LMFDB - Embedded newform 756.2.bf.b.271.4

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			271.4
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.b.703.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.02662 - 0.972657i) q^{2} +(0.107877 + 1.99709i) q^{4} +(-2.11960 - 1.22375i) q^{5} +(1.64814 + 2.06969i) q^{7} +(1.83173 - 2.15517i) q^{8} +O(q^{10})$	\(q+(-1.02662 - 0.972657i) q^{2} +(0.107877 + 1.99709i) q^{4} +(-2.11960 - 1.22375i) q^{5} +(1.64814 + 2.06969i) q^{7} +(1.83173 - 2.15517i) q^{8} +(0.985722 + 3.31796i) q^{10} +(-5.38874 + 3.11119i) q^{11} -2.57290i q^{13} +(0.321089 - 3.72785i) q^{14} +(-3.97673 + 0.430879i) q^{16} +(5.44664 - 3.14462i) q^{17} +(2.28953 - 3.96558i) q^{19} +(2.21528 - 4.36504i) q^{20} +(8.55829 + 2.04740i) q^{22} +(1.66922 + 0.963723i) q^{23} +(0.495133 + 0.857595i) q^{25} +(-2.50255 + 2.64138i) q^{26} +(-3.95556 + 3.51476i) q^{28} +6.67305 q^{29} +(1.50045 + 2.59886i) q^{31} +(4.50166 + 3.42564i) q^{32} +(-8.65024 - 2.06940i) q^{34} +(-0.960619 - 6.40383i) q^{35} +(1.60049 - 2.77213i) q^{37} +(-6.20762 + 1.84420i) q^{38} +(-6.51993 + 2.32651i) q^{40} -2.33285i q^{41} -5.77146i q^{43} +(-6.79465 - 10.4262i) q^{44} +(-0.776271 - 2.61295i) q^{46} +(4.53242 - 7.85038i) q^{47} +(-1.56724 + 6.82230i) q^{49} +(0.325835 - 1.36201i) q^{50} +(5.13832 - 0.277557i) q^{52} +(-2.91237 - 5.04437i) q^{53} +15.2293 q^{55} +(7.47949 + 0.239095i) q^{56} +(-6.85065 - 6.49058i) q^{58} +(1.10526 + 1.91436i) q^{59} +(-8.57935 - 4.95329i) q^{61} +(0.987410 - 4.12745i) q^{62} +(-1.28950 - 7.89539i) q^{64} +(-3.14859 + 5.45352i) q^{65} +(13.4028 - 7.73809i) q^{67} +(6.86765 + 10.5382i) q^{68} +(-5.24255 + 7.50862i) q^{70} -0.552999i q^{71} +(6.82352 - 3.93956i) q^{73} +(-4.33942 + 1.28918i) q^{74} +(8.16661 + 4.14460i) q^{76} +(-15.3206 - 6.02534i) q^{77} +(-10.7489 - 6.20587i) q^{79} +(8.95635 + 3.95323i) q^{80} +(-2.26906 + 2.39494i) q^{82} +0.324649 q^{83} -15.3929 q^{85} +(-5.61365 + 5.92507i) q^{86} +(-3.16560 + 17.3125i) q^{88} +(8.69544 + 5.02031i) q^{89} +(5.32512 - 4.24052i) q^{91} +(-1.74457 + 3.43754i) q^{92} +(-12.2888 + 3.65083i) q^{94} +(-9.70578 + 5.60363i) q^{95} +17.2188i q^{97} +(8.24471 - 5.47949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.02662	−	0.972657i	−0.725926	−	0.687772i
$2$	−1.02662	−	0.972657i	−0.725926	−	0.687772i
$3$		0			0
$3$		0			0
$4$	0.107877	+	1.99709i	0.0539384	+	0.998544i
$5$	−2.11960	−	1.22375i	−0.947913	−	0.547278i	−0.0554813	−	0.998460i	$-0.517669\pi$
$5$	−2.11960	−	1.22375i	−0.947913	−	0.547278i	−0.892432	+	0.451182i	$0.851003\pi$
$6$		0			0
$7$	1.64814	+	2.06969i	0.622940	+	0.782270i
$7$	1.64814	+	2.06969i	0.622940	+	0.782270i
$8$	1.83173	−	2.15517i	0.647616	−	0.761967i
$9$		0			0
$10$	0.985722	+	3.31796i	0.311713	+	1.04923i
$11$	−5.38874	+	3.11119i	−1.62477	+	0.938060i	−0.639146	+	0.769085i	$0.720712\pi$
$11$	−5.38874	+	3.11119i	−1.62477	+	0.938060i	−0.985620	+	0.168974i	$0.945954\pi$
$12$		0			0
$13$		−	2.57290i		−	0.713595i	−0.934182	−	0.356798i	$-0.883869\pi$
$13$		−	2.57290i		−	0.713595i	0.934182	−	0.356798i	$-0.116131\pi$
$14$	0.321089	−	3.72785i	0.0858147	−	0.996311i
$15$		0			0
$16$	−3.97673	+	0.430879i	−0.994181	+	0.107720i
$17$	5.44664	−	3.14462i	1.32101	−	0.762683i	0.337116	−	0.941463i	$-0.390548\pi$
$17$	5.44664	−	3.14462i	1.32101	−	0.762683i	0.983889	+	0.178780i	$0.0572151\pi$
$18$		0			0
$19$	2.28953	−	3.96558i	0.525254	−	0.909767i	−0.474313	−	0.880356i	$-0.657303\pi$
$19$	2.28953	−	3.96558i	0.525254	−	0.909767i	0.999567	−	0.0294111i	$-0.00936320\pi$
$20$	2.21528	−	4.36504i	0.495352	−	0.976053i
$21$		0			0
$22$	8.55829	+	2.04740i	1.82463	+	0.436507i
$23$	1.66922	+	0.963723i	0.348056	+	0.200950i	0.663829	−	0.747885i	$-0.268930\pi$
$23$	1.66922	+	0.963723i	0.348056	+	0.200950i	−0.315773	+	0.948835i	$0.602264\pi$
$24$		0			0
$25$	0.495133	+	0.857595i	0.0990266	+	0.171519i
$26$	−2.50255	+	2.64138i	−0.490791	+	0.518018i
$27$		0			0
$28$	−3.95556	+	3.51476i	−0.747530	+	0.664228i
$29$	6.67305			1.23915			0.619577	−	0.784936i	$-0.287304\pi$
$29$	6.67305			1.23915			0.619577	+	0.784936i	$0.287304\pi$
$30$		0			0
$31$	1.50045	+	2.59886i	0.269489	+	0.466768i	0.968730	−	0.248118i	$-0.0798120\pi$
$31$	1.50045	+	2.59886i	0.269489	+	0.466768i	−0.699241	+	0.714886i	$0.746479\pi$
$32$	4.50166	+	3.42564i	0.795789	+	0.605574i
$33$		0			0
$34$	−8.65024	−	2.06940i	−1.48350	−	0.354899i
$35$	−0.960619	−	6.40383i	−0.162374	−	1.08245i
$36$		0			0
$37$	1.60049	−	2.77213i	0.263119	−	0.455736i	−0.703950	−	0.710250i	$-0.748582\pi$
$37$	1.60049	−	2.77213i	0.263119	−	0.455736i	0.967069	+	0.254514i	$0.0819154\pi$
$38$	−6.20762	+	1.84420i	−1.00701	+	0.299169i
$39$		0			0
$40$	−6.51993	+	2.32651i	−1.03089	+	0.367853i
$41$		−	2.33285i		−	0.364330i	−0.983268	−	0.182165i	$-0.941689\pi$
$41$		−	2.33285i		−	0.364330i	0.983268	−	0.182165i	$-0.0583105\pi$
$42$		0			0
$43$		−	5.77146i		−	0.880140i	−0.897964	−	0.440070i	$-0.854954\pi$
$43$		−	5.77146i		−	0.880140i	0.897964	−	0.440070i	$-0.145046\pi$
$44$	−6.79465	−	10.4262i	−1.02433	−	1.57180i
$45$		0			0
$46$	−0.776271	−	2.61295i	−0.114455	−	0.385258i
$47$	4.53242	−	7.85038i	0.661122	−	1.14510i	−0.319200	−	0.947688i	$-0.603414\pi$
$47$	4.53242	−	7.85038i	0.661122	−	1.14510i	0.980321	−	0.197409i	$-0.0632526\pi$
$48$		0			0
$49$	−1.56724	+	6.82230i	−0.223891	+	0.974614i
$50$	0.325835	−	1.36201i	0.0460801	−	0.192618i
$51$		0			0
$52$	5.13832	−	0.277557i	0.712556	−	0.0384902i
$53$	−2.91237	−	5.04437i	−0.400045	−	0.692898i	0.593686	−	0.804697i	$-0.297672\pi$
$53$	−2.91237	−	5.04437i	−0.400045	−	0.692898i	−0.993731	+	0.111799i	$0.964339\pi$
$54$		0			0
$55$	15.2293			2.05352
$56$	7.47949	+	0.239095i	0.999489	+	0.0319504i
$57$		0			0
$58$	−6.85065	−	6.49058i	−0.899534	−	0.852255i
$59$	1.10526	+	1.91436i	0.143892	+	0.249229i	0.928959	−	0.370182i	$-0.120705\pi$
$59$	1.10526	+	1.91436i	0.143892	+	0.249229i	−0.785067	+	0.619411i	$0.787371\pi$
$60$		0			0
$61$	−8.57935	−	4.95329i	−1.09847	−	0.634204i	−0.162654	−	0.986683i	$-0.552005\pi$
$61$	−8.57935	−	4.95329i	−1.09847	−	0.634204i	−0.935820	+	0.352479i	$0.885339\pi$
$62$	0.987410	−	4.12745i	0.125401	−	0.524186i
$63$		0			0
$64$	−1.28950	−	7.89539i	−0.161187	−	0.986924i
$65$	−3.14859	+	5.45352i	−0.390535	+	0.676427i
$66$		0			0
$67$	13.4028	−	7.73809i	1.63741	−	0.945358i	0.655687	−	0.755033i	$-0.272379\pi$
$67$	13.4028	−	7.73809i	1.63741	−	0.945358i	0.981721	−	0.190325i	$-0.0609541\pi$
$68$	6.86765	+	10.5382i	0.832825	+	1.27794i
$69$		0			0
$70$	−5.24255	+	7.50862i	−0.626604	+	0.897452i
$71$		−	0.552999i		−	0.0656289i	−0.999461	−	0.0328145i	$-0.989553\pi$
$71$		−	0.552999i		−	0.0656289i	0.999461	−	0.0328145i	$-0.0104470\pi$
$72$		0			0
$73$	6.82352	−	3.93956i	0.798633	−	0.461091i	−0.0443602	−	0.999016i	$-0.514125\pi$
$73$	6.82352	−	3.93956i	0.798633	−	0.461091i	0.842993	+	0.537925i	$0.180792\pi$
$74$	−4.33942	+	1.28918i	−0.504448	+	0.149865i
$75$		0			0
$76$	8.16661	+	4.14460i	0.936774	+	0.475418i
$77$	−15.3206	−	6.02534i	−1.74595	−	0.686651i
$78$		0			0
$79$	−10.7489	−	6.20587i	−1.20934	−	0.698215i	−0.246728	−	0.969085i	$-0.579355\pi$
$79$	−10.7489	−	6.20587i	−1.20934	−	0.698215i	−0.962616	+	0.270869i	$0.912689\pi$
$80$	8.95635	+	3.95323i	1.00135	+	0.441985i
$81$		0			0
$82$	−2.26906	+	2.39494i	−0.250576	+	0.264477i
