LMFDB - Embedded newform 756.2.ck.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(5,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 5, 15]))

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

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

chi := DirichletCharacter("756.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.ck (of order $18$, degree $6$, 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:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	756.5
Dual form			756.2.ck.a.605.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +O(q^{10})$	\(q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +(3.93578 - 0.693985i) q^{11} +(1.87975 - 2.24020i) q^{13} +(-4.57548 + 5.12720i) q^{15} +7.25945 q^{17} +2.16772i q^{19} +(1.44981 - 4.34719i) q^{21} +(-0.423740 + 0.504993i) q^{23} +(-10.0933 - 3.67365i) q^{25} +(0.474237 - 5.17447i) q^{27} +(-5.27940 - 6.29175i) q^{29} +(-0.711008 - 1.95348i) q^{31} +(-6.42955 - 2.56454i) q^{33} +(10.4796 - 0.604570i) q^{35} +(-0.0940596 - 0.162916i) q^{37} +(-4.81025 + 1.58660i) q^{39} +(0.931145 + 0.781324i) q^{41} +(-0.546157 - 0.198785i) q^{43} +(11.4118 - 3.38228i) q^{45} +(-7.42893 - 2.70391i) q^{47} +(-6.25889 + 3.13470i) q^{49} +(-10.6926 - 6.61564i) q^{51} +(-5.15055 + 2.97367i) q^{53} -15.8561i q^{55} +(1.97547 - 3.19288i) q^{57} +(10.3271 + 8.66550i) q^{59} +(3.62963 - 9.97232i) q^{61} +(-6.09711 + 5.08186i) q^{63} +(-7.45790 - 8.88798i) q^{65} +(1.33647 - 7.57947i) q^{67} +(1.08434 - 0.357657i) q^{69} +(-0.923830 - 0.533373i) q^{71} +(2.88569 + 1.66605i) q^{73} +(11.5188 + 14.6092i) q^{75} +(4.18269 + 9.71128i) q^{77} +(2.48404 + 14.0877i) q^{79} +(-5.41408 + 7.18942i) q^{81} +(6.12280 - 5.13764i) q^{83} +(5.00139 - 28.3643i) q^{85} +(2.04241 + 14.0785i) q^{87} +8.66443 q^{89} +(6.91226 + 3.47624i) q^{91} +(-0.732970 + 3.52528i) q^{93} +(8.46975 + 1.49345i) q^{95} +(3.49318 - 9.59744i) q^{97} +(7.13314 + 9.63672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) $ 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	−1.47292	−	0.911314i	−0.850394	−	0.526147i
$3$	−1.47292	−	0.911314i	−0.850394	−	0.526147i
$4$		0			0
$5$	0.688949	−	3.90722i	0.308107	−	1.74736i	−0.300398	−	0.953814i	$-0.597120\pi$
$5$	0.688949	−	3.90722i	0.308107	−	1.74736i	0.608506	−	0.793550i	$-0.291769\pi$
$6$		0			0
$7$	0.608733	+	2.57477i	0.230079	+	0.973172i
$7$	0.608733	+	2.57477i	0.230079	+	0.973172i
$8$		0			0
$9$	1.33902	+	2.68459i	0.446338	+	0.894864i
$10$		0			0
$11$	3.93578	−	0.693985i	1.18668	−	0.209244i	0.454749	−	0.890620i	$-0.349729\pi$
$11$	3.93578	−	0.693985i	1.18668	−	0.209244i	0.731934	+	0.681376i	$0.238618\pi$
$12$		0			0
$13$	1.87975	−	2.24020i	0.521349	−	0.621319i	−0.439550	−	0.898218i	$-0.644862\pi$
$13$	1.87975	−	2.24020i	0.521349	−	0.621319i	0.960899	+	0.276899i	$0.0893066\pi$
$14$		0			0
$15$	−4.57548	+	5.12720i	−1.18138	+	1.32384i
$16$		0			0
$17$	7.25945			1.76068			0.880338	−	0.474347i	$-0.157316\pi$
$17$	7.25945			1.76068			0.880338	+	0.474347i	$0.157316\pi$
$18$		0			0
$19$			2.16772i			0.497308i	0.968592	+	0.248654i	$0.0799882\pi$
$19$			2.16772i			0.497308i	−0.968592	+	0.248654i	$0.920012\pi$
$20$		0			0
$21$	1.44981	−	4.34719i	0.316373	−	0.948635i
$22$		0			0
$23$	−0.423740	+	0.504993i	−0.0883558	+	0.105298i	−0.808411	−	0.588618i	$-0.799672\pi$
$23$	−0.423740	+	0.504993i	−0.0883558	+	0.105298i	0.720055	+	0.693917i	$0.244116\pi$
$24$		0			0
$25$	−10.0933	−	3.67365i	−2.01866	−	0.734731i
$26$		0			0
$27$	0.474237	−	5.17447i	0.0912669	−	0.995826i
$28$		0			0
$29$	−5.27940	−	6.29175i	−0.980360	−	1.16835i	−0.985725	−	0.168362i	$-0.946152\pi$
$29$	−5.27940	−	6.29175i	−0.980360	−	1.16835i	0.00536483	−	0.999986i	$-0.498292\pi$
$30$		0			0
$31$	−0.711008	−	1.95348i	−0.127701	−	0.350855i	0.859322	−	0.511435i	$-0.170886\pi$
$31$	−0.711008	−	1.95348i	−0.127701	−	0.350855i	−0.987023	+	0.160580i	$0.948664\pi$
$32$		0			0
$33$	−6.42955	−	2.56454i	−1.11924	−	0.446430i
$34$		0			0
$35$	10.4796	−	0.604570i	1.77137	−	0.102191i
$36$		0			0
$37$	−0.0940596	−	0.162916i	−0.0154633	−	0.0267832i	0.858190	−	0.513332i	$-0.171589\pi$
$37$	−0.0940596	−	0.162916i	−0.0154633	−	0.0267832i	−0.873654	+	0.486549i	$0.838256\pi$
$38$		0			0
$39$	−4.81025	+	1.58660i	−0.770257	+	0.254060i
$40$		0			0
$41$	0.931145	+	0.781324i	0.145420	+	0.122022i	0.712596	−	0.701575i	$-0.247519\pi$
$41$	0.931145	+	0.781324i	0.145420	+	0.122022i	−0.567175	+	0.823597i	$0.691964\pi$
$42$		0			0
$43$	−0.546157	−	0.198785i	−0.0832882	−	0.0303144i	0.300040	−	0.953927i	$-0.403000\pi$
$43$	−0.546157	−	0.198785i	−0.0832882	−	0.0303144i	−0.383328	+	0.923612i	$0.625222\pi$
$44$		0			0
$45$	11.4118	−	3.38228i	1.70117	−	0.504201i
$46$		0			0
$47$	−7.42893	−	2.70391i	−1.08362	−	0.394406i	−0.262367	−	0.964968i	$-0.584503\pi$
$47$	−7.42893	−	2.70391i	−1.08362	−	0.394406i	−0.821254	+	0.570563i	$0.806725\pi$
$48$		0			0
$49$	−6.25889	+	3.13470i	−0.894127	+	0.447814i
$50$		0			0
$51$	−10.6926	−	6.61564i	−1.49727	−	0.926375i
$52$		0			0
$53$	−5.15055	+	2.97367i	−0.707482	+	0.408465i	−0.810128	−	0.586253i	$-0.800602\pi$
$53$	−5.15055	+	2.97367i	−0.707482	+	0.408465i	0.102646	+	0.994718i	$0.467269\pi$
$54$		0			0
$55$		−	15.8561i		−	2.13804i
$56$		0			0
$57$	1.97547	−	3.19288i	0.261657	−	0.422908i
$58$		0			0
$59$	10.3271	+	8.66550i	1.34448	+	1.12815i	0.980451	+	0.196765i	$0.0630435\pi$
$59$	10.3271	+	8.66550i	1.34448	+	1.12815i	0.364029	+	0.931388i	$0.381401\pi$
$60$		0			0
$61$	3.62963	−	9.97232i	0.464726	−	1.27682i	−0.457167	−	0.889381i	$-0.651136\pi$
$61$	3.62963	−	9.97232i	0.464726	−	1.27682i	0.921893	−	0.387444i	$-0.126642\pi$
$62$		0			0
$63$	−6.09711	+	5.08186i	−0.768163	+	0.640254i
$64$		0			0
$65$	−7.45790	−	8.88798i	−0.925039	−	1.10242i
$66$		0			0
$67$	1.33647	−	7.57947i	0.163275	−	0.925980i	−0.787550	−	0.616251i	$-0.788651\pi$
$67$	1.33647	−	7.57947i	0.163275	−	0.925980i	0.950825	−	0.309729i	$-0.100238\pi$
$68$		0			0
$69$	1.08434	−	0.357657i	0.130540	−	0.0430569i
$70$		0			0
$71$	−0.923830	−	0.533373i	−0.109638	−	0.0632998i	0.444178	−	0.895939i	$-0.353496\pi$
$71$	−0.923830	−	0.533373i	−0.109638	−	0.0632998i	−0.553816	+	0.832639i	$0.686829\pi$
$72$		0			0
$73$	2.88569	+	1.66605i	0.337744	+	0.194997i	0.659274	−	0.751903i	$-0.270864\pi$
$73$	2.88569	+	1.66605i	0.337744	+	0.194997i	−0.321530	+	0.946899i	$0.604197\pi$
$74$		0			0
$75$	11.5188	+	14.6092i	1.33008	+	1.68692i
$76$		0			0
$77$	4.18269	+	9.71128i	0.476662	+	1.10670i
$78$		0			0
$79$	2.48404	+	14.0877i	0.279476	+	1.58499i	0.724375	+	0.689406i	$0.242128\pi$
$79$	2.48404	+	14.0877i	0.279476	+	1.58499i	−0.444899	+	0.895581i	$0.646760\pi$
$80$		0			0
$81$	−5.41408	+	7.18942i	−0.601564	+	0.798825i
$82$		0			0
$83$	6.12280	−	5.13764i	0.672064	−	0.563929i	−0.241611	−	0.970373i	$-0.577676\pi$
