−0.977294	+	0.211889i
$225$		0			0
$226$	−1.11475	+	3.50855i	−0.0741523	+	0.233385i
$227$	−2.20721	−	3.82300i	−0.146498	−	0.253742i	0.783433	−	0.621476i	$-0.213467\pi$
$227$	−2.20721	−	3.82300i	−0.146498	−	0.253742i	−0.929931	+	0.367735i	$0.880133\pi$
$228$		0			0
$229$	−16.5530	−	9.55686i	−1.09385	−	0.631535i	−0.159252	−	0.987238i	$-0.550908\pi$
$229$	−16.5530	−	9.55686i	−1.09385	−	0.631535i	−0.934599	+	0.355703i	$0.884241\pi$
$230$	−2.12830	+	0.466912i	−0.140336	+	0.0307873i
$231$		0			0
$232$	17.2576	−	13.0617i	1.13302	−	0.857545i
$233$	7.20579	−	12.4808i	0.472067	−	0.817644i	−0.527422	−	0.849603i	$-0.676841\pi$
$233$	7.20579	−	12.4808i	0.472067	−	0.817644i	0.999489	+	0.0319592i	$0.0101747\pi$
$234$		0			0
$235$	−1.49522	+	0.863264i	−0.0975372	+	0.0563131i
$236$	2.31660	−	25.1983i	0.150798	−	1.64027i
$237$		0			0
$238$	2.97271	+	7.09312i	0.192692	+	0.459779i
$239$		−	13.3320i		−	0.862375i	−0.902262	−	0.431187i	$-0.858095\pi$
$239$		−	13.3320i		−	0.862375i	0.902262	−	0.431187i	$-0.141905\pi$
$240$		0			0
$241$	−21.3015	+	12.2984i	−1.37215	+	0.792210i	−0.991198	−	0.132386i	$-0.957736\pi$
$241$	−21.3015	+	12.2984i	−1.37215	+	0.792210i	−0.380950	+	0.924596i	$0.624403\pi$
$242$	−6.08171	−	6.66648i	−0.390947	−	0.428538i
$243$		0			0
$244$	−4.98250	−	10.8092i	−0.318972	−	0.691989i
$245$	5.61446	+	0.916424i	0.358694	+	0.0585482i
$246$		0			0
$247$	−14.0104	−	8.08893i	−0.891463	−	0.514687i
$248$	−2.67789	−	1.13003i	−0.170046	−	0.0717570i
$249$		0			0
$250$	10.2300	+	3.25033i	0.647004	+	0.205569i
$251$	−1.47312			−0.0929824			−0.0464912	−	0.998919i	$-0.514804\pi$
$251$	−1.47312			−0.0929824			−0.0464912	+	0.998919i	$0.514804\pi$
$252$		0			0
$253$	−4.07465			−0.256171
$254$	−9.03337	−	2.87013i	−0.566804	−	0.180088i
$255$		0			0
$256$	−12.4362	+	10.0668i	−0.777265	+	0.629174i
$257$	9.23212	+	5.33017i	0.575884	+	0.332487i	0.759496	−	0.650512i	$-0.225446\pi$
$257$	9.23212	+	5.33017i	0.575884	+	0.332487i	−0.183612	+	0.982999i	$0.558779\pi$
$258$		0			0
$259$	5.24051	−	14.6885i	0.325630	−	0.912700i
$260$	−7.58777	+	3.49757i	−0.470573	+	0.216910i
$261$		0			0
$262$	14.0592	+	15.4110i	0.868579	+	0.952094i
$263$	−23.1783	+	13.3820i	−1.42924	+	0.825170i	−0.997060	−	0.0766200i	$-0.975587\pi$
$263$	−23.1783	+	13.3820i	−1.42924	+	0.825170i	−0.432175	+	0.901790i	$0.642254\pi$
$264$		0			0
$265$			5.39919i			0.331670i
$266$	9.37200	+	7.12961i	0.574634	+	0.437145i
$267$		0			0
$268$	15.9103	+	1.46271i	0.971878	+	0.0893492i
$269$	−17.3592	+	10.0223i	−1.05841	+	0.611073i	−0.924992	−	0.379987i	$-0.875929\pi$
$269$	−17.3592	+	10.0223i	−1.05841	+	0.611073i	−0.133418	+	0.991060i	$0.542595\pi$
$270$		0			0
$271$	−4.36814	+	7.56584i	−0.265346	+	0.459592i	−0.967654	−	0.252281i	$-0.918819\pi$
$271$	−4.36814	+	7.56584i	−0.265346	+	0.459592i	0.702309	+	0.711873i	$0.252153\pi$
$272$	6.25146	+	5.34027i	0.379051	+	0.323802i
$273$		0			0
$274$	27.8917	−	6.11893i	1.68500	−	0.369658i
$275$	8.07716	+	4.66335i	0.487071	+	0.281211i
$276$		0			0
$277$	5.73771	+	9.93800i	0.344746	+	0.597117i	0.985308	−	0.170790i	$-0.0546319\pi$
$277$	5.73771	+	9.93800i	0.344746	+	0.597117i	−0.640562	+	0.767906i	$0.721299\pi$
$278$	−9.63552	+	30.3266i	−0.577900	+	1.81887i
$279$		0			0
$280$	5.80052	−	1.82731i	0.346647	−	0.109203i
$281$	19.6940			1.17484			0.587422	−	0.809281i	$-0.300143\pi$
$281$	19.6940			1.17484			0.587422	+	0.809281i	$0.300143\pi$
$282$		0			0
$283$	−1.80656	−	3.12905i	−0.107389	−	0.186003i	0.807323	−	0.590110i	$-0.200916\pi$
$283$	−1.80656	−	3.12905i	−0.107389	−	0.186003i	−0.914712	+	0.404107i	$0.867582\pi$
$284$	−12.7649	+	18.0601i	−0.757459	+	1.07167i
$285$		0			0
$286$	−15.2613	+	3.34806i	−0.902420	+	0.197975i
$287$	−1.21452	−	6.64034i	−0.0716906	−	0.391967i
$288$		0			0
$289$	−6.38752	+	11.0635i	−0.375737	+	0.650795i
$290$	−6.49710	+	5.92719i	−0.381523	+	0.348057i
$291$		0			0
$292$	−19.8773	−	1.82741i	−1.16323	−	0.106941i
$293$			26.8845i			1.57061i	0.619110	+	0.785304i	$0.287494\pi$
$293$			26.8845i			1.57061i	−0.619110	+	0.785304i	$0.712506\pi$
$294$		0			0
$295$			10.2822i			0.598656i
$296$	−2.06675	−	16.5435i	−0.120127	−	0.961574i
$297$		0			0
$298$	−11.3366	−	12.4266i	−0.656711	−	0.719855i
$299$	4.87279	−	8.43991i	0.281800	−	0.488093i
$300$		0			0
$301$	4.89421	+	26.7590i	0.282097	+	1.54236i
$302$	−2.92137	−	13.3163i	−0.168106	−	0.766269i
$303$		0			0
$304$	12.3777	+	2.29527i	0.709908	+	0.131643i
$305$	2.41819	+	4.18842i	0.138465	+	0.239828i
$306$		0			0
$307$	9.99662			0.570537			0.285269	−	0.958448i	$-0.407917\pi$
$307$	9.99662			0.570537			0.285269	+	0.958448i	$0.407917\pi$
$308$	11.3274	−	1.01336i	0.645440	−	0.0577414i
$309$		0			0
$310$	1.12560	+	0.357631i	0.0639297	+	0.0203121i
$311$	9.81325	+	16.9970i	0.556458	+	0.963814i	0.997788	+	0.0664690i	$0.0211733\pi$
$311$	9.81325	+	16.9970i	0.556458	+	0.963814i	−0.441330	+	0.897345i	$0.645493\pi$
$312$		0			0
$313$	19.3657	+	11.1808i	1.09462	+	0.631977i	0.934802	−	0.355171i	$-0.115577\pi$
$313$	19.3657	+	11.1808i	1.09462	+	0.631977i	0.159814	+	0.987147i	$0.448911\pi$
$314$	1.81304	+	8.26428i	0.102316	+	0.466380i
$315$		0			0
$316$	−6.59780	−	14.3135i	−0.371155	−	0.805197i
$317$	−1.16986	+	2.02626i	−0.0657061	+	0.113806i	−0.897007	−	0.442016i	$-0.854263\pi$
$317$	−1.16986	+	2.02626i	−0.0657061	+	0.113806i	0.831301	+	0.555823i	$0.187597\pi$
$318$		0			0
$319$	−14.2427	+	8.22304i	−0.797439	+	0.460402i
$320$	4.65763	−	4.53598i	0.260370	−	0.253569i
$321$		0			0
$322$	−4.29489	+	5.64570i	−0.239345	+	0.314623i
$323$		−	6.46892i		−	0.359940i