$83$	0.324649			0.0356348			0.0178174	−	0.999841i	$-0.494328\pi$
$83$	0.324649			0.0356348			0.0178174	+	0.999841i	$0.494328\pi$
$84$		0			0
$85$	−15.3929			−1.66960
$86$	−5.61365	+	5.92507i	−0.605336	+	0.638917i
$87$		0			0
$88$	−3.16560	+	17.3125i	−0.337454	+	1.84552i
$89$	8.69544	+	5.02031i	0.921714	+	0.532152i	0.884182	−	0.467143i	$-0.154717\pi$
$89$	8.69544	+	5.02031i	0.921714	+	0.532152i	0.0375328	+	0.999295i	$0.488050\pi$
$90$		0			0
$91$	5.32512	−	4.24052i	0.558224	−	0.444527i
$92$	−1.74457	+	3.43754i	−0.181884	+	0.358388i
$93$		0			0
$94$	−12.2888	+	3.65083i	−1.26749	+	0.376554i
$95$	−9.70578	+	5.60363i	−0.995792	+	0.574921i
$96$		0			0
$97$			17.2188i			1.74830i	0.485655	+	0.874150i	$0.338581\pi$
$97$			17.2188i			1.74830i	−0.485655	+	0.874150i	$0.661419\pi$
$98$	8.24471	−	5.47949i	0.832841	−	0.553512i
$99$		0			0
$100$	−1.65928	+	1.08134i	−0.165928	+	0.108134i
$101$	8.66353	−	5.00189i	0.862053	−	0.497707i	−0.00264624	−	0.999996i	$-0.500842\pi$
$101$	8.66353	−	5.00189i	0.862053	−	0.497707i	0.864699	+	0.502290i	$0.167509\pi$
$102$		0			0
$103$	2.27637	−	3.94278i	0.224297	−	0.388494i	−0.731811	−	0.681507i	$-0.761325\pi$
$103$	2.27637	−	3.94278i	0.224297	−	0.388494i	0.956108	+	0.293014i	$0.0946581\pi$
$104$	−5.54504	−	4.71288i	−0.543736	−	0.462136i
$105$		0			0
$106$	−1.91656	+	8.01136i	−0.186153	+	0.778132i
$107$	−5.77417	−	3.33372i	−0.558210	−	0.322283i	0.194217	−	0.980959i	$-0.437783\pi$
$107$	−5.77417	−	3.33372i	−0.558210	−	0.322283i	−0.752427	+	0.658676i	$0.771117\pi$
$108$		0			0
$109$	−3.72303	−	6.44848i	−0.356602	−	0.617652i	0.630789	−	0.775954i	$-0.282731\pi$
$109$	−3.72303	−	6.44848i	−0.356602	−	0.617652i	−0.987391	+	0.158302i	$0.949398\pi$
$110$	−15.6346	−	14.8129i	−1.49070	−	1.41235i
$111$		0			0
$112$	−7.44600	−	7.52044i	−0.703581	−	0.710615i
$113$	−8.00634			−0.753173			−0.376586	−	0.926381i	$-0.622902\pi$
$113$	−8.00634			−0.753173			−0.376586	+	0.926381i	$0.622902\pi$
$114$		0			0
$115$	−2.35871	−	4.08541i	−0.219951	−	0.380966i
$116$	0.719866	+	13.3267i	0.0668379	+	1.23735i
$117$		0			0
$118$	0.727343	−	3.04035i	0.0669574	−	0.279887i
$119$	15.4853	+	6.09008i	1.41953	+	0.558277i
$120$		0			0
$121$	13.8590	−	24.0045i	1.25991	−	2.18223i
$122$	3.98984	+	13.4299i	0.361223	+	1.21588i
$123$		0			0
$124$	−5.02828	+	3.27689i	−0.451553	+	0.294273i
$125$			9.81383i			0.877776i
$126$		0			0
$127$			6.12138i			0.543185i	0.962412	+	0.271593i	$0.0875503\pi$
$127$			6.12138i			0.543185i	−0.962412	+	0.271593i	$0.912450\pi$
$128$	−6.35569	+	9.35977i	−0.561769	+	0.827294i
$129$		0			0
$130$	8.53680	−	2.53617i	0.748727	−	0.222437i
$131$	−1.37188	+	2.37617i	−0.119862	+	0.207607i	−0.919713	−	0.392592i	$-0.871578\pi$
$131$	−1.37188	+	2.37617i	−0.119862	+	0.207607i	0.799851	+	0.600199i	$0.204912\pi$
$132$		0			0
$133$	11.9810	−	1.79723i	1.03889	−	0.155840i
$134$	−21.2860	−	5.09225i	−1.83883	−	0.439904i
$135$		0			0
$136$	3.19962	−	17.4985i	0.274365	−	1.50049i
$137$	6.87292	+	11.9042i	0.587193	+	1.01705i	0.994598	+	0.103801i	$0.0331004\pi$
$137$	6.87292	+	11.9042i	0.587193	+	1.01705i	−0.407405	+	0.913248i	$0.633566\pi$
$138$		0			0
$139$	−4.98365			−0.422708			−0.211354	−	0.977410i	$-0.567787\pi$
$139$	−4.98365			−0.422708			−0.211354	+	0.977410i	$0.567787\pi$
$140$	12.6854	−	2.60927i	1.07211	−	0.220523i
$141$		0			0
$142$	−0.537878	+	0.567717i	−0.0451378	+	0.0476418i
$143$	8.00480	+	13.8647i	0.669395	+	1.15943i
$144$		0			0
$145$	−14.1442	−	8.16615i	−1.17461	−	0.678161i
$146$	−10.8370	−	2.59253i	−0.896874	−	0.214559i
$147$		0			0
$148$	5.70885	+	2.89727i	0.469264	+	0.238154i
$149$	−1.31303	+	2.27423i	−0.107567	+	0.186312i	−0.914784	−	0.403943i	$-0.867639\pi$
$149$	−1.31303	+	2.27423i	−0.107567	+	0.186312i	0.807217	+	0.590255i	$0.200973\pi$
$150$		0			0
$151$	6.48887	−	3.74635i	0.528056	−	0.304874i	−0.212168	−	0.977233i	$-0.568052\pi$
$151$	6.48887	−	3.74635i	0.528056	−	0.304874i	0.740225	+	0.672360i	$0.234719\pi$
$152$	−4.35269	−	12.1982i	−0.353050	−	0.989406i
$153$		0			0
$154$	9.86780	+	21.0874i	0.795170	+	1.69927i
$155$		−	7.34471i		−	0.589941i
$156$		0			0
$157$	−1.55994	+	0.900633i	−0.124497	+	0.0718783i	−0.560955	−	0.827846i	$-0.689566\pi$
$157$	−1.55994	+	0.900633i	−0.124497	+	0.0718783i	0.436458	+	0.899725i	$0.356233\pi$
$158$	4.99878	+	16.8260i	0.397682	+	1.33861i
$159$		0			0
$160$	−5.34959	−	12.7699i	−0.422922	−	1.00955i
$161$	0.756502	+	5.04312i	0.0596207	+	0.397453i
$162$		0			0
$163$	11.5485	+	6.66750i	0.904545	+	0.522239i	0.878672	−	0.477426i	$-0.158430\pi$
$163$	11.5485	+	6.66750i	0.904545	+	0.522239i	0.0258729	+	0.999665i	$0.491763\pi$
$164$	4.65891	−	0.251660i	0.363800	−	0.0196514i
$165$		0			0
$166$	−0.333289	−	0.315772i	−0.0258683	−	0.0245087i
$167$	0.785920			0.0608163			0.0304082	−	0.999538i	$-0.490319\pi$
$167$	0.785920			0.0608163			0.0304082	+	0.999538i	$0.490319\pi$
$168$		0			0
$169$	6.38016			0.490782
$170$	15.8026	+	14.9720i	1.21201	+	1.14830i
$171$		0			0
$172$	11.5261	−	0.622606i	0.878858	−	0.0474733i
$173$	3.25836	+	1.88122i	0.247729	+	0.143026i	0.618724	−	0.785609i	$-0.287650\pi$
$173$	3.25836	+	1.88122i	0.247729	+	0.143026i	−0.370995	+	0.928635i	$0.620983\pi$
$174$		0			0
$175$	−0.958906	+	2.43821i	−0.0724865	+	0.184312i
$176$	20.0890	−	14.6942i	1.51427	−	1.10762i
$177$		0			0
$178$	−4.04382	−	13.6116i	−0.303097	−	1.02023i
$179$	−0.443533	+	0.256074i	−0.0331512	+	0.0191399i	−0.516484	−	0.856297i	$-0.672759\pi$
$179$	−0.443533	+	0.256074i	−0.0331512	+	0.0191399i	0.483333	+	0.875437i	$0.339426\pi$
$180$		0			0
$181$			19.0777i			1.41804i	0.705190	+	0.709019i	$0.250862\pi$
$181$			19.0777i			1.41804i	−0.705190	+	0.709019i	$0.749138\pi$
$182$	−9.59141	−	0.826132i	−0.710963	−	0.0612370i
$183$		0			0
$184$	5.13454	−	1.83216i	0.378524	−	0.135069i
$185$	−6.78480	+	3.91721i	−0.498828	+	0.287999i
$186$		0			0
$187$	−19.5670	+	33.8911i	−1.43088	+	2.47836i
$188$	16.1669	+	8.20477i	1.17909	+	0.598395i
$189$		0			0
$190$	15.4145	+	3.68762i	1.11829	+	0.267528i
$191$	−11.0333	−	6.37009i	−0.798342	−	0.460923i	0.0445488	−	0.999007i	$-0.485815\pi$
$191$	−11.0333	−	6.37009i	−0.798342	−	0.460923i	−0.842891	+	0.538084i	$0.819148\pi$
$192$		0			0
$193$	7.29027	+	12.6271i	0.524765	+	0.908920i	0.999584	+	0.0288363i	$0.00918015\pi$
$193$	7.29027	+	12.6271i	0.524765	+	0.908920i	−0.474819	+	0.880083i	$0.657487\pi$
$194$	16.7480	−	17.6770i	1.20243	−	1.26914i
$195$		0			0
$196$	−13.7938	−	2.39395i	−0.985272	−	0.170996i
$197$	−23.8488			−1.69916			−0.849578	−	0.527464i	$-0.823143\pi$
$197$	−23.8488			−1.69916			−0.849578	+	0.527464i	$0.823143\pi$
$198$		0			0
$199$	−5.78805	−	10.0252i	−0.410304	−	0.710668i	0.584619	−	0.811308i	$-0.301244\pi$
$199$	−5.78805	−	10.0252i	−0.410304	−	0.710668i	−0.994923	+	0.100641i	$0.967911\pi$
$200$	2.75521	+	0.503792i	0.194823	+	0.0356235i
$201$		0			0
$202$	−13.7592	−	3.29162i	−0.968096	−	0.231598i
$203$	10.9981	+	13.8111i	0.771918	+	0.969352i
$204$		0			0
$205$	−2.85483	+	4.94471i	−0.199390	+	0.345353i
$206$	−6.17192	+	1.83360i	−0.430018	+	0.127753i
$207$		0			0
$208$	1.10861	+	10.2317i	0.0768683	+	0.709443i
$209$			28.4927i			1.97088i
$210$		0			0
$211$			5.18513i			0.356959i	0.983944	+	0.178479i	$0.0571178\pi$
$211$			5.18513i			0.356959i	−0.983944	+	0.178479i	$0.942882\pi$
$212$	9.75988	−	6.36043i	0.670311	−	0.436836i