$83$	6.12280	−	5.13764i	0.672064	−	0.563929i	0.913676	+	0.406444i	$0.133231\pi$
$84$		0			0
$85$	5.00139	−	28.3643i	0.542477	−	3.07654i
$86$		0			0
$87$	2.04241	+	14.0785i	0.218969	+	1.50937i
$88$		0			0
$89$	8.66443			0.918428			0.459214	−	0.888326i	$-0.348131\pi$
$89$	8.66443			0.918428			0.459214	+	0.888326i	$0.348131\pi$
$90$		0			0
$91$	6.91226	+	3.47624i	0.724602	+	0.364409i
$92$		0			0
$93$	−0.732970	+	3.52528i	−0.0760054	+	0.365554i
$94$		0			0
$95$	8.46975	+	1.49345i	0.868978	+	0.153224i
$96$		0			0
$97$	3.49318	−	9.59744i	0.354679	−	0.974472i	−0.626167	−	0.779689i	$-0.715377\pi$
$97$	3.49318	−	9.59744i	0.354679	−	0.974472i	0.980846	−	0.194783i	$-0.0624004\pi$
$98$		0			0
$99$	7.13314	+	9.63672i	0.716907	+	0.968526i
$100$		0			0
$101$	−8.98912	+	7.54277i	−0.894451	+	0.750534i	−0.969098	−	0.246676i	$-0.920662\pi$
$101$	−8.98912	+	7.54277i	−0.894451	+	0.750534i	0.0746466	+	0.997210i	$0.476217\pi$
$102$		0			0
$103$	−6.28666	−	1.10851i	−0.619443	−	0.109224i	−0.144885	−	0.989449i	$-0.546281\pi$
$103$	−6.28666	−	1.10851i	−0.619443	−	0.109224i	−0.474558	+	0.880224i	$0.657392\pi$
$104$		0			0
$105$	−15.9866	−	8.65971i	−1.56013	−	0.845101i
$106$		0			0
$107$	11.1821	+	6.45600i	1.08102	+	0.624125i	0.931170	−	0.364584i	$-0.118789\pi$
$107$	11.1821	+	6.45600i	1.08102	+	0.624125i	0.149846	+	0.988709i	$0.452122\pi$
$108$		0			0
$109$	1.15230	+	1.99583i	0.110370	+	0.191166i	0.915919	−	0.401362i	$-0.131463\pi$
$109$	1.15230	+	1.99583i	0.110370	+	0.191166i	−0.805550	+	0.592528i	$0.798130\pi$
$110$		0			0
$111$	−0.00992484	+	0.325681i	−0.000942024	+	0.0309122i
$112$		0			0
$113$	−5.63872	−	15.4922i	−0.530446	−	1.45739i	−0.858542	−	0.512744i	$-0.828629\pi$
$113$	−5.63872	−	15.4922i	−0.530446	−	1.45739i	0.328096	−	0.944644i	$-0.393593\pi$
$114$		0			0
$115$	1.68119	+	2.00356i	0.156771	+	0.186833i
$116$		0			0
$117$	8.53103	+	2.04670i	0.788694	+	0.189218i
$118$		0			0
$119$	4.41907	+	18.6914i	0.405095	+	1.71344i
$120$		0			0
$121$	4.67215	−	1.70052i	0.424740	−	0.154593i
$122$		0			0
$123$	−0.659476	−	1.99940i	−0.0594630	−	0.180280i
$124$		0			0
$125$	−11.3888	+	19.7260i	−1.01865	+	1.76435i
$126$		0			0
$127$	−2.99863	−	5.19378i	−0.266085	−	0.460873i	0.701762	−	0.712411i	$-0.252397\pi$
$127$	−2.99863	−	5.19378i	−0.266085	−	0.460873i	−0.967847	+	0.251538i	$0.919064\pi$
$128$		0			0
$129$	0.623293	+	0.790516i	0.0548779	+	0.0696010i
$130$		0			0
$131$	−5.03254	−	4.22280i	−0.439695	−	0.368948i	0.395900	−	0.918293i	$-0.370433\pi$
$131$	−5.03254	−	4.22280i	−0.439695	−	0.368948i	−0.835595	+	0.549346i	$0.814877\pi$
$132$		0			0
$133$	−5.58137	+	1.31956i	−0.483966	+	0.114420i
$134$		0			0
$135$	−19.8911	−	5.41789i	−1.71195	−	0.466298i
$136$		0			0
$137$	−5.48611	+	15.0730i	−0.468710	+	1.28777i	0.450067	+	0.892995i	$0.351400\pi$
$137$	−5.48611	+	15.0730i	−0.468710	+	1.28777i	−0.918777	+	0.394776i	$0.870822\pi$
$138$		0			0
$139$	−22.1082	−	3.89827i	−1.87519	−	0.330647i	−0.884476	−	0.466587i	$-0.845484\pi$
$139$	−22.1082	−	3.89827i	−1.87519	−	0.330647i	−0.990717	+	0.135939i	$0.956595\pi$
$140$		0			0
$141$	8.47814	+	10.7527i	0.713989	+	0.905544i
$142$		0			0
$143$	5.84362	−	10.1214i	0.488668	−	0.846398i
$144$		0			0
$145$	−28.2205	+	16.2931i	−2.34358	+	1.35307i
$146$		0			0
$147$	12.0756	+	1.08664i	0.995976	+	0.0896244i
$148$		0			0
$149$	0.744457	+	2.04538i	0.0609883	+	0.167564i	0.966444	−	0.256876i	$-0.0826932\pi$
$149$	0.744457	+	2.04538i	0.0609883	+	0.167564i	−0.905456	+	0.424440i	$0.860471\pi$
$150$		0			0
$151$	3.62566	+	20.5621i	0.295052	+	1.67332i	0.666992	+	0.745065i	$0.267582\pi$
$151$	3.62566	+	20.5621i	0.295052	+	1.67332i	−0.371940	+	0.928257i	$0.621307\pi$
$152$		0			0
$153$	9.72052	+	19.4887i	0.785857	+	1.57557i
$154$		0			0
$155$	−8.12252	+	1.43222i	−0.652417	+	0.115039i
$156$		0			0
$157$	−8.45553	+	10.0769i	−0.674825	+	0.804225i	−0.989432	−	0.144997i	$-0.953683\pi$
$157$	−8.45553	+	10.0769i	−0.674825	+	0.804225i	0.314607	+	0.949222i	$0.398127\pi$
$158$		0			0
$159$	10.2963	+	0.313771i	0.816551	+	0.0248837i
$160$		0			0
$161$	−1.55819	−	0.783626i	−0.122802	−	0.0617584i
$162$		0			0
$163$	−2.50840	+	4.34468i	−0.196473	+	0.340302i	−0.947383	−	0.320104i	$-0.896282\pi$
$163$	−2.50840	+	4.34468i	−0.196473	+	0.340302i	0.750909	+	0.660405i	$0.229616\pi$
$164$		0			0
$165$	−14.4499	+	23.3548i	−1.12492	+	1.81817i
$166$		0			0
$167$	3.96921	−	1.44467i	0.307147	−	0.111792i	−0.183848	−	0.982955i	$-0.558856\pi$
$167$	3.96921	−	1.44467i	0.307147	−	0.111792i	0.490995	+	0.871162i	$0.336633\pi$
$168$		0			0
$169$	0.772396	+	4.38048i	0.0594151	+	0.336960i
$170$		0			0
$171$	−5.81943	+	2.90260i	−0.445023	+	0.221968i
$172$		0			0
$173$	11.7887	−	9.89186i	0.896275	−	0.752064i	−0.0731834	−	0.997318i	$-0.523316\pi$
$173$	11.7887	−	9.89186i	0.896275	−	0.752064i	0.969459	+	0.245254i	$0.0788714\pi$
$174$		0			0
$175$	3.31470	−	28.2242i	0.250568	−	2.13355i
$176$		0			0
$177$	−7.31412	−	22.1749i	−0.549763	−	1.66677i
$178$		0			0
$179$		−	4.06742i		−	0.304013i	−0.988379	−	0.152007i	$-0.951426\pi$
$179$		−	4.06742i		−	0.304013i	0.988379	−	0.152007i	$-0.0485735\pi$
$180$		0			0
$181$	−6.60441	+	3.81306i	−0.490902	+	0.283422i	−0.724948	−	0.688803i	$-0.758136\pi$
$181$	−6.60441	+	3.81306i	−0.490902	+	0.283422i	0.234047	+	0.972225i	$0.424803\pi$
$182$		0			0
$183$	−14.4341	+	11.3807i	−1.06700	+	0.841289i
$184$		0			0
$185$	−0.701351	+	0.255271i	−0.0515644	+	0.0187679i
$186$		0			0
$187$	28.5716	−	5.03795i	2.08936	−	0.368411i
$188$		0			0
$189$	13.6117	−	1.92882i	0.990109	−	0.140301i
$190$		0			0
$191$	15.7820	−	2.78279i	1.14194	−	0.201356i	0.429488	−	0.903072i	$-0.358694\pi$
$191$	15.7820	−	2.78279i	1.14194	−	0.201356i	0.712456	+	0.701717i	$0.247583\pi$
$192$		0			0
$193$	17.2269	−	6.27007i	1.24002	−	0.451329i	0.363000	−	0.931789i	$-0.381752\pi$
$193$	17.2269	−	6.27007i	1.24002	−	0.451329i	0.877017	+	0.480460i	$0.159530\pi$
$194$		0			0
$195$	2.88519	+	19.8878i	0.206613	+	1.42420i
$196$		0			0
$197$	8.35914	−	4.82615i	0.595564	−	0.343849i	−0.171731	−	0.985144i	$-0.554936\pi$
$197$	8.35914	−	4.82615i	0.595564	−	0.343849i	0.767294	+	0.641295i	$0.221603\pi$
$198$		0			0
$199$			10.5741i			0.749581i	0.927110	+	0.374790i	$0.122285\pi$
$199$			10.5741i			0.749581i	−0.927110	+	0.374790i	$0.877715\pi$
$200$		0			0
$201$	−8.87579	+	9.94605i	−0.626050	+	0.701540i
$202$		0			0
$203$	12.9861	−	17.4232i	0.911443	−	1.22287i
$204$		0			0
$205$	3.69432	−	3.09990i	0.258022	−	0.216506i
$206$		0			0
$207$	−1.92310	−	0.461375i	−0.133664	−	0.0320678i
$208$		0			0
$209$	1.50436	+	8.53166i	0.104059	+	0.590147i
$210$		0			0
$211$	−17.5093	+	6.37285i	−1.20539	+	0.438725i	−0.865101	−	0.501597i	$-0.832746\pi$
$211$	−17.5093	+	6.37285i	−1.20539	+	0.438725i	−0.340286	+	0.940322i	$0.610524\pi$
$212$		0			0
$213$	0.874661	+	1.62752i	0.0599308	+	0.111516i
