LMFDB - Embedded newform 756.2.bq.a.25.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

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, 10, 12]))

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

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

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.20
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52539 - 0.820472i) q^{3} +(-3.26720 - 1.18916i) q^{5} +(-0.0267571 + 2.64562i) q^{7} +(1.65365 - 2.50309i) q^{9} +O(q^{10})$	\(q+(1.52539 - 0.820472i) q^{3} +(-3.26720 - 1.18916i) q^{5} +(-0.0267571 + 2.64562i) q^{7} +(1.65365 - 2.50309i) q^{9} +(3.29257 - 1.19840i) q^{11} +(-1.03945 - 5.89501i) q^{13} +(-5.95944 + 0.866704i) q^{15} +4.38787 q^{17} -7.42646 q^{19} +(2.12984 + 4.05756i) q^{21} +(-1.34542 - 7.63027i) q^{23} +(5.43025 + 4.55652i) q^{25} +(0.468756 - 5.17497i) q^{27} +(1.19802 - 6.79431i) q^{29} +(-5.74085 + 4.81715i) q^{31} +(4.03921 - 4.52949i) q^{33} +(3.23349 - 8.61193i) q^{35} +(1.60801 - 2.78515i) q^{37} +(-6.42226 - 8.13937i) q^{39} +(-0.347466 - 1.97058i) q^{41} +(4.39481 + 3.68768i) q^{43} +(-8.37938 + 6.21162i) q^{45} +(-0.990964 - 0.831517i) q^{47} +(-6.99857 - 0.141578i) q^{49} +(6.69323 - 3.60012i) q^{51} +(1.46375 - 2.53528i) q^{53} -12.1826 q^{55} +(-11.3283 + 6.09320i) q^{57} +(0.292690 + 1.65993i) q^{59} +(1.85426 + 1.55590i) q^{61} +(6.57796 + 4.44190i) q^{63} +(-3.61404 + 20.4962i) q^{65} +(8.99190 + 3.27278i) q^{67} +(-8.31272 - 10.5353i) q^{69} +(5.74781 + 9.95550i) q^{71} +(1.33876 + 2.31880i) q^{73} +(12.0218 + 2.49512i) q^{75} +(3.08240 + 8.74294i) q^{77} +(-3.00314 + 1.09305i) q^{79} +(-3.53088 - 8.27846i) q^{81} +(-1.36108 + 7.71907i) q^{83} +(-14.3360 - 5.21789i) q^{85} +(-3.74709 - 11.3469i) q^{87} +7.65419 q^{89} +(15.6237 - 2.59225i) q^{91} +(-4.80472 + 12.0583i) q^{93} +(24.2637 + 8.83127i) q^{95} +(7.06016 + 5.92418i) q^{97} +(2.44507 - 10.2233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.52539	−	0.820472i	0.880686	−	0.473700i
$3$	1.52539	−	0.820472i	0.880686	−	0.473700i
$4$		0			0
$5$	−3.26720	−	1.18916i	−1.46114	−	0.531810i	−0.515458	−	0.856915i	$-0.672378\pi$
$5$	−3.26720	−	1.18916i	−1.46114	−	0.531810i	−0.945678	+	0.325105i	$0.894600\pi$
$6$		0			0
$7$	−0.0267571	+	2.64562i	−0.0101132	+	0.999949i
$7$	−0.0267571	+	2.64562i	−0.0101132	+	0.999949i
$8$		0			0
$9$	1.65365	−	2.50309i	0.551217	−	0.834362i
$10$		0			0
$11$	3.29257	−	1.19840i	0.992747	−	0.361330i	0.205963	−	0.978560i	$-0.433967\pi$
$11$	3.29257	−	1.19840i	0.992747	−	0.361330i	0.786783	+	0.617229i	$0.211745\pi$
$12$		0			0
$13$	−1.03945	−	5.89501i	−0.288291	−	1.63498i	−0.693286	−	0.720663i	$-0.743838\pi$
$13$	−1.03945	−	5.89501i	−0.288291	−	1.63498i	0.404994	−	0.914319i	$-0.367273\pi$
$14$		0			0
$15$	−5.95944	+	0.866704i	−1.53872	+	0.223782i
$16$		0			0
$17$	4.38787			1.06421			0.532107	−	0.846677i	$-0.321400\pi$
$17$	4.38787			1.06421			0.532107	+	0.846677i	$0.321400\pi$
$18$		0			0
$19$	−7.42646			−1.70375			−0.851873	−	0.523748i	$-0.824533\pi$
$19$	−7.42646			−1.70375			−0.851873	+	0.523748i	$0.824533\pi$
$20$		0			0
$21$	2.12984	+	4.05756i	0.464769	+	0.885432i
$22$		0			0
$23$	−1.34542	−	7.63027i	−0.280540	−	1.59102i	−0.720795	−	0.693149i	$-0.756223\pi$
$23$	−1.34542	−	7.63027i	−0.280540	−	1.59102i	0.440255	−	0.897873i	$-0.354888\pi$
$24$		0			0
$25$	5.43025	+	4.55652i	1.08605	+	0.911304i
$26$		0			0
$27$	0.468756	−	5.17497i	0.0902121	−	0.995923i
$28$		0			0
$29$	1.19802	−	6.79431i	0.222467	−	1.26167i	−0.645002	−	0.764180i	$-0.723144\pi$
$29$	1.19802	−	6.79431i	0.222467	−	1.26167i	0.867469	−	0.497491i	$-0.165745\pi$
$30$		0			0
$31$	−5.74085	+	4.81715i	−1.03109	+	0.865185i	−0.990980	−	0.134010i	$-0.957214\pi$
$31$	−5.74085	+	4.81715i	−1.03109	+	0.865185i	−0.0401074	+	0.999195i	$0.512770\pi$
$32$		0			0
$33$	4.03921	−	4.52949i	0.703136	−	0.788482i
$34$		0			0
$35$	3.23349	−	8.61193i	0.546559	−	1.45568i
$36$		0			0
$37$	1.60801	−	2.78515i	0.264355	−	0.457876i	−0.703040	−	0.711151i	$-0.748174\pi$
$37$	1.60801	−	2.78515i	0.264355	−	0.457876i	0.967394	+	0.253275i	$0.0815077\pi$
$38$		0			0
$39$	−6.42226	−	8.13937i	−1.02839	−	1.30334i
$40$		0			0
$41$	−0.347466	−	1.97058i	−0.0542651	−	0.307753i	0.945579	−	0.325392i	$-0.105496\pi$
$41$	−0.347466	−	1.97058i	−0.0542651	−	0.307753i	−0.999844	+	0.0176390i	$0.994385\pi$
$42$		0			0
$43$	4.39481	+	3.68768i	0.670202	+	0.562366i	0.913125	−	0.407679i	$-0.133662\pi$
$43$	4.39481	+	3.68768i	0.670202	+	0.562366i	−0.242923	+	0.970046i	$0.578106\pi$
$44$		0			0
$45$	−8.37938	+	6.21162i	−1.24912	+	0.925973i
$46$		0			0
$47$	−0.990964	−	0.831517i	−0.144547	−	0.121289i	0.567647	−	0.823272i	$-0.307854\pi$
$47$	−0.990964	−	0.831517i	−0.144547	−	0.121289i	−0.712194	+	0.701983i	$0.752298\pi$
$48$		0			0
$49$	−6.99857	−	0.141578i	−0.999795	−	0.0202254i
$50$		0			0
$51$	6.69323	−	3.60012i	0.937239	−	0.504118i
$52$		0			0
$53$	1.46375	−	2.53528i	0.201061	−	0.348248i	−0.747810	−	0.663913i	$-0.768894\pi$
$53$	1.46375	−	2.53528i	0.201061	−	0.348248i	0.948871	+	0.315666i	$0.102228\pi$
$54$		0			0
$55$	−12.1826			−1.64270
$56$		0			0
$57$	−11.3283	+	6.09320i	−1.50047	+	0.807065i
$58$		0			0
$59$	0.292690	+	1.65993i	0.0381050	+	0.216104i	0.997915	−	0.0645476i	$-0.0205604\pi$
$59$	0.292690	+	1.65993i	0.0381050	+	0.216104i	−0.959810	+	0.280652i	$0.909449\pi$
$60$		0			0
$61$	1.85426	+	1.55590i	0.237413	+	0.199213i	0.753730	−	0.657185i	$-0.228253\pi$
$61$	1.85426	+	1.55590i	0.237413	+	0.199213i	−0.516317	+	0.856398i	$0.672697\pi$
$62$		0			0
$63$	6.57796	+	4.44190i	0.828745	+	0.559627i
$64$		0			0
$65$	−3.61404	+	20.4962i	−0.448267	+	2.54225i
$66$		0			0
$67$	8.99190	+	3.27278i	1.09853	+	0.399834i	0.826776	−	0.562531i	$-0.190172\pi$
$67$	8.99190	+	3.27278i	1.09853	+	0.399834i	0.271759	+	0.962365i	$0.412395\pi$
$68$		0			0
$69$	−8.31272	−	10.5353i	−1.00073	−	1.26830i