$213$		0			0
$214$	2.68528	+	9.03873i	0.183562	+	0.617875i
$215$	−7.06283	+	12.2332i	−0.481681	+	0.834296i
$216$		0			0
$217$	−2.90587	+	7.38876i	−0.197263	+	0.501581i
$218$	−2.45004	+	10.2413i	−0.165937	+	0.693631i
$219$		0			0
$220$	1.64289	+	30.4143i	0.110763	+	2.05053i
$221$	−8.09081	−	14.0137i	−0.544247	−	0.942663i
$222$		0			0
$223$	3.17961			0.212923			0.106461	−	0.994317i	$-0.466048\pi$
$223$	3.17961			0.212923			0.106461	+	0.994317i	$0.466048\pi$
$224$	0.329370	+	14.9630i	0.0220069	+	0.999758i
$225$		0			0
$226$	8.21943	+	7.78742i	0.546748	+	0.518012i
$227$	4.98711	+	8.63792i	0.331006	+	0.573319i	0.982709	−	0.185155i	$-0.0592787\pi$
$227$	4.98711	+	8.63792i	0.331006	+	0.573319i	−0.651703	+	0.758474i	$0.725945\pi$
$228$		0			0
$229$	19.4966	+	11.2564i	1.28837	+	0.743842i	0.978364	−	0.206892i	$-0.0663350\pi$
$229$	19.4966	+	11.2564i	1.28837	+	0.743842i	0.310008	+	0.950734i	$0.399668\pi$
$230$	−1.55221	+	6.48836i	−0.102350	+	0.427830i
$231$		0			0
$232$	12.2232	−	14.3815i	0.802495	−	0.944194i
$233$	−1.65167	+	2.86077i	−0.108204	+	0.187416i	−0.915043	−	0.403357i	$-0.867843\pi$
$233$	−1.65167	+	2.86077i	−0.108204	+	0.187416i	0.806838	+	0.590772i	$0.201177\pi$
$234$		0			0
$235$	−19.2138	+	11.0931i	−1.25337	+	0.723635i
$236$	−3.70392	+	2.41381i	−0.241104	+	0.157126i
$237$		0			0
$238$	−9.97383	−	21.3140i	−0.646508	−	1.38158i
$239$		−	27.0248i		−	1.74809i	−0.485845	−	0.874045i	$-0.661488\pi$
$239$		−	27.0248i		−	1.74809i	0.485845	−	0.874045i	$-0.338512\pi$
$240$		0			0
$241$	4.74441	−	2.73918i	0.305614	−	0.176446i	−0.339348	−	0.940661i	$-0.610206\pi$
$241$	4.74441	−	2.73918i	0.305614	−	0.176446i	0.644962	+	0.764215i	$0.276873\pi$
$242$	−37.5761	+	11.1633i	−2.41548	+	0.717607i
$243$		0			0
$244$	8.96665	−	17.6681i	0.574031	−	1.13108i
$245$	11.6707	−	12.5426i	0.745615	−	0.801319i
$246$		0			0
$247$	−10.2031	−	5.89074i	−0.649206	−	0.374819i
$248$	8.34939	+	1.52669i	0.530187	+	0.0969449i
$249$		0			0
$250$	9.54549	−	10.0750i	0.603710	−	0.637201i
$251$	11.5888			0.731476			0.365738	−	0.930718i	$-0.380817\pi$
$251$	11.5888			0.731476			0.365738	+	0.930718i	$0.380817\pi$
$252$		0			0
$253$	−11.9933			−0.754012
$254$	5.95401	−	6.28430i	0.373588	−	0.394312i
$255$		0			0
$256$	15.6287	−	3.42697i	0.976793	−	0.214186i
$257$	−13.9722	−	8.06685i	−0.871562	−	0.503196i	−0.00369473	−	0.999993i	$-0.501176\pi$
$257$	−13.9722	−	8.06685i	−0.871562	−	0.503196i	−0.867867	+	0.496797i	$0.834509\pi$
$258$		0			0
$259$	8.37530	−	1.25635i	0.520416	−	0.0780659i
$260$	−11.2308	−	5.69971i	−0.696507	−	0.353481i
$261$		0			0
$262$	3.71959	−	1.10504i	0.229797	−	0.0682695i
$263$	6.45544	−	3.72705i	0.398060	−	0.229820i	−0.287587	−	0.957755i	$-0.592853\pi$
$263$	6.45544	−	3.72705i	0.398060	−	0.229820i	0.685646	+	0.727935i	$0.259520\pi$
$264$		0			0
$265$			14.2561i			0.875743i
$266$	−14.0480	−	9.80835i	−0.861337	−	0.601388i
$267$		0			0
$268$	16.8995	+	25.9317i	1.03230	+	1.58403i
$269$	12.4710	−	7.20015i	0.760372	−	0.439001i	−0.0690575	−	0.997613i	$-0.521999\pi$
$269$	12.4710	−	7.20015i	0.760372	−	0.439001i	0.829429	+	0.558612i	$0.188666\pi$
$270$		0			0
$271$	3.12187	−	5.40724i	0.189640	−	0.328467i	−0.755490	−	0.655160i	$-0.772601\pi$
$271$	3.12187	−	5.40724i	0.189640	−	0.328467i	0.945130	+	0.326693i	$0.105934\pi$
$272$	−20.3049	+	14.8521i	−1.23116	+	0.900543i
$273$		0			0
$274$	4.52290	−	18.9061i	0.273239	−	1.14216i
$275$	−5.33629	−	3.08091i	−0.321790	−	0.185786i
$276$		0			0
$277$	−9.24825	−	16.0184i	−0.555673	−	0.962454i	−0.997851	−	0.0655269i	$-0.979127\pi$
$277$	−9.24825	−	16.0184i	−0.555673	−	0.962454i	0.442177	−	0.896928i	$-0.354206\pi$
$278$	5.11629	+	4.84738i	0.306855	+	0.290727i
$279$		0			0
$280$	−15.5609	−	9.65982i	−0.929944	−	0.577285i
$281$	17.1045			1.02037			0.510184	−	0.860066i	$-0.329577\pi$
$281$	17.1045			1.02037			0.510184	+	0.860066i	$0.329577\pi$
$282$		0			0
$283$	3.83828	+	6.64810i	0.228162	+	0.395189i	0.957263	−	0.289217i	$-0.0933950\pi$
$283$	3.83828	+	6.64810i	0.228162	+	0.395189i	−0.729101	+	0.684406i	$0.760062\pi$
$284$	1.10439	−	0.0596557i	0.0655334	−	0.00353992i
$285$		0			0
$286$	5.26777	−	22.0197i	0.311490	−	1.30205i
$287$	4.82828	−	3.84488i	0.285004	−	0.226956i
$288$		0			0
$289$	11.2773	−	19.5328i	0.663370	−	1.14899i
$290$	6.57777	+	22.1409i	0.386260	+	1.30016i
$291$		0			0
$292$	8.60375	+	13.2022i	0.503497	+	0.772600i
$293$		−	27.9991i		−	1.63573i	−0.575412	−	0.817863i	$-0.695158\pi$
$293$		−	27.9991i		−	1.63573i	0.575412	−	0.817863i	$-0.304842\pi$
$294$		0			0
$295$		−	5.41024i		−	0.314996i
$296$	−3.04274	−	8.52714i	−0.176855	−	0.495630i
$297$		0			0
$298$	3.56002	−	1.05763i	0.206226	−	0.0612671i
$299$	2.47957	−	4.29473i	0.143397	−	0.248371i
$300$		0			0
$301$	11.9451	−	9.51220i	0.688506	−	0.548274i
$302$	−10.3055	−	2.46538i	−0.593014	−	0.141867i
$303$		0			0
$304$	−7.39615	+	16.7565i	−0.424198	+	0.961054i
$305$	12.1232	+	20.9980i	0.694172	+	1.20234i
$306$		0			0
$307$	−26.2995			−1.50099			−0.750495	−	0.660876i	$-0.770185\pi$
$307$	−26.2995			−1.50099			−0.750495	+	0.660876i	$0.770185\pi$
$308$	10.3804	−	31.2466i	0.591478	−	1.78044i
$309$		0			0
$310$	−7.14388	+	7.54019i	−0.405745	+	0.428254i
$311$	0.235693	+	0.408233i	0.0133649	+	0.0231488i	0.872631	−	0.488381i	$-0.162412\pi$
$311$	0.235693	+	0.408233i	0.0133649	+	0.0231488i	−0.859266	+	0.511530i	$0.829079\pi$
$312$		0			0
$313$	−15.0754	−	8.70377i	−0.852110	−	0.491966i	0.00925198	−	0.999957i	$-0.497055\pi$
$313$	−15.0754	−	8.70377i	−0.852110	−	0.491966i	−0.861362	+	0.507991i	$0.830388\pi$
$314$	2.47747	+	0.592685i	0.139812	+	0.0334472i
$315$		0			0
$316$	11.2341	−	22.1359i	0.631969	−	1.24524i
$317$	0.566218	−	0.980719i	0.0318020	−	0.0550827i	−0.849686	−	0.527288i	$-0.823209\pi$
$317$	0.566218	−	0.980719i	0.0318020	−	0.0550827i	0.881488	+	0.472206i	$0.156542\pi$
$318$		0			0
$319$	−35.9593	+	20.7611i	−2.01334	+	1.16240i
$320$	−6.92877	+	18.3131i	−0.387330	+	1.02373i
$321$		0			0
$322$	4.12859	−	5.91316i	0.230077	−	0.329527i
$323$		−	28.7988i		−	1.60241i
$324$		0			0
$325$	2.20651	−	1.27393i	0.122395	−	0.0706649i
$326$	−5.37062	−	18.0776i	−0.297451	−	1.00123i
$327$		0			0
$328$	−5.02769	−	4.27316i	−0.277608	−	0.235946i
$329$	23.7180	−	3.55786i	1.30761	−	0.196151i
$330$		0			0
$331$	−6.52502	−	3.76722i	−0.358648	−	0.207065i	0.309840	−	0.950789i	$-0.399725\pi$
$331$	−6.52502	−	3.76722i	−0.358648	−	0.207065i	−0.668487	+	0.743723i	$0.733058\pi$
$332$	0.0350221	+	0.648352i	0.00192209	+	0.0355830i
$333$		0			0
$334$	−0.806837	−	0.764431i	−0.0441482	−	0.0418278i
$335$	−37.8780			−2.06949
$336$		0			0
$337$	−27.7651			−1.51246			−0.756230	−	0.654305i	$-0.772961\pi$
$337$	−27.7651			−1.51246			−0.756230	+	0.654305i	$0.772961\pi$
$338$	−6.54997	−	6.20571i	−0.356271	−	0.337546i
$339$		0			0
$340$	−1.66054	−	30.7411i	−0.0900554	−	1.66717i
$341$	−16.1711	−	9.33637i	−0.875713	−	0.505593i
$342$		0			0
$343$	−16.7031	+	8.00043i	−0.901882	+	0.431983i
$344$	−12.4385	−	10.5718i	−0.670637	−	0.569992i
$345$		0			0
$346$	−1.51530	−	5.10055i	−0.0814633	−	0.274207i
$347$	−25.4909	+	14.7172i	−1.36842	+	0.790060i	−0.990727	−	0.135869i	$-0.956618\pi$
$347$	−25.4909	+	14.7172i	−1.36842	+	0.790060i	−0.377698	+	0.925929i	$0.623284\pi$
$348$		0			0
$349$		−	1.30460i		−	0.0698335i	−0.999390	−	0.0349168i	$-0.988883\pi$