$214$		0			0
$215$	−1.15297	+	1.99701i	−0.0786320	+	0.136195i
$216$		0			0
$217$	4.59694	−	3.01983i	0.312061	−	0.204999i
$218$		0			0
$219$	−2.73210	−	5.08373i	−0.184618	−	0.343527i
$220$		0			0
$221$	13.6460	−	16.2626i	0.917926	−	1.09394i
$222$		0			0
$223$	−13.0786	+	2.30611i	−0.875808	+	0.154429i	−0.593440	−	0.804878i	$-0.702231\pi$
$223$	−13.0786	+	2.30611i	−0.875808	+	0.154429i	−0.282367	+	0.959306i	$0.591120\pi$
$224$		0			0
$225$	−3.65279	−	32.0154i	−0.243520	−	2.13436i
$226$		0			0
$227$	−2.26914	−	12.8689i	−0.150608	−	0.854141i	−0.962692	−	0.270600i	$-0.912778\pi$
$227$	−2.26914	−	12.8689i	−0.150608	−	0.854141i	0.812084	−	0.583541i	$-0.198333\pi$
$228$		0			0
$229$	4.91506	+	13.5040i	0.324796	+	0.892370i	0.989405	+	0.145179i	$0.0463758\pi$
$229$	4.91506	+	13.5040i	0.324796	+	0.892370i	−0.664609	+	0.747191i	$0.731402\pi$
$230$		0			0
$231$	2.68923	−	18.1157i	0.176939	−	1.19193i
$232$		0			0
$233$	−6.49516	+	3.74998i	−0.425512	+	0.245669i	−0.697433	−	0.716650i	$-0.745674\pi$
$233$	−6.49516	+	3.74998i	−0.425512	+	0.245669i	0.271921	+	0.962320i	$0.412341\pi$
$234$		0			0
$235$	−15.6829	+	27.1636i	−1.02304	+	1.77196i
$236$		0			0
$237$	9.17949	−	23.0138i	0.596272	−	1.49491i
$238$		0			0
$239$	−2.35845	−	0.415858i	−0.152555	−	0.0268996i	0.0968488	−	0.995299i	$-0.469124\pi$
$239$	−2.35845	−	0.415858i	−0.152555	−	0.0268996i	−0.249404	+	0.968399i	$0.580235\pi$
$240$		0			0
$241$	8.28691	−	22.7681i	0.533807	−	1.46662i	−0.320700	−	0.947181i	$-0.603918\pi$
$241$	8.28691	−	22.7681i	0.533807	−	1.46662i	0.854506	−	0.519441i	$-0.173860\pi$
$242$		0			0
$243$	14.5263	−	5.65556i	0.931865	−	0.362804i
$244$		0			0
$245$	7.93590	+	26.6145i	0.507006	+	1.70034i
$246$		0			0
$247$	4.85611	+	4.07476i	0.308987	+	0.259271i
$248$		0			0
$249$	−13.7004	+	1.98757i	−0.868229	+	0.125957i
$250$		0			0
$251$	14.5178	+	25.1456i	0.916356	+	1.58717i	0.804904	+	0.593405i	$0.202217\pi$
$251$	14.5178	+	25.1456i	0.916356	+	1.58717i	0.111452	+	0.993770i	$0.464450\pi$
$252$		0			0
$253$	−1.31729	+	2.28161i	−0.0828173	+	0.143444i
$254$		0			0
$255$	−33.2155	+	37.2207i	−2.08003	+	2.33085i
$256$		0			0
$257$	13.6563	−	4.97049i	0.851857	−	0.310051i	0.121060	−	0.992645i	$-0.461371\pi$
$257$	13.6563	−	4.97049i	0.851857	−	0.310051i	0.730797	+	0.682594i	$0.239148\pi$
$258$		0			0
$259$	0.362214	−	0.341354i	0.0225069	−	0.0212107i
$260$		0			0
$261$	9.82158	−	22.5978i	0.607940	−	1.39877i
$262$		0			0
$263$	−8.03518	−	9.57596i	−0.495471	−	0.590479i	0.459129	−	0.888369i	$-0.348161\pi$
$263$	−8.03518	−	9.57596i	−0.495471	−	0.590479i	−0.954600	+	0.297891i	$0.903717\pi$
$264$		0			0
$265$	8.07033	+	22.1730i	0.495756	+	1.36208i
$266$		0			0
$267$	−12.7621	−	7.89602i	−0.781025	−	0.483228i
$268$		0			0
$269$	9.04697	+	15.6698i	0.551604	+	0.955406i	0.998159	+	0.0606497i	$0.0193173\pi$
$269$	9.04697	+	15.6698i	0.551604	+	0.955406i	−0.446555	+	0.894756i	$0.647349\pi$
$270$		0			0
$271$	−10.9167	−	6.30277i	−0.663143	−	0.382866i	0.130330	−	0.991471i	$-0.458396\pi$
$271$	−10.9167	−	6.30277i	−0.663143	−	0.382866i	−0.793474	+	0.608605i	$0.791730\pi$
$272$		0			0
$273$	−7.01330	−	11.4195i	−0.424464	−	0.691138i
$274$		0			0
$275$	−42.2744	−	7.45412i	−2.54924	−	0.449500i
$276$		0			0
$277$	−12.1089	+	10.1606i	−0.727555	+	0.610491i	−0.929464	−	0.368914i	$-0.879730\pi$
$277$	−12.1089	+	10.1606i	−0.727555	+	0.610491i	0.201909	+	0.979404i	$0.435285\pi$
$278$		0			0
$279$	4.29224	−	4.52450i	0.256970	−	0.270875i
$280$		0			0
$281$	0.386386	−	1.06159i	0.0230499	−	0.0633290i	−0.927634	−	0.373490i	$-0.878161\pi$
$281$	0.386386	−	1.06159i	0.0230499	−	0.0633290i	0.950684	+	0.310161i	$0.100383\pi$
$282$		0			0
$283$	19.0304	+	3.35557i	1.13124	+	0.199468i	0.707770	−	0.706443i	$-0.249701\pi$
$283$	19.0304	+	3.35557i	1.13124	+	0.199468i	0.423469	+	0.905911i	$0.360812\pi$
$284$		0			0
$285$	−11.1143	−	9.91833i	−0.658355	−	0.587511i
$286$		0			0
$287$	−1.44491	+	2.87310i	−0.0852904	+	0.169594i
$288$		0			0
$289$	35.6997			2.09998
$290$		0			0
$291$	−13.8915	+	10.9529i	−0.814332	+	0.642071i
$292$		0			0
$293$	3.55249	−	20.1472i	0.207539	−	1.17701i	−0.685856	−	0.727738i	$-0.740572\pi$
$293$	3.55249	−	20.1472i	0.207539	−	1.17701i	0.893394	−	0.449273i	$-0.148317\pi$
$294$		0			0
$295$	40.9729	−	34.3804i	2.38554	−	2.00170i
$296$		0			0
$297$	−1.72451	−	20.6947i	−0.100066	−	1.20083i
$298$		0			0
$299$	0.334761	+	1.89852i	0.0193597	+	0.109794i
$300$		0			0
$301$	0.179362	−	1.52724i	0.0103382	−	0.0880285i
$302$		0			0
$303$	20.1141	−	2.91802i	1.15553	−	0.167636i
$304$		0			0
$305$	−36.4634	−	21.0522i	−2.08789	−	1.20544i
$306$		0			0
$307$	−24.4057	−	14.0906i	−1.39291	−	0.804194i	−0.399269	−	0.916834i	$-0.630736\pi$
$307$	−24.4057	−	14.0906i	−1.39291	−	0.804194i	−0.993636	+	0.112640i	$0.964069\pi$
$308$		0			0
$309$	8.24958	+	7.36187i	0.469302	+	0.418802i
$310$		0			0
$311$	−1.80190	+	10.2191i	−0.102176	+	0.579470i	0.890135	+	0.455698i	$0.150610\pi$
$311$	−1.80190	+	10.2191i	−0.102176	+	0.579470i	−0.992311	+	0.123772i	$0.960501\pi$
$312$		0			0
$313$	13.1554	+	15.6780i	0.743586	+	0.886171i	0.996692	−	0.0812672i	$-0.0258967\pi$
$313$	13.1554	+	15.6780i	0.743586	+	0.886171i	−0.253106	+	0.967438i	$0.581452\pi$
$314$		0			0
$315$	15.6554	+	27.3239i	0.882079	+	1.53953i
$316$		0			0
$317$	−1.39302	+	3.82728i	−0.0782396	+	0.214962i	−0.972645	−	0.232295i	$-0.925377\pi$
$317$	−1.39302	+	3.82728i	−0.0782396	+	0.214962i	0.894406	+	0.447256i	$0.147599\pi$
$318$		0			0
$319$	−25.1449	−	21.0991i	−1.40785	−	1.18132i
$320$		0			0
$321$	−10.5870	−	19.6996i	−0.590908	−	1.09953i
$322$		0			0
$323$			15.7364i			0.875598i
$324$		0			0
$325$	−27.2026	+	15.7054i	−1.50893	+	0.871179i
$326$		0			0
$327$	0.121586	−	3.98981i	0.00672373	−	0.220637i
$328$		0			0
$329$	2.43971	−	20.7737i	0.134506	−	1.14529i
$330$		0			0
$331$	3.67758	+	1.33853i	0.202138	+	0.0735722i	0.441105	−	0.897455i	$-0.354587\pi$
$331$	3.67758	+	1.33853i	0.202138	+	0.0735722i	−0.238967	+	0.971028i	$0.576809\pi$
$332$		0			0
$333$	0.311416	−	0.470659i	0.0170655	−	0.0257919i
$334$		0			0
$335$	−28.6939	−	10.4437i	−1.56772	−	0.570602i
$336$		0			0
$337$	7.46671	+	6.26531i	0.406737	+	0.341293i	0.823091	−	0.567910i	$-0.192248\pi$
$337$	7.46671	+	6.26531i	0.406737	+	0.341293i	−0.416354	+	0.909203i	$0.636692\pi$
$338$		0			0
$339$	−5.81289	+	27.9576i	−0.315713	+	1.51845i
$340$		0			0
$341$	−4.15406	−	7.19503i	−0.224955	−	0.389633i
$342$		0			0
$343$	−11.8811	−	14.2070i	−0.641520	−	0.767106i
$344$		0			0
$345$	−0.650390	−	4.48318i	−0.0350158	−	0.241366i
$346$		0			0
$347$	−0.307897	−	0.845941i	−0.0165288	−	0.0454125i	0.931154	−	0.364627i	$-0.118803\pi$
$347$	−0.307897	−	0.845941i	−0.0165288	−	0.0454125i	−0.947683	+	0.319214i	$0.896581\pi$
$348$		0			0
$349$	14.2878	+	17.0276i	0.764810	+	0.911465i	0.998142	−	0.0609324i	$-0.0194074\pi$