$70$		0			0
$71$	5.74781	+	9.95550i	0.682139	+	1.18150i	0.974327	+	0.225139i	$0.0722836\pi$
$71$	5.74781	+	9.95550i	0.682139	+	1.18150i	−0.292187	+	0.956361i	$0.594383\pi$
$72$		0			0
$73$	1.33876	+	2.31880i	0.156690	+	0.271395i	0.933673	−	0.358126i	$-0.116584\pi$
$73$	1.33876	+	2.31880i	0.156690	+	0.271395i	−0.776983	+	0.629522i	$0.783251\pi$
$74$		0			0
$75$	12.0218	+	2.49512i	1.38815	+	0.288112i
$76$		0			0
$77$	3.08240	+	8.74294i	0.351272	+	0.996350i
$78$		0			0
$79$	−3.00314	+	1.09305i	−0.337880	+	0.122978i	−0.505387	−	0.862893i	$-0.668650\pi$
$79$	−3.00314	+	1.09305i	−0.337880	+	0.122978i	0.167507	+	0.985871i	$0.446428\pi$
$80$		0			0
$81$	−3.53088	−	8.27846i	−0.392320	−	0.919829i
$82$		0			0
$83$	−1.36108	+	7.71907i	−0.149398	+	0.847278i	0.814332	+	0.580399i	$0.197103\pi$
$83$	−1.36108	+	7.71907i	−0.149398	+	0.847278i	−0.963730	+	0.266879i	$0.914008\pi$
$84$		0			0
$85$	−14.3360	−	5.21789i	−1.55496	−	0.565960i
$86$		0			0
$87$	−3.74709	−	11.3469i	−0.401730	−	1.21652i
$88$		0			0
$89$	7.65419			0.811343			0.405671	−	0.914019i	$-0.367038\pi$
$89$	7.65419			0.811343			0.405671	+	0.914019i	$0.367038\pi$
$90$		0			0
$91$	15.6237	−	2.59225i	1.63781	−	0.271742i
$92$		0			0
$93$	−4.80472	+	12.0583i	−0.498227	+	1.25038i
$94$		0			0
$95$	24.2637	+	8.83127i	2.48940	+	0.906069i
$96$		0			0
$97$	7.06016	+	5.92418i	0.716851	+	0.601509i	0.926512	−	0.376265i	$-0.122792\pi$
$97$	7.06016	+	5.92418i	0.716851	+	0.601509i	−0.209661	+	0.977774i	$0.567236\pi$
$98$		0			0
$99$	2.44507	−	10.2233i	0.245739	−	1.02748i
$100$		0			0
$101$	−0.591148	+	3.35257i	−0.0588215	+	0.333593i	−0.999991	−	0.00434289i	$-0.998618\pi$
$101$	−0.591148	+	3.35257i	−0.0588215	+	0.333593i	0.941169	+	0.337936i	$0.109729\pi$
$102$		0			0
$103$	−0.200581	−	0.0730055i	−0.0197638	−	0.00719345i	0.332119	−	0.943237i	$-0.392236\pi$
$103$	−0.200581	−	0.0730055i	−0.0197638	−	0.00719345i	−0.351883	+	0.936044i	$0.614459\pi$
$104$		0			0
$105$	−2.13351	−	15.7896i	−0.208209	−	1.54090i
$106$		0			0
$107$	−7.32933	−	12.6948i	−0.708553	−	1.22725i	−0.965394	−	0.260796i	$-0.916015\pi$
$107$	−7.32933	−	12.6948i	−0.708553	−	1.22725i	0.256841	−	0.966454i	$-0.417318\pi$
$108$		0			0
$109$	8.31916	−	14.4092i	0.796831	−	1.38015i	−0.124839	−	0.992177i	$-0.539841\pi$
$109$	8.31916	−	14.4092i	0.796831	−	1.38015i	0.921670	−	0.387975i	$-0.126825\pi$
$110$		0			0
$111$	0.167705	−	5.56777i	0.0159179	−	0.528470i
$112$		0			0
$113$	5.35453	−	4.49298i	0.503712	−	0.422664i	−0.355198	−	0.934791i	$-0.615587\pi$
$113$	5.35453	−	4.49298i	0.503712	−	0.422664i	0.858910	+	0.512127i	$0.171142\pi$
$114$		0			0
$115$	−4.67787	+	26.5295i	−0.436214	+	2.47389i
$116$		0			0
$117$	−16.4746	−	7.14646i	−1.52308	−	0.660690i
$118$		0			0
$119$	−0.117407	+	11.6086i	−0.0107626	+	1.06416i
$120$		0			0
$121$	0.978360	−	0.820942i	0.0889418	−	0.0746311i
$122$		0			0
$123$	−2.14683	−	2.72082i	−0.193573	−	0.245328i
$124$		0			0
$125$	−3.63106	−	6.28918i	−0.324772	−	0.562522i
$126$		0			0
$127$	−5.61712	+	9.72914i	−0.498439	+	0.863322i	−0.999998	−	0.00180157i	$-0.999427\pi$
$127$	−5.61712	+	9.72914i	−0.498439	+	0.863322i	0.501559	+	0.865123i	$0.332760\pi$
$128$		0			0
$129$	9.72945	+	2.01935i	0.856631	+	0.177794i
$130$		0			0
$131$	−0.525763	−	2.98175i	−0.0459361	−	0.260517i	0.953187	−	0.302381i	$-0.0977814\pi$
$131$	−0.525763	−	2.98175i	−0.0459361	−	0.260517i	−0.999123	+	0.0418641i	$0.986670\pi$
$132$		0			0
$133$	0.198710	−	19.6476i	0.0172304	−	1.70366i
$134$		0			0
$135$	−7.68539	+	16.3502i	−0.661453	+	1.40720i
$136$		0			0
$137$	−5.37211	−	4.50774i	−0.458970	−	0.385122i	0.383782	−	0.923424i	$-0.374622\pi$
$137$	−5.37211	−	4.50774i	−0.458970	−	0.385122i	−0.842752	+	0.538302i	$0.819066\pi$
$138$		0			0
$139$	14.5397	+	5.29203i	1.23324	+	0.448864i	0.874708	−	0.484651i	$-0.161053\pi$
$139$	14.5397	+	5.29203i	1.23324	+	0.448864i	0.358537	+	0.933515i	$0.383276\pi$
$140$		0			0
$141$	−2.19385	−	0.455333i	−0.184755	−	0.0383459i
$142$		0			0
$143$	−10.4870	−	18.1641i	−0.876969	−	1.51895i
$144$		0			0
$145$	−11.9937	+	20.7737i	−0.996023	+	1.72516i
$146$		0			0
$147$	−10.7917	+	5.52617i	−0.890087	+	0.455791i
$148$		0			0
$149$	0.693312	−	0.581758i	0.0567984	−	0.0476595i	−0.613947	−	0.789348i	$-0.710419\pi$
$149$	0.693312	−	0.581758i	0.0567984	−	0.0476595i	0.670745	+	0.741688i	$0.265975\pi$
$150$		0			0
$151$	12.0497	−	4.38574i	0.980592	−	0.356906i	0.198521	−	0.980097i	$-0.436386\pi$
$151$	12.0497	−	4.38574i	0.980592	−	0.356906i	0.782070	+	0.623190i	$0.214164\pi$
$152$		0			0
$153$	7.25600	−	10.9832i	0.586613	−	0.887940i
$154$		0			0
$155$	24.4849	−	8.91176i	1.96667	−	0.715810i
$156$		0			0
$157$	0.858958	+	4.87139i	0.0685523	+	0.388780i	0.999708	+	0.0241580i	$0.00769049\pi$
$157$	0.858958	+	4.87139i	0.0685523	+	0.388780i	−0.931156	+	0.364621i	$0.881198\pi$
$158$		0			0
$159$	0.152660	−	5.06826i	0.0121067	−	0.401940i
$160$		0			0
$161$	20.2228	−	3.35531i	1.59378	−	0.264435i
$162$		0			0
$163$	5.46856	+	9.47182i	0.428331	+	0.741891i	0.996725	−	0.0808658i	$-0.0257685\pi$
$163$	5.46856	+	9.47182i	0.428331	+	0.741891i	−0.568394	+	0.822756i	$0.692435\pi$
$164$		0			0
$165$	−18.5832	+	9.99545i	−1.44670	+	0.778145i
$166$		0			0
$167$	−6.46519	+	5.42494i	−0.500291	+	0.419794i	−0.857697	−	0.514155i	$-0.828106\pi$
$167$	−6.46519	+	5.42494i	−0.500291	+	0.419794i	0.357406	+	0.933949i	$0.383661\pi$
$168$		0			0
$169$	−21.4547	+	7.80887i	−1.65036	+	0.600682i
$170$		0			0
$171$	−12.2808	+	18.5891i	−0.939134	+	1.42154i
$172$		0			0
$173$	0.0999513	−	0.566852i	0.00759915	−	0.0430969i	−0.980772	−	0.195155i	$-0.937479\pi$
$173$	0.0999513	−	0.566852i	0.00759915	−	0.0430969i	0.988372	+	0.152058i	$0.0485901\pi$
$174$		0			0
$175$	−12.2001	+	14.2444i	−0.922241	+	1.07678i
$176$		0			0
$177$	1.80839	+	2.29190i	0.135927	+	0.172270i
$178$		0			0
$179$	−9.63569			−0.720205			−0.360103	−	0.932913i	$-0.617258\pi$