$349$		−	1.30460i		−	0.0698335i	0.999390	−	0.0349168i	$-0.0111166\pi$
$350$	3.35597	−	1.57042i	0.179384	−	0.0839424i
$351$		0			0
$352$	−34.9161	−	4.45437i	−1.86104	−	0.237419i
$353$	4.50430	−	2.60056i	0.239740	−	0.138414i	−0.375317	−	0.926896i	$-0.622466\pi$
$353$	4.50430	−	2.60056i	0.239740	−	0.138414i	0.615057	+	0.788483i	$0.289133\pi$
$354$		0			0
$355$	−0.676733	+	1.17214i	−0.0359173	+	0.0622105i
$356$	−9.08797	+	17.9071i	−0.481662	+	0.949076i
$357$		0			0
$358$	0.704410	+	0.168516i	0.0372292	+	0.00890637i
$359$	1.79011	+	1.03352i	0.0944783	+	0.0545470i	0.546495	−	0.837463i	$-0.315962\pi$
$359$	1.79011	+	1.03352i	0.0944783	+	0.0545470i	−0.452016	+	0.892010i	$0.649295\pi$
$360$		0			0
$361$	−0.983906	−	1.70418i	−0.0517845	−	0.0896934i
$362$	18.5561	−	19.5855i	0.975287	−	1.02939i
$363$		0			0
$364$	9.04315	+	10.1773i	0.473990	+	0.533434i
$365$	−19.2842			−1.00938
$366$		0			0
$367$	−6.58035	−	11.3975i	−0.343492	−	0.594945i	0.641587	−	0.767050i	$-0.278276\pi$
$367$	−6.58035	−	11.3975i	−0.343492	−	0.594945i	−0.985079	+	0.172105i	$0.944943\pi$
$368$	−7.05326	−	3.11323i	−0.367677	−	0.162288i
$369$		0			0
$370$	10.7755	+	2.57782i	0.560190	+	0.134014i
$371$	5.64028	−	14.3416i	0.292829	−	0.744576i
$372$		0			0
$373$	4.41023	−	7.63875i	0.228353	−	0.395519i	−0.728967	−	0.684549i	$-0.759999\pi$
$373$	4.41023	−	7.63875i	0.228353	−	0.395519i	0.957320	+	0.289029i	$0.0933326\pi$
$374$	53.0522	−	15.7611i	2.74327	−	0.814987i
$375$		0			0
$376$	−8.61671	−	24.1479i	−0.444373	−	1.24534i
$377$		−	17.1691i		−	0.884254i
$378$		0			0
$379$			2.81003i			0.144342i	0.997392	+	0.0721708i	$0.0229927\pi$
$379$			2.81003i			0.144342i	−0.997392	+	0.0721708i	$0.977007\pi$
$380$	−12.2380	−	18.7788i	−0.627795	−	0.963332i
$381$		0			0
$382$	5.13106	+	17.2713i	0.262528	+	0.883674i
$383$	9.13019	−	15.8139i	0.466531	−	0.808055i	−0.532738	−	0.846280i	$-0.678837\pi$
$383$	9.13019	−	15.8139i	0.466531	−	0.808055i	0.999269	+	0.0382251i	$0.0121704\pi$
$384$		0			0
$385$	25.1001	+	31.5199i	1.27922	+	1.60640i
$386$	4.79755	−	20.0541i	0.244189	−	1.02073i
$387$		0			0
$388$	−34.3874	+	1.85750i	−1.74576	+	0.0943005i
$389$	−2.63882	−	4.57056i	−0.133793	−	0.231737i	0.791343	−	0.611373i	$-0.209382\pi$
$389$	−2.63882	−	4.57056i	−0.133793	−	0.231737i	−0.925136	+	0.379636i	$0.876049\pi$
$390$		0			0
$391$	12.1222			0.613044
$392$	11.8324	+	15.8743i	0.597628	+	0.801773i
$393$		0			0
$394$	24.4835	+	23.1967i	1.23346	+	1.16863i
$395$	15.1889	+	26.3079i	0.764236	+	1.32370i
$396$		0			0
$397$	18.0245	+	10.4064i	0.904622	+	0.522284i	0.878697	−	0.477380i	$-0.158414\pi$
$397$	18.0245	+	10.4064i	0.904622	+	0.522284i	0.0259250	+	0.999664i	$0.491747\pi$
$398$	−3.80898	+	15.9218i	−0.190927	+	0.798088i
$399$		0			0
$400$	−2.33853	−	3.19708i	−0.116926	−	0.159854i
$401$	−1.76065	+	3.04954i	−0.0879227	+	0.152287i	−0.906633	−	0.421920i	$-0.861356\pi$
$401$	−1.76065	+	3.04954i	−0.0879227	+	0.152287i	0.818710	+	0.574207i	$0.194690\pi$
$402$		0			0
$403$	6.68661	−	3.86051i	0.333084	−	0.192306i
$404$	10.9238	+	16.7622i	0.543480	+	0.833953i
$405$		0			0
$406$	2.14264	−	24.8761i	0.106338	−	1.23458i
$407$			19.9177i			0.987286i
$408$		0			0
$409$	−14.7533	+	8.51782i	−0.729504	+	0.421179i	−0.818241	−	0.574876i	$-0.805050\pi$
$409$	−14.7533	+	8.51782i	−0.729504	+	0.421179i	0.0887367	+	0.996055i	$0.471717\pi$
$410$	7.74032	−	2.29954i	0.382267	−	0.113566i
$411$		0			0
$412$	8.11965	+	4.12077i	0.400026	+	0.203016i
$413$	−2.14051	+	5.44268i	−0.105328	+	0.267817i
$414$		0			0
$415$	−0.688125	−	0.397289i	−0.0337787	−	0.0195022i
$416$	8.81385	−	11.5823i	0.432135	−	0.567871i
$417$		0			0
$418$	27.7136	−	29.2510i	1.35552	−	1.43071i
$419$	7.44368			0.363648			0.181824	−	0.983331i	$-0.441800\pi$
$419$	7.44368			0.363648			0.181824	+	0.983331i	$0.441800\pi$
$420$		0			0
$421$	−38.8499			−1.89343			−0.946713	−	0.322077i	$-0.895619\pi$
$421$	−38.8499			−1.89343			−0.946713	+	0.322077i	$0.895619\pi$
$422$	5.04335	−	5.32313i	0.245506	−	0.259126i
$423$		0			0
$424$	−16.2062	−	2.96330i	−0.787040	−	0.143911i
$425$	5.39362	+	3.11401i	0.261629	+	0.151052i
$426$		0			0
$427$	−3.88823	−	25.9203i	−0.188165	−	1.25437i
$428$	6.03483	−	11.8912i	0.291705	−	0.574781i
$429$		0			0
$430$	19.1495	−	5.68906i	0.923471	−	0.274351i
$431$	2.70724	−	1.56303i	0.130403	−	0.0752883i	−0.433379	−	0.901212i	$-0.642679\pi$
$431$	2.70724	−	1.56303i	0.130403	−	0.0752883i	0.563782	+	0.825923i	$0.309346\pi$
$432$		0			0
$433$			29.0993i			1.39842i	0.714916	+	0.699210i	$0.246465\pi$
$433$			29.0993i			1.39842i	−0.714916	+	0.699210i	$0.753535\pi$
$434$	10.1699	−	4.75899i	0.488172	−	0.228439i
$435$		0			0
$436$	12.4765	−	8.13086i	0.597518	−	0.389398i
$437$	7.64345	−	4.41295i	0.365636	−	0.211100i
$438$		0			0
$439$	4.20567	−	7.28443i	0.200725	−	0.347667i	−0.748037	−	0.663657i	$-0.769003\pi$
$439$	4.20567	−	7.28443i	0.200725	−	0.347667i	0.948762	+	0.315990i	$0.102337\pi$
$440$	27.8960	−	32.8217i	1.32989	−	1.56471i
$441$		0			0
$442$	−5.32437	+	22.2563i	−0.253254	+	1.05862i
$443$	11.9568	+	6.90325i	0.568084	+	0.327984i	0.756384	−	0.654128i	$-0.226964\pi$
$443$	11.9568	+	6.90325i	0.568084	+	0.327984i	−0.188300	+	0.982112i	$0.560298\pi$
$444$		0			0
$445$	−12.2872	−	21.2821i	−0.582470	−	1.00887i
$446$	−3.26424	−	3.09267i	−0.154566	−	0.146442i
$447$		0			0
$448$	14.2157	−	15.6816i	0.671630	−	0.740886i
$449$	13.7739			0.650029			0.325014	−	0.945709i	$-0.394631\pi$
$449$	13.7739			0.650029			0.325014	+	0.945709i	$0.394631\pi$
$450$		0			0
$451$	7.25795	+	12.5711i	0.341763	+	0.591952i
$452$	−0.863698	−	15.9894i	−0.0406249	−	0.752077i
$453$		0			0
$454$	3.28190	−	13.7186i	0.154027	−	0.643844i
$455$	−16.4764	+	2.47158i	−0.772428	+	0.115870i
$456$		0			0
$457$	2.31431	−	4.00851i	0.108259	−	0.187510i	−0.806806	−	0.590816i	$-0.798806\pi$
$457$	2.31431	−	4.00851i	0.108259	−	0.187510i	0.915065	+	0.403306i	$0.132139\pi$
$458$	−9.06692	−	30.5195i	−0.423669	−	1.42608i
$459$		0			0
$460$	7.90448	−	5.15128i	0.368548	−	0.240180i
$461$		−	16.0348i		−	0.746815i	−0.927667	−	0.373408i	$-0.878189\pi$
$461$		−	16.0348i		−	0.746815i	0.927667	−	0.373408i	$-0.121811\pi$
$462$		0			0
$463$			35.3655i			1.64357i	0.569796	+	0.821786i	$0.307022\pi$
$463$			35.3655i			1.64357i	−0.569796	+	0.821786i	$0.692978\pi$
$464$	−26.5369	+	2.87527i	−1.23194	+	0.133481i
$465$		0			0
$466$	4.47818	−	1.33041i	0.207448	−	0.0616299i
$467$	−2.39295	+	4.14472i	−0.110733	+	0.191795i	−0.916066	−	0.401028i	$-0.868653\pi$
$467$	−2.39295	+	4.14472i	−0.110733	+	0.191795i	0.805333	+	0.592822i	$0.201986\pi$
$468$		0			0
$469$	38.1051	+	14.9861i	1.75953	+	0.691993i
$470$	30.5150	+	7.30011i	1.40755	+	0.336729i
$471$		0			0
$472$	6.15031	+	1.12459i	0.283091	+	0.0517633i
$473$	17.9561	+	31.1009i	0.825623	+	1.43002i
$474$		0			0
$475$	4.53449			0.208057
$476$	−10.4919	+	31.5824i	−0.480897	+	1.44758i
$477$		0			0
$478$	−26.2859	+	27.7441i	−1.20229	+	1.26898i
$479$	−6.85002	−	11.8646i	−0.312985	−	0.542106i	0.666022	−	0.745932i	$-0.267996\pi$
$479$	−6.85002	−	11.8646i	−0.312985	−	0.542106i	−0.979007	+	0.203826i	$0.934662\pi$
$480$		0			0
$481$	−7.13243	−	4.11791i	−0.325211	−	0.187761i
$482$	−7.53496	−	1.80259i	−0.343208	−	0.0821058i
$483$		0			0
$484$	49.4343	+	25.0882i	2.24701	+	1.14037i
$485$	21.0715	−	36.4969i	0.956807	−	1.65724i
$486$		0			0