$349$	14.2878	+	17.0276i	0.764810	+	0.911465i	−0.233332	+	0.972397i	$0.574963\pi$
$350$		0			0
$351$	−10.7004	−	10.7891i	−0.571144	−	0.575879i
$352$		0			0
$353$	25.6896	+	9.35025i	1.36732	+	0.497663i	0.918309	−	0.395863i	$-0.129555\pi$
$353$	25.6896	+	9.35025i	1.36732	+	0.497663i	0.449010	+	0.893527i	$0.351777\pi$
$354$		0			0
$355$	−2.72048	+	3.24214i	−0.144388	+	0.172075i
$356$		0			0
$357$	10.5248	−	31.5582i	0.557031	−	1.67024i
$358$		0			0
$359$			2.55839i			0.135027i	0.997718	+	0.0675135i	$0.0215066\pi$
$359$			2.55839i			0.135027i	−0.997718	+	0.0675135i	$0.978493\pi$
$360$		0			0
$361$	14.3010			0.752685
$362$		0			0
$363$	−8.43143	−	1.75305i	−0.442535	−	0.0920112i
$364$		0			0
$365$	8.49772	−	10.1272i	0.444791	−	0.530082i
$366$		0			0
$367$	−5.82671	+	1.02741i	−0.304152	+	0.0536302i	−0.323641	−	0.946180i	$-0.604907\pi$
$367$	−5.82671	+	1.02741i	−0.304152	+	0.0536302i	0.0194893	+	0.999810i	$0.493796\pi$
$368$		0			0
$369$	−0.850718	+	3.54595i	−0.0442866	+	0.184595i
$370$		0			0
$371$	−10.7918	−	11.4513i	−0.560284	−	0.594522i
$372$		0			0
$373$	−3.00818	+	17.0603i	−0.155758	+	0.883346i	0.802332	+	0.596878i	$0.203592\pi$
$373$	−3.00818	+	17.0603i	−0.155758	+	0.883346i	−0.958090	+	0.286468i	$0.907519\pi$
$374$		0			0
$375$	34.7514	−	18.6761i	1.79455	−	0.964430i
$376$		0			0
$377$	−24.0187			−1.23703
$378$		0			0
$379$	−33.5463			−1.72316			−0.861579	−	0.507623i	$-0.830524\pi$
$379$	−33.5463			−1.72316			−0.861579	+	0.507623i	$0.830524\pi$
$380$		0			0
$381$	−0.316405	+	10.3827i	−0.0162099	+	0.531924i
$382$		0			0
$383$	0.383922	−	2.17733i	0.0196175	−	0.111256i	−0.973427	−	0.228999i	$-0.926455\pi$
$383$	0.383922	−	2.17733i	0.0196175	−	0.111256i	0.993044	+	0.117743i	$0.0375658\pi$
$384$		0			0
$385$	40.8258	−	9.65213i	2.08068	−	0.491918i
$386$		0			0
$387$	−0.197656	−	1.73239i	−0.0100474	−	0.0880621i
$388$		0			0
$389$	−33.7290	+	5.94734i	−1.71013	+	0.301542i	−0.941215	−	0.337808i	$-0.890315\pi$
$389$	−33.7290	+	5.94734i	−1.71013	+	0.301542i	−0.768916	+	0.639350i	$0.779203\pi$
$390$		0			0
$391$	−3.07612	+	3.66597i	−0.155566	+	0.185396i
$392$		0			0
$393$	3.56425	+	10.8061i	0.179793	+	0.545095i
$394$		0			0
$395$	56.7551			2.85566
$396$		0			0
$397$		−	21.5352i		−	1.08082i	−0.841401	−	0.540411i	$-0.818269\pi$
$397$		−	21.5352i		−	1.08082i	0.841401	−	0.540411i	$-0.181731\pi$
$398$		0			0
$399$	9.42347	+	3.14277i	0.471764	+	0.157335i
$400$		0			0
$401$	−16.6603	+	19.8550i	−0.831975	+	0.991509i	0.168008	+	0.985786i	$0.446266\pi$
$401$	−16.6603	+	19.8550i	−0.831975	+	0.991509i	−0.999984	+	0.00572381i	$0.998178\pi$
$402$		0			0
$403$	−5.71270	−	2.07925i	−0.284570	−	0.103575i
$404$		0			0
$405$	24.3607	+	26.1072i	1.21049	+	1.29727i
$406$		0			0
$407$	−0.483259	−	0.575926i	−0.0239543	−	0.0285476i
$408$		0			0
$409$	3.98666	+	10.9532i	0.197127	+	0.541603i	0.998391	−	0.0567086i	$-0.0180606\pi$
$409$	3.98666	+	10.9532i	0.197127	+	0.541603i	−0.801263	+	0.598312i	$0.795838\pi$
$410$		0			0
$411$	21.8168	−	17.2018i	1.07615	−	0.848502i
$412$		0			0
$413$	−16.0252	+	31.8650i	−0.788549	+	1.56797i
$414$		0			0
$415$	−15.8556	−	27.4627i	−0.778321	−	1.34809i
$416$		0			0
$417$	29.0112	+	25.8894i	1.42068	+	1.26781i
$418$		0			0
$419$	−6.52747	−	5.47720i	−0.318888	−	0.267579i	0.469266	−	0.883057i	$-0.344518\pi$
$419$	−6.52747	−	5.47720i	−0.318888	−	0.267579i	−0.788154	+	0.615478i	$0.788963\pi$
$420$		0			0
$421$	21.6891	+	7.89419i	1.05706	+	0.384739i	0.811324	−	0.584597i	$-0.198747\pi$
$421$	21.6891	+	7.89419i	1.05706	+	0.384739i	0.245739	+	0.969336i	$0.420969\pi$
$422$		0			0
$423$	−2.68855	−	23.5642i	−0.130722	−	1.14573i
$424$		0			0
$425$	−73.2717	−	26.6687i	−3.55420	−	1.29362i
$426$		0			0
$427$	27.8859	+	3.27498i	1.34949	+	0.158487i
$428$		0			0
$429$	−17.8310	+	9.58276i	−0.860890	+	0.462660i
$430$		0			0
$431$	4.15301	−	2.39774i	0.200043	−	0.115495i	−0.396632	−	0.917978i	$-0.629821\pi$
$431$	4.15301	−	2.39774i	0.200043	−	0.115495i	0.596676	+	0.802482i	$0.296488\pi$
$432$		0			0
$433$			21.7041i			1.04303i	0.853242	+	0.521516i	$0.174633\pi$
$433$			21.7041i			1.04303i	−0.853242	+	0.521516i	$0.825367\pi$
$434$		0			0
$435$	56.4148	+	1.71919i	2.70488	+	0.0824290i
$436$		0			0
$437$	−1.09468	−	0.918547i	−0.0523657	−	0.0439401i
$438$		0			0
$439$	−6.09546	+	16.7471i	−0.290921	+	0.799298i	0.705012	+	0.709195i	$0.250942\pi$
$439$	−6.09546	+	16.7471i	−0.290921	+	0.799298i	−0.995933	+	0.0901022i	$0.971281\pi$
$440$		0			0
$441$	−16.7961	−	12.6052i	−0.799816	−	0.600246i
$442$		0			0
$443$	14.9000	+	17.7571i	0.707919	+	0.843666i	0.993398	−	0.114720i	$-0.0365969\pi$
$443$	14.9000	+	17.7571i	0.707919	+	0.843666i	−0.285478	+	0.958385i	$0.592153\pi$
$444$		0			0
$445$	5.96935	−	33.8539i	0.282974	−	1.60483i
$446$		0			0
$447$	0.767452	−	3.69112i	0.0362992	−	0.174584i
$448$		0			0
$449$	10.5855	+	6.11156i	0.499563	+	0.288423i	0.728533	−	0.685011i	$-0.240203\pi$
$449$	10.5855	+	6.11156i	0.499563	+	0.288423i	−0.228970	+	0.973433i	$0.573536\pi$
$450$		0			0
$451$	4.20701	+	2.42892i	0.198100	+	0.114373i
$452$		0			0
$453$	13.3982	−	33.5906i	0.629503	−	1.57822i
$454$		0			0
$455$	18.3446	−	24.6128i	0.860010	−	1.15387i
$456$		0			0
$457$	2.69680	+	15.2943i	0.126151	+	0.715438i	0.980618	+	0.195932i	$0.0627731\pi$
$457$	2.69680	+	15.2943i	0.126151	+	0.715438i	−0.854467	+	0.519506i	$0.826116\pi$
$458$		0			0
$459$	3.44270	−	37.5638i	0.160691	−	1.75333i
$460$		0			0
$461$	26.6254	−	22.3413i	1.24007	−	1.04054i	0.242547	−	0.970140i	$-0.422017\pi$
$461$	26.6254	−	22.3413i	1.24007	−	1.04054i	0.997519	−	0.0703997i	$-0.0224275\pi$
$462$		0			0
$463$	4.43131	−	25.1312i	0.205941	−	1.16795i	−0.690012	−	0.723798i	$-0.742395\pi$
$463$	4.43131	−	25.1312i	0.205941	−	1.16795i	0.895953	−	0.444149i	$-0.146494\pi$
$464$		0			0
$465$	13.2691	+	5.29261i	0.615338	+	0.245439i
$466$		0			0
$467$	−13.5982			−0.629249			−0.314625	−	0.949216i	$-0.601879\pi$
$467$	−13.5982			−0.629249			−0.314625	+	0.949216i	$0.601879\pi$
$468$		0			0
$469$	20.3289	−	1.17278i	0.938704	−	0.0541541i
$470$		0			0
$471$	21.6376	−	7.13689i	0.997008	−	0.328851i
$472$		0			0
$473$	−2.28751	−	0.403350i	−0.105180	−	0.0185460i
$474$		0			0
$475$	7.96344	−	21.8794i	0.365388	−	1.00389i
$476$		0			0
$477$	−14.8798	−	9.84533i	−0.681297	−	0.450787i
$478$		0			0
$479$	−19.3576	+	16.2429i	−0.884470	+	0.742159i	−0.967093	−	0.254422i	$-0.918115\pi$
$479$	−19.3576	+	16.2429i	−0.884470	+	0.742159i	0.0826230	+	0.996581i	$0.473670\pi$
$480$		0			0
$481$	−0.541772	−	0.0955291i	−0.0247027	−	0.00435575i
$482$		0			0
$483$	1.58096	+	2.57422i	0.0719363	+	0.117131i
$484$		0			0
$485$	−35.0927	−	20.2608i	−1.59348	−	0.919995i
$486$		0			0
$487$	4.72827	+	8.18961i	0.214258	+	0.371107i	0.953043	−	0.302835i	$-0.0979332\pi$