$324$		0			0
$325$	−19.3186	+	11.1536i	−1.07160	+	0.618691i
$326$	10.2969	−	9.39364i	0.570290	−	0.520265i
$327$		0			0
$328$	−4.35521	−	5.75424i	−0.240476	−	0.317725i
$329$	−1.88878	+	5.29402i	−0.104132	+	0.291869i
$330$		0			0
$331$	−25.7526	−	14.8683i	−1.41549	−	0.817234i	−0.419592	−	0.907713i	$-0.637827\pi$
$331$	−25.7526	−	14.8683i	−1.41549	−	0.817234i	−0.995898	+	0.0904788i	$0.971160\pi$
$332$	28.5906	+	20.2078i	1.56911	+	1.10905i
$333$		0			0
$334$	−8.76999	+	27.6025i	−0.479873	+	1.51034i
$335$	−6.49226			−0.354710
$336$		0			0
$337$	−1.92824			−0.105038			−0.0525191	−	0.998620i	$-0.516725\pi$
$337$	−1.92824			−0.105038			−0.0525191	+	0.998620i	$0.516725\pi$
$338$	5.74871	−	18.0934i	0.312689	−	0.984149i
$339$		0			0
$340$	−2.72821	−	1.92830i	−0.147958	−	0.104577i
$341$	1.91270	+	1.10430i	0.103579	+	0.0598011i
$342$		0			0
$343$	15.8592	−	9.56478i	0.856317	−	0.516450i
$344$	17.5504	+	23.1882i	0.946256	+	1.25022i
$345$		0			0
$346$	4.17559	−	3.80932i	0.224481	−	0.204790i
$347$	11.6827	−	6.74504i	0.627163	−	0.362093i	−0.152490	−	0.988305i	$-0.548729\pi$
$347$	11.6827	−	6.74504i	0.627163	−	0.362093i	0.779652	+	0.626212i	$0.215396\pi$
$348$		0			0
$349$			22.7410i			1.21730i	0.793439	+	0.608650i	$0.208288\pi$
$349$			22.7410i			1.21730i	−0.793439	+	0.608650i	$0.791712\pi$
$350$	14.9751	−	6.27605i	0.800455	−	0.335469i
$351$		0			0
$352$	10.3253	−	6.41898i	0.550339	−	0.342133i
$353$	22.4215	−	12.9450i	1.19337	−	0.688995i	0.234304	−	0.972163i	$-0.424719\pi$
$353$	22.4215	−	12.9450i	1.19337	−	0.688995i	0.959070	+	0.283169i	$0.0913856\pi$
$354$		0			0
$355$	4.49328	−	7.78259i	0.238479	−	0.413057i
$356$	−0.468798	−	1.01703i	−0.0248463	−	0.0539024i
$357$		0			0
$358$	−5.58110	−	25.4401i	−0.294970	−	1.34455i
$359$	0.384185	+	0.221809i	0.0202765	+	0.0117066i	0.510104	−	0.860113i	$-0.329607\pi$
$359$	0.384185	+	0.221809i	0.0202765	+	0.0117066i	−0.489827	+	0.871819i	$0.662940\pi$
$360$		0			0
$361$	4.54765	+	7.87677i	0.239350	+	0.414567i
$362$	−11.8298	−	3.75862i	−0.621761	−	0.197549i
$363$		0			0
$364$	−11.4473	+	24.6746i	−0.599999	+	1.29330i
$365$	8.11098			0.424548
$366$		0			0
$367$	−13.6052	−	23.5650i	−0.710188	−	1.23008i	−0.964786	−	0.263035i	$-0.915277\pi$
$367$	−13.6052	−	23.5650i	−0.710188	−	1.23008i	0.254599	−	0.967047i	$-0.418057\pi$
$368$	−1.38268	+	7.45633i	−0.0720770	+	0.388688i
$369$		0			0
$370$	1.45169	+	6.61719i	0.0754699	+	0.344011i
$371$	11.3841	+	13.3930i	0.591035	+	0.695329i
$372$		0			0
$373$	−8.63311	+	14.9530i	−0.447005	+	0.774236i	−0.998189	−	0.0601476i	$-0.980843\pi$
$373$	−8.63311	+	14.9530i	−0.447005	+	0.774236i	0.551184	+	0.834384i	$0.314176\pi$
$374$	−4.21061	−	4.61547i	−0.217726	−	0.238660i
$375$		0			0
$376$	0.744896	+	5.96261i	0.0384151	+	0.307498i
$377$		−	39.3350i		−	2.02586i
$378$		0			0
$379$			30.0266i			1.54236i	0.636616	+	0.771181i	$0.280334\pi$
$379$			30.0266i			1.54236i	−0.636616	+	0.771181i	$0.719666\pi$
$380$	−5.09380	−	0.468297i	−0.261307	−	0.0240231i
$381$		0			0
$382$	22.9455	−	20.9328i	1.17399	−	1.07101i
$383$	−10.5011	+	18.1884i	−0.536581	+	0.929386i	0.462504	+	0.886617i	$0.346951\pi$
$383$	−10.5011	+	18.1884i	−0.536581	+	0.929386i	−0.999085	+	0.0427689i	$0.986382\pi$
$384$		0			0
$385$	−4.54576	+	0.831417i	−0.231673	+	0.0423729i
$386$	0.968807	−	0.212539i	0.0493110	−	0.0108179i
$387$		0			0
$388$	−2.13254	+	3.01718i	−0.108263	+	0.153174i
$389$	4.55328	+	7.88652i	0.230861	+	0.399862i	0.958062	−	0.286562i	$-0.0925125\pi$
$389$	4.55328	+	7.88652i	0.230861	+	0.399862i	−0.727201	+	0.686425i	$0.759179\pi$
$390$		0			0
$391$	3.89688			0.197074
$392$	10.5356	−	16.7631i	0.532129	−	0.846663i
$393$		0			0
$394$	10.2603	−	32.2931i	0.516908	−	1.62690i
$395$	3.20215	+	5.54628i	0.161118	+	0.279064i
$396$		0			0
$397$	−3.92841	−	2.26807i	−0.197161	−	0.113831i	0.398169	−	0.917312i	$-0.369646\pi$
$397$	−3.92841	−	2.26807i	−0.197161	−	0.113831i	−0.595331	+	0.803481i	$0.702979\pi$
$398$	3.03005	−	0.664739i	0.151883	−	0.0333203i
$399$		0			0
$400$	11.2745	−	13.1982i	0.563725	−	0.659911i
$401$	12.5118	−	21.6711i	0.624810	−	1.08220i	−0.363767	−	0.931490i	$-0.618510\pi$
$401$	12.5118	−	21.6711i	0.624810	−	1.08220i	0.988577	−	0.150714i	$-0.0481571\pi$
$402$		0			0
$403$	−4.57472	+	2.64122i	−0.227883	+	0.131568i
$404$	32.5333	+	2.99094i	1.61859	+	0.148805i
$405$		0			0
$406$	−3.61898	+	28.4018i	−0.179607	+	1.40956i
$407$			12.6686i			0.627961i
$408$		0			0
$409$	3.37147	−	1.94652i	0.166708	−	0.0962490i	−0.414325	−	0.910129i	$-0.635982\pi$
$409$	3.37147	−	1.94652i	0.166708	−	0.0962490i	0.581033	+	0.813880i	$0.302649\pi$
$410$	1.97632	+	2.16634i	0.0976034	+	0.106988i
$411$		0			0
$412$	−8.66417	+	3.99374i	−0.426853	+	0.196758i
$413$	21.6800	+	25.5057i	1.06680	+	1.25505i
$414$		0			0
$415$	−12.3204	−	7.11320i	−0.604786	−	0.349173i
$416$	0.948004	+	29.0633i	0.0464797	+	1.42495i
$417$		0			0
$418$	−9.11665	−	2.89659i	−0.445910	−	0.141677i
$419$	−11.4873			−0.561192			−0.280596	−	0.959826i	$-0.590532\pi$
$419$	−11.4873			−0.561192			−0.280596	+	0.959826i	$0.590532\pi$
$420$		0			0
$421$	−7.14186			−0.348073			−0.174037	−	0.984739i	$-0.555681\pi$
$421$	−7.14186			−0.348073			−0.174037	+	0.984739i	$0.555681\pi$
$422$	−14.8857	−	4.72956i	−0.724625	−	0.230231i
$423$		0			0
$424$	17.3129	+	7.30578i	0.840787	+	0.354800i
$425$	−7.72479	−	4.45991i	−0.374707	−	0.216337i
$426$		0			0
$427$	14.8297	+	5.29088i	0.717659	+	0.256044i
$428$	3.91905	+	8.50214i	0.189435	+	0.410967i
$429$		0			0
$430$	−7.96409	−	8.72985i	−0.384063	−	0.420991i