$179$	−9.63569			−0.720205			−0.360103	+	0.932913i	$0.617258\pi$
$180$		0			0
$181$	5.17791	−	8.96840i	0.384871	−	0.666616i	−0.606880	−	0.794793i	$-0.707579\pi$
$181$	5.17791	−	8.96840i	0.384871	−	0.666616i	0.991751	+	0.128177i	$0.0409126\pi$
$182$		0			0
$183$	4.10505	+	0.852002i	0.303454	+	0.0629818i
$184$		0			0
$185$	−8.56567	+	7.18745i	−0.629761	+	0.528432i
$186$		0			0
$187$	14.4474	−	5.25841i	1.05650	−	0.384533i
$188$		0			0
$189$	13.6784	+	1.37861i	0.994959	+	0.100279i
$190$		0			0
$191$	6.03399	−	2.19619i	0.436604	−	0.158911i	−0.114361	−	0.993439i	$-0.536482\pi$
$191$	6.03399	−	2.19619i	0.436604	−	0.158911i	0.550965	+	0.834528i	$0.314260\pi$
$192$		0			0
$193$	−0.162204	+	0.136105i	−0.0116757	+	0.00979707i	−0.648607	−	0.761124i	$-0.724648\pi$
$193$	−0.162204	+	0.136105i	−0.0116757	+	0.00979707i	0.636931	+	0.770921i	$0.280204\pi$
$194$		0			0
$195$	11.3038	+	34.2301i	0.809479	+	2.45127i
$196$		0			0
$197$	−8.20961	+	14.2195i	−0.584910	+	1.01309i	0.409976	+	0.912096i	$0.365537\pi$
$197$	−8.20961	+	14.2195i	−0.584910	+	1.01309i	−0.994887	+	0.100998i	$0.967796\pi$
$198$		0			0
$199$	10.1650			0.720580			0.360290	−	0.932840i	$-0.382678\pi$
$199$	10.1650			0.720580			0.360290	+	0.932840i	$0.382678\pi$
$200$		0			0
$201$	16.4014	−	2.38532i	1.15687	−	0.168247i
$202$		0			0
$203$	17.9431	+	3.35130i	1.25936	+	0.235215i
$204$		0			0
$205$	−1.20810	+	6.85147i	−0.0843772	+	0.478527i
$206$		0			0
$207$	−21.3241	−	9.25010i	−1.48213	−	0.642926i
$208$		0			0
$209$	−24.4521	+	8.89984i	−1.69139	+	0.615615i
$210$		0			0
$211$	6.88213	−	5.77479i	0.473785	−	0.397553i	−0.374388	−	0.927272i	$-0.622147\pi$
$211$	6.88213	−	5.77479i	0.473785	−	0.397553i	0.848173	+	0.529719i	$0.177703\pi$
$212$		0			0
$213$	16.9359	+	10.4701i	1.16043	+	0.717402i
$214$		0			0
$215$	−9.97346	−	17.2745i	−0.680184	−	1.17811i
$216$		0			0
$217$	−12.5907	−	15.3170i	−0.854713	−	1.03978i
$218$		0			0
$219$	3.94465	+	2.43867i	0.266555	+	0.164790i
$220$		0			0
$221$	−4.56097	−	25.8665i	−0.306804	−	1.73997i
$222$		0			0
$223$	−5.48910	+	1.99787i	−0.367577	+	0.133787i	−0.519203	−	0.854651i	$-0.673771\pi$
$223$	−5.48910	+	1.99787i	−0.367577	+	0.133787i	0.151626	+	0.988438i	$0.451549\pi$
$224$		0			0
$225$	20.3851	−	6.05749i	1.35901	−	0.403833i
$226$		0			0
$227$	11.8439	−	4.31084i	0.786111	−	0.286121i	0.0823923	−	0.996600i	$-0.473744\pi$
$227$	11.8439	−	4.31084i	0.786111	−	0.286121i	0.703718	+	0.710479i	$0.251522\pi$
$228$		0			0
$229$	−18.3542	+	15.4010i	−1.21288	+	1.01773i	−0.213714	+	0.976896i	$0.568556\pi$
$229$	−18.3542	+	15.4010i	−1.21288	+	1.01773i	−0.999166	+	0.0408306i	$0.987000\pi$
$230$		0			0
$231$	11.8752	+	10.8074i	0.781331	+	0.711074i
$232$		0			0
$233$	−13.8029	+	23.9073i	−0.904255	+	1.56622i	−0.0823419	+	0.996604i	$0.526240\pi$
$233$	−13.8029	+	23.9073i	−0.904255	+	1.56622i	−0.821914	+	0.569612i	$0.807093\pi$
$234$		0			0
$235$	2.24887	+	3.89515i	0.146700	+	0.254091i
$236$		0			0
$237$	−3.68415	+	4.13133i	−0.239311	+	0.268359i
$238$		0			0
$239$	26.6847	+	9.71243i	1.72609	+	0.628245i	0.998340	−	0.0575984i	$-0.0183443\pi$
$239$	26.6847	+	9.71243i	1.72609	+	0.628245i	0.727749	+	0.685843i	$0.240567\pi$
$240$		0			0
$241$	−3.81497	−	3.20114i	−0.245744	−	0.206204i	0.511593	−	0.859228i	$-0.329056\pi$
$241$	−3.81497	−	3.20114i	−0.245744	−	0.206204i	−0.757337	+	0.653024i	$0.773500\pi$
$242$		0			0
$243$	−12.1782	−	9.73092i	−0.781234	−	0.624239i
$244$		0			0
$245$	22.6973	+	8.78500i	1.45008	+	0.561253i
$246$		0			0
$247$	7.71943	+	43.7791i	0.491176	+	2.78560i
$248$		0			0
$249$	4.25710	+	12.8913i	0.269783	+	0.816956i
$250$		0			0
$251$	0.694758	−	1.20336i	0.0438527	−	0.0759551i	−0.843266	−	0.537497i	$-0.819370\pi$
$251$	0.694758	−	1.20336i	0.0438527	−	0.0759551i	0.887119	+	0.461541i	$0.152703\pi$
$252$		0			0
$253$	−13.5740	−	23.5108i	−0.853389	−	1.47811i
$254$		0			0
$255$	−26.1492	+	3.80298i	−1.63753	+	0.238152i
$256$		0			0
$257$	12.0485	−	10.1099i	0.751568	−	0.630640i	−0.184349	−	0.982861i	$-0.559018\pi$
$257$	12.0485	−	10.1099i	0.751568	−	0.630640i	0.935917	+	0.352221i	$0.114573\pi$
$258$		0			0
$259$	7.32541	+	4.32869i	0.455179	+	0.268972i
$260$		0			0
$261$	−15.0256	−	14.2342i	−0.930063	−	0.881072i
$262$		0			0
$263$	−3.55765	+	20.1764i	−0.219374	+	1.24413i	0.653779	+	0.756685i	$0.273182\pi$
$263$	−3.55765	+	20.1764i	−0.219374	+	1.24413i	−0.873153	+	0.487446i	$0.837929\pi$
$264$		0			0
$265$	−7.79721	+	6.54264i	−0.478979	+	0.401911i
$266$		0			0
$267$	11.6757	−	6.28005i	0.714539	−	0.384333i
$268$		0			0
$269$	7.18380	−	12.4427i	0.438004	−	0.758645i	−0.559531	−	0.828809i	$-0.689019\pi$
$269$	7.18380	−	12.4427i	0.438004	−	0.758645i	0.997535	+	0.0701639i	$0.0223522\pi$
$270$		0			0
$271$	0.845318	+	1.46413i	0.0513494	+	0.0889398i	0.890558	−	0.454870i	$-0.150314\pi$
$271$	0.845318	+	1.46413i	0.0513494	+	0.0889398i	−0.839208	+	0.543810i	$0.816981\pi$
$272$		0			0
$273$	21.7055	−	16.7731i	1.31368	−	1.01515i
$274$		0			0
$275$	23.3400	+	8.49506i	1.40745	+	0.512272i
$276$		0			0
$277$	−4.56857	+	25.9096i	−0.274499	+	1.55676i	0.466052	+	0.884757i	$0.345676\pi$
$277$	−4.56857	+	25.9096i	−0.274499	+	1.55676i	−0.740550	+	0.672001i	$0.765435\pi$
$278$		0			0
$279$	2.56437	+	22.3357i	0.153525	+	1.33720i
$280$		0			0
$281$	−24.9113	−	20.9030i	−1.48608	−	1.24697i	−0.899381	−	0.437165i	$-0.855983\pi$
$281$	−24.9113	−	20.9030i	−1.48608	−	1.24697i	−0.586700	−	0.809805i	$-0.699573\pi$
$282$		0			0
$283$	−30.8631	−	11.2332i	−1.83462	−	0.667746i	−0.991515	−	0.129995i	$-0.958504\pi$
$283$	−30.8631	−	11.2332i	−1.83462	−	0.667746i	−0.843103	−	0.537751i	$-0.819274\pi$
$284$		0			0
$285$	44.2575	−	6.43654i	2.62159	−	0.381268i
$286$		0			0
$287$	5.22269	−	0.866535i	0.308286	−	0.0511500i
$288$		0			0
$289$	2.25339			0.132552
$290$		0			0
$291$	15.6302	+	3.24404i	0.916256	+	0.190169i
$292$		0			0