$487$	−14.7351	+	8.50730i	−0.667710	+	0.385503i	−0.795209	−	0.606336i	$-0.792639\pi$
$487$	−14.7351	+	8.50730i	−0.667710	+	0.385503i	0.127498	+	0.991839i	$0.459305\pi$
$488$	−26.3903	+	9.41683i	−1.19463	+	0.426280i
$489$		0			0
$490$	−24.1810	+	1.52485i	−1.09239	+	0.0688855i
$491$			36.2436i			1.63565i	0.575466	+	0.817826i	$0.304821\pi$
$491$			36.2436i			1.63565i	−0.575466	+	0.817826i	$0.695179\pi$
$492$		0			0
$493$	36.3457	−	20.9842i	1.63693	−	0.945081i
$494$	4.74495	+	15.9716i	0.213485	+	0.718597i
$495$		0			0
$496$	−7.08667	−	9.68842i	−0.318201	−	0.435023i
$497$	1.14454	−	0.911422i	0.0513395	−	0.0408829i
$498$		0			0
$499$	−30.5399	−	17.6322i	−1.36715	−	0.789326i	−0.376589	−	0.926381i	$-0.622903\pi$
$499$	−30.5399	−	17.6322i	−1.36715	−	0.789326i	−0.990563	+	0.137055i	$0.956236\pi$
$500$	−19.5991	+	1.05868i	−0.876498	+	0.0473458i
$501$		0			0
$502$	−11.8972	−	11.2719i	−0.530998	−	0.503089i
$503$	−42.6851			−1.90323			−0.951617	−	0.307286i	$-0.900579\pi$
$503$	−42.6851			−1.90323			−0.951617	+	0.307286i	$0.900579\pi$
$504$		0			0
$505$	−24.4843			−1.08954
$506$	12.3125	+	11.6654i	0.547358	+	0.518589i
$507$		0			0
$508$	−12.2249	+	0.660355i	−0.542394	+	0.0292985i
$509$	−15.6979	−	9.06318i	−0.695797	−	0.401719i	0.109983	−	0.993933i	$-0.464920\pi$
$509$	−15.6979	−	9.06318i	−0.695797	−	0.401719i	−0.805780	+	0.592215i	$0.798254\pi$
$510$		0			0
$511$	19.3998	+	7.62961i	0.858198	+	0.337514i
$512$	−19.3779	−	11.6832i	−0.856391	−	0.516328i
$513$		0			0
$514$	6.49779	+	21.8717i	0.286605	+	0.964719i
$515$	−9.64996	+	5.57141i	−0.425228	+	0.245506i
$516$		0			0
$517$			56.4049i			2.48069i
$518$	−9.82021	−	6.85650i	−0.431475	−	0.301257i
$519$		0			0
$520$	5.98588	+	16.7752i	0.262498	+	0.735639i
$521$	−13.4962	+	7.79201i	−0.591277	+	0.341374i	−0.765602	−	0.643314i	$-0.777559\pi$
$521$	−13.4962	+	7.79201i	−0.591277	+	0.341374i	0.174325	+	0.984688i	$0.444226\pi$
$522$		0			0
$523$	4.20000	−	7.27461i	0.183653	−	0.318096i	−0.759469	−	0.650544i	$-0.774541\pi$
$523$	4.20000	−	7.27461i	0.183653	−	0.318096i	0.943122	+	0.332447i	$0.107874\pi$
$524$	−4.89341	−	2.48343i	−0.213770	−	0.108489i
$525$		0			0
$526$	−10.2524	−	2.45268i	−0.447026	−	0.106942i
$527$	16.3448	+	9.43669i	0.711992	+	0.411069i
$528$		0			0
$529$	−9.64248	−	16.7013i	−0.419238	−	0.726142i
$530$	13.8663	−	14.6355i	0.602311	−	0.635725i
$531$		0			0
$532$	4.88171	+	23.7333i	0.211649	+	1.02897i
$533$	−6.00220			−0.259984
$534$		0			0
$535$	8.15928	+	14.1323i	0.352757	+	0.610992i
$536$	7.87342	−	43.0593i	0.340080	−	1.85988i
$537$		0			0
$538$	−19.8062	−	4.73825i	−0.853907	−	0.204280i
$539$	−12.7800	−	41.6396i	−0.550475	−	1.79354i
$540$		0			0
$541$	−7.24728	+	12.5527i	−0.311585	+	0.539681i	−0.978706	−	0.205269i	$-0.934193\pi$
$541$	−7.24728	+	12.5527i	−0.311585	+	0.539681i	0.667121	+	0.744950i	$0.267527\pi$
$542$	−8.46436	+	2.51465i	−0.363575	+	0.108013i
$543$		0			0
$544$	35.2913	+	4.50223i	1.51310	+	0.193032i
$545$			18.2242i			0.780641i
$546$		0			0
$547$			39.9222i			1.70695i	0.521133	+	0.853476i	$0.325510\pi$
$547$			39.9222i			1.70695i	−0.521133	+	0.853476i	$0.674490\pi$
$548$	−23.0324	+	15.0100i	−0.983895	+	0.641196i
$549$		0			0
$550$	2.48165	+	8.35328i	0.105818	+	0.356185i
$551$	15.2781	−	26.4625i	0.650871	−	1.12734i
$552$		0			0
$553$	−4.87148	−	32.4750i	−0.207156	−	1.38098i
$554$	−6.08605	+	25.4401i	−0.258572	+	1.08085i
$555$		0			0
$556$	−0.537620	−	9.95279i	−0.0228002	−	0.422092i
$557$	1.74788	+	3.02741i	0.0740599	+	0.128276i	0.900677	−	0.434489i	$-0.143071\pi$
$557$	1.74788	+	3.02741i	0.0740599	+	0.128276i	−0.826617	+	0.562765i	$0.809738\pi$
$558$		0			0
$559$	−14.8494			−0.628063
$560$	6.57939	+	25.0524i	0.278030	+	1.05866i
$561$		0			0
$562$	−17.5597	−	16.6368i	−0.740711	−	0.701780i
$563$	−9.26245	−	16.0430i	−0.390366	−	0.676133i	0.602132	−	0.798397i	$-0.294318\pi$
$563$	−9.26245	−	16.0430i	−0.390366	−	0.676133i	−0.992498	+	0.122263i	$0.960985\pi$
$564$		0			0
$565$	16.9702	+	9.79776i	0.713943	+	0.412195i
$566$	2.52588	−	10.5584i	0.106171	−	0.443801i
$567$		0			0
$568$	−1.19181	−	1.01295i	−0.0500071	−	0.0425023i
$569$	10.5321	−	18.2421i	0.441528	−	0.764750i	−0.556275	−	0.830998i	$-0.687770\pi$
$569$	10.5321	−	18.2421i	0.441528	−	0.764750i	0.997803	+	0.0662488i	$0.0211031\pi$
$570$		0			0
$571$	26.9402	−	15.5539i	1.12741	−	0.650911i	0.184129	−	0.982902i	$-0.441054\pi$
$571$	26.9402	−	15.5539i	1.12741	−	0.650911i	0.943283	+	0.331991i	$0.107720\pi$
$572$	−26.8255	+	17.4820i	−1.12163	+	0.730958i
$573$		0			0
$574$	−8.69653	−	0.749054i	−0.362986	−	0.0312649i
$575$			1.90868i			0.0795976i
$576$		0			0
$577$	22.0773	−	12.7463i	0.919089	−	0.530637i	0.0357450	−	0.999361i	$-0.488620\pi$
$577$	22.0773	−	12.7463i	0.919089	−	0.530637i	0.883344	+	0.468724i	$0.155286\pi$
$578$	−30.5762	+	9.08377i	−1.27180	+	0.377835i
$579$		0			0
$580$	14.7827	−	29.1281i	0.613818	−	1.20948i
$581$	0.535068	+	0.671923i	0.0221984	+	0.0278760i
$582$		0			0
$583$	31.3880	+	18.1219i	1.29996	+	0.750531i
$584$	4.00846	−	21.9221i	0.165871	−	0.907141i
$585$		0			0
$586$	−27.2336	+	28.7443i	−1.12501	+	1.18742i
$587$	33.1819			1.36956			0.684781	−	0.728749i	$-0.259898\pi$
$587$	33.1819			1.36956			0.684781	+	0.728749i	$0.259898\pi$
$588$		0			0
$589$	13.7413			0.566201
$590$	−5.26231	+	5.55423i	−0.216646	+	0.228664i
$591$		0			0
$592$	−5.17026	+	11.7136i	−0.212496	+	0.481427i
$593$	39.2414	+	22.6560i	1.61145	+	0.930372i	0.989034	+	0.147685i	$0.0471823\pi$
$593$	39.2414	+	22.6560i	1.61145	+	0.930372i	0.622417	+	0.782686i	$0.286151\pi$
$594$		0			0
$595$	−25.3698	−	31.8586i	−1.04006	−	1.30608i
$596$	−4.68349	−	2.37690i	−0.191843	−	0.0973615i
$597$		0			0
$598$	−6.72286	+	1.99727i	−0.274918	+	0.0816745i
$599$	−16.5466	+	9.55321i	−0.676078	+	0.390334i	−0.798376	−	0.602160i	$-0.794307\pi$
$599$	−16.5466	+	9.55321i	−0.676078	+	0.390334i	0.122298	+	0.992493i	$0.460974\pi$
$600$		0			0
$601$		−	35.6488i		−	1.45414i	−0.686561	−	0.727072i	$-0.740881\pi$
$601$		−	35.6488i		−	1.45414i	0.686561	−	0.727072i	$-0.259119\pi$
$602$	−21.5152	−	1.85315i	−0.876893	−	0.0755289i
$603$		0			0
$604$	8.18179	+	12.5547i	0.332912	+	0.510843i
$605$	−58.7512	+	33.9200i	−2.38857	+	1.37904i
$606$		0			0
$607$	13.1893	−	22.8446i	0.535337	−	0.927232i	−0.463809	−	0.885935i	$-0.653518\pi$
$607$	13.1893	−	22.8446i	0.535337	−	0.927232i	0.999147	−	0.0412967i	$-0.0131489\pi$
$608$	23.8914	−	10.0086i	0.968923	−	0.405903i
$609$		0			0
$610$	7.97798	−	33.3485i	0.323019	−	1.35024i
$611$	−20.1983	−	11.6615i	−0.817135	−	0.471773i
$612$		0			0
$613$	−3.27374	−	5.67029i	−0.132225	−	0.229021i	0.792309	−	0.610120i	$-0.208879\pi$
$613$	−3.27374	−	5.67029i	−0.132225	−	0.229021i	−0.924534	+	0.381099i	$0.875546\pi$
$614$	26.9994	+	25.5804i	1.08961	+	1.03234i
$615$		0			0
$616$	−41.0489	+	21.9817i	−1.65391	+	0.885669i
$617$	−13.6839			−0.550894			−0.275447	−	0.961316i	$-0.588826\pi$
$617$	−13.6839			−0.550894			−0.275447	+	0.961316i	$0.588826\pi$
$618$		0			0
$619$	4.99878	+	8.65815i	0.200918	+	0.348000i	0.948824	−	0.315804i	$-0.102274\pi$
$619$	4.99878	+	8.65815i	0.200918	+	0.348000i	−0.747906	+	0.663804i	$0.768941\pi$
$620$	14.6680	−	0.792323i	0.589082	−	0.0318205i
$621$		0			0
$622$	0.155104	−	0.648347i	0.00621911	−	0.0259963i
$623$	3.94084	+	26.2711i	0.157886	+	1.05253i
$624$		0			0