$431$	−17.9137	+	10.3425i	−0.862873	+	0.498180i	−0.864973	−	0.501818i	$-0.832665\pi$
$431$	−17.9137	+	10.3425i	−0.862873	+	0.498180i	0.00210056	+	0.999998i	$0.499331\pi$
$432$		0			0
$433$			14.4701i			0.695389i	0.937608	+	0.347695i	$0.113035\pi$
$433$			14.4701i			0.695389i	−0.937608	+	0.347695i	$0.886965\pi$
$434$	3.54617	−	1.48619i	0.170222	−	0.0713395i
$435$		0			0
$436$	−1.53661	+	16.7141i	−0.0735902	+	0.800462i
$437$	5.16723	−	2.98330i	0.247182	−	0.142711i
$438$		0			0
$439$	−2.54215	+	4.40313i	−0.121330	+	0.210150i	−0.920292	−	0.391231i	$-0.872049\pi$
$439$	−2.54215	+	4.40313i	−0.121330	+	0.210150i	0.798962	+	0.601381i	$0.205383\pi$
$440$	−3.93916	+	2.98143i	−0.187792	+	0.142134i
$441$		0			0
$442$	14.5955	−	3.20200i	0.694238	−	0.152303i
$443$	−4.97946	−	2.87489i	−0.236581	−	0.136590i	0.377023	−	0.926204i	$-0.376948\pi$
$443$	−4.97946	−	2.87489i	−0.236581	−	0.136590i	−0.613605	+	0.789614i	$0.710281\pi$
$444$		0			0
$445$	0.227525	+	0.394084i	0.0107857	+	0.0186814i
$446$	−8.74016	+	27.5086i	−0.413858	+	1.30257i
$447$		0			0
$448$	1.98943	−	21.0723i	0.0939919	−	0.995573i
$449$	18.3848			0.867630			0.433815	−	0.901002i	$-0.357167\pi$
$449$	18.3848			0.867630			0.433815	+	0.901002i	$0.357167\pi$
$450$		0			0
$451$	2.74183	+	4.74898i	0.129108	+	0.223621i
$452$	−4.25151	−	3.00497i	−0.199974	−	0.141342i
$453$		0			0
$454$	6.09792	−	1.33777i	0.286190	−	0.0627849i
$455$	3.71405	−	10.4100i	0.174117	−	0.488029i
$456$		0			0
$457$	14.5364	−	25.1777i	0.679982	−	1.17776i	−0.295003	−	0.955496i	$-0.595321\pi$
$457$	14.5364	−	25.1777i	0.679982	−	1.17776i	0.974986	−	0.222268i	$-0.0713459\pi$
$458$	19.9695	−	18.2178i	0.933112	−	0.851262i
$459$		0			0
$460$	0.282103	−	3.06851i	0.0131531	−	0.143070i
$461$			27.4011i			1.27620i	0.769954	+	0.638099i	$0.220279\pi$
$461$			27.4011i			1.27620i	−0.769954	+	0.638099i	$0.779721\pi$
$462$		0			0
$463$			33.6619i			1.56440i	0.623027	+	0.782200i	$0.285903\pi$
$463$			33.6619i			1.56440i	−0.623027	+	0.782200i	$0.714097\pi$
$464$	10.2145	+	28.8536i	0.474198	+	1.33949i
$465$		0			0
$466$	13.7361	+	15.0568i	0.636311	+	0.697494i
$467$	7.28260	−	12.6138i	0.336998	−	0.583698i	−0.646868	−	0.762602i	$-0.723922\pi$
$467$	7.28260	−	12.6138i	0.336998	−	0.583698i	0.983867	+	0.178903i	$0.0572549\pi$
$468$		0			0
$469$	−16.1044	+	13.6889i	−0.743632	+	0.632093i
$470$	−0.523218	−	2.38496i	−0.0241342	−	0.110010i
$471$		0			0
$472$	32.9707	+	13.9132i	1.51760	+	0.640405i
$473$	−11.0489	−	19.1373i	−0.508029	−	0.879933i
$474$		0			0
$475$	−13.6573			−0.626641
$476$	−10.8333	+	0.969149i	−0.496542	+	0.0444209i
$477$		0			0
$478$	17.9691	+	5.70923i	0.821888	+	0.261134i
$479$	3.36750	+	5.83269i	0.153865	+	0.266502i	0.932645	−	0.360795i	$-0.117495\pi$
$479$	3.36750	+	5.83269i	0.153865	+	0.266502i	−0.778780	+	0.627297i	$0.784161\pi$
$480$		0			0
$481$	−26.2408	−	15.1502i	−1.19648	−	0.690788i
$482$	−7.45398	−	33.9771i	−0.339519	−	1.54762i
$483$		0			0
$484$	11.5896	−	5.34222i	0.526801	−	0.242828i
$485$	0.750659	−	1.30018i	0.0340857	−	0.0590381i
$486$		0			0
$487$	−4.48186	+	2.58760i	−0.203093	+	0.117256i	−0.598097	−	0.801424i	$-0.704076\pi$
$487$	−4.48186	+	2.58760i	−0.203093	+	0.117256i	0.395005	+	0.918679i	$0.370743\pi$
$488$	16.7026	−	2.08661i	0.756089	−	0.0944566i
$489$		0			0
$490$	−3.63948	+	7.17482i	−0.164415	+	0.324125i
$491$			4.23104i			0.190944i	0.995432	+	0.0954720i	$0.0304360\pi$
$491$			4.23104i			0.190944i	−0.995432	+	0.0954720i	$0.969564\pi$
$492$		0			0
$493$	13.6214	−	7.86430i	0.613475	−	0.354190i
$494$	16.9022	−	15.4196i	0.760465	−	0.693759i
$495$		0			0
$496$	2.66984	−	3.12539i	0.119879	−	0.140334i
$497$	−5.26369	−	28.7792i	−0.236109	−	1.29092i
$498$		0			0
$499$	−24.9498	−	14.4048i	−1.11691	−	0.644846i	−0.176297	−	0.984337i	$-0.556412\pi$
$499$	−24.9498	−	14.4048i	−1.11691	−	0.644846i	−0.940609	+	0.339491i	$0.889745\pi$
$500$	−8.76172	+	12.3963i	−0.391836	+	0.554380i
$501$		0			0
$502$	0.630842	−	1.98550i	0.0281558	−	0.0886170i
$503$	33.0972			1.47573			0.737865	−	0.674948i	$-0.235834\pi$
$503$	33.0972			1.47573			0.737865	+	0.674948i	$0.235834\pi$
$504$		0			0
$505$	−13.2753			−0.590744
$506$	1.74491	−	5.49188i	0.0775706	−	0.244144i
$507$		0			0
$508$	7.73682	−	10.9462i	0.343266	−	0.485661i
$509$	16.1832	+	9.34337i	0.717308	+	0.414138i	0.813761	−	0.581200i	$-0.197416\pi$
$509$	16.1832	+	9.34337i	0.717308	+	0.414138i	−0.0964533	+	0.995338i	$0.530750\pi$
$510$		0			0
$511$	20.1197	−	17.1019i	0.890044	−	0.756544i
$512$	−8.24255	−	21.0727i	−0.364273	−	0.931292i
$513$		0			0
$514$	−11.1376	+	10.1607i	−0.491259	+	0.448167i
$515$	3.35725	−	1.93831i	0.147938	−	0.0854120i
$516$		0			0
$517$		−	4.56602i		−	0.200813i
$518$	17.5533	+	13.3534i	0.771246	+	0.586715i
$519$		0			0
$520$	−1.46474	−	11.7247i	−0.0642333	−	0.514163i
$521$	−17.4125	+	10.0531i	−0.762855	+	0.440435i	−0.830320	−	0.557287i	$-0.811842\pi$
$521$	−17.4125	+	10.0531i	−0.762855	+	0.440435i	0.0674646	+	0.997722i	$0.478509\pi$
$522$		0			0
$523$	−10.3935	+	18.0021i	−0.454476	+	0.787175i	−0.998658	−	0.0517922i	$-0.983507\pi$
$523$	−10.3935	+	18.0021i	−0.454476	+	0.787175i	0.544182	+	0.838967i	$0.316840\pi$
$524$	−26.7919	+	12.3497i	−1.17041	+	0.539499i
$525$		0			0
$526$	−8.11073	−	36.9708i	−0.353645	−	1.61200i
$527$	−1.82926	−	1.05612i	−0.0796837	−	0.0460054i
$528$		0			0
$529$	−9.70286	−	16.8058i	−0.421863	−	0.730689i
$530$	−7.27713	−	2.31213i	−0.316098	−	0.100432i
$531$		0			0
$532$	−13.6228	+	9.57860i	−0.590625	+	0.415285i
$533$	−13.1156			−0.568099
$534$		0			0