$293$	−0.212842	−	0.0774683i	−0.0124344	−	0.00452575i	0.335795	−	0.941935i	$-0.390995\pi$
$293$	−0.212842	−	0.0774683i	−0.0124344	−	0.00452575i	−0.348230	+	0.937409i	$0.613217\pi$
$294$		0			0
$295$	1.01765	−	5.77138i	0.0592498	−	0.336022i
$296$		0			0
$297$	−4.65825	−	17.6007i	−0.270299	−	1.02130i
$298$		0			0
$299$	−43.5820	+	15.8626i	−2.52041	+	0.917356i
$300$		0			0
$301$	−9.87378	+	11.5283i	−0.569115	+	0.664480i
$302$		0			0
$303$	1.84896	+	5.59901i	0.106220	+	0.321655i
$304$		0			0
$305$	−4.20799	−	7.28846i	−0.240949	−	0.417336i
$306$		0			0
$307$	−8.70036	−	15.0695i	−0.496556	−	0.860060i	0.503436	−	0.864032i	$-0.332069\pi$
$307$	−8.70036	−	15.0695i	−0.496556	−	0.860060i	−0.999992	+	0.00397242i	$0.998736\pi$
$308$		0			0
$309$	−0.365864	+	0.0532090i	−0.0208133	+	0.00302695i
$310$		0			0
$311$	−11.5529	−	4.20492i	−0.655107	−	0.238439i	−0.00698441	−	0.999976i	$-0.502223\pi$
$311$	−11.5529	−	4.20492i	−0.655107	−	0.238439i	−0.648122	+	0.761536i	$0.724445\pi$
$312$		0			0
$313$	5.49085	−	31.1402i	0.310361	−	1.76015i	−0.286767	−	0.958000i	$-0.592581\pi$
$313$	5.49085	−	31.1402i	0.310361	−	1.76015i	0.597128	−	0.802146i	$-0.296308\pi$
$314$		0			0
$315$	−16.2093	−	22.3348i	−0.913293	−	1.25843i
$316$		0			0
$317$	7.34057	+	6.15947i	0.412288	+	0.345951i	0.825220	−	0.564811i	$-0.191051\pi$
$317$	7.34057	+	6.15947i	0.412288	+	0.345951i	−0.412932	+	0.910762i	$0.635495\pi$
$318$		0			0
$319$	−4.19772	−	23.8064i	−0.235027	−	1.33290i
$320$		0			0
$321$	−21.5958	−	13.3510i	−1.20536	−	0.745180i
$322$		0			0
$323$	−32.5863			−1.81315
$324$		0			0
$325$	21.2163	−	36.7477i	1.17687	−	2.03839i
$326$		0			0
$327$	0.867639	−	28.8054i	0.0479805	−	1.59294i
$328$		0			0
$329$	2.22639	−	2.59946i	0.122745	−	0.143313i
$330$		0			0
$331$	2.59517	+	2.17761i	0.142643	+	0.119692i	0.711317	−	0.702871i	$-0.248099\pi$
$331$	2.59517	+	2.17761i	0.142643	+	0.119692i	−0.568674	+	0.822563i	$0.692543\pi$
$332$		0			0
$333$	−4.31239	−	8.63064i	−0.236317	−	0.472956i
$334$		0			0
$335$	−25.4864	−	21.3857i	−1.39247	−	1.16842i
$336$		0			0
$337$	3.53607	+	20.0541i	0.192622	+	1.09241i	0.915765	+	0.401715i	$0.131586\pi$
$337$	3.53607	+	20.0541i	0.192622	+	1.09241i	−0.723142	+	0.690699i	$0.757303\pi$
$338$		0			0
$339$	4.48139	−	11.2468i	0.243396	−	0.610843i
$340$		0			0
$341$	−13.1293	+	22.7406i	−0.710991	+	1.23147i
$342$		0			0
$343$	0.561822	−	18.5117i	0.0303355	−	0.999540i
$344$		0			0
$345$	14.6311	+	44.3060i	0.787715	+	2.38536i
$346$		0			0
$347$	14.9289	−	12.5268i	0.801424	−	0.672474i	−0.147121	−	0.989119i	$-0.547001\pi$
$347$	14.9289	−	12.5268i	0.801424	−	0.672474i	0.948544	+	0.316644i	$0.102556\pi$
$348$		0			0
$349$	2.12044	−	12.0256i	0.113505	−	0.643717i	−0.873975	−	0.485971i	$-0.838466\pi$
$349$	2.12044	−	12.0256i	0.113505	−	0.643717i	0.987480	−	0.157746i	$-0.0504228\pi$
$350$		0			0
$351$	−30.9937	+	2.61580i	−1.65432	+	0.139621i
$352$		0			0
$353$	−9.22047	−	7.73689i	−0.490756	−	0.411793i	0.363541	−	0.931578i	$-0.381568\pi$
$353$	−9.22047	−	7.73689i	−0.490756	−	0.411793i	−0.854297	+	0.519785i	$0.826012\pi$
$354$		0			0
$355$	−6.94052	−	39.3617i	−0.368365	−	2.08910i
$356$		0			0
$357$	9.34545	+	17.8040i	0.494614	+	0.942289i
$358$		0			0
$359$	−0.703960			−0.0371536			−0.0185768	−	0.999827i	$-0.505914\pi$
$359$	−0.703960			−0.0371536			−0.0185768	+	0.999827i	$0.505914\pi$
$360$		0			0
$361$	36.1523			1.90275
$362$		0			0
$363$	0.818824	−	2.05498i	0.0429771	−	0.107858i
$364$		0			0
$365$	−1.61656	−	9.16799i	−0.0846148	−	0.479874i
$366$		0			0
$367$	4.23558	−	1.54162i	0.221095	−	0.0804721i	−0.229097	−	0.973403i	$-0.573577\pi$
$367$	4.23558	−	1.54162i	0.221095	−	0.0804721i	0.450193	+	0.892931i	$0.351355\pi$
$368$		0			0
$369$	−5.50712	−	2.38891i	−0.286689	−	0.124362i
$370$		0			0
$371$	6.66822	+	3.94035i	0.346197	+	0.204573i
$372$		0			0
$373$	7.30724	+	2.65962i	0.378355	+	0.137710i	0.524195	−	0.851598i	$-0.324366\pi$
$373$	7.30724	+	2.65962i	0.378355	+	0.137710i	−0.145840	+	0.989308i	$0.546589\pi$
$374$		0			0
$375$	−10.6989	−	6.61429i	−0.552489	−	0.341561i
$376$		0			0
$377$	−41.2978			−2.12695
$378$		0			0
$379$	−10.8099			−0.555267			−0.277634	−	0.960687i	$-0.589550\pi$
$379$	−10.8099			−0.555267			−0.277634	+	0.960687i	$0.589550\pi$
$380$		0			0
$381$	−0.585832	+	19.4495i	−0.0300131	+	0.996426i
$382$		0			0
$383$	30.5881	+	11.1332i	1.56298	+	0.568878i	0.971417	−	0.237381i	$-0.0762889\pi$
$383$	30.5881	+	11.1332i	1.56298	+	0.568878i	0.591563	+	0.806259i	$0.298511\pi$
$384$		0			0
$385$	0.325970	−	32.2304i	0.0166130	−	1.64261i
$386$		0			0
$387$	16.4981	−	4.90245i	0.838644	−	0.249205i
$388$		0			0
$389$	−11.8567	+	4.31549i	−0.601159	+	0.218804i	−0.624630	−	0.780921i	$-0.714750\pi$
$389$	−11.8567	+	4.31549i	−0.601159	+	0.218804i	0.0234715	+	0.999725i	$0.492528\pi$
$390$		0			0
$391$	−5.90354	−	33.4806i	−0.298555	−	1.69319i
$392$		0			0
$393$	−3.24844	−	4.11697i	−0.163862	−	0.207674i
$394$		0			0
$395$	11.1117			0.559089
$396$		0			0
$397$	0.801634			0.0402329			0.0201164	−	0.999798i	$-0.493596\pi$
$397$	0.801634			0.0402329			0.0201164	+	0.999798i	$0.493596\pi$
$398$		0			0
$399$	−15.8172	−	30.1333i	−0.791849	−	1.50855i
$400$		0			0
$401$	−2.40808	−	13.6569i	−0.120254	−	0.681994i	−0.984014	−	0.178091i	$-0.943008\pi$
$401$	−2.40808	−	13.6569i	−0.120254	−	0.681994i	0.863760	−	0.503903i	$-0.168103\pi$
$402$		0			0
$403$	34.3645	+	28.8352i	1.71182	+	1.43638i
$404$		0			0
$405$	1.69164	+	31.2462i	0.0840584	+	1.55263i
$406$		0			0
$407$	1.95676	−	11.0973i	0.0969929	−	0.550074i
$408$		0			0
$409$	11.4708	−	9.62517i	0.567196	−	0.475934i	−0.313518	−	0.949582i	$-0.601508\pi$
$409$	11.4708	−	9.62517i	0.567196	−	0.475934i	0.880714	+	0.473648i	$0.157063\pi$
$410$		0			0
$411$	−11.8931	−	2.46840i	−0.586641	−	0.121757i
$412$		0			0
$413$	−4.39937	+	0.729932i	−0.216479	+	0.0359176i
$414$		0			0
$415$	13.6261	−	23.6012i	0.668881	−	1.15854i