$625$	14.4854	−	25.0894i	0.579414	−	1.00357i
$626$	7.01082	+	23.5986i	0.280209	+	0.943189i
$627$		0			0
$628$	−1.96693	−	3.01819i	−0.0784889	−	0.120439i
$629$		−	20.1318i		−	0.802706i
$630$		0			0
$631$		−	10.6994i		−	0.425938i	−0.977059	−	0.212969i	$-0.931687\pi$
$631$		−	10.6994i		−	0.425938i	0.977059	−	0.212969i	$-0.0683134\pi$
$632$	−33.0638	+	11.7981i	−1.31521	+	0.469305i
$633$		0			0
$634$	−1.53519	+	0.456085i	−0.0609703	+	0.0181134i
$635$	7.49105	−	12.9749i	0.297273	−	0.514892i
$636$		0			0
$637$	17.5531	+	4.03236i	0.695480	+	0.159768i
$638$	57.1098	+	13.6624i	2.26100	+	0.540900i
$639$		0			0
$640$	24.9255	−	12.0612i	0.985268	−	0.476760i
$641$	8.21994	+	14.2373i	0.324668	+	0.562342i	0.981445	−	0.191743i	$-0.0614141\pi$
$641$	8.21994	+	14.2373i	0.324668	+	0.562342i	−0.656777	+	0.754085i	$0.728081\pi$
$642$		0			0
$643$	29.5305			1.16457			0.582285	−	0.812985i	$-0.302159\pi$
$643$	29.5305			1.16457			0.582285	+	0.812985i	$0.302159\pi$
$644$	−9.98994	+	2.05484i	−0.393659	+	0.0809719i
$645$		0			0
$646$	−28.0114	+	29.5653i	−1.10209	+	1.16323i
$647$	19.9948	+	34.6321i	0.786078	+	1.36153i	0.928353	+	0.371700i	$0.121225\pi$
$647$	19.9948	+	34.6321i	0.786078	+	1.36153i	−0.142274	+	0.989827i	$0.545442\pi$
$648$		0			0
$649$	−11.9119	−	6.87733i	−0.467583	−	0.269959i
$650$	−3.50433	−	0.838343i	−0.137451	−	0.0328825i
$651$		0			0
$652$	−12.0698	+	23.7826i	−0.472689	+	0.931397i
$653$	−1.75468	+	3.03919i	−0.0686658	+	0.118933i	−0.898314	−	0.439354i	$-0.855208\pi$
$653$	−1.75468	+	3.03919i	−0.0686658	+	0.118933i	0.829648	+	0.558286i	$0.188541\pi$
$654$		0			0
$655$	5.81567	−	3.35768i	0.227237	−	0.131195i
$656$	1.00518	+	9.27711i	0.0392455	+	0.362210i
$657$		0			0
$658$	−27.8098	−	19.4169i	−1.08414	−	0.756949i
$659$			13.7591i			0.535978i	0.963422	+	0.267989i	$0.0863591\pi$
$659$			13.7591i			0.535978i	−0.963422	+	0.267989i	$0.913641\pi$
$660$		0			0
$661$	−20.1812	+	11.6516i	−0.784958	+	0.453196i	−0.838184	−	0.545387i	$-0.816383\pi$
$661$	−20.1812	+	11.6516i	−0.784958	+	0.453196i	0.0532268	+	0.998582i	$0.483049\pi$
$662$	3.03447	+	10.2141i	0.117938	+	0.396982i
$663$		0			0
$664$	0.594670	−	0.699673i	0.0230777	−	0.0271526i
$665$	−27.5943	−	10.8524i	−1.07006	−	0.420836i
$666$		0			0
$667$	11.1388	+	6.43096i	0.431294	+	0.249008i
$668$	0.0847825	+	1.56955i	0.00328033	+	0.0607278i
$669$		0			0
$670$	38.8861	+	36.8423i	1.50230	+	1.42334i
$671$	61.6425			2.37968
$672$		0			0
$673$	−27.1327			−1.04589			−0.522945	−	0.852366i	$-0.675167\pi$
$673$	−27.1327			−1.04589			−0.522945	+	0.852366i	$0.675167\pi$
$674$	28.5041	+	27.0059i	1.09794	+	1.04023i
$675$		0			0
$676$	0.688271	+	12.7418i	0.0264720	+	0.490067i
$677$	−33.2762	−	19.2120i	−1.27891	−	0.738378i	−0.302261	−	0.953225i	$-0.597741\pi$
$677$	−33.2762	−	19.2120i	−1.27891	−	0.738378i	−0.976648	+	0.214847i	$0.931075\pi$
$678$		0			0
$679$	−35.6375	+	28.3790i	−1.36764	+	1.08909i
$680$	−28.1958	+	33.1744i	−1.08126	+	1.27218i
$681$		0			0
$682$	7.52038	+	25.3138i	0.287970	+	0.969314i
$683$	35.9959	−	20.7822i	1.37734	−	0.795210i	0.385505	−	0.922706i	$-0.374027\pi$
$683$	35.9959	−	20.7822i	1.37734	−	0.795210i	0.991839	+	0.127496i	$0.0406940\pi$
$684$		0			0
$685$		−	33.6430i		−	1.28543i
$686$	24.9293	+	8.03301i	0.951806	+	0.306702i
$687$		0			0
$688$	2.48680	+	22.9515i	0.0948084	+	0.875018i
$689$	−12.9787	+	7.49325i	−0.494448	+	0.285470i
$690$		0			0
$691$	11.9417	−	20.6836i	0.454283	−	0.786842i	−0.544363	−	0.838850i	$-0.683229\pi$
$691$	11.9417	−	20.6836i	0.454283	−	0.786842i	0.998647	+	0.0520076i	$0.0165620\pi$
$692$	−3.40545	+	6.71017i	−0.129456	+	0.255083i
$693$		0			0
$694$	40.4841	+	9.68504i	1.53676	+	0.367639i
$695$	10.5633	+	6.09874i	0.400690	+	0.231339i
$696$		0			0
$697$	−7.33593	−	12.7062i	−0.277868	−	0.481282i
$698$	−1.26893	+	1.33932i	−0.0480296	+	0.0506940i
$699$		0			0
$700$	−4.97277	−	1.65199i	−0.187953	−	0.0624395i
$701$	11.6837			0.441287			0.220643	−	0.975355i	$-0.429184\pi$
$701$	11.6837			0.441287			0.220643	+	0.975355i	$0.429184\pi$
$702$		0			0
$703$	−7.32875	−	12.6938i	−0.276409	−	0.478754i
$704$	31.5129	+	38.5343i	1.18769	+	1.45232i
$705$		0			0
$706$	−7.15363	−	1.71137i	−0.269231	−	0.0644081i
$707$	24.6311	+	9.68698i	0.926348	+	0.364317i
$708$		0			0
$709$	−14.8364	+	25.6973i	−0.557191	+	0.965084i	0.440538	+	0.897734i	$0.354788\pi$
$709$	−14.8364	+	25.6973i	−0.557191	+	0.965084i	−0.997729	+	0.0673499i	$0.978546\pi$
$710$	1.83483	−	0.545103i	0.0688600	−	0.0204574i
$711$		0			0
$712$	26.7473	−	9.54425i	1.00240	−	0.357686i
$713$			5.78407i			0.216615i
$714$		0			0
$715$		−	39.1835i		−	1.46538i
$716$	−0.559250	−	0.858151i	−0.0209001	−	0.0320706i
$717$		0			0
$718$	−0.832492	−	2.80219i	−0.0310683	−	0.104577i
$719$	−7.24634	+	12.5510i	−0.270243	+	0.468075i	−0.968924	−	0.247359i	$-0.920437\pi$
$719$	−7.24634	+	12.5510i	−0.270243	+	0.468075i	0.698681	+	0.715433i	$0.253771\pi$
$720$		0			0
$721$	11.9121	−	1.78690i	0.443630	−	0.0665476i
$722$	−0.647485	+	2.70653i	−0.0240969	+	0.100727i
$723$		0			0
$724$	−38.0999	+	2.05804i	−1.41597	+	0.0764866i
$725$	3.30404	+	5.72277i	0.122709	+	0.212538i
$726$		0			0
$727$	36.0100			1.33554			0.667769	−	0.744368i	$-0.267249\pi$
$727$	36.0100			1.33554			0.667769	+	0.744368i	$0.267249\pi$
$728$	0.615168	−	19.2440i	0.0227997	−	0.713231i
$729$		0			0
$730$	19.7974	+	18.7569i	0.732735	+	0.694223i
$731$	−18.1491	−	31.4351i	−0.671267	−	1.16267i
$732$		0			0
$733$	10.0265	+	5.78879i	0.370336	+	0.213814i	0.673605	−	0.739091i	$-0.264745\pi$
$733$	10.0265	+	5.78879i	0.370336	+	0.213814i	−0.303269	+	0.952905i	$0.598078\pi$
$734$	−4.33037	+	18.1013i	−0.159837	+	0.668130i
$735$		0			0
$736$	4.21288	+	10.0565i	0.155289	+	0.370687i
$737$	−48.1493	+	83.3971i	−1.77360	+	3.07197i
$738$		0			0
$739$	25.9584	−	14.9871i	0.954894	−	0.551308i	0.0602959	−	0.998181i	$-0.480796\pi$
$739$	25.9584	−	14.9871i	0.954894	−	0.551308i	0.894598	+	0.446872i	$0.147462\pi$
$740$	−8.55493	−	13.1273i	−0.314485	−	0.482568i
$741$		0			0
$742$	−19.7398	+	9.23719i	−0.724671	+	0.339108i
$743$		−	38.6790i		−	1.41899i	−0.704709	−	0.709497i	$-0.748922\pi$
$743$		−	38.6790i		−	1.41899i	0.704709	−	0.709497i	$-0.251078\pi$
$744$		0			0
$745$	5.56618	−	3.21364i	0.203929	−	0.117739i
$746$	−11.9575	+	3.55241i	−0.437795	+	0.130063i
$747$		0			0
$748$	−69.7944	−	35.4210i	−2.55193	−	1.29512i
$749$	−2.61690	−	17.4452i	−0.0956194	−	0.637434i
$750$		0			0
$751$	31.2191	+	18.0244i	1.13920	+	0.657718i	0.946233	−	0.323486i	$-0.104855\pi$
$751$	31.2191	+	18.0244i	1.13920	+	0.657718i	0.192969	+	0.981205i	$0.438188\pi$
$752$	−14.6416	+	33.1717i	−0.533925	+	1.20965i
$753$		0			0
$754$	−16.6997	+	17.6261i	−0.608165	+	0.641903i
$755$	−18.3384			−0.667402
$756$		0			0
$757$	−13.8059			−0.501782			−0.250891	−	0.968015i	$-0.580724\pi$
$757$	−13.8059			−0.501782			−0.250891	+	0.968015i	$0.580724\pi$
$758$	2.73320	−	2.88482i	0.0992742	−	0.104781i
$759$		0			0
$760$	−5.70163	+	31.1819i	−0.206820	+	1.13109i
$761$	43.8402	+	25.3112i	1.58921	+	0.917529i	0.993438	+	0.114374i	$0.0364863\pi$
$761$	43.8402	+	25.3112i	1.58921	+	0.917529i	0.595770	+	0.803155i	$0.296847\pi$
$762$		0			0
$763$	7.21026	−	18.3335i	0.261029	−	0.663719i
$764$	11.5314	−	22.7217i	0.417191	−	0.822042i
$765$		0			0
$766$	−24.7547	+	7.35430i	−0.894425	+	0.265721i