$535$	−1.90206	−	3.29446i	−0.0822332	−	0.142432i
$536$	−8.78483	+	20.8178i	−0.379447	+	0.899194i
$537$		0			0
$538$	−6.07447	−	27.6890i	−0.261889	−	1.19376i
$539$	−9.52296	+	11.6471i	−0.410183	+	0.501674i
$540$		0			0
$541$	15.1843	−	26.3000i	0.652824	−	1.13072i	−0.329611	−	0.944117i	$-0.606917\pi$
$541$	15.1843	−	26.3000i	0.652824	−	1.13072i	0.982435	−	0.186607i	$-0.0597492\pi$
$542$	−8.32678	−	9.12742i	−0.357666	−	0.392056i
$543$		0			0
$544$	−9.87481	+	6.13894i	−0.423379	+	0.263205i
$545$		−	6.82026i		−	0.292148i
$546$		0			0
$547$		−	13.2770i		−	0.567685i	−0.958871	−	0.283842i	$-0.908391\pi$
$547$		−	13.2770i		−	0.567685i	0.958871	−	0.283842i	$-0.0916092\pi$
$548$	−3.69699	+	40.2132i	−0.157928	+	1.71782i
$549$		0			0
$550$	−9.74428	+	8.88954i	−0.415498	+	0.379051i
$551$	12.0412	−	20.8560i	0.512972	−	0.888493i
$552$		0			0
$553$	19.6374	+	7.00615i	0.835066	+	0.297932i
$554$	−15.8517	+	3.47758i	−0.673475	+	0.147748i
$555$		0			0
$556$	−36.7485	−	25.9739i	−1.55848	−	1.10154i
$557$	15.4608	+	26.7788i	0.655093	+	1.13465i	0.981870	+	0.189553i	$0.0607040\pi$
$557$	15.4608	+	26.7788i	0.655093	+	1.13465i	−0.326777	+	0.945101i	$0.605963\pi$
$558$		0			0
$559$	52.8527			2.23543
$560$	−0.0211051	+	8.60057i	−0.000891853	+	0.363440i
$561$		0			0
$562$	−8.43365	+	26.5439i	−0.355752	+	1.11969i
$563$	−11.6019	−	20.0950i	−0.488960	−	0.846904i	0.510959	−	0.859605i	$-0.329290\pi$
$563$	−11.6019	−	20.0950i	−0.488960	−	0.846904i	−0.999919	+	0.0127010i	$0.995957\pi$
$564$		0			0
$565$	1.83209	+	1.05776i	0.0770764	+	0.0445001i
$566$	4.99102	−	1.09494i	0.209788	−	0.0460238i
$567$		0			0
$568$	−18.8754	−	24.9388i	−0.791994	−	1.04641i
$569$	−6.30064	+	10.9130i	−0.264137	+	0.457498i	−0.967337	−	0.253494i	$-0.918420\pi$
$569$	−6.30064	+	10.9130i	−0.264137	+	0.457498i	0.703200	+	0.710992i	$0.251754\pi$
$570$		0			0
$571$	36.0513	−	20.8142i	1.50870	−	0.871049i	0.508752	−	0.860913i	$-0.330107\pi$
$571$	36.0513	−	20.8142i	1.50870	−	0.871049i	0.999949	−	0.0101362i	$-0.00322649\pi$
$572$	2.02286	−	22.0032i	0.0845800	−	0.920001i
$573$		0			0
$574$	9.47008	+	1.20669i	0.395273	+	0.0503661i
$575$		−	8.22719i		−	0.343097i
$576$		0			0
$577$	19.5101	−	11.2642i	0.812218	−	0.468934i	−0.0355075	−	0.999369i	$-0.511305\pi$
$577$	19.5101	−	11.2642i	0.812218	−	0.468934i	0.847726	+	0.530435i	$0.177971\pi$
$578$	−12.1762	−	13.3470i	−0.506465	−	0.555162i
$579$		0			0
$580$	−5.20649	−	11.2951i	−0.216188	−	0.469006i
$581$	−45.5596	+	8.33282i	−1.89013	+	0.345704i
$582$		0			0
$583$	−12.3658	−	7.13942i	−0.512141	−	0.295685i
$584$	10.9752	−	26.0084i	0.454156	−	1.07623i
$585$		0			0
$586$	−36.2354	−	11.5129i	−1.49687	−	0.475593i
$587$	−8.49214			−0.350508			−0.175254	−	0.984523i	$-0.556075\pi$
$587$	−8.49214			−0.350508			−0.175254	+	0.984523i	$0.556075\pi$
$588$		0			0
$589$	−3.23410			−0.133259
$590$	−13.8586	−	4.40322i	−0.570550	−	0.181278i
$591$		0			0
$592$	23.1827	+	4.29893i	0.952805	+	0.176685i
$593$	0.699256	+	0.403715i	0.0287150	+	0.0165786i	0.514289	−	0.857617i	$-0.328056\pi$
$593$	0.699256	+	0.403715i	0.0287150	+	0.0165786i	−0.485574	+	0.874196i	$0.661389\pi$
$594$		0			0
$595$	4.34745	−	0.795145i	0.178228	−	0.0325978i
$596$	21.6036	−	9.95814i	0.884916	−	0.407901i
$597$		0			0
$598$	9.28877	+	10.1819i	0.379846	+	0.416369i
$599$	−27.9459	+	16.1346i	−1.14184	+	0.659240i	−0.946885	−	0.321572i	$-0.895789\pi$
$599$	−27.9459	+	16.1346i	−1.14184	+	0.659240i	−0.194953	+	0.980813i	$0.562455\pi$
$600$		0			0
$601$			2.37514i			0.0968838i	0.998826	+	0.0484419i	$0.0154256\pi$
$601$			2.37514i			0.0968838i	−0.998826	+	0.0484419i	$0.984574\pi$
$602$	−38.1621	−	4.86265i	−1.55537	−	0.198187i
$603$		0			0
$604$	19.1990	+	1.76506i	0.781198	+	0.0718191i
$605$	−4.49082	+	2.59277i	−0.182578	+	0.105411i
$606$		0			0
$607$	−8.99848	+	15.5858i	−0.365237	+	0.632609i	−0.988814	−	0.149153i	$-0.952345\pi$
$607$	−8.99848	+	15.5858i	−0.365237	+	0.632609i	0.623577	+	0.781762i	$0.285679\pi$
$608$	−8.39417	+	15.6999i	−0.340429	+	0.636717i
$609$		0			0
$610$	−6.68079	+	1.46565i	−0.270497	+	0.0593423i
$611$	9.45770	+	5.46041i	0.382618	+	0.220904i
$612$		0			0
$613$	8.95667	+	15.5134i	0.361757	+	0.626581i	0.988250	−	0.152846i	$-0.0488438\pi$
$613$	8.95667	+	15.5134i	0.361757	+	0.626581i	−0.626493	+	0.779427i	$0.715510\pi$
$614$	−4.28091	+	13.4736i	−0.172763	+	0.543751i
$615$		0			0
$616$	−3.48499	+	15.7013i	−0.140414	+	0.632622i
$617$	−7.48143			−0.301191			−0.150596	−	0.988595i	$-0.548119\pi$
$617$	−7.48143			−0.301191			−0.150596	+	0.988595i	$0.548119\pi$
$618$		0			0
$619$	−14.6007	−	25.2892i	−0.586852	−	1.01646i	−0.994642	−	0.103381i	$-0.967034\pi$
$619$	−14.6007	−	25.2892i	−0.586852	−	1.01646i	0.407790	−	0.913076i	$-0.366300\pi$
$620$	−0.964043	+	1.36395i	−0.0387169	+	0.0547777i
$621$		0			0
$622$	−27.1113	+	5.94774i	−1.08706	+	0.238482i
$623$	1.39531	+	0.497814i	0.0559019	+	0.0199445i
$624$		0			0
$625$	−7.76474	+	13.4489i	−0.310589	+	0.537957i
$626$	−23.3628	+	21.3135i	−0.933765	+	0.851857i
$627$		0			0
$628$	−11.9152	−	1.09542i	−0.475467	−	0.0437118i
$629$		−	12.1159i		−	0.483094i
$630$		0			0
$631$			3.89890i			0.155213i	0.996984	+	0.0776063i	$0.0247277\pi$
$631$			3.89890i			0.155213i	−0.996984	+	0.0776063i	$0.975272\pi$
$632$	22.1174	−	2.76308i	0.879783	−	0.109909i
$633$		0			0
$634$	−2.23006	−	2.44448i	−0.0885670	−	0.0970828i
$635$	−2.72338	+	4.71702i	−0.108074	+	0.187189i
$636$		0			0
$637$	−12.7365	−	33.6536i	−0.504639	−	1.33341i
$638$	−4.98392	−	22.7180i	−0.197315	−	0.899414i
$639$		0			0
$640$	4.11912	+	8.22011i	0.162822	+	0.324928i