$487$	4.72827	+	8.18961i	0.214258	+	0.371107i	−0.738784	+	0.673942i	$0.764600\pi$
$488$		0			0
$489$	7.65406	−	4.11345i	0.346128	−	0.186017i
$490$		0			0
$491$	11.9824	+	32.9213i	0.540757	+	1.48572i	0.845863	+	0.533400i	$0.179086\pi$
$491$	11.9824	+	32.9213i	0.540757	+	1.48572i	−0.305106	+	0.952319i	$0.598692\pi$
$492$		0			0
$493$	−38.3256	−	45.6746i	−1.72610	−	2.05708i
$494$		0			0
$495$	42.5672	−	21.2316i	1.91325	−	0.954288i
$496$		0			0
$497$	0.810948	−	2.70333i	0.0363760	−	0.121261i
$498$		0			0
$499$	−27.3282	+	9.94666i	−1.22338	+	0.445274i	−0.871325	−	0.490706i	$-0.836739\pi$
$499$	−27.3282	+	9.94666i	−1.22338	+	0.445274i	−0.352054	+	0.935980i	$0.614517\pi$
$500$		0			0
$501$	−7.16290	−	1.48930i	−0.320015	−	0.0665369i
$502$		0			0
$503$	4.77536	−	8.27117i	0.212923	−	0.368793i	−0.739705	−	0.672931i	$-0.765035\pi$
$503$	4.77536	−	8.27117i	0.212923	−	0.368793i	0.952628	+	0.304138i	$0.0983684\pi$
$504$		0			0
$505$	23.2782	+	40.3191i	1.03587	+	1.79418i
$506$		0			0
$507$	2.85431	−	7.15601i	0.126764	−	0.317809i
$508$		0			0
$509$	−15.5398	−	13.0395i	−0.688791	−	0.577964i	0.229770	−	0.973245i	$-0.426203\pi$
$509$	−15.5398	−	13.0395i	−0.688791	−	0.577964i	−0.918560	+	0.395281i	$0.870647\pi$
$510$		0			0
$511$	−2.53309	+	8.44416i	−0.112057	+	0.373548i
$512$		0			0
$513$	11.2168	+	1.02801i	0.495233	+	0.0453878i
$514$		0			0
$515$	−8.66237	+	23.7997i	−0.381710	+	1.04874i
$516$		0			0
$517$	−31.1151	−	5.48643i	−1.36844	−	0.241293i
$518$		0			0
$519$	−26.3784	+	3.82680i	−1.15788	+	0.167978i
$520$		0			0
$521$	7.07494	−	12.2542i	0.309959	−	0.536864i	−0.668394	−	0.743807i	$-0.733018\pi$
$521$	7.07494	−	12.2542i	0.309959	−	0.536864i	0.978353	+	0.206943i	$0.0663514\pi$
$522$		0			0
$523$	−27.6390	+	15.9574i	−1.20857	+	0.697767i	−0.962446	−	0.271472i	$-0.912489\pi$
$523$	−27.6390	+	15.9574i	−1.20857	+	0.697767i	−0.246121	+	0.969239i	$0.579156\pi$
$524$		0			0
$525$	−30.6034	+	38.5513i	−1.33564	+	1.68252i
$526$		0			0
$527$	−5.16153	−	14.1812i	−0.224840	−	0.617742i
$528$		0			0
$529$	3.91845	+	22.2226i	0.170367	+	0.966200i
$530$		0			0
$531$	−9.43514	+	39.3274i	−0.409450	+	1.70666i
$532$		0			0
$533$	3.50064	−	0.617257i	0.151630	−	0.0267364i
$534$		0			0
$535$	32.9290	−	39.2432i	1.42364	−	1.69663i
$536$		0			0
$537$	−3.70670	+	5.99101i	−0.159956	+	0.258531i
$538$		0			0
$539$	−22.4582	+	16.6811i	−0.967343	+	0.718504i
$540$		0			0
$541$	6.59562	−	11.4239i	0.283568	−	0.491154i	−0.688693	−	0.725053i	$-0.741815\pi$
$541$	6.59562	−	11.4239i	0.283568	−	0.491154i	0.972261	+	0.233899i	$0.0751486\pi$
$542$		0			0
$543$	13.2027	+	0.402340i	0.566581	+	0.0172661i
$544$		0			0
$545$	8.59204	−	3.12725i	0.368043	−	0.133957i
$546$		0			0
$547$	1.86468	+	10.5751i	0.0797281	+	0.452161i	0.998370	+	0.0570699i	$0.0181758\pi$
$547$	1.86468	+	10.5751i	0.0797281	+	0.452161i	−0.918642	+	0.395091i	$0.870713\pi$
$548$		0			0
$549$	31.6317	−	3.60902i	1.35001	−	0.154029i
$550$		0			0
$551$	13.6387	−	11.4442i	0.581029	−	0.487541i
$552$		0			0
$553$	−34.7604	+	14.9715i	−1.47816	+	0.636651i
$554$		0			0
$555$	1.26567	+	0.263156i	0.0537247	+	0.0111703i
$556$		0			0
$557$			32.7388i			1.38719i	0.720367	+	0.693593i	$0.243974\pi$
$557$			32.7388i			1.38719i	−0.720367	+	0.693593i	$0.756026\pi$
$558$		0			0
$559$	−1.47196	+	0.849835i	−0.0622571	+	0.0359442i
$560$		0			0
$561$	−46.6750	−	18.6172i	−1.97062	−	0.786018i
$562$		0			0
$563$	−8.37882	+	3.04964i	−0.353125	+	0.128527i	−0.512491	−	0.858693i	$-0.671277\pi$
$563$	−8.37882	+	3.04964i	−0.353125	+	0.128527i	0.159366	+	0.987220i	$0.449055\pi$
$564$		0			0
$565$	−64.4165	+	11.3584i	−2.71002	+	0.477850i
$566$		0			0
$567$	−21.8068	−	9.56357i	−0.915801	−	0.401632i
$568$		0			0
$569$	−27.9792	+	4.93349i	−1.17295	+	0.206823i	−0.725973	−	0.687723i	$-0.758610\pi$
$569$	−27.9792	+	4.93349i	−1.17295	+	0.206823i	−0.446976	+	0.894546i	$0.647499\pi$
$570$		0			0
$571$	9.22186	−	3.35648i	0.385923	−	0.140464i	−0.141770	−	0.989900i	$-0.545279\pi$
$571$	9.22186	−	3.35648i	0.385923	−	0.140464i	0.527693	+	0.849435i	$0.323057\pi$
$572$		0			0
$573$	−25.7817	−	10.2835i	−1.07704	−	0.429599i
$574$		0			0
$575$	6.13209	−	3.54037i	0.255726	−	0.147643i
$576$		0			0
$577$			2.15118i			0.0895546i	0.998997	+	0.0447773i	$0.0142578\pi$
$577$			2.15118i			0.0895546i	−0.998997	+	0.0447773i	$0.985742\pi$
$578$		0			0
$579$	−31.0879	−	6.46374i	−1.29197	−	0.268624i
$580$		0			0
$581$	16.9554	+	12.6374i	0.703428	+	0.524286i
$582$		0			0
$583$	−18.2077	+	15.2781i	−0.754088	+	0.632755i
$584$		0			0
$585$	13.8744	−	31.9226i	0.573635	−	1.31984i
$586$		0			0
$587$	−6.62516	−	37.5732i	−0.273450	−	1.55081i	−0.743844	−	0.668354i	$-0.766999\pi$
$587$	−6.62516	−	37.5732i	−0.273450	−	1.55081i	0.470394	−	0.882456i	$-0.344112\pi$
$588$		0			0
$589$	4.23458	−	1.54126i	0.174483	−	0.0635066i
$590$		0			0
$591$	−16.7105	−	0.509238i	−0.687379	−	0.0209473i
$592$		0			0
$593$	8.09994	−	14.0295i	0.332625	−	0.576123i	−0.650401	−	0.759591i	$-0.725399\pi$
$593$	8.09994	−	14.0295i	0.332625	−	0.576123i	0.983026	+	0.183468i	$0.0587324\pi$
$594$		0			0
$595$	76.0761	−	4.38885i	3.11882	−	0.179925i
$596$		0			0
$597$	9.63635	−	15.5749i	0.394390	−	0.637439i
$598$		0			0
$599$	13.0624	−	15.5671i	0.533714	−	0.636056i	−0.430052	−	0.902804i	$-0.641505\pi$
$599$	13.0624	−	15.5671i	0.533714	−	0.636056i	0.963766	+	0.266748i	$0.0859492\pi$
$600$		0			0
$601$	5.94613	−	1.04846i	0.242548	−	0.0427677i	−0.0510527	−	0.998696i	$-0.516258\pi$
$601$	5.94613	−	1.04846i	0.242548	−	0.0427677i	0.293600	+	0.955928i	$0.405147\pi$
$602$		0			0
$603$	22.1373	−	6.56116i	0.901502	−	0.267191i
$604$		0			0
$605$	−3.42545	−	19.4267i	−0.139264	−	0.789807i
$606$		0			0
$607$	0.239855	+	0.658996i	0.00973542	+	0.0267478i	0.944465	−	0.328612i	$-0.106581\pi$
$607$	0.239855	+	0.658996i	0.00973542	+	0.0267478i	−0.934730	+	0.355359i	$0.884358\pi$
$608$		0			0
$609$	−35.0055	+	13.8288i	−1.41850	+	0.560370i
$610$		0			0
$611$	−20.0218	+	11.5596i	−0.809996	+	0.467651i
$612$		0			0
$613$	−16.1127	+	27.9080i	−0.650785	+	1.12719i	0.332148	+	0.943227i	$0.392227\pi$
$613$	−16.1127	+	27.9080i	−0.650785	+	1.12719i	−0.982933	+	0.183965i	$0.941107\pi$
$614$		0			0
$615$	−8.26643	+	1.19924i	−0.333335	+	0.0483580i
$616$		0			0
$617$	18.1880	+	3.20704i	0.732222	+	0.129110i	0.527314	−	0.849671i	$-0.323199\pi$
$617$	18.1880	+	3.20704i	0.732222	+	0.129110i	0.204908	+	0.978781i	$0.434310\pi$
$618$		0			0
$619$	−3.07549	+	8.44985i	−0.123615	+	0.339628i	−0.986029	−	0.166575i	$-0.946729\pi$
$619$	−3.07549	+	8.44985i	−0.123615	+	0.339628i	0.862414	+	0.506203i	$0.168951\pi$
$620$		0			0
$621$	2.41212	+	2.43211i	0.0967949	+	0.0975973i
$622$		0			0
$623$	5.27433	+	22.3089i	0.211311	+	0.893789i
$624$		0			0
$625$	28.0869	+	23.5677i	1.12348	+	0.942709i
$626$		0			0
$627$	5.55920	−	13.9374i	0.222013	−	0.556607i