$767$	4.92547	−	2.84372i	0.177848	−	0.102681i
$768$		0			0
$769$			45.9839i			1.65822i	0.559084	+	0.829111i	$0.311153\pi$
$769$			45.9839i			1.65822i	−0.559084	+	0.829111i	$0.688847\pi$
$770$	4.88996	−	56.7726i	0.176222	−	2.04594i
$771$		0			0
$772$	−24.4310	+	15.9215i	−0.879292	+	0.573027i
$773$	19.7997	−	11.4313i	0.712144	−	0.411157i	−0.0997101	−	0.995017i	$-0.531792\pi$
$773$	19.7997	−	11.4313i	0.712144	−	0.411157i	0.811855	+	0.583860i	$0.198458\pi$
$774$		0			0
$775$	−1.48584	+	2.57356i	−0.0533731	+	0.0924449i
$776$	37.1093	+	31.5402i	1.33215	+	1.13223i
$777$		0			0
$778$	−1.73654	+	7.25887i	−0.0622580	+	0.260243i
$779$	−9.25112	−	5.34114i	−0.331456	−	0.191366i
$780$		0			0
$781$	1.72049	+	2.97997i	0.0615638	+	0.106632i
$782$	−12.4448	−	11.7907i	−0.445025	−	0.421635i
$783$		0			0
$784$	3.29290	−	27.8057i	0.117603	−	0.993061i
$785$	4.40860			0.157350
$786$		0			0
$787$	−4.30888	−	7.46319i	−0.153595	−	0.266034i	0.778952	−	0.627084i	$-0.215752\pi$
$787$	−4.30888	−	7.46319i	−0.153595	−	0.266034i	−0.932546	+	0.361050i	$0.882418\pi$
$788$	−2.57273	−	47.6281i	−0.0916497	−	1.69668i
$789$		0			0
$790$	9.99545	−	41.7817i	0.355622	−	1.48653i
$791$	−13.1956	−	16.5706i	−0.469182	−	0.589184i
$792$		0			0
$793$	−12.7443	+	22.0738i	−0.452565	+	0.783865i
$794$	−8.38230	−	28.2150i	−0.297477	−	1.00131i
$795$		0			0
$796$	19.3968	−	12.6407i	0.687502	−	0.448039i
$797$			13.6259i			0.482656i	0.970444	+	0.241328i	$0.0775829\pi$
$797$			13.6259i			0.482656i	−0.970444	+	0.241328i	$0.922417\pi$
$798$		0			0
$799$		−	57.0110i		−	2.01690i
$800$	−0.708894	+	5.55675i	−0.0250632	+	0.196461i
$801$		0			0
$802$	4.77367	−	1.41819i	0.168564	−	0.0500781i
$803$	−24.5135	+	42.4586i	−0.865061	+	1.49833i
$804$		0			0
$805$	4.56804	−	11.6152i	0.161002	−	0.409380i
$806$	−10.6195	−	2.54051i	−0.374057	−	0.0894857i
$807$		0			0
$808$	5.08936	−	27.8335i	0.179043	−	0.979179i
$809$	−18.9151	−	32.7619i	−0.665020	−	1.15185i	−0.979280	−	0.202511i	$-0.935090\pi$
$809$	−18.9151	−	32.7619i	−0.665020	−	1.15185i	0.314260	−	0.949337i	$-0.398244\pi$
$810$		0			0
$811$	28.8329			1.01246			0.506229	−	0.862399i	$-0.331039\pi$
$811$	28.8329			1.01246			0.506229	+	0.862399i	$0.331039\pi$
$812$	−26.3956	+	23.4542i	−0.926305	+	0.823080i
$813$		0			0
$814$	19.3731	−	20.4478i	0.679028	−	0.716697i
$815$	−16.3187	−	28.2649i	−0.571620	−	0.990075i
$816$		0			0
$817$	−22.8872	−	13.2139i	−0.800722	−	0.462297i
$818$	23.4309	+	5.60538i	0.819242	+	0.195987i
$819$		0			0
$820$	−10.1830	−	5.16793i	−0.355605	−	0.180472i
$821$	−17.4506	+	30.2252i	−0.609028	+	1.05487i	0.382372	+	0.924008i	$0.375107\pi$
$821$	−17.4506	+	30.2252i	−0.609028	+	1.05487i	−0.991401	+	0.130860i	$0.958226\pi$
$822$		0			0
$823$	−8.48099	+	4.89650i	−0.295629	+	0.170681i	−0.640477	−	0.767977i	$-0.721264\pi$
$823$	−8.48099	+	4.89650i	−0.295629	+	0.170681i	0.344849	+	0.938658i	$0.387930\pi$
$824$	−4.32766	−	12.1281i	−0.150761	−	0.422502i
$825$		0			0
$826$	7.49135	−	3.50556i	0.260657	−	0.121974i
$827$			31.5615i			1.09750i	0.835986	+	0.548751i	$0.184896\pi$
$827$			31.5615i			1.09750i	−0.835986	+	0.548751i	$0.815104\pi$
$828$		0			0
$829$	−40.1351	+	23.1720i	−1.39395	+	0.804797i	−0.993750	−	0.111631i	$-0.964392\pi$
$829$	−40.1351	+	23.1720i	−1.39395	+	0.804797i	−0.400199	+	0.916428i	$0.631059\pi$
$830$	0.320013	+	1.07717i	0.0111078	+	0.0373892i
$831$		0			0
$832$	−20.3141	+	3.31776i	−0.704264	+	0.115023i
$833$	12.9174	+	42.0870i	0.447560	+	1.45823i
$834$		0			0
$835$	−1.66584	−	0.961770i	−0.0576486	−	0.0332834i
$836$	−56.9024	+	3.07370i	−1.96801	+	0.106306i
$837$		0			0
$838$	−7.64180	−	7.24015i	−0.263981	−	0.250107i
$839$	10.3847			0.358521			0.179260	−	0.983802i	$-0.442630\pi$
$839$	10.3847			0.358521			0.179260	+	0.983802i	$0.442630\pi$
$840$		0			0
$841$	15.5295			0.535501
$842$	39.8839	+	37.7876i	1.37449	+	1.30225i
$843$		0			0
$844$	−10.3552	+	0.559355i	−0.356439	+	0.0192538i
$845$	−13.5234	−	7.80773i	−0.465219	−	0.268594i
$846$		0			0
$847$	72.5236	−	10.8790i	2.49194	−	0.373809i
$848$	13.7552	+	18.8052i	0.472356	+	0.645773i
$849$		0			0
$850$	−2.50831	−	8.44304i	−0.0860344	−	0.289594i
$851$	5.34313	−	3.08486i	0.183160	−	0.105748i
$852$		0			0
$853$			15.1171i			0.517600i	0.965931	+	0.258800i	$0.0833271\pi$
$853$			15.1171i			0.517600i	−0.965931	+	0.258800i	$0.916673\pi$
$854$	−21.2199	+	30.3921i	−0.726129	+	1.04000i
$855$		0			0
$856$	−17.7615	+	6.33782i	−0.607074	+	0.216622i
$857$	26.0794	−	15.0569i	0.890854	−	0.514335i	0.0166324	−	0.999862i	$-0.494705\pi$
$857$	26.0794	−	15.0569i	0.890854	−	0.514335i	0.874222	+	0.485527i	$0.161372\pi$
$858$		0			0
$859$	19.9677	−	34.5851i	0.681289	−	1.18003i	−0.293298	−	0.956021i	$-0.594753\pi$
$859$	19.9677	−	34.5851i	0.681289	−	1.18003i	0.974588	−	0.224007i	$-0.0719138\pi$
$860$	−25.1927	−	12.7854i	−0.859063	−	0.435979i
$861$		0			0
$862$	−4.29958	−	1.02859i	−0.146444	−	0.0350339i
$863$	12.7729	+	7.37443i	0.434794	+	0.251029i	0.701387	−	0.712781i	$-0.252564\pi$
$863$	12.7729	+	7.37443i	0.434794	+	0.251029i	−0.266593	+	0.963809i	$0.585898\pi$
$864$		0			0
$865$	−4.60428	−	7.97484i	−0.156550	−	0.271153i
$866$	28.3036	−	29.8737i	0.961795	−	1.01515i
$867$		0			0
$868$	−15.0695	−	5.00620i	−0.511491	−	0.169922i
$869$	77.2306			2.61987
$870$		0			0
$871$	−19.9094	−	34.4840i	−0.674603	−	1.16845i
$872$	−20.7171	−	3.78814i	−0.701571	−	0.128283i
$873$		0			0
$874$	−12.1392	−	2.90405i	−0.410613	−	0.0982311i
$875$	−20.3116	+	16.1746i	−0.686657	+	0.546802i
$876$		0			0
$877$	24.6714	−	42.7322i	0.833095	−	1.44296i	−0.0624763	−	0.998046i	$-0.519900\pi$
$877$	24.6714	−	42.7322i	0.833095	−	1.44296i	0.895572	−	0.444917i	$-0.146767\pi$
$878$	−11.4028	+	3.38763i	−0.384828	+	0.114327i
$879$		0			0
$880$	−60.5627	+	6.56198i	−2.04157	+	0.221204i
$881$			4.71976i			0.159013i	0.996834	+	0.0795065i	$0.0253344\pi$
$881$			4.71976i			0.159013i	−0.996834	+	0.0795065i	$0.974666\pi$
$882$		0			0
$883$			47.6089i			1.60217i	0.598552	+	0.801084i	$0.295743\pi$
$883$			47.6089i			1.60217i	−0.598552	+	0.801084i	$0.704257\pi$
$884$	27.1138	−	17.6698i	0.911935	−	0.594300i
$885$		0			0
$886$	−5.56052	−	18.7168i	−0.186809	−	0.628804i
$887$	−25.2856	+	43.7960i	−0.849008	+	1.47052i	0.0330869	+	0.999452i	$0.489466\pi$
$887$	−25.2856	+	43.7960i	−0.849008	+	1.47052i	−0.882095	+	0.471072i	$0.843867\pi$
$888$		0			0
$889$	−12.6694	+	10.0889i	−0.424917	+	0.338372i
$890$	−8.08593	+	33.7998i	−0.271041	+	1.13297i
$891$		0			0
$892$	0.343006	+	6.34997i	0.0114847	+	0.212613i
$893$	−20.7542	−	35.9474i	−0.694514	−	1.20293i
$894$		0			0
$895$	1.25348			0.0418994
$896$	−29.8469	+	2.27194i	−0.997115	+	0.0759002i
$897$		0			0
$898$	−14.1405	−	13.3972i	−0.471873	−	0.447072i
$899$	10.0126	+	17.3423i	0.333938	+	0.578397i
$900$		0			0
$901$	−31.7253	−	18.3166i	−1.05692	−	0.610214i
$902$	4.77628	−	19.9652i	0.159033	−	0.664769i
$903$		0			0
$904$	−14.6655	+	17.2550i	−0.487767	+	0.573893i
$905$	23.3464	−	40.4372i	0.776061	−	1.34418i
$906$		0			0
$907$	−27.0285	+	15.6049i	−0.897465	+	0.518152i	−0.876377	−	0.481626i	$-0.840046\pi$
$907$	−27.0285	+	15.6049i	−0.897465	+	0.518152i	−0.0210884	+	0.999778i	$0.506713\pi$
$908$	−16.7127	+	10.8915i	−0.554631	+	0.361448i
$909$		0			0
$910$	19.3190	+	13.4886i	0.640418	+	0.447142i
$911$			14.8737i			0.492789i	0.969170	+	0.246394i	$0.0792459\pi$