$641$	1.10624	+	1.91606i	0.0436938	+	0.0756799i	0.887045	−	0.461683i	$-0.152754\pi$
$641$	1.10624	+	1.91606i	0.0436938	+	0.0756799i	−0.843351	+	0.537362i	$0.819421\pi$
$642$		0			0
$643$	32.8438			1.29523			0.647616	−	0.761967i	$-0.275766\pi$
$643$	32.8438			1.29523			0.647616	+	0.761967i	$0.275766\pi$
$644$	−5.77016	−	8.20642i	−0.227376	−	0.323378i
$645$		0			0
$646$	8.71892	+	2.77022i	0.343041	+	0.108993i
$647$	−16.0315	−	27.7674i	−0.630263	−	1.09165i	−0.987498	−	0.157633i	$-0.949614\pi$
$647$	−16.0315	−	27.7674i	−0.630263	−	1.09165i	0.357234	−	0.934015i	$-0.383720\pi$
$648$		0			0
$649$	−23.5496	−	13.5963i	−0.924401	−	0.533703i
$650$	−6.76013	−	30.8144i	−0.265154	−	1.20864i
$651$		0			0
$652$	8.25144	+	17.9010i	0.323151	+	0.701056i
$653$	−15.9326	+	27.5961i	−0.623491	+	1.07992i	0.365340	+	0.930874i	$0.380953\pi$
$653$	−15.9326	+	27.5961i	−0.623491	+	1.07992i	−0.988831	+	0.149044i	$0.952380\pi$
$654$		0			0
$655$	10.3815	−	5.99375i	0.405638	−	0.234195i
$656$	9.62072	−	3.40586i	0.375626	−	0.132976i
$657$		0			0
$658$	−6.32653	−	4.81282i	−0.246634	−	0.187623i
$659$		−	16.2660i		−	0.633634i	−0.948487	−	0.316817i	$-0.897386\pi$
$659$		−	16.2660i		−	0.633634i	0.948487	−	0.316817i	$-0.102614\pi$
$660$		0			0
$661$	37.3471	−	21.5624i	1.45263	−	0.838679i	0.454004	−	0.891000i	$-0.349995\pi$
$661$	37.3471	−	21.5624i	1.45263	−	0.838679i	0.998630	+	0.0523206i	$0.0166618\pi$
$662$	31.0679	−	28.3427i	1.20749	−	1.10157i
$663$		0			0
$664$	−39.4800	+	29.8812i	−1.53212	+	1.15961i
$665$	5.15594	−	4.38259i	0.199939	−	0.169949i
$666$		0			0
$667$	12.5637	+	7.25363i	0.486467	+	0.280862i
$668$	−33.4475	−	23.6407i	−1.29412	−	0.914687i
$669$		0			0
$670$	2.78022	−	8.75039i	0.107409	−	0.338057i
$671$	−12.7904			−0.493768
$672$		0			0
$673$	20.3814			0.785645			0.392822	−	0.919614i	$-0.371499\pi$
$673$	20.3814			0.785645			0.392822	+	0.919614i	$0.371499\pi$
$674$	0.825743	−	2.59892i	0.0318064	−	0.100107i
$675$		0			0
$676$	21.9248	+	15.4964i	0.843260	+	0.596017i
$677$	−31.8523	−	18.3900i	−1.22419	−	0.706784i	−0.258378	−	0.966044i	$-0.583188\pi$
$677$	−31.8523	−	18.3900i	−1.22419	−	0.706784i	−0.965807	+	0.259260i	$0.916521\pi$
$678$		0			0
$679$	−0.879366	−	4.80792i	−0.0337470	−	0.184511i
$680$	3.76731	−	2.85136i	0.144470	−	0.109345i
$681$		0			0
$682$	−2.30748	+	2.10507i	−0.0883580	+	0.0806074i
$683$	29.7576	−	17.1805i	1.13864	−	0.657395i	0.192548	−	0.981288i	$-0.438325\pi$
$683$	29.7576	−	17.1805i	1.13864	−	0.657395i	0.946094	+	0.323892i	$0.104992\pi$
$684$		0			0
$685$		−	16.4091i		−	0.626961i
$686$	6.10011	+	25.4713i	0.232903	+	0.972500i
$687$		0			0
$688$	−38.7692	+	13.7248i	−1.47806	+	0.523253i
$689$	29.5761	−	17.0758i	1.12676	−	0.650535i
$690$		0			0
$691$	−24.0149	+	41.5950i	−0.913568	+	1.58235i	−0.104584	+	0.994516i	$0.533351\pi$
$691$	−24.0149	+	41.5950i	−0.913568	+	1.58235i	−0.808984	+	0.587830i	$0.799982\pi$
$692$	3.34613	+	7.25923i	0.127201	+	0.275954i
$693$		0			0
$694$	4.08812	+	18.6347i	0.155183	+	0.707363i
$695$	15.8359	+	9.14286i	0.600690	+	0.346808i
$696$		0			0
$697$	−2.62221	−	4.54180i	−0.0993234	−	0.172033i
$698$	−30.6508	−	9.73851i	−1.16015	−	0.368608i
$699$		0			0
$700$	2.04609	+	22.8714i	0.0773349	+	0.864458i
$701$	1.33206			0.0503111			0.0251555	−	0.999684i	$-0.491992\pi$
$701$	1.33206			0.0503111			0.0251555	+	0.999684i	$0.491992\pi$
$702$		0			0
$703$	−9.27549	−	16.0656i	−0.349832	−	0.605926i
$704$	4.22997	+	16.6654i	0.159423	+	0.628102i
$705$		0			0
$706$	7.84589	+	35.7636i	0.295284	+	1.34598i
$707$	−32.9301	+	27.9909i	−1.23847	+	1.05271i
$708$		0			0
$709$	15.9986	−	27.7104i	0.600840	−	1.04068i	−0.391855	−	0.920027i	$-0.628166\pi$
$709$	15.9986	−	27.7104i	0.600840	−	1.04068i	0.992694	−	0.120658i	$-0.0385003\pi$
$710$	8.56534	+	9.38891i	0.321451	+	0.352360i
$711$		0			0
$712$	1.57153	−	0.196327i	0.0588954	−	0.00735768i
$713$		−	1.94823i		−	0.0729617i
$714$		0			0
$715$			8.97849i			0.335777i
$716$	36.6786	+	3.37203i	1.37074	+	0.126019i
$717$		0			0
$718$	−0.463480	+	0.422824i	−0.0172969	+	0.0157797i
$719$	1.60377	−	2.77780i	0.0598104	−	0.103595i	−0.834570	−	0.550902i	$-0.814284\pi$
$719$	1.60377	−	2.77780i	0.0598104	−	0.103595i	0.894380	+	0.447308i	$0.147617\pi$
$720$		0			0
$721$	4.24092	−	11.8868i	0.157940	−	0.442687i
$722$	−12.5639	+	2.75630i	−0.467581	+	0.102579i
$723$		0			0
$724$	10.1319	−	14.3349i	0.376549	−	0.532751i
$725$	−16.6033	−	28.7577i	−0.616630	−	1.06803i
$726$		0			0
$727$	50.4852			1.87239			0.936197	−	0.351477i	$-0.114320\pi$
$727$	50.4852			1.87239			0.936197	+	0.351477i	$0.114320\pi$
$728$	−28.3548	−	25.9954i	−1.05090	−	0.963453i
$729$		0			0
$730$	−3.47341	+	10.9321i	−0.128557	+	0.404616i
$731$	10.5669	+	18.3024i	0.390830	+	0.676938i
$732$		0			0
$733$	−4.98706	−	2.87928i	−0.184201	−	0.106349i	0.405064	−	0.914288i	$-0.367249\pi$
$733$	−4.98706	−	2.87928i	−0.184201	−	0.106349i	−0.589265	+	0.807940i	$0.700583\pi$
$734$	37.5875	−	8.24604i	1.38738	−	0.304367i
$735$		0			0
$736$	−9.45767	−	5.05666i	−0.348614	−	0.186391i
$737$	8.58479	−	14.8693i	0.316225	−	0.547718i
$738$		0			0
$739$	−22.7520	+	13.1359i	−0.836945	+	0.483210i	−0.856225	−	0.516604i	$-0.827196\pi$
$739$	−22.7520	+	13.1359i	−0.836945	+	0.483210i	0.0192796	+	0.999814i	$0.493863\pi$
$740$	−9.54043	−	0.877096i	−0.350713	−	0.0322427i
$741$		0			0
$742$	−22.9264	+	9.60841i	−0.841655	+	0.352736i
$743$			1.42155i			0.0521516i	0.999660	+	0.0260758i	$0.00830112\pi$
$743$			1.42155i			0.0521516i	−0.999660	+	0.0260758i	$0.991699\pi$
$744$		0			0