$628$		0			0
$629$	−0.682821	−	1.18268i	−0.0272259	−	0.0471566i
$630$		0			0
$631$	−5.62050	+	9.73499i	−0.223749	+	0.387544i	−0.955943	−	0.293552i	$-0.905163\pi$
$631$	−5.62050	+	9.73499i	−0.223749	+	0.387544i	0.732195	+	0.681095i	$0.238496\pi$
$632$		0			0
$633$	31.5975	+	6.56970i	1.25589	+	0.261122i
$634$		0			0
$635$	−22.3592	+	8.13807i	−0.887296	+	0.322949i
$636$		0			0
$637$	−4.74280	+	19.9136i	−0.187917	+	0.789005i
$638$		0			0
$639$	0.194868	−	3.19430i	0.00770886	−	0.126365i
$640$		0			0
$641$	−10.7267	−	12.7836i	−0.423679	−	0.504920i	0.511409	−	0.859338i	$-0.329124\pi$
$641$	−10.7267	−	12.7836i	−0.423679	−	0.504920i	−0.935087	+	0.354417i	$0.884679\pi$
$642$		0			0
$643$	7.25386	+	19.9298i	0.286064	+	0.785955i	0.996607	+	0.0823015i	$0.0262270\pi$
$643$	7.25386	+	19.9298i	0.286064	+	0.785955i	−0.710543	+	0.703654i	$0.751551\pi$
$644$		0			0
$645$	3.51814	−	1.89072i	0.138527	−	0.0744470i
$646$		0			0
$647$	−15.2203	−	26.3623i	−0.598371	−	1.03641i	−0.993062	−	0.117595i	$-0.962482\pi$
$647$	−15.2203	−	26.3623i	−0.598371	−	1.03641i	0.394691	−	0.918814i	$-0.370852\pi$
$648$		0			0
$649$	46.6591	+	26.9386i	1.83153	+	1.05743i
$650$		0			0
$651$	−9.52296	+	0.258723i	−0.373234	+	0.0101402i
$652$		0			0
$653$	2.31357	+	0.407944i	0.0905369	+	0.0159641i	0.218733	−	0.975785i	$-0.429808\pi$
$653$	2.31357	+	0.407944i	0.0905369	+	0.0159641i	−0.128196	+	0.991749i	$0.540919\pi$
$654$		0			0
$655$	−19.9666	+	16.7540i	−0.780159	+	0.654631i
$656$		0			0
$657$	−0.608692	+	9.97776i	−0.0237473	+	0.389269i
$658$		0			0
$659$	16.2406	−	44.6206i	0.632643	−	1.73817i	−0.0410456	−	0.999157i	$-0.513069\pi$
$659$	16.2406	−	44.6206i	0.632643	−	1.73817i	0.673689	−	0.739015i	$-0.264709\pi$
$660$		0			0
$661$	−7.28366	−	1.28431i	−0.283302	−	0.0499537i	0.0301917	−	0.999544i	$-0.490388\pi$
$661$	−7.28366	−	1.28431i	−0.283302	−	0.0499537i	−0.313493	+	0.949590i	$0.601499\pi$
$662$		0			0
$663$	−34.9198	+	11.5179i	−1.35617	+	0.447317i
$664$		0			0
$665$	1.31054	+	22.7168i	0.0508204	+	0.880919i
$666$		0			0
$667$	5.41438			0.209646
$668$		0			0
$669$	21.3654	+	8.52198i	0.826033	+	0.329479i
$670$		0			0
$671$	7.36478	−	41.7678i	0.284314	−	1.61243i
$672$		0			0
$673$	−14.2500	+	11.9572i	−0.549297	+	0.460915i	−0.874703	−	0.484660i	$-0.838943\pi$
$673$	−14.2500	+	11.9572i	−0.549297	+	0.460915i	0.325406	+	0.945574i	$0.394499\pi$
$674$		0			0
$675$	−23.7958	+	50.4852i	−0.915901	+	1.94317i
$676$		0			0
$677$	−5.37940	−	30.5081i	−0.206747	−	1.17252i	−0.894667	−	0.446735i	$-0.852587\pi$
$677$	−5.37940	−	30.5081i	−0.206747	−	1.17252i	0.687919	−	0.725787i	$-0.258524\pi$
$678$		0			0
$679$	26.8376	+	3.15186i	1.02993	+	0.120957i
$680$		0			0
$681$	−8.38536	+	21.0229i	−0.321328	+	0.805598i
$682$		0			0
$683$	−1.32267	−	0.763644i	−0.0506106	−	0.0292200i	0.474481	−	0.880266i	$-0.342636\pi$
$683$	−1.32267	−	0.763644i	−0.0506106	−	0.0292200i	−0.525092	+	0.851046i	$0.675969\pi$
$684$		0			0
$685$	55.1138	+	31.8200i	2.10579	+	1.21578i
$686$		0			0
$687$	5.06688	−	24.3695i	0.193313	−	0.929756i
$688$		0			0
$689$	−3.02013	+	17.1280i	−0.115058	+	0.652525i
$690$		0			0
$691$	29.8290	+	35.5488i	1.13475	+	1.35234i	0.927400	+	0.374071i	$0.122038\pi$
$691$	29.8290	+	35.5488i	1.13475	+	1.35234i	0.207347	+	0.978267i	$0.433517\pi$
$692$		0			0
$693$	−20.4702	+	24.2324i	−0.777597	+	0.920512i
$694$		0			0
$695$	−30.4628	+	83.6960i	−1.15552	+	3.17477i
$696$		0			0
$697$	6.75961	+	5.67198i	0.256038	+	0.214842i
$698$		0			0
$699$	12.9843	+	0.395685i	0.491111	+	0.0149662i
$700$		0			0
$701$			13.6944i			0.517231i	0.965980	+	0.258615i	$0.0832662\pi$
$701$			13.6944i			0.517231i	−0.965980	+	0.258615i	$0.916734\pi$
$702$		0			0
$703$	0.353155	−	0.203894i	0.0133195	−	0.00769002i
$704$		0			0
$705$	47.8544	−	25.7179i	1.80230	−	0.968593i
$706$		0			0
$707$	−24.8929	−	18.5534i	−0.936193	−	0.697772i
$708$		0			0
$709$	42.3406	+	15.4107i	1.59013	+	0.578761i	0.977376	−	0.211510i	$-0.0678380\pi$
$709$	42.3406	+	15.4107i	1.59013	+	0.578761i	0.612757	+	0.790271i	$0.290060\pi$
$710$		0			0
$711$	−34.4935	+	25.5322i	−1.29361	+	0.957534i
$712$		0			0
$713$	1.28778	+	0.468712i	0.0482276	+	0.0175534i
$714$		0			0
$715$	−35.5208	−	29.8055i	−1.32840	−	1.11466i
$716$		0			0
$717$	3.09484	+	2.76181i	0.115579	+	0.103142i
$718$		0			0
$719$	6.57011	+	11.3798i	0.245024	+	0.424394i	0.962138	−	0.272562i	$-0.0878709\pi$
$719$	6.57011	+	11.3798i	0.245024	+	0.424394i	−0.717115	+	0.696955i	$0.754538\pi$
$720$		0			0
$721$	−0.972744	−	16.8615i	−0.0362269	−	0.627955i
$722$		0			0
$723$	−32.9549	+	25.9837i	−1.22560	+	0.966345i
$724$		0			0
$725$	30.1728	+	82.8991i	1.12059	+	3.07879i
$726$		0			0
$727$	25.2352	+	30.0742i	0.935922	+	1.11539i	0.993129	+	0.117026i	$0.0373361\pi$
$727$	25.2352	+	30.0742i	0.935922	+	1.11539i	−0.0572067	+	0.998362i	$0.518219\pi$
$728$		0			0
$729$	−26.5502	−	4.90784i	−0.983341	−	0.181772i
$730$		0			0
$731$	−3.96480	−	1.44307i	−0.146644	−	0.0533739i
$732$		0			0
$733$	2.95168	−	3.51767i	0.109023	−	0.129928i	−0.708773	−	0.705436i	$-0.750751\pi$
$733$	2.95168	−	3.51767i	0.109023	−	0.129928i	0.817796	+	0.575508i	$0.195196\pi$
$734$		0			0
$735$	12.5652	−	46.4333i	0.463474	−	1.71272i
$736$		0			0
$737$		−	30.7586i		−	1.13301i
$738$		0			0
$739$	1.73047			0.0636564			0.0318282	−	0.999493i	$-0.489867\pi$
$739$	1.73047			0.0636564			0.0318282	+	0.999493i	$0.489867\pi$
$740$		0			0
$741$	−3.43930	−	10.4273i	−0.126346	−	0.383055i
$742$		0			0
$743$	−8.04882	+	9.59220i	−0.295282	+	0.351904i	−0.893205	−	0.449650i	$-0.851549\pi$
$743$	−8.04882	+	9.59220i	−0.295282	+	0.351904i	0.597922	+	0.801554i	$0.295993\pi$
$744$		0			0
$745$	8.50464	−	1.49960i	0.311586	−	0.0549410i
$746$		0			0
$747$	21.9910	+	9.55784i	0.804608	+	0.349703i
$748$		0			0
$749$	−9.81580	+	32.7214i	−0.358661	+	1.19561i
$750$		0			0
$751$	7.15576	−	40.5823i	0.261117	−	1.48087i	−0.518751	−	0.854926i	$-0.673603\pi$
$751$	7.15576	−	40.5823i	0.261117	−	1.48087i	0.779868	−	0.625944i	$-0.215286\pi$
$752$		0			0
$753$	1.53187	−	50.2678i	0.0558244	−	1.83186i
$754$		0			0
$755$	82.8387			3.01481
$756$		0			0
$757$	−20.9608			−0.761832			−0.380916	−	0.924610i	$-0.624391\pi$
$757$	−20.9608			−0.761832			−0.380916	+	0.924610i	$0.624391\pi$
$758$		0			0
$759$	4.01953	−	2.16018i	0.145900	−	0.0784095i
$760$		0			0
$761$	−5.11286	+	28.9965i	−0.185341	+	1.05112i	0.740175	+	0.672414i	$0.234742\pi$
$761$	−5.11286	+	28.9965i	−0.185341	+	1.05112i	−0.925516	+	0.378707i	$0.876369\pi$
$762$		0			0
$763$	−4.43737	+	4.18183i	−0.160644	+	0.151392i
$764$		0			0
$765$	82.8436	−	24.5535i	2.99521	−	0.887735i
$766$		0			0
$767$	38.8249	−	6.84588i	1.40189	−	0.247190i
$768$		0			0
$769$	−32.3467	+	38.5493i	−1.16645	+	1.39012i	−0.261178	+	0.965291i	$0.584111\pi$
$769$	−32.3467	+	38.5493i	−1.16645	+	1.39012i	−0.905272	+	0.424832i	$0.860333\pi$