$416$		0			0
$417$	26.5208	−	3.85702i	1.29873	−	0.188879i
$418$		0			0
$419$	−1.18086	−	6.69698i	−0.0576887	−	0.327169i	0.942282	−	0.334820i	$-0.108676\pi$
$419$	−1.18086	−	6.69698i	−0.0576887	−	0.327169i	−0.999971	+	0.00765141i	$0.997564\pi$
$420$		0			0
$421$	23.9380	+	20.0864i	1.16667	+	0.978951i	0.999975	−	0.00705792i	$-0.00224662\pi$
$421$	23.9380	+	20.0864i	1.16667	+	0.978951i	0.166693	+	0.986009i	$0.446691\pi$
$422$		0			0
$423$	−3.72007	+	1.10543i	−0.180876	+	0.0537478i
$424$		0			0
$425$	23.8272	+	19.9934i	1.15579	+	0.969823i
$426$		0			0
$427$	−4.16594	+	4.86402i	−0.201604	+	0.235386i
$428$		0			0
$429$	−30.8999	−	19.1030i	−1.49186	−	0.922302i
$430$		0			0
$431$	14.1593	−	24.5246i	0.682029	−	1.18131i	−0.292331	−	0.956317i	$-0.594431\pi$
$431$	14.1593	−	24.5246i	0.682029	−	1.18131i	0.974361	−	0.224992i	$-0.0722357\pi$
$432$		0			0
$433$	31.6192			1.51952			0.759761	−	0.650203i	$-0.225316\pi$
$433$	31.6192			1.51952			0.759761	+	0.650203i	$0.225316\pi$
$434$		0			0
$435$	−1.25087	+	41.5286i	−0.0599747	+	1.99114i
$436$		0			0
$437$	9.99173	+	56.6659i	0.477969	+	2.71070i
$438$		0			0
$439$	20.7938	+	17.4481i	0.992433	+	0.832750i	0.985918	−	0.167229i	$-0.0534818\pi$
$439$	20.7938	+	17.4481i	0.992433	+	0.832750i	0.00651475	+	0.999979i	$0.497926\pi$
$440$		0			0
$441$	−11.9276	+	17.2839i	−0.567979	+	0.823043i
$442$		0			0
$443$	4.08778	−	23.1829i	0.194216	−	1.10145i	−0.719315	−	0.694685i	$-0.755544\pi$
$443$	4.08778	−	23.1829i	0.194216	−	1.10145i	0.913531	−	0.406770i	$-0.133345\pi$
$444$		0			0
$445$	−25.0078	−	9.10208i	−1.18548	−	0.431480i
$446$		0			0
$447$	0.580258	−	1.45625i	0.0274452	−	0.0688784i
$448$		0			0
$449$	9.19456	+	15.9255i	0.433918	+	0.751569i	0.997207	−	0.0746918i	$-0.0237973\pi$
$449$	9.19456	+	15.9255i	0.433918	+	0.751569i	−0.563288	+	0.826260i	$0.690464\pi$
$450$		0			0
$451$	−3.50559	−	6.07186i	−0.165072	−	0.285913i
$452$		0			0
$453$	14.7822	−	16.5764i	0.694527	−	0.778828i
$454$		0			0
$455$	−54.1285	−	10.1098i	−2.53758	−	0.473954i
$456$		0			0
$457$	6.11496	−	2.22566i	0.286046	−	0.104112i	−0.195013	−	0.980801i	$-0.562475\pi$
$457$	6.11496	−	2.22566i	0.286046	−	0.104112i	0.481058	+	0.876689i	$0.340253\pi$
$458$		0			0
$459$	2.05684	−	22.7071i	0.0960050	−	1.05988i
$460$		0			0
$461$	3.22312	−	18.2792i	0.150116	−	0.851349i	−0.813000	−	0.582263i	$-0.802167\pi$
$461$	3.22312	−	18.2792i	0.150116	−	0.851349i	0.963116	−	0.269086i	$-0.0867216\pi$
$462$		0			0
$463$	11.3897	+	4.14551i	0.529324	+	0.192658i	0.592837	−	0.805323i	$-0.298008\pi$
$463$	11.3897	+	4.14551i	0.529324	+	0.192658i	−0.0635123	+	0.997981i	$0.520230\pi$
$464$		0			0
$465$	30.0372	−	33.6831i	1.39294	−	1.56202i
$466$		0			0
$467$	35.0219			1.62062			0.810311	−	0.586000i	$-0.199298\pi$
$467$	35.0219			1.62062			0.810311	+	0.586000i	$0.199298\pi$
$468$		0			0
$469$	−8.89912	+	23.7015i	−0.410923	+	1.09444i
$470$		0			0
$471$	5.30709	+	6.72604i	0.244538	+	0.309920i
$472$		0			0
$473$	18.8895	+	6.87522i	0.868541	+	0.316123i
$474$		0			0
$475$	−40.3275	−	33.8388i	−1.85035	−	1.55263i
$476$		0			0
$477$	−3.92550	−	7.85635i	−0.179736	−	0.359718i
$478$		0			0
$479$	−1.03708	+	5.88157i	−0.0473854	+	0.268736i	−0.999291	−	0.0376564i	$-0.988011\pi$
$479$	−1.03708	+	5.88157i	−0.0473854	+	0.268736i	0.951905	+	0.306392i	$0.0991219\pi$
$480$		0			0
$481$	−18.0899	−	6.58419i	−0.824830	−	0.300213i
$482$		0			0
$483$	28.0947	−	21.7104i	1.27835	−	0.987857i
$484$		0			0
$485$	−16.0221	−	27.7512i	−0.727528	−	1.26012i
$486$		0			0
$487$	−12.6121	+	21.8448i	−0.571509	+	0.989883i	0.424902	+	0.905239i	$0.360309\pi$
$487$	−12.6121	+	21.8448i	−0.571509	+	0.989883i	−0.996411	+	0.0846438i	$0.973025\pi$
$488$		0			0
$489$	16.1131	+	9.96146i	0.728658	+	0.450473i
$490$		0			0
$491$	−15.2705	+	12.8135i	−0.689148	+	0.578264i	−0.918663	−	0.395041i	$-0.870730\pi$
$491$	−15.2705	+	12.8135i	−0.689148	+	0.578264i	0.229515	+	0.973305i	$0.426286\pi$
$492$		0			0
$493$	5.25675	−	29.8125i	0.236752	−	1.34269i
$494$		0			0
$495$	−20.1457	+	30.4940i	−0.905482	+	1.37060i
$496$		0			0
$497$	−26.4922	+	14.9401i	−1.18834	+	0.670156i
$498$		0			0
$499$	18.6892	−	15.6821i	0.836642	−	0.702026i	−0.120163	−	0.992754i	$-0.538342\pi$
$499$	18.6892	−	15.6821i	0.836642	−	0.702026i	0.956806	+	0.290728i	$0.0938974\pi$
$500$		0			0
$501$	−5.41095	+	13.5797i	−0.241743	+	0.606695i
$502$		0			0
$503$	−2.43264	−	4.21345i	−0.108466	−	0.187869i	0.806683	−	0.590984i	$-0.201261\pi$
$503$	−2.43264	−	4.21345i	−0.108466	−	0.187869i	−0.915149	+	0.403116i	$0.867927\pi$
$504$		0			0
$505$	5.91815	−	10.2505i	0.263354	−	0.456143i
$506$		0			0
$507$	−26.3199	+	29.5146i	−1.16891	+	1.31079i
$508$		0			0
$509$	−2.44819	−	13.8844i	−0.108514	−	0.615413i	−0.989758	−	0.142753i	$-0.954405\pi$
$509$	−2.44819	−	13.8844i	−0.108514	−	0.615413i	0.881244	−	0.472661i	$-0.156706\pi$
$510$		0			0
$511$	−6.17048	+	3.47980i	−0.272966	+	0.153937i
$512$		0			0
$513$	−3.48120	+	38.4317i	−0.153699	+	1.69680i
$514$		0			0
$515$	0.568522	+	0.477047i	0.0250521	+	0.0210212i
$516$		0			0
$517$	−4.25930	−	1.55026i	−0.187324	−	0.0681803i
$518$		0			0
$519$	−0.312621	−	0.946679i	−0.0137225	−	0.0415546i
$520$		0			0
$521$	−9.43934	−	16.3494i	−0.413545	−	0.716281i	0.581729	−	0.813382i	$-0.302376\pi$
$521$	−9.43934	−	16.3494i	−0.413545	−	0.716281i	−0.995275	+	0.0971013i	$0.969043\pi$
$522$		0			0
$523$	−7.77749	+	13.4710i	−0.340086	+	0.589046i	−0.984448	−	0.175674i	$-0.943789\pi$
$523$	−7.77749	+	13.4710i	−0.340086	+	0.589046i	0.644363	+	0.764720i	$0.277123\pi$
$524$		0			0
$525$	−6.92279	+	31.7382i	−0.302135	+	1.38517i
$526$		0			0
$527$	−25.1901	+	21.1370i	−1.09730	+	0.920742i
$528$		0			0
$529$	−34.7979	+	12.6654i	−1.51295	+	0.550670i
$530$		0			0
$531$	4.63895	+	2.01231i	0.201313	+	0.0873270i
$532$		0			0
$533$	−11.2554	+	4.09664i	−0.487526	+	0.177445i
$534$		0			0