$745$	−8.37108	+	4.83304i	−0.306693	+	0.177069i
$746$	−16.4569	−	18.0393i	−0.602530	−	0.660464i
$747$		0			0
$748$	8.02395	−	3.69863i	0.293385	−	0.135235i
$749$	−11.6645	−	4.16162i	−0.426211	−	0.152062i
$750$		0			0
$751$	−41.4368	−	23.9235i	−1.51205	−	0.872982i	−0.999901	−	0.0140857i	$-0.995516\pi$
$751$	−41.4368	−	23.9235i	−1.51205	−	0.872982i	−0.512149	−	0.858897i	$-0.671150\pi$
$752$	−8.35551	−	1.54942i	−0.304694	−	0.0565014i
$753$		0			0
$754$	53.0165	+	16.8447i	1.93075	+	0.613447i
$755$	−7.83423			−0.285117
$756$		0			0
$757$	31.0162			1.12730			0.563651	−	0.826013i	$-0.309396\pi$
$757$	31.0162			1.12730			0.563651	+	0.826013i	$0.309396\pi$
$758$	−40.4704	−	12.8584i	−1.46995	−	0.467040i
$759$		0			0
$760$	2.81253	−	6.66498i	0.102021	−	0.241764i
$761$	−10.0676	−	5.81256i	−0.364952	−	0.210705i	0.306299	−	0.951935i	$-0.400909\pi$
$761$	−10.0676	−	5.81256i	−0.364952	−	0.210705i	−0.671251	+	0.741230i	$0.734243\pi$
$762$		0			0
$763$	−14.3805	−	16.9180i	−0.520607	−	0.612473i
$764$	18.3875	+	39.8905i	0.665236	+	1.44319i
$765$		0			0
$766$	−20.0178	−	21.9425i	−0.723272	−	0.792816i
$767$	56.3249	−	32.5192i	2.03377	−	1.17420i
$768$		0			0
$769$		−	27.9395i		−	1.00752i	−0.863843	−	0.503762i	$-0.831949\pi$
$769$		−	27.9395i		−	1.00752i	0.863843	−	0.503762i	$-0.168051\pi$
$770$	0.826057	−	6.48290i	0.0297690	−	0.233628i
$771$		0			0
$772$	−0.128414	+	1.39679i	−0.00462171	+	0.0502716i
$773$	−46.4286	+	26.8056i	−1.66992	+	0.964129i	−0.702243	+	0.711938i	$0.747818\pi$
$773$	−46.4286	+	26.8056i	−1.66992	+	0.964129i	−0.967677	+	0.252191i	$0.918849\pi$
$774$		0			0
$775$	−2.22971	+	3.86197i	−0.0800935	+	0.138726i
$776$	−3.15337	−	4.16634i	−0.113200	−	0.149563i
$777$		0			0
$778$	−12.5795	+	2.75971i	−0.450996	+	0.0989404i
$779$	−6.95405	−	4.01492i	−0.249155	−	0.143850i
$780$		0			0
$781$	11.8830	+	20.5820i	0.425209	+	0.736483i
$782$	−1.66878	+	5.25229i	−0.0596756	+	0.187822i
$783$		0			0
$784$	18.0818	+	21.3787i	0.645780	+	0.763523i
$785$	4.86202			0.173533
$786$		0			0
$787$	20.7021	+	35.8571i	0.737950	+	1.27817i	0.953417	+	0.301656i	$0.0975393\pi$
$787$	20.7021	+	35.8571i	0.737950	+	1.27817i	−0.215467	+	0.976511i	$0.569127\pi$
$788$	39.1314	+	27.6581i	1.39400	+	0.985280i
$789$		0			0
$790$	−8.84666	+	1.94080i	−0.314750	+	0.0690505i
$791$	6.77485	−	1.23912i	0.240886	−	0.0440579i
$792$		0			0
$793$	15.2958	−	26.4931i	0.543169	−	0.940796i
$794$	4.73923	−	4.32352i	0.168189	−	0.153436i
$795$		0			0
$796$	−0.401628	+	4.36862i	−0.0142353	+	0.154842i
$797$			10.5390i			0.373311i	0.982425	+	0.186656i	$0.0597648\pi$
$797$			10.5390i			0.373311i	−0.982425	+	0.186656i	$0.940235\pi$
$798$		0			0
$799$			4.36682i			0.154487i
$800$	12.9607	+	20.8479i	0.458229	+	0.737085i
$801$		0			0
$802$	23.8507	+	26.1440i	0.842198	+	0.923177i
$803$	−10.7253	+	18.5767i	−0.378486	+	0.655557i
$804$		0			0
$805$	2.64008	+	3.10594i	0.0930505	+	0.109470i
$806$	−1.60082	−	7.29695i	−0.0563865	−	0.257024i
$807$		0			0
$808$	−17.9632	+	42.5682i	−0.631942	+	1.49754i
$809$	19.6904	+	34.1047i	0.692276	+	1.19906i	0.971090	+	0.238712i	$0.0767252\pi$
$809$	19.6904	+	34.1047i	0.692276	+	1.19906i	−0.278814	+	0.960345i	$0.589941\pi$
$810$		0			0
$811$	−5.44942			−0.191355			−0.0956775	−	0.995412i	$-0.530502\pi$
$811$	−5.44942			−0.191355			−0.0956775	+	0.995412i	$0.530502\pi$
$812$	−36.7307	−	17.0404i	−1.28899	−	0.598000i
$813$		0			0
$814$	−17.0750	−	5.42516i	−0.598479	−	0.190152i
$815$	−4.00472	−	6.93638i	−0.140279	−	0.242971i
$816$		0			0
$817$	28.0232	+	16.1792i	0.980407	+	0.566038i
$818$	1.17977	+	5.37769i	0.0412497	+	0.188027i
$819$		0			0
$820$	−3.76617	+	1.73601i	−0.131520	+	0.0606242i
$821$	−16.0464	+	27.7932i	−0.560024	+	0.969990i	0.437469	+	0.899233i	$0.355875\pi$
$821$	−16.0464	+	27.7932i	−0.560024	+	0.969990i	−0.997494	+	0.0707570i	$0.977459\pi$
$822$		0			0
$823$	−28.0465	+	16.1927i	−0.977640	+	0.564440i	−0.901557	−	0.432661i	$-0.857575\pi$
$823$	−28.0465	+	16.1927i	−0.977640	+	0.564440i	−0.0760829	+	0.997101i	$0.524241\pi$
$824$	−1.67253	−	13.3880i	−0.0582654	−	0.466393i
$825$		0			0
$826$	−43.6611	+	18.2983i	−1.51917	+	0.636679i
$827$		−	15.1100i		−	0.525426i	−0.964874	−	0.262713i	$-0.915383\pi$
$827$		−	15.1100i		−	0.525426i	0.964874	−	0.262713i	$-0.0846173\pi$
$828$		0			0
$829$	−26.0615	+	15.0466i	−0.905153	+	0.522590i	−0.878868	−	0.477064i	$-0.841701\pi$
$829$	−26.0615	+	15.0466i	−0.905153	+	0.522590i	−0.0262843	+	0.999655i	$0.508368\pi$
$830$	14.8634	−	13.5596i	0.515914	−	0.470660i
$831$		0			0
$832$	−39.5780	−	11.1682i	−1.37212	−	0.387188i
$833$	9.10751	−	11.1389i	0.315557	−	0.385941i
$834$		0			0
$835$	14.4134	+	8.32158i	0.498796	+	0.287980i
$836$	7.80815	−	11.0472i	0.270050	−	0.382074i
$837$		0			0
$838$	4.91927	−	15.4828i	0.169934	−	0.534845i
$839$	14.7609			0.509602			0.254801	−	0.966993i	$-0.417990\pi$
$839$	14.7609			0.509602			0.254801	+	0.966993i	$0.417990\pi$
$840$		0			0
$841$	29.5542			1.01911
$842$	3.05840	−	9.62593i	0.105399	−	0.331732i
$843$		0			0
$844$	12.7492	−	18.0379i	0.438845	−	0.620889i
$845$	−9.44796	−	5.45478i	−0.325020	−	0.187650i
$846$		0			0
$847$	−5.67287	+	15.9003i	−0.194922	+	0.546342i
$848$	−17.2608	+	20.2060i	−0.592740	+	0.693877i
$849$		0			0
$850$	9.31917	−	8.50172i	0.319645	−	0.291607i
$851$	9.67795	−	5.58757i	0.331756	−	0.191539i
$852$		0			0
$853$			6.60254i			0.226067i	0.993591	+	0.113033i	$0.0360567\pi$
$853$			6.60254i			0.226067i	−0.993591	+	0.113033i	$0.963943\pi$
$854$	−13.4817	+	17.7220i	−0.461336	+	0.606434i
$855$		0			0
$856$	−13.1376	+	1.64126i	−0.449035	+	0.0560969i