$770$		0			0
$771$	−24.6444	−	5.12402i	−0.887546	−	0.184537i
$772$		0			0
$773$	25.1223			0.903587			0.451793	−	0.892123i	$-0.350784\pi$
$773$	25.1223			0.903587			0.451793	+	0.892123i	$0.350784\pi$
$774$		0			0
$775$			22.3290i			0.802081i
$776$		0			0
$777$	−0.844595	+	0.172698i	−0.0302997	+	0.00619552i
$778$		0			0
$779$	−1.69369	+	2.01846i	−0.0606827	+	0.0723188i
$780$		0			0
$781$	−4.00614	−	1.45812i	−0.143351	−	0.0521755i
$782$		0			0
$783$	−35.0601	+	24.3343i	−1.25295	+	0.869637i
$784$		0			0
$785$	33.5473	+	39.9801i	1.19736	+	1.42695i
$786$		0			0
$787$	−4.03975	−	11.0991i	−0.144001	−	0.395641i	0.846634	−	0.532176i	$-0.178626\pi$
$787$	−4.03975	−	11.0991i	−0.144001	−	0.395641i	−0.990635	+	0.136535i	$0.956403\pi$
$788$		0			0
$789$	3.10852	+	21.4272i	0.110666	+	0.762830i
$790$		0			0
$791$	36.4565	−	23.9490i	1.29624	−	0.851530i
$792$		0			0
$793$	−15.5172	−	26.8765i	−0.551031	−	0.954414i
$794$		0			0
$795$	8.31961	−	40.0138i	0.295066	−	1.41914i
$796$		0			0
$797$	−25.6797	−	21.5478i	−0.909621	−	0.763262i	0.0624261	−	0.998050i	$-0.480116\pi$
$797$	−25.6797	−	21.5478i	−0.909621	−	0.763262i	−0.972047	+	0.234787i	$0.924561\pi$
$798$		0			0
$799$	−53.9300	−	19.6289i	−1.90790	−	0.694421i
$800$		0			0
$801$	11.6018	+	23.2605i	0.409930	+	0.821869i
$802$		0			0
$803$	12.5136	+	4.55459i	0.441597	+	0.160728i
$804$		0			0
$805$	−4.13531	+	5.54830i	−0.145751	+	0.195552i
$806$		0			0
$807$	0.954605	−	31.3251i	0.0336037	−	1.10270i
$808$		0			0
$809$	24.0879	−	13.9072i	0.846887	−	0.488950i	−0.0127126	−	0.999919i	$-0.504047\pi$
$809$	24.0879	−	13.9072i	0.846887	−	0.488950i	0.859599	+	0.510969i	$0.170713\pi$
$810$		0			0
$811$		−	15.5701i		−	0.546741i	−0.961909	−	0.273371i	$-0.911861\pi$
$811$		−	15.5701i		−	0.546741i	0.961909	−	0.273371i	$-0.0881385\pi$
$812$		0			0
$813$	10.3357	+	19.2321i	0.362489	+	0.674497i
$814$		0			0
$815$	15.2475	+	12.7942i	0.534096	+	0.448160i
$816$		0			0
$817$	0.430909	−	1.18391i	0.0150756	−	0.0414199i
$818$		0			0
$819$	−0.0766675	+	23.2114i	−0.00267898	+	0.811070i
$820$		0			0
$821$	−3.92828	−	4.68154i	−0.137098	−	0.163387i	0.693127	−	0.720815i	$-0.256232\pi$
$821$	−3.92828	−	4.68154i	−0.137098	−	0.163387i	−0.830225	+	0.557429i	$0.811788\pi$
$822$		0			0
$823$	−2.25795	+	12.8055i	−0.0787072	+	0.446371i	0.919831	+	0.392315i	$0.128326\pi$
$823$	−2.25795	+	12.8055i	−0.0787072	+	0.446371i	−0.998538	+	0.0540552i	$0.982785\pi$
$824$		0			0
$825$	55.4740	+	49.5046i	1.93136	+	1.72353i
$826$		0			0
$827$	−2.45676	−	1.41841i	−0.0854297	−	0.0493229i	0.456677	−	0.889633i	$-0.349040\pi$
$827$	−2.45676	−	1.41841i	−0.0854297	−	0.0493229i	−0.542106	+	0.840310i	$0.682373\pi$
$828$		0			0
$829$	−42.1583	−	24.3401i	−1.46422	−	0.845366i	−0.465015	−	0.885303i	$-0.653951\pi$
$829$	−42.1583	−	24.3401i	−1.46422	−	0.845366i	−0.999202	+	0.0399371i	$0.987284\pi$
$830$		0			0
$831$	27.0950	−	3.93076i	0.939916	−	0.136357i
$832$		0			0
$833$	−45.4361	+	22.7562i	−1.57427	+	0.788455i
$834$		0			0
$835$	−2.91008	−	16.5039i	−0.100708	−	0.571141i
$836$		0			0
$837$	−10.4454	+	2.75267i	−0.361046	+	0.0951464i
$838$		0			0
$839$	−9.21649	+	7.73356i	−0.318189	+	0.266992i	−0.787867	−	0.615846i	$-0.788814\pi$
$839$	−9.21649	+	7.73356i	−0.318189	+	0.266992i	0.469678	+	0.882838i	$0.344370\pi$
$840$		0			0
$841$	−6.67819	+	37.8739i	−0.230282	+	1.30600i
$842$		0			0
$843$	−1.53656	+	1.21152i	−0.0529218	+	0.0417269i
$844$		0			0
$845$	17.6476			0.607097
$846$		0			0
$847$	7.22254	+	10.9945i	0.248170	+	0.377777i
$848$		0			0
$849$	−24.9724	−	22.2852i	−0.857049	−	0.764825i
$850$		0			0
$851$	0.122128	+	0.0215345i	0.00418650	+	0.000738193i
$852$		0			0
$853$	2.46979	−	6.78570i	0.0845641	−	0.232338i	−0.890202	−	0.455566i	$-0.849437\pi$
$853$	2.46979	−	6.78570i	0.0845641	−	0.232338i	0.974766	+	0.223228i	$0.0716593\pi$
$854$		0			0
$855$	7.33183	+	24.7376i	0.250743	+	0.846007i
$856$		0			0
$857$	−8.21388	+	6.89226i	−0.280581	+	0.235435i	−0.772207	−	0.635371i	$-0.780847\pi$
$857$	−8.21388	+	6.89226i	−0.280581	+	0.235435i	0.491626	+	0.870806i	$0.336403\pi$
$858$		0			0
$859$	1.41545	+	0.249581i	0.0482944	+	0.00851560i	0.197743	−	0.980254i	$-0.436639\pi$
$859$	1.41545	+	0.249581i	0.0482944	+	0.00851560i	−0.149449	+	0.988769i	$0.547750\pi$
$860$		0			0
$861$	4.74654	−	2.91510i	0.161762	−	0.0993463i
$862$		0			0
$863$	−8.11258	−	4.68380i	−0.276156	−	0.159439i	0.355526	−	0.934666i	$-0.384302\pi$
$863$	−8.11258	−	4.68380i	−0.276156	−	0.159439i	−0.631682	+	0.775228i	$0.717635\pi$
$864$		0			0
$865$	−30.5279	−	52.8759i	−1.03798	−	1.79784i
$866$		0			0
$867$	−52.5829	−	32.5336i	−1.78581	−	1.10490i
$868$		0			0
$869$	19.5533	+	53.7221i	0.663299	+	1.82240i
$870$		0			0
$871$	−14.4673	−	17.2415i	−0.490206	−	0.584204i
$872$		0			0
$873$	30.4426	−	3.47334i	1.03033	−	0.117555i
$874$		0			0
$875$	−57.7226	−	17.3157i	−1.95138	−	0.585377i
$876$		0			0
$877$	24.5016	−	8.91784i	0.827359	−	0.301134i	0.106584	−	0.994304i	$-0.466009\pi$
$877$	24.5016	−	8.91784i	0.827359	−	0.301134i	0.720775	+	0.693170i	$0.243786\pi$
$878$		0			0
$879$	−23.5930	+	26.4378i	−0.795770	+	0.891726i
$880$		0			0
$881$	−15.3210	+	26.5368i	−0.516179	+	0.894048i	0.483645	+	0.875264i	$0.339313\pi$
$881$	−15.3210	+	26.5368i	−0.516179	+	0.894048i	−0.999824	+	0.0187834i	$0.994021\pi$
$882$		0			0
$883$	2.50187	+	4.33337i	0.0841946	+	0.145829i	0.905048	−	0.425310i	$-0.139835\pi$
$883$	2.50187	+	4.33337i	0.0841946	+	0.145829i	−0.820853	+	0.571139i	$0.806502\pi$
$884$		0			0
$885$	−91.6813	+	13.3005i	−3.08183	+	0.447092i
$886$		0			0
$887$	−24.9127	−	20.9042i	−0.836486	−	0.701895i	0.120284	−	0.992739i	$-0.461619\pi$
$887$	−24.9127	−	20.9042i	−0.836486	−	0.701895i	−0.956770	+	0.290844i	$0.906064\pi$
$888$		0			0
$889$	11.5474	−	10.8824i	0.387288	−	0.364984i
$890$		0			0
$891$	−16.3193	+	32.0533i	−0.546716	+	1.07383i
$892$		0			0
$893$	5.86131	−	16.1038i	0.196141	−	0.538893i
$894$		0			0
$895$	−15.8923	−	2.80225i	−0.531222	−	0.0936687i
$896$		0			0
$897$	1.23707	−	3.10145i	0.0413046	−	0.103554i
$898$		0			0
$899$	−8.53709	+	14.7867i	−0.284728	+	0.493163i
$900$		0			0
$901$	−37.3901	+	21.5872i	−1.24565	+	0.719174i
$902$		0			0
$903$	−1.65598	+	2.08605i	−0.0551075	+	0.0694194i
$904$		0			0
$905$	10.3484	+	28.4319i	0.343991	+	0.945108i
$906$		0			0
$907$	−3.36434	−	19.0801i	−0.111711	−	0.633545i	−0.988326	−	0.152353i	$-0.951315\pi$
$907$	−3.36434	−	19.0801i	−0.111711	−	0.633545i	0.876615	−	0.481192i	$-0.159796\pi$
$908$		0			0
$909$	−32.2858	−	14.0323i	−1.07085	−	0.465420i
$910$		0			0
$911$	−12.8670	+	2.26880i	−0.426304	+	0.0751688i	−0.382684	−	0.923879i	$-0.625000\pi$
$911$	−12.8670	+	2.26880i	−0.426304	+	0.0751688i	−0.0436198	+	0.999048i	$0.513889\pi$
$912$		0			0
$913$	20.5326	−	24.4697i	0.679528	−	0.809830i
$914$		0			0