$911$			14.8737i			0.492789i	−0.969170	+	0.246394i	$0.920754\pi$
$912$		0			0
$913$	−1.74945	+	1.01004i	−0.0578983	+	0.0334276i
$914$	−6.27481	+	1.86416i	−0.207552	+	0.0616610i
$915$		0			0
$916$	−20.3767	+	40.1507i	−0.673266	+	1.32662i
$917$	−7.17899	+	1.07690i	−0.237071	+	0.0355623i
$918$		0			0
$919$	−20.9884	−	12.1177i	−0.692345	−	0.399726i	0.112145	−	0.993692i	$-0.464228\pi$
$919$	−20.9884	−	12.1177i	−0.692345	−	0.399726i	−0.804490	+	0.593966i	$0.797561\pi$
$920$	−13.1253	−	2.39996i	−0.432728	−	0.0791244i
$921$		0			0
$922$	−15.5964	+	16.4616i	−0.513639	+	0.542133i
$923$	−1.42281			−0.0468325
$924$		0			0
$925$	3.16982			0.104223
$926$	34.3985	−	36.3067i	1.13040	−	1.19311i
$927$		0			0
$928$	30.0398	+	22.8595i	0.986105	+	0.750399i
$929$	−31.1972	−	18.0117i	−1.02355	−	0.590945i	−0.108417	−	0.994105i	$-0.534578\pi$
$929$	−31.1972	−	18.0117i	−1.02355	−	0.590945i	−0.915129	+	0.403161i	$0.867912\pi$
$930$		0			0
$931$	23.4662	+	21.8349i	0.769072	+	0.715609i
$932$	−5.89140	−	2.98992i	−0.192979	−	0.0979380i
$933$		0			0
$934$	6.48803	−	1.92751i	0.212295	−	0.0630699i
$935$	82.9485	−	47.8904i	2.71271	−	1.56618i
$936$		0			0
$937$			10.1913i			0.332935i	0.986047	+	0.166468i	$0.0532361\pi$
$937$			10.1913i			0.332935i	−0.986047	+	0.166468i	$0.946764\pi$
$938$	−24.5430	−	52.4482i	−0.801357	−	1.71249i
$939$		0			0
$940$	−24.2267	−	37.1750i	−0.790186	−	1.21252i
$941$	−7.06748	+	4.08041i	−0.230393	+	0.133018i	−0.610753	−	0.791821i	$-0.709133\pi$
$941$	−7.06748	+	4.08041i	−0.230393	+	0.133018i	0.380360	+	0.924838i	$0.375800\pi$
$942$		0			0
$943$	2.24822	−	3.89403i	0.0732122	−	0.126807i
$944$	−5.22016	−	7.13666i	−0.169902	−	0.232278i
$945$		0			0
$946$	11.8165	−	49.3938i	0.384187	−	1.60593i
$947$	−35.3088	−	20.3855i	−1.14738	−	0.662441i	−0.199134	−	0.979972i	$-0.563813\pi$
$947$	−35.3088	−	20.3855i	−1.14738	−	0.662441i	−0.948248	+	0.317531i	$0.897146\pi$
$948$		0			0
$949$	−10.1361	−	17.5563i	−0.329032	−	0.569900i
$950$	−4.65517	−	4.41050i	−0.151034	−	0.143096i
$951$		0			0
$952$	41.4900	−	22.2179i	1.34470	−	0.720087i
$953$	10.4835			0.339594			0.169797	−	0.985479i	$-0.445689\pi$
$953$	10.4835			0.339594			0.169797	+	0.985479i	$0.445689\pi$
$954$		0			0
$955$	15.5908	+	27.0041i	0.504506	+	0.873831i
$956$	53.9709	−	2.91535i	1.74554	−	0.0942891i
$957$		0			0
$958$	−4.50783	+	18.8431i	−0.145641	+	0.608792i
$959$	−13.3105	+	33.8447i	−0.429820	+	1.09290i
$960$		0			0
$961$	10.9973	−	19.0479i	0.354752	−	0.614448i
$962$	3.31695	+	11.1649i	0.106943	+	0.359971i
$963$		0			0
$964$	5.98220	+	9.17950i	0.192674	+	0.295652i
$965$		−	35.6859i		−	1.14877i
$966$		0			0
$967$		−	2.75486i		−	0.0885903i	−0.999018	−	0.0442951i	$-0.985896\pi$
$967$		−	2.75486i		−	0.0885903i	0.999018	−	0.0442951i	$-0.0141042\pi$
$968$	−26.3478	−	73.8385i	−0.846849	−	2.37326i
$969$		0			0
$970$	−57.1312	+	16.9729i	−1.83437	+	0.544968i
$971$	−24.3255	+	42.1330i	−0.780643	+	1.35211i	0.150925	+	0.988545i	$0.451775\pi$
$971$	−24.3255	+	42.1330i	−0.780643	+	1.35211i	−0.931568	+	0.363568i	$0.881559\pi$
$972$		0			0
$973$	−8.21377	−	10.3146i	−0.263321	−	0.330671i
$974$	23.4019	+	5.59846i	0.749847	+	0.179386i
$975$		0			0
$976$	36.2520	+	16.0012i	1.16040	+	0.512186i
$977$	−7.70115	−	13.3388i	−0.246382	−	0.426745i	0.716138	−	0.697959i	$-0.245908\pi$
$977$	−7.70115	−	13.3388i	−0.246382	−	0.426745i	−0.962519	+	0.271214i	$0.912575\pi$
$978$		0			0
$979$	−62.4766			−1.99676
$980$	26.3077	+	21.9544i	0.840370	+	0.701307i
$981$		0			0
$982$	35.2526	−	37.2082i	1.12496	−	1.18736i
$983$	−12.3097	−	21.3210i	−0.392617	−	0.680033i	0.600177	−	0.799867i	$-0.295097\pi$
$983$	−12.3097	−	21.3210i	−0.392617	−	0.680033i	−0.992794	+	0.119835i	$0.961764\pi$
$984$		0			0
$985$	50.5498	+	29.1850i	1.61065	+	0.929910i
$986$	−57.7235	−	13.8092i	−1.83829	−	0.439775i
$987$		0			0
$988$	10.6637	−	21.0119i	0.339256	−	0.668478i
$989$	5.56209	−	9.63382i	0.176864	−	0.306338i
$990$		0			0
$991$	22.8459	−	13.1901i	0.725723	−	0.418997i	−0.0911322	−	0.995839i	$-0.529049\pi$
$991$	22.8459	−	13.1901i	0.725723	−	0.418997i	0.816856	+	0.576842i	$0.195715\pi$
$992$	−2.14823	+	16.8392i	−0.0682064	+	0.534644i
$993$		0			0
$994$	−2.06150	−	0.177562i	−0.0653868	−	0.00563193i
$995$			28.3325i			0.898202i
$996$		0			0
$997$	22.4382	−	12.9547i	0.710623	−	0.410279i	−0.100668	−	0.994920i	$-0.532098\pi$
$997$	22.4382	−	12.9547i	0.710623	−	0.410279i	0.811292	+	0.584641i	$0.198765\pi$
$998$	14.2026	+	47.8063i	0.449575	+	1.51328i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.b.271.4	yes	32
3.2	odd	2		756.2.bf.c.271.13	yes	32
4.3	odd	2		756.2.bf.c.271.15	yes	32
7.3	odd	6		756.2.bf.c.703.15	yes	32
12.11	even	2	inner	756.2.bf.b.271.2	✓	32
21.17	even	6	inner	756.2.bf.b.703.2	yes	32
28.3	even	6	inner	756.2.bf.b.703.4	yes	32
84.59	odd	6		756.2.bf.c.703.13	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.b.271.2	✓	32	12.11	even	2	inner
756.2.bf.b.271.4	yes	32	1.1	even	1	trivial
756.2.bf.b.703.2	yes	32	21.17	even	6	inner
756.2.bf.b.703.4	yes	32	28.3	even	6	inner
756.2.bf.c.271.13	yes	32	3.2	odd	2
756.2.bf.c.271.15	yes	32	4.3	odd	2
756.2.bf.c.703.13	yes	32	84.59	odd	6
756.2.bf.c.703.15	yes	32	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.02662 - 0.972657i) q^{2} +(0.107877 + 1.99709i) q^{4} +(-2.11960 - 1.22375i) q^{5} +(1.64814 + 2.06969i) q^{7} +(1.83173 - 2.15517i) q^{8} +O(q^{10})\)	\(q+(-1.02662 - 0.972657i) q^{2} +(0.107877 + 1.99709i) q^{4} +(-2.11960 - 1.22375i) q^{5} +(1.64814 + 2.06969i) q^{7} +(1.83173 - 2.15517i) q^{8} +(0.985722 + 3.31796i) q^{10} +(-5.38874 + 3.11119i) q^{11} -2.57290i q^{13} +(0.321089 - 3.72785i) q^{14} +(-3.97673 + 0.430879i) q^{16} +(5.44664 - 3.14462i) q^{17} +(2.28953 - 3.96558i) q^{19} +(2.21528 - 4.36504i) q^{20} +(8.55829 + 2.04740i) q^{22} +(1.66922 + 0.963723i) q^{23} +(0.495133 + 0.857595i) q^{25} +(-2.50255 + 2.64138i) q^{26} +(-3.95556 + 3.51476i) q^{28} +6.67305 q^{29} +(1.50045 + 2.59886i) q^{31} +(4.50166 + 3.42564i) q^{32} +(-8.65024 - 2.06940i) q^{34} +(-0.960619 - 6.40383i) q^{35} +(1.60049 - 2.77213i) q^{37} +(-6.20762 + 1.84420i) q^{38} +(-6.51993 + 2.32651i) q^{40} -2.33285i q^{41} -5.77146i q^{43} +(-6.79465 - 10.4262i) q^{44} +(-0.776271 - 2.61295i) q^{46} +(4.53242 - 7.85038i) q^{47} +(-1.56724 + 6.82230i) q^{49} +(0.325835 - 1.36201i) q^{50} +(5.13832 - 0.277557i) q^{52} +(-2.91237 - 5.04437i) q^{53} +15.2293 q^{55} +(7.47949 + 0.239095i) q^{56} +(-6.85065 - 6.49058i) q^{58} +(1.10526 + 1.91436i) q^{59} +(-8.57935 - 4.95329i) q^{61} +(0.987410 - 4.12745i) q^{62} +(-1.28950 - 7.89539i) q^{64} +(-3.14859 + 5.45352i) q^{65} +(13.4028 - 7.73809i) q^{67} +(6.86765 + 10.5382i) q^{68} +(-5.24255 + 7.50862i) q^{70} -0.552999i q^{71} +(6.82352 - 3.93956i) q^{73} +(-4.33942 + 1.28918i) q^{74} +(8.16661 + 4.14460i) q^{76} +(-15.3206 - 6.02534i) q^{77} +(-10.7489 - 6.20587i) q^{79} +(8.95635 + 3.95323i) q^{80} +(-2.26906 + 2.39494i) q^{82} +0.324649 q^{83} -15.3929 q^{85} +(-5.61365 + 5.92507i) q^{86} +(-3.16560 + 17.3125i) q^{88} +(8.69544 + 5.02031i) q^{89} +(5.32512 - 4.24052i) q^{91} +(-1.74457 + 3.43754i) q^{92} +(-12.2888 + 3.65083i) q^{94} +(-9.70578 + 5.60363i) q^{95} +17.2188i q^{97} +(8.24471 - 5.47949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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