$857$	2.44768	−	1.41317i	0.0836111	−	0.0482729i	−0.457612	−	0.889152i	$-0.651295\pi$
$857$	2.44768	−	1.41317i	0.0836111	−	0.0482729i	0.541223	+	0.840879i	$0.317962\pi$
$858$		0			0
$859$	8.29006	−	14.3588i	0.282853	−	0.489916i	−0.689233	−	0.724540i	$-0.742052\pi$
$859$	8.29006	−	14.3588i	0.282853	−	0.489916i	0.972086	+	0.234624i	$0.0753858\pi$
$860$	15.1768	−	6.99572i	0.517523	−	0.238552i
$861$		0			0
$862$	−6.26850	−	28.5734i	−0.213506	−	0.973215i
$863$	3.90041	+	2.25190i	0.132771	+	0.0766557i	0.564915	−	0.825149i	$-0.308909\pi$
$863$	3.90041	+	2.25190i	0.132771	+	0.0766557i	−0.432143	+	0.901805i	$0.642242\pi$
$864$		0			0
$865$	−1.62400	−	2.81285i	−0.0552176	−	0.0956397i
$866$	−19.5031	−	6.19661i	−0.662742	−	0.210570i
$867$		0			0
$868$	0.484521	+	5.41603i	0.0164457	+	0.183832i
$869$	−16.9370			−0.574547
$870$		0			0
$871$	20.5328	+	35.5638i	0.695726	+	1.20503i
$872$	−21.8696	−	9.22866i	−0.740598	−	0.312522i
$873$		0			0
$874$	1.80816	+	8.24204i	0.0611618	+	0.278791i
$875$	−3.61295	−	19.7537i	−0.122140	−	0.667798i
$876$		0			0
$877$	−1.22271	+	2.11780i	−0.0412880	+	0.0715130i	−0.885931	−	0.463817i	$-0.846479\pi$
$877$	−1.22271	+	2.11780i	−0.0412880	+	0.0715130i	0.844643	+	0.535330i	$0.179813\pi$
$878$	−4.84598	−	5.31193i	−0.163544	−	0.179269i
$879$		0			0
$880$	−2.33154	−	6.58603i	−0.0785961	−	0.222015i
$881$		−	46.1550i		−	1.55500i	−0.628883	−	0.777500i	$-0.716487\pi$
$881$		−	46.1550i		−	1.55500i	0.628883	−	0.777500i	$-0.283513\pi$
$882$		0			0
$883$		−	6.58454i		−	0.221587i	−0.993843	−	0.110794i	$-0.964661\pi$
$883$		−	6.58454i		−	0.221587i	0.993843	−	0.110794i	$-0.0353393\pi$
$884$	−1.93461	+	21.0433i	−0.0650680	+	0.707763i
$885$		0			0
$886$	6.00722	−	5.48028i	0.201816	−	0.184114i
$887$	3.75381	−	6.50180i	0.126041	−	0.218309i	−0.796099	−	0.605167i	$-0.793106\pi$
$887$	3.75381	−	6.50180i	0.126041	−	0.218309i	0.922139	+	0.386858i	$0.126440\pi$
$888$		0			0
$889$	3.19032	+	17.4430i	0.107000	+	0.585021i
$890$	−0.628589	+	0.137901i	−0.0210703	+	0.00462246i
$891$		0			0
$892$	−33.3337	−	23.5603i	−1.11610	−	0.788857i
$893$	3.34306	+	5.79036i	0.111871	+	0.193767i
$894$		0			0
$895$	−14.9668			−0.500286
$896$	27.5497	+	11.7053i	0.920371	+	0.391047i
$897$		0			0
$898$	−7.87300	+	24.7793i	−0.262726	+	0.826896i
$899$	−3.93171	−	6.80993i	−0.131130	−	0.227124i
$900$		0			0
$901$	11.8264	+	6.82796i	0.393993	+	0.227472i
$902$	−7.57492	+	1.66180i	−0.252217	+	0.0553319i
$903$		0			0
$904$	5.87080	−	4.44343i	0.195260	−	0.147786i
$905$	−3.56645	+	6.17726i	−0.118553	+	0.205339i
$906$		0			0
$907$	−22.8284	+	13.1800i	−0.758005	+	0.437634i	−0.828579	−	0.559872i	$-0.810850\pi$
$907$	−22.8284	+	13.1800i	−0.758005	+	0.437634i	0.0705742	+	0.997507i	$0.477517\pi$
$908$	−0.808268	+	8.79177i	−0.0268233	+	0.291765i
$909$		0			0
$910$	12.4403	+	9.46380i	0.412393	+	0.313722i
$911$			41.7614i			1.38362i	0.722081	+	0.691808i	$0.243186\pi$
$911$			41.7614i			1.38362i	−0.722081	+	0.691808i	$0.756814\pi$
$912$		0			0
$913$	32.5829	−	18.8118i	1.07834	−	0.622578i
$914$	27.7100	+	30.3744i	0.916566	+	1.00469i
$915$		0			0
$916$	16.0026	+	34.7167i	0.528742	+	1.14707i
$917$	13.1140	−	36.7570i	0.433064	−	1.21382i
$918$		0			0
$919$	−17.1773	−	9.91735i	−0.566628	−	0.327143i	0.189173	−	0.981944i	$-0.439419\pi$
$919$	−17.1773	−	9.91735i	−0.566628	−	0.327143i	−0.755802	+	0.654801i	$0.772753\pi$
$920$	4.01499	+	1.69427i	0.132370	+	0.0558584i
$921$		0			0
$922$	−36.9318	−	11.7341i	−1.21628	−	0.386443i
$923$	−56.8428			−1.87100
$924$		0			0
$925$	−25.5795			−0.841047
$926$	−45.3701	−	14.4152i	−1.49095	−	0.473713i
$927$		0			0
$928$	−43.2636	+	1.41120i	−1.42020	+	0.0463249i
$929$	48.7429	+	28.1417i	1.59920	+	0.923301i	0.991641	+	0.129029i	$0.0411862\pi$
$929$	48.7429	+	28.1417i	1.59920	+	0.923301i	0.607563	+	0.794271i	$0.292147\pi$
$930$		0			0
$931$	3.54893	−	21.7425i	0.116311	−	0.712581i
$932$	−26.1761	+	12.0659i	−0.857428	+	0.395231i
$933$		0			0
$934$	13.8825	+	15.2173i	0.454249	+	0.497926i
$935$	−3.10917	+	1.79508i	−0.101681	+	0.0587054i
$936$		0			0
$937$		−	2.78557i		−	0.0910006i	−0.998964	−	0.0455003i	$-0.985512\pi$
$937$		−	2.78557i		−	0.0910006i	0.998964	−	0.0455003i	$-0.0144882\pi$
$938$	−11.5536	−	27.5678i	−0.377239	−	0.900122i
$939$		0			0
$940$	3.43855	+	0.316122i	0.112153	+	0.0103108i
$941$	42.7539	−	24.6840i	1.39374	−	0.804674i	0.400009	−	0.916511i	$-0.369007\pi$
$941$	42.7539	−	24.6840i	1.39374	−	0.804674i	0.993727	+	0.111837i	$0.0356735\pi$
$942$		0			0
$943$	2.41860	−	4.18913i	0.0787603	−	0.136417i
$944$	−32.8716	+	38.4804i	−1.06988	+	1.25243i
$945$		0			0
$946$	30.5251	−	6.69666i	0.992457	−	0.217727i
$947$	42.7332	+	24.6720i	1.38864	+	0.801734i	0.993162	−	0.116740i	$-0.0372445\pi$
$947$	42.7332	+	24.6720i	1.38864	+	0.801734i	0.395481	+	0.918474i	$0.370578\pi$
$948$		0			0
$949$	−25.6522	−	44.4310i	−0.832706	−	1.44229i
$950$	5.84855	−	18.4076i	0.189752	−	0.597221i
$951$		0			0
$952$	3.33295	−	15.0163i	0.108021	−	0.486681i
$953$	−34.4944			−1.11738			−0.558691	−	0.829376i	$-0.688696\pi$
$953$	−34.4944			−1.11738			−0.558691	+	0.829376i	$0.688696\pi$
$954$		0			0
$955$	−8.92412	−	15.4570i	−0.288778	−	0.500178i
$956$	−15.3900	+	21.7742i	−0.497749	+	0.704228i
$957$		0			0
$958$	−9.30349	+	2.04102i	−0.300582	+	0.0659423i
$959$	−34.5985	−	40.7037i	−1.11724	−	1.31439i
$960$		0			0
$961$	14.9720	−	25.9323i	0.482968	−	0.836525i
$962$	31.6569	−	28.8801i	1.02066	−	0.931130i
$963$		0			0
$964$	48.9871	+	4.50361i	1.57777	+	0.145051i
$965$		−	0.569966i		−	0.0183478i