$915$	34.5228	+	64.2379i	1.14129	+	2.12364i
$916$		0			0
$917$	7.80927	−	15.5282i	0.257885	−	0.512786i
$918$		0			0
$919$	−22.2263	+	38.4971i	−0.733178	+	1.26990i	0.222340	+	0.974969i	$0.428630\pi$
$919$	−22.2263	+	38.4971i	−0.733178	+	1.26990i	−0.955518	+	0.294932i	$0.904703\pi$
$920$		0			0
$921$	23.1067	+	42.9956i	0.761393	+	1.41675i
$922$		0			0
$923$	−2.93143	+	1.06695i	−0.0964892	+	0.0351192i
$924$		0			0
$925$	0.350873	+	1.98990i	0.0115366	+	0.0654275i
$926$		0			0
$927$	−5.44204	−	18.3614i	−0.178740	−	0.603068i
$928$		0			0
$929$	20.4425	−	17.1533i	0.670695	−	0.562780i	−0.242576	−	0.970132i	$-0.577992\pi$
$929$	20.4425	−	17.1533i	0.670695	−	0.562780i	0.913271	+	0.407352i	$0.133548\pi$
$930$		0			0
$931$	−6.79513	−	13.5675i	−0.222701	−	0.444656i
$932$		0			0
$933$	11.9668	−	13.4098i	0.391776	−	0.439018i
$934$		0			0
$935$		−	115.107i		−	3.76439i
$936$		0			0
$937$	9.13851	−	5.27612i	0.298542	−	0.172363i	−0.343246	−	0.939246i	$-0.611526\pi$
$937$	9.13851	−	5.27612i	0.298542	−	0.172363i	0.641788	+	0.766882i	$0.278193\pi$
$938$		0			0
$939$	−5.08934	−	35.0811i	−0.166084	−	1.14483i
$940$		0			0
$941$	−25.6527	+	9.33682i	−0.836255	+	0.304372i	−0.724423	−	0.689355i	$-0.757894\pi$
$941$	−25.6527	+	9.33682i	−0.836255	+	0.304372i	−0.111831	+	0.993727i	$0.535672\pi$
$942$		0			0
$943$	−0.789126	+	0.139144i	−0.0256975	+	0.00453116i
$944$		0			0
$945$	1.84148	−	54.5130i	0.0599033	−	1.77331i
$946$		0			0
$947$	18.0429	−	3.18145i	0.586315	−	0.103383i	0.127381	−	0.991854i	$-0.459343\pi$
$947$	18.0429	−	3.18145i	0.586315	−	0.103383i	0.458933	+	0.888471i	$0.348232\pi$
$948$		0			0
$949$	9.15665	−	3.33275i	0.297237	−	0.108186i
$950$		0			0
$951$	5.53966	−	4.36783i	0.179636	−	0.141636i
$952$		0			0
$953$	−52.3480	+	30.2231i	−1.69572	+	0.979023i	−0.745983	+	0.665965i	$0.768020\pi$
$953$	−52.3480	+	30.2231i	−1.69572	+	0.979023i	−0.949734	+	0.313058i	$0.898647\pi$
$954$		0			0
$955$		−	63.5810i		−	2.05743i
$956$		0			0
$957$	17.8087	+	53.9923i	0.575674	+	1.74532i
$958$		0			0
$959$	−42.1490	−	4.95007i	−1.36106	−	0.159846i
$960$		0			0
$961$	20.4368	−	17.1485i	0.659253	−	0.553179i
$962$		0			0
$963$	−2.35870	+	38.6641i	−0.0760081	+	1.24593i
$964$		0			0
$965$	−12.6301	−	71.6290i	−0.406578	−	2.30582i
$966$		0			0
$967$	1.14038	−	0.415063i	0.0366721	−	0.0133475i	−0.323619	−	0.946187i	$-0.604900\pi$
$967$	1.14038	−	0.415063i	0.0366721	−	0.0133475i	0.360291	+	0.932840i	$0.382677\pi$
$968$		0			0
$969$	14.3408	−	23.1786i	0.460694	−	0.744603i
$970$		0			0
$971$	−5.22774	+	9.05472i	−0.167766	+	0.290580i	−0.937634	−	0.347624i	$-0.886989\pi$
$971$	−5.22774	+	9.05472i	−0.167766	+	0.290580i	0.769868	+	0.638203i	$0.220322\pi$
$972$		0			0
$973$	−3.42083	−	59.2965i	−0.109667	−	1.90096i
$974$		0			0
$975$	54.3799	+	1.65718i	1.74155	+	0.0530722i
$976$		0			0
$977$	1.16217	−	1.38502i	0.0371812	−	0.0443108i	−0.747133	−	0.664674i	$-0.768570\pi$
$977$	1.16217	−	1.38502i	0.0371812	−	0.0443108i	0.784315	+	0.620363i	$0.213015\pi$
$978$		0			0
$979$	34.1013	−	6.01298i	1.08988	−	0.192176i
$980$		0			0
$981$	−3.81506	+	5.76589i	−0.121805	+	0.184091i
$982$		0			0
$983$	−5.11132	−	28.9877i	−0.163026	−	0.924565i	−0.951077	−	0.308955i	$-0.900021\pi$
$983$	−5.11132	−	28.9877i	−0.163026	−	0.924565i	0.788051	−	0.615610i	$-0.211090\pi$
$984$		0			0
$985$	−13.0978	−	35.9860i	−0.417332	−	1.14661i
$986$		0			0
$987$	−22.5249	+	28.3748i	−0.716976	+	0.903181i
$988$		0			0
$989$	0.331814	−	0.191573i	0.0105511	−	0.00609166i
$990$		0			0
$991$	1.23131	−	2.13269i	0.0391138	−	0.0677471i	−0.845806	−	0.533491i	$-0.820880\pi$
$991$	1.23131	−	2.13269i	0.0391138	−	0.0677471i	0.884920	+	0.465744i	$0.154213\pi$
$992$		0			0
$993$	−4.19698	−	5.32298i	−0.133187	−	0.168920i
$994$		0			0
$995$	41.3155	+	7.28504i	1.30979	+	0.230951i
$996$		0			0
$997$	9.78734	−	26.8905i	0.309968	−	0.851630i	−0.682693	−	0.730705i	$-0.739192\pi$
$997$	9.78734	−	26.8905i	0.309968	−	0.851630i	0.992662	−	0.120926i	$-0.0385862\pi$
$998$		0			0
$999$	−0.887610	+	0.409447i	−0.0280827	+	0.0129543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.ck.a.5.6	yes	144
7.3	odd	6		756.2.ca.a.437.13	yes	144
27.11	odd	18		756.2.ca.a.173.13	✓	144
189.38	even	18	inner	756.2.ck.a.605.6	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.ca.a.173.13	✓	144	27.11	odd	18
756.2.ca.a.437.13	yes	144	7.3	odd	6
756.2.ck.a.5.6	yes	144	1.1	even	1	trivial
756.2.ck.a.605.6	yes	144	189.38	even	18	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.ck (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +O(q^{10})\)	\(q+(-1.47292 - 0.911314i) q^{3} +(0.688949 - 3.90722i) q^{5} +(0.608733 + 2.57477i) q^{7} +(1.33902 + 2.68459i) q^{9} +(3.93578 - 0.693985i) q^{11} +(1.87975 - 2.24020i) q^{13} +(-4.57548 + 5.12720i) q^{15} +7.25945 q^{17} +2.16772i q^{19} +(1.44981 - 4.34719i) q^{21} +(-0.423740 + 0.504993i) q^{23} +(-10.0933 - 3.67365i) q^{25} +(0.474237 - 5.17447i) q^{27} +(-5.27940 - 6.29175i) q^{29} +(-0.711008 - 1.95348i) q^{31} +(-6.42955 - 2.56454i) q^{33} +(10.4796 - 0.604570i) q^{35} +(-0.0940596 - 0.162916i) q^{37} +(-4.81025 + 1.58660i) q^{39} +(0.931145 + 0.781324i) q^{41} +(-0.546157 - 0.198785i) q^{43} +(11.4118 - 3.38228i) q^{45} +(-7.42893 - 2.70391i) q^{47} +(-6.25889 + 3.13470i) q^{49} +(-10.6926 - 6.61564i) q^{51} +(-5.15055 + 2.97367i) q^{53} -15.8561i q^{55} +(1.97547 - 3.19288i) q^{57} +(10.3271 + 8.66550i) q^{59} +(3.62963 - 9.97232i) q^{61} +(-6.09711 + 5.08186i) q^{63} +(-7.45790 - 8.88798i) q^{65} +(1.33647 - 7.57947i) q^{67} +(1.08434 - 0.357657i) q^{69} +(-0.923830 - 0.533373i) q^{71} +(2.88569 + 1.66605i) q^{73} +(11.5188 + 14.6092i) q^{75} +(4.18269 + 9.71128i) q^{77} +(2.48404 + 14.0877i) q^{79} +(-5.41408 + 7.18942i) q^{81} +(6.12280 - 5.13764i) q^{83} +(5.00139 - 28.3643i) q^{85} +(2.04241 + 14.0785i) q^{87} +8.66443 q^{89} +(6.91226 + 3.47624i) q^{91} +(-0.732970 + 3.52528i) q^{93} +(8.46975 + 1.49345i) q^{95} +(3.49318 - 9.59744i) q^{97} +(7.13314 + 9.63672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} - 6 q^{11} + 12 q^{15} + 33 q^{21} + 21 q^{23} - 6 q^{29} + 27 q^{35} + 39 q^{39} - 54 q^{47} + 18 q^{49} - 9 q^{51} - 45 q^{53} + 3 q^{57} + 45 q^{59} + 39 q^{63} + 24 q^{65} - 36 q^{69} + 36 q^{71} + 45 q^{75} + 21 q^{77} - 18 q^{79} + 18 q^{81} + 36 q^{85} - 45 q^{87} + 9 q^{91} - 48 q^{93} - 66 q^{95}+O(q^{100}) \) 144 * q + 6 * q^9 - 6 * q^11 + 12 * q^15 + 33 * q^21 + 21 * q^23 - 6 * q^29 + 27 * q^35 + 39 * q^39 - 54 * q^47 + 18 * q^49 - 9 * q^51 - 45 * q^53 + 3 * q^57 + 45 * q^59 + 39 * q^63 + 24 * q^65 - 36 * q^69 + 36 * q^71 + 45 * q^75 + 21 * q^77 - 18 * q^79 + 18 * q^81 + 36 * q^85 - 45 * q^87 + 9 * q^91 - 48 * q^93 - 66 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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