$535$	8.85022	+	50.1921i	0.382628	+	2.16999i
$536$		0			0
$537$	−14.6982	+	7.90582i	−0.634275	+	0.341161i
$538$		0			0
$539$	−23.2129	+	7.92091i	−0.999852	+	0.341178i
$540$		0			0
$541$	−3.86682	−	6.69754i	−0.166248	−	0.287950i	0.770850	−	0.637017i	$-0.219832\pi$
$541$	−3.86682	−	6.69754i	−0.166248	−	0.287950i	−0.937098	+	0.349067i	$0.886498\pi$
$542$		0			0
$543$	0.540025	−	17.9287i	0.0231747	−	0.769393i
$544$		0			0
$545$	−44.3152	+	37.1849i	−1.89826	+	1.59283i
$546$		0			0
$547$	22.3267	−	8.12624i	0.954620	−	0.347453i	0.182697	−	0.983169i	$-0.441517\pi$
$547$	22.3267	−	8.12624i	0.954620	−	0.347453i	0.771923	+	0.635716i	$0.219295\pi$
$548$		0			0
$549$	6.96085	−	2.06844i	0.297082	−	0.0882787i
$550$		0			0
$551$	−8.89705	+	50.4577i	−0.379027	+	2.14957i
$552$		0			0
$553$	−2.81145	−	7.97441i	−0.119555	−	0.339106i
$554$		0			0
$555$	−7.16891	+	17.9916i	−0.304303	+	0.763700i
$556$		0			0
$557$	5.79541			0.245560			0.122780	−	0.992434i	$-0.460819\pi$
$557$	5.79541			0.245560			0.122780	+	0.992434i	$0.460819\pi$
$558$		0			0
$559$	17.1707	−	29.7406i	0.726245	−	1.25789i
$560$		0			0
$561$	17.7235	−	19.8748i	0.748288	−	0.839114i
$562$		0			0
$563$	2.46243	−	2.06622i	0.103779	−	0.0870809i	−0.589422	−	0.807825i	$-0.700644\pi$
$563$	2.46243	−	2.06622i	0.103779	−	0.0870809i	0.693201	+	0.720745i	$0.256200\pi$
$564$		0			0
$565$	−22.8372	+	8.31206i	−0.960768	+	0.349691i
$566$		0			0
$567$	21.9961	−	9.11984i	0.923749	−	0.382997i
$568$		0			0
$569$	9.53640	−	3.47097i	0.399787	−	0.145511i	−0.134299	−	0.990941i	$-0.542878\pi$
$569$	9.53640	−	3.47097i	0.399787	−	0.145511i	0.534086	+	0.845430i	$0.320656\pi$
$570$		0			0
$571$	−4.74370	+	3.98044i	−0.198518	+	0.166576i	−0.736628	−	0.676299i	$-0.763583\pi$
$571$	−4.74370	+	3.98044i	−0.198518	+	0.166576i	0.538110	+	0.842875i	$0.319138\pi$
$572$		0			0
$573$	7.40229	−	8.30077i	0.309235	−	0.346770i
$574$		0			0
$575$	27.4615	−	47.5647i	1.14522	−	1.98359i
$576$		0			0
$577$	−15.9795			−0.665237			−0.332619	−	0.943061i	$-0.607932\pi$
$577$	−15.9795			−0.665237			−0.332619	+	0.943061i	$0.607932\pi$
$578$		0			0
$579$	−0.135754	+	0.340698i	−0.00564176	+	0.0141589i
$580$		0			0
$581$	−20.3853	−	3.80743i	−0.845723	−	0.157959i
$582$		0			0
$583$	1.78121	−	10.1017i	0.0737701	−	0.418371i
$584$		0			0
$585$	45.3275	+	42.9399i	1.87406	+	1.77535i
$586$		0			0
$587$	−16.3306	+	5.94384i	−0.674035	+	0.245329i	−0.656284	−	0.754514i	$-0.727873\pi$
$587$	−16.3306	+	5.94384i	−0.674035	+	0.245329i	−0.0177506	+	0.999842i	$0.505650\pi$
$588$		0			0
$589$	42.6342	−	35.7743i	1.75671	−	1.47406i
$590$		0			0
$591$	−0.856213	+	28.4260i	−0.0352199	+	1.16929i
$592$		0			0
$593$	13.1645	+	22.8016i	0.540603	+	0.936351i	0.998869	+	0.0475366i	$0.0151371\pi$
$593$	13.1645	+	22.8016i	0.540603	+	0.936351i	−0.458267	+	0.888815i	$0.651530\pi$
$594$		0			0
$595$	14.1881	−	37.7880i	0.581656	−	1.54916i
$596$		0			0
$597$	15.5057	−	8.34013i	0.634605	−	0.341339i
$598$		0			0
$599$	−4.88082	−	27.6805i	−0.199425	−	1.13099i	−0.905975	−	0.423331i	$-0.860861\pi$
$599$	−4.88082	−	27.6805i	−0.199425	−	1.13099i	0.706550	−	0.707663i	$-0.250250\pi$
$600$		0			0
$601$	6.46808	−	2.35419i	0.263839	−	0.0960294i	−0.206714	−	0.978401i	$-0.566277\pi$
$601$	6.46808	−	2.35419i	0.263839	−	0.0960294i	0.470552	+	0.882372i	$0.344055\pi$
$602$		0			0
$603$	23.0615	−	17.0954i	0.939137	−	0.696181i
$604$		0			0
$605$	−4.17273	+	1.51875i	−0.169646	+	0.0617459i
$606$		0			0
$607$	−12.9948	+	10.9039i	−0.527441	+	0.442576i	−0.867217	−	0.497931i	$-0.834093\pi$
$607$	−12.9948	+	10.9039i	−0.527441	+	0.442576i	0.339775	+	0.940507i	$0.389649\pi$
$608$		0			0
$609$	30.1199	−	9.60975i	1.22052	−	0.389407i
$610$		0			0
$611$	−3.87175	+	6.70606i	−0.156634	+	0.271298i
$612$		0			0
$613$	−3.41409	−	5.91338i	−0.137894	−	0.238839i	0.788805	−	0.614643i	$-0.210700\pi$
$613$	−3.41409	−	5.91338i	−0.137894	−	0.238839i	−0.926699	+	0.375804i	$0.877367\pi$
$614$		0			0
$615$	3.77861	+	11.4424i	0.152368	+	0.461402i
$616$		0			0
$617$	−9.44105	−	3.43626i	−0.380083	−	0.138339i	0.144912	−	0.989445i	$-0.453710\pi$
$617$	−9.44105	−	3.43626i	−0.380083	−	0.138339i	−0.524994	+	0.851106i	$0.675932\pi$
$618$		0			0
$619$	−2.99240	−	2.51092i	−0.120275	−	0.100923i	0.580666	−	0.814142i	$-0.302792\pi$
$619$	−2.99240	−	2.51092i	−0.120275	−	0.100923i	−0.700941	+	0.713219i	$0.747237\pi$
$620$		0			0
$621$	−40.1171	+	3.38578i	−1.60984	+	0.135867i
$622$		0			0
$623$	−0.204804	+	20.2501i	−0.00820529	+	0.811301i
$624$		0			0
$625$	−1.77016	−	10.0391i	−0.0708062	−	0.401562i
$626$		0			0
$627$	−29.9970	+	33.6381i	−1.19797	+	1.34337i
$628$		0			0
$629$	7.05572	−	12.2209i	0.281330	−	0.487278i
$630$		0			0
$631$	−2.08631	−	3.61360i	−0.0830549	−	0.143855i	0.821506	−	0.570200i	$-0.193134\pi$
$631$	−2.08631	−	3.61360i	−0.0830549	−	0.143855i	−0.904561	+	0.426345i	$0.859801\pi$
$632$		0			0
$633$	5.75990	−	14.4554i	0.228936	−	0.574552i
$634$		0			0
$635$	29.9218	−	25.1074i	1.18741	−	0.996355i
$636$		0			0
$637$	6.44005	+	41.4038i	0.255164	+	1.64048i
$638$		0			0
$639$	34.4243	+	2.07566i	1.36181	+	0.0821117i
$640$		0			0
$641$	3.61496	−	20.5015i	0.142782	−	0.809759i	−0.826339	−	0.563174i	$-0.809580\pi$
$641$	3.61496	−	20.5015i	0.142782	−	0.809759i	0.969121	−	0.246586i	$-0.0793086\pi$
$642$		0			0
$643$	25.9774	−	21.7976i	1.02445	−	0.859614i	0.0342676	−	0.999413i	$-0.489090\pi$
$643$	25.9774	−	21.7976i	1.02445	−	0.859614i	0.990180	+	0.139799i	$0.0446457\pi$
$644$		0			0
$645$	−29.3867	−	18.1675i	−1.15710	−	0.715345i
$646$		0			0
$647$	6.43141	−	11.1395i	0.252845	−	0.437940i	−0.711463	−	0.702723i	$-0.751967\pi$
$647$	6.43141	−	11.1395i	0.252845	−	0.437940i	0.964308	+	0.264784i	$0.0853005\pi$
$648$		0			0
$649$	2.95296	+	5.11467i	0.115914	+	0.200768i
$650$		0			0
$651$	−31.7729	−	13.0341i	−1.24528	−	0.510846i
$652$		0			0
$653$	22.7601	+	8.28400i	0.890671	+	0.324178i	0.746508	−	0.665376i	$-0.231729\pi$