$966$		0			0
$967$			5.11586i			0.164515i	0.996611	+	0.0822575i	$0.0262130\pi$
$967$			5.11586i			0.164515i	−0.996611	+	0.0822575i	$0.973787\pi$
$968$	2.23726	+	17.9084i	0.0719083	+	0.575599i
$969$		0			0
$970$	1.43095	+	1.56854i	0.0459450	+	0.0503626i
$971$	−21.5432	+	37.3139i	−0.691354	+	1.19746i	0.280040	+	0.959988i	$0.409652\pi$
$971$	−21.5432	+	37.3139i	−0.691354	+	1.19746i	−0.971394	+	0.237472i	$0.923681\pi$
$972$		0			0
$973$	58.5594	−	10.7105i	1.87733	−	0.343362i
$974$	−1.56833	−	7.14884i	−0.0502525	−	0.229064i
$975$		0			0
$976$	−4.34025	+	23.4056i	−0.138928	+	0.749194i
$977$	−11.9965	−	20.7786i	−0.383803	−	0.664766i	0.607800	−	0.794090i	$-0.292052\pi$
$977$	−11.9965	−	20.7786i	−0.383803	−	0.664766i	−0.991602	+	0.129325i	$0.958719\pi$
$978$		0			0
$979$	−1.20344			−0.0384620
$980$	−8.11180	−	7.97787i	−0.259122	−	0.254844i
$981$		0			0
$982$	−5.70267	−	1.81188i	−0.181980	−	0.0578194i
$983$	−17.1303	−	29.6706i	−0.546372	−	0.946344i	−0.998519	−	0.0544009i	$-0.982675\pi$
$983$	−17.1303	−	29.6706i	−0.546372	−	0.946344i	0.452147	−	0.891943i	$-0.350658\pi$
$984$		0			0
$985$	−16.8628	−	9.73572i	−0.537292	−	0.310206i
$986$	4.76649	+	21.7269i	0.151796	+	0.691925i
$987$		0			0
$988$	13.5447	+	29.3843i	0.430913	+	0.934839i
$989$	−9.74636	+	16.8812i	−0.309916	+	0.536791i
$990$		0			0
$991$	2.24015	−	1.29335i	0.0711608	−	0.0410847i	−0.463997	−	0.885837i	$-0.653585\pi$
$991$	2.24015	−	1.29335i	0.0711608	−	0.0410847i	0.535158	+	0.844752i	$0.320252\pi$
$992$	3.06913	+	4.93686i	0.0974450	+	0.156746i
$993$		0			0
$994$	41.0432	+	5.22976i	1.30181	+	0.165878i
$995$		−	1.78263i		−	0.0565132i
$996$		0			0
$997$	−17.1394	+	9.89541i	−0.542809	+	0.313391i	−0.746217	−	0.665703i	$-0.768132\pi$
$997$	−17.1394	+	9.89541i	−0.542809	+	0.313391i	0.203408	+	0.979094i	$0.434798\pi$
$998$	30.0994	−	27.4592i	0.952780	−	0.869204i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.c.271.7	yes	32
3.2	odd	2		756.2.bf.b.271.10	yes	32
4.3	odd	2		756.2.bf.b.271.5	✓	32
7.3	odd	6		756.2.bf.b.703.5	yes	32
12.11	even	2	inner	756.2.bf.c.271.12	yes	32
21.17	even	6	inner	756.2.bf.c.703.12	yes	32
28.3	even	6	inner	756.2.bf.c.703.7	yes	32
84.59	odd	6		756.2.bf.b.703.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.5	✓	32	4.3	odd	2
756.2.bf.b.271.10	yes	32	3.2	odd	2
756.2.bf.b.703.5	yes	32	7.3	odd	6
756.2.bf.b.703.10	yes	32	84.59	odd	6
756.2.bf.c.271.7	yes	32	1.1	even	1	trivial
756.2.bf.c.271.12	yes	32	12.11	even	2	inner
756.2.bf.c.703.7	yes	32	28.3	even	6	inner
756.2.bf.c.703.12	yes	32	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.428236 + 1.34782i) q^{2} +(-1.63323 - 1.15437i) q^{4} +(0.703801 + 0.406340i) q^{5} +(2.60258 - 0.476010i) q^{7} +(2.25528 - 1.70695i) q^{8} +O(q^{10})\)	\(q+(-0.428236 + 1.34782i) q^{2} +(-1.63323 - 1.15437i) q^{4} +(0.703801 + 0.406340i) q^{5} +(2.60258 - 0.476010i) q^{7} +(2.25528 - 1.70695i) q^{8} +(-0.849065 + 0.774587i) q^{10} +(-1.86129 + 1.07462i) q^{11} -5.14045i q^{13} +(-0.472941 + 3.71165i) q^{14} +(1.33487 + 3.77069i) q^{16} +(1.78009 - 1.02773i) q^{17} +(1.57359 - 2.72553i) q^{19} +(-0.680403 - 1.47609i) q^{20} +(-0.651317 - 2.96887i) q^{22} +(1.64186 + 0.947931i) q^{23} +(-2.16978 - 3.75816i) q^{25} +(6.92839 + 2.20132i) q^{26} +(-4.80010 - 2.22690i) q^{28} +7.65207 q^{29} +(-0.513811 - 0.889946i) q^{31} +(-5.65385 + 0.184421i) q^{32} +(0.622902 + 2.83935i) q^{34} +(2.02512 + 0.722515i) q^{35} +(2.94725 - 5.10478i) q^{37} +(2.99966 + 3.28808i) q^{38} +(2.28088 - 0.284945i) q^{40} -2.55145i q^{41} +10.2817i q^{43} +(4.28041 + 0.393518i) q^{44} +(-1.98074 + 1.80700i) q^{46} +(-1.06224 + 1.83986i) q^{47} +(6.54683 - 2.47771i) q^{49} +(5.99450 - 1.31509i) q^{50} +(-5.93396 + 8.39552i) q^{52} +(3.32185 + 5.75361i) q^{53} -1.74664 q^{55} +(5.05703 - 5.51602i) q^{56} +(-3.27689 + 10.3136i) q^{58} +(6.32614 + 10.9572i) q^{59} +(5.15384 + 2.97557i) q^{61} +(1.41952 - 0.311417i) q^{62} +(2.17261 - 7.69933i) q^{64} +(2.08877 - 3.61785i) q^{65} +(-6.91842 + 3.99435i) q^{67} +(-4.09368 - 0.376351i) q^{68} +(-1.84105 + 2.42009i) q^{70} -11.0579i q^{71} +(8.64340 - 4.99027i) q^{73} +(5.61820 + 6.15840i) q^{74} +(-5.71629 + 2.63492i) q^{76} +(-4.33262 + 3.68277i) q^{77} +(6.82469 + 3.94024i) q^{79} +(-0.592698 + 3.19623i) q^{80} +(3.43889 + 1.09262i) q^{82} -17.5056 q^{83} +1.67044 q^{85} +(-13.8579 - 4.40300i) q^{86} +(-2.36342 + 5.60070i) q^{88} +(0.484920 + 0.279969i) q^{89} +(-2.44690 - 13.3784i) q^{91} +(-1.58728 - 3.44350i) q^{92} +(-2.02491 - 2.21961i) q^{94} +(2.21498 - 1.27882i) q^{95} -1.84737i q^{97} +(0.535915 + 9.88498i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 6 q^{11} + 17 q^{14} - 4 q^{16} - 8 q^{20} + 2 q^{22} + 14 q^{25} - 15 q^{26} - 13 q^{28} - 15 q^{32} - 6 q^{35} + 4 q^{37} + q^{38} - 15 q^{40} + 42 q^{44} - 9 q^{46} + 4 q^{47} + 14 q^{49} - 9 q^{52} - 45 q^{56} + 10 q^{58} + 16 q^{59} - 42 q^{64} + 49 q^{68} - 33 q^{70} + 36 q^{73} + 54 q^{74} + 15 q^{80} - 51 q^{82} - 20 q^{83} + 16 q^{85} - 78 q^{86} - 2 q^{88} - 27 q^{94} - 24 q^{95} + 46 q^{98}+O(q^{100}) \) 32 * q + 6 * q^11 + 17 * q^14 - 4 * q^16 - 8 * q^20 + 2 * q^22 + 14 * q^25 - 15 * q^26 - 13 * q^28 - 15 * q^32 - 6 * q^35 + 4 * q^37 + q^38 - 15 * q^40 + 42 * q^44 - 9 * q^46 + 4 * q^47 + 14 * q^49 - 9 * q^52 - 45 * q^56 + 10 * q^58 + 16 * q^59 - 42 * q^64 + 49 * q^68 - 33 * q^70 + 36 * q^73 + 54 * q^74 + 15 * q^80 - 51 * q^82 - 20 * q^83 + 16 * q^85 - 78 * q^86 - 2 * q^88 - 27 * q^94 - 24 * q^95 + 46 * q^98

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