$653$	22.7601	+	8.28400i	0.890671	+	0.324178i	0.144163	+	0.989554i	$0.453951\pi$
$654$		0			0
$655$	−1.82801	+	10.3672i	−0.0714264	+	0.405079i
$656$		0			0
$657$	8.01800	+	0.483455i	0.312812	+	0.0188614i
$658$		0			0
$659$	16.6294	+	13.9537i	0.647790	+	0.543560i	0.906399	−	0.422422i	$-0.138820\pi$
$659$	16.6294	+	13.9537i	0.647790	+	0.543560i	−0.258610	+	0.965982i	$0.583264\pi$
$660$		0			0
$661$	15.8044	+	5.75233i	0.614720	+	0.223740i	0.630567	−	0.776135i	$-0.282822\pi$
$661$	15.8044	+	5.75233i	0.614720	+	0.223740i	−0.0158471	+	0.999874i	$0.505044\pi$
$662$		0			0
$663$	−28.1800	−	35.7145i	−1.09442	−	1.38704i
$664$		0			0
$665$	−24.0134	+	63.9562i	−0.931199	+	2.48011i
$666$		0			0
$667$	−53.4543			−2.06976
$668$		0			0
$669$	−6.73384	+	7.55119i	−0.260345	+	0.291946i
$670$		0			0
$671$	7.96985	+	2.90079i	0.307673	+	0.111984i
$672$		0			0
$673$	−6.07205	+	34.4363i	−0.234060	+	1.32742i	0.610523	+	0.791998i	$0.290959\pi$
$673$	−6.07205	+	34.4363i	−0.234060	+	1.32742i	−0.844583	+	0.535424i	$0.820152\pi$
$674$		0			0
$675$	26.1253	−	25.9655i	1.00556	−	0.999411i
$676$		0			0
$677$	−13.3050	+	4.84262i	−0.511352	+	0.186117i	−0.584793	−	0.811183i	$-0.698824\pi$
$677$	−13.3050	+	4.84262i	−0.511352	+	0.186117i	0.0734409	+	0.997300i	$0.476602\pi$
$678$		0			0
$679$	−15.8620	+	18.5200i	−0.608728	+	0.710731i
$680$		0			0
$681$	14.5298	−	16.2934i	0.556781	−	0.624363i
$682$		0			0
$683$	−11.1850	−	19.3731i	−0.427984	−	0.741289i	0.568710	−	0.822538i	$-0.307443\pi$
$683$	−11.1850	−	19.3731i	−0.427984	−	0.741289i	−0.996694	+	0.0812485i	$0.974109\pi$
$684$		0			0
$685$	12.1913	+	21.1160i	0.465806	+	0.806800i
$686$		0			0
$687$	−15.3613	+	38.5517i	−0.586070	+	1.47084i
$688$		0			0
$689$	−16.4670	−	5.99350i	−0.627343	−	0.228334i
$690$		0			0
$691$	−2.83797	+	16.0950i	−0.107962	+	0.612281i	0.882034	+	0.471185i	$0.156174\pi$
$691$	−2.83797	+	16.0950i	−0.107962	+	0.612281i	−0.989996	+	0.141096i	$0.954937\pi$
$692$		0			0
$693$	26.9815	+	6.74226i	1.02494	+	0.256117i
$694$		0			0
$695$	−41.2111	−	34.5802i	−1.56323	−	1.31170i
$696$		0			0
$697$	−1.52464	−	8.64664i	−0.0577497	−	0.327515i
$698$		0			0
$699$	−1.43956	+	47.7928i	−0.0544490	+	1.80769i
$700$		0			0
$701$	−11.2951			−0.426609			−0.213305	−	0.976986i	$-0.568423\pi$
$701$	−11.2951			−0.426609			−0.213305	+	0.976986i	$0.568423\pi$
$702$		0			0
$703$	−11.9418	+	20.6838i	−0.450393	+	0.780104i
$704$		0			0
$705$	6.62627	+	4.09650i	0.249560	+	0.154283i
$706$		0			0
$707$	−8.85379	−	1.65366i	−0.332981	−	0.0621921i
$708$		0			0
$709$	26.7821	+	22.4728i	1.00582	+	0.843985i	0.987780	−	0.155852i	$-0.0498123\pi$
$709$	26.7821	+	22.4728i	1.00582	+	0.843985i	0.0180419	+	0.999837i	$0.494257\pi$
$710$		0			0
$711$	−2.23014	+	9.32466i	−0.0836368	+	0.349702i
$712$		0			0
$713$	44.4800	+	37.3232i	1.66579	+	1.39776i
$714$		0			0
$715$	12.6632	+	71.8163i	0.473575	+	2.68578i
$716$		0			0
$717$	48.6734	−	7.07876i	1.81774	−	0.264361i
$718$		0			0
$719$	22.6244	−	39.1866i	0.843748	−	1.46141i	−0.0429568	−	0.999077i	$-0.513678\pi$
$719$	22.6244	−	39.1866i	0.843748	−	1.46141i	0.886704	−	0.462337i	$-0.152989\pi$
$720$		0			0
$721$	0.198512	−	0.528707i	0.00739296	−	0.0196901i
$722$		0			0
$723$	−8.44578	−	1.75292i	−0.314102	−	0.0651919i
$724$		0			0
$725$	37.4640	−	31.4360i	1.39138	−	1.16750i
$726$		0			0
$727$	3.81097	−	21.6131i	0.141341	−	0.801585i	−0.828892	−	0.559409i	$-0.811028\pi$
$727$	3.81097	−	21.6131i	0.141341	−	0.801585i	0.970233	−	0.242175i	$-0.0778609\pi$
$728$		0			0
$729$	−26.5605	−	4.85159i	−0.983724	−	0.179689i
$730$		0			0
$731$	19.2838	+	16.1811i	0.713239	+	0.598478i
$732$		0			0
$733$	−3.37814	−	19.1584i	−0.124774	−	0.707630i	−0.981442	−	0.191761i	$-0.938580\pi$
$733$	−3.37814	−	19.1584i	−0.124774	−	0.707630i	0.856667	−	0.515869i	$-0.172531\pi$
$734$		0			0
$735$	41.8302	−	5.22196i	1.54293	−	0.192615i
$736$		0			0
$737$	33.5285			1.23504
$738$		0			0
$739$	8.25157			0.303539			0.151770	−	0.988416i	$-0.451503\pi$
$739$	8.25157			0.303539			0.151770	+	0.988416i	$0.451503\pi$
$740$		0			0
$741$	47.6947	+	60.4467i	1.75211	+	2.22057i
$742$		0			0
$743$	6.24479	+	35.4160i	0.229099	+	1.29929i	0.854691	+	0.519136i	$0.173746\pi$
$743$	6.24479	+	35.4160i	0.229099	+	1.29929i	−0.625592	+	0.780150i	$0.715143\pi$
$744$		0			0
$745$	−2.95699	+	1.07626i	−0.108336	+	0.0394310i
$746$		0			0
$747$	17.0707	+	16.1715i	0.624586	+	0.591686i
$748$		0			0
$749$	33.7816	−	19.0509i	1.23435	−	0.696105i
$750$		0			0
$751$	−15.2038	−	5.53373i	−0.554795	−	0.201929i	0.0493809	−	0.998780i	$-0.484275\pi$
$751$	−15.2038	−	5.53373i	−0.554795	−	0.201929i	−0.604175	+	0.796851i	$0.706497\pi$
$752$		0			0
$753$	0.0724591	−	2.40562i	0.00264056	−	0.0876657i
$754$		0			0
$755$	−44.5841			−1.62258
$756$		0			0
$757$	−10.7440			−0.390498			−0.195249	−	0.980754i	$-0.562552\pi$
$757$	−10.7440			−0.390498			−0.195249	+	0.980754i	$0.562552\pi$
$758$		0			0
$759$	−39.9957	−	24.7262i	−1.45175	−	0.897504i
$760$		0			0
$761$	−31.2042	−	11.3574i	−1.13115	−	0.411705i	−0.292441	−	0.956283i	$-0.594468\pi$
$761$	−31.2042	−	11.3574i	−1.13115	−	0.411705i	−0.838710	+	0.544578i	$0.816690\pi$
$762$		0			0
$763$	37.8986	+	22.3949i	1.37202	+	0.810748i
$764$		0			0
$765$	−36.7676	+	27.2558i	−1.32934	+	0.985434i
$766$		0			0
$767$	9.48107	−	3.45083i	0.342342	−	0.124602i
$768$		0			0
$769$	−8.96256	−	50.8292i	−0.323198	−	1.83295i	−0.522045	−	0.852918i	$-0.674831\pi$
$769$	−8.96256	−	50.8292i	−0.323198	−	1.83295i	0.198847	−	0.980031i	$-0.436280\pi$
$770$		0			0
$771$	10.0839	−	25.3071i	0.363161	−	0.911414i
$772$		0			0
$773$	−24.5047			−0.881373			−0.440687	−	0.897661i	$-0.645265\pi$
$773$	−24.5047			−0.881373			−0.440687	+	0.897661i	$0.645265\pi$
$774$		0			0
$775$	−53.1237			−1.90826
$776$		0			0
$777$	14.7257	+	0.592661i	0.528282	+	0.0212616i
$778$		0			0
$779$	2.58044	+	14.6344i	0.0924540	+	0.524333i
$780$		0			0
$781$	30.8557	+	25.8910i	1.10410	+	0.926452i
$782$		0			0
$783$	−34.5987	−	9.38458i	−1.23646	−	0.335378i
$784$		0			0
$785$	2.98649	−	16.9372i	0.106593	−	0.604516i
$786$		0			0
$787$	−15.3991	+	12.9213i	−0.548917	+	0.460596i	−0.874574	−	0.484892i	$-0.838859\pi$
$787$	−15.3991	+	12.9213i	−0.548917	+	0.460596i	0.325657	+	0.945488i	$0.394414\pi$
$788$		0			0
$789$	11.1274	+	33.6959i	0.396145	+	1.19961i
$790$		0			0
$791$	11.7434	+	14.2862i	0.417548	+	0.507960i
$792$		0			0
$793$	7.24467	−	12.5481i	0.257266	−	0.445598i
$794$		0			0
$795$	−6.52576	+	16.3775i	−0.231445	+	0.580850i
$796$		0			0
$797$	−3.65576	−	20.7328i	−0.129494	−	0.734394i	−0.978537	−	0.206071i	$-0.933932\pi$
$797$	−3.65576	−	20.7328i	−0.129494	−	0.734394i	0.849043	−	0.528323i	$-0.177179\pi$
$798$		0			0
$799$	−4.34822	−	3.64859i	−0.153829	−	0.129078i
$800$		0			0
$801$	12.6574	−	19.1591i	0.447226	−	0.676954i
$802$		0			0
$803$	7.18680	+	6.03045i	0.253617	+	0.212810i
$804$		0			0
$805$	−70.0618	−	13.0857i	−2.46935	−	0.461211i
$806$		0			0
$807$	0.749227	−	24.8741i	0.0263740	−	0.875611i
$808$		0			0
$809$	−8.58203	+	14.8645i	−0.301728	+	0.522608i	−0.976527	−	0.215393i	$-0.930897\pi$
$809$	−8.58203	+	14.8645i	−0.301728	+	0.522608i	0.674799	+	0.738001i	$0.264230\pi$
$810$		0			0
$811$	−10.1728			−0.357214			−0.178607	−	0.983920i	$-0.557159\pi$
$811$	−10.1728			−0.357214			−0.178607	+	0.983920i	$0.557159\pi$
$812$		0			0
$813$	2.49072	+	1.53982i	0.0873535	+	0.0540038i
$814$		0			0
$815$	−6.60333	−	37.4493i	−0.231304	−	1.31179i
$816$		0			0
$817$	−32.6379	−	27.3864i	−1.14185	−	0.958130i
$818$		0			0
$819$	19.3476	−	43.3943i	0.676060	−	1.51632i
$820$		0			0
$821$	−4.34257	+	24.6279i	−0.151557	+	0.859520i	0.810310	+	0.586001i	$0.199299\pi$
$821$	−4.34257	+	24.6279i	−0.151557	+	0.859520i	−0.961867	+	0.273519i	$0.911812\pi$
$822$		0			0
$823$	−47.0643	−	17.1300i	−1.64056	−	0.597115i	−0.653422	−	0.756994i	$-0.726667\pi$
$823$	−47.0643	−	17.1300i	−1.64056	−	0.597115i	−0.987137	+	0.159879i	$0.948890\pi$
$824$		0			0
$825$	42.5726	−	6.19150i	1.48219	−	0.215560i
$826$		0			0
$827$	21.7913	+	37.7437i	0.757759	+	1.31248i	0.943991	+	0.329972i	$0.107039\pi$
$827$	21.7913	+	37.7437i	0.757759	+	1.31248i	−0.186231	+	0.982506i	$0.559627\pi$
$828$		0			0
$829$	22.7935	+	39.4795i	0.791651	+	1.37118i	0.924944	+	0.380102i	$0.124111\pi$
$829$	22.7935	+	39.4795i	0.791651	+	1.37118i	−0.133294	+	0.991077i	$0.542555\pi$
$830$		0			0
$831$	14.2893	+	43.2708i	0.495689	+	1.50105i
$832$		0			0
$833$	−30.7088	−	0.621225i	−1.06400	−	0.0215242i
$834$		0			0
$835$	27.5742	−	10.0362i	0.954244	−	0.347316i
$836$		0			0
$837$	22.2375	+	31.9668i	0.768641	+	1.10493i
$838$		0			0
$839$	1.52431	−	8.64481i	0.0526251	−	0.298452i	−0.947124	−	0.320869i	$-0.896025\pi$
$839$	1.52431	−	8.64481i	0.0526251	−	0.298452i	0.999749	+	0.0224171i	$0.00713619\pi$
$840$		0			0
$841$	−17.4763	−	6.36085i	−0.602631	−	0.219340i
$842$		0			0
$843$	−55.1498	−	11.4463i	−1.89946	−	0.394233i
$844$		0			0
$845$	79.3828			2.73085
$846$		0			0
$847$	2.14572	+	2.61033i	0.0737277	+	0.0896920i
$848$		0			0
$849$	−56.2949	+	8.18718i	−1.93203	+	0.280983i
$850$		0			0
$851$	−23.4149	−	8.52232i	−0.802652	−	0.292141i
$852$		0			0
$853$	15.3438	+	12.8750i	0.525362	+	0.440831i	0.866496	−	0.499184i	$-0.166367\pi$
$853$	15.3438	+	12.8750i	0.525362	+	0.440831i	−0.341135	+	0.940014i	$0.610811\pi$
$854$		0			0
$855$	62.2291	−	46.1303i	2.12819	−	1.57762i
$856$		0			0
$857$	−6.67634	+	37.8634i	−0.228059	+	1.29339i	0.628690	+	0.777656i	$0.283591\pi$
$857$	−6.67634	+	37.8634i	−0.228059	+	1.29339i	−0.856749	+	0.515733i	$0.827520\pi$
$858$		0			0
$859$	30.0103	+	10.9229i	1.02394	+	0.372683i	0.798770	−	0.601637i	$-0.205485\pi$
$859$	30.0103	+	10.9229i	1.02394	+	0.372683i	0.225168	+	0.974320i	$0.427707\pi$
$860$		0			0
$861$	7.25569	−	5.60688i	0.247273	−	0.191082i
$862$		0			0
$863$	−25.6447	−	44.4180i	−0.872957	−	1.51201i	−0.858923	−	0.512105i	$-0.828866\pi$
$863$	−25.6447	−	44.4180i	−0.872957	−	1.51201i	−0.0140341	−	0.999902i	$-0.504467\pi$
$864$		0			0
$865$	−1.00064	+	1.73316i	−0.0340228	+	0.0589292i
$866$		0			0
$867$	3.43730	−	1.84884i	0.116737	−	0.0627900i
$868$		0			0
$869$	−8.57814	+	7.19791i	−0.290993	+	0.244172i
$870$		0			0
$871$	9.94647	−	56.4092i	0.337023	−	1.91135i
$872$		0			0
$873$	26.5038	−	7.87567i	0.897017	−	0.266551i
$874$		0			0
$875$	16.7359	−	9.43811i	0.565777	−	0.319067i
$876$		0			0
$877$	25.5949	−	21.4767i	0.864278	−	0.725215i	−0.0986074	−	0.995126i	$-0.531439\pi$
$877$	25.5949	−	21.4767i	0.864278	−	0.725215i	0.962885	+	0.269911i	$0.0869944\pi$
$878$		0			0
$879$	−0.388229	+	0.0564617i	−0.0130946	+	0.00190440i
$880$		0			0
$881$	11.5544	+	20.0128i	0.389277	+	0.674247i	0.992352	−	0.123437i	$-0.0393916\pi$
$881$	11.5544	+	20.0128i	0.389277	+	0.674247i	−0.603076	+	0.797684i	$0.706058\pi$
$882$		0			0
$883$	−14.6561	+	25.3851i	−0.493218	+	0.854278i	−0.999969	−	0.00781380i	$-0.997513\pi$
$883$	−14.6561	+	25.3851i	−0.493218	+	0.854278i	0.506752	+	0.862092i	$0.330846\pi$
$884$		0			0
$885$	−3.18294	−	9.63857i	−0.106993	−	0.323997i
$886$		0			0
$887$	10.1864	+	57.7698i	0.342025	+	1.93972i	0.341948	+	0.939719i	$0.388913\pi$
$887$	10.1864	+	57.7698i	0.342025	+	1.93972i	7.68838e−5		1.00000i	$0.499976\pi$
$888$		0			0
$889$	−25.5893	−	15.1211i	−0.858237	−	0.507144i
$890$		0			0
$891$	−21.5465	−	23.0260i	−0.721836	−	0.771400i
$892$		0			0
$893$	7.35935	+	6.17523i	0.246271	+	0.206646i
$894$		0			0
$895$	31.4817	+	11.4584i	1.05232	+	0.383012i
$896$		0			0
$897$	−53.4650	+	59.9545i	−1.78514	+	2.00182i
$898$		0			0
$899$	25.8515	+	44.7762i	0.862197	+	1.49337i
$900$		0			0
$901$	6.42272	−	11.1245i	0.213972	−	0.370610i
$902$		0			0
$903$	−5.60275	+	25.6864i	−0.186448	+	0.854789i
$904$		0			0
$905$	−27.5822	+	23.1442i	−0.916862	+	0.769338i
$906$		0			0
$907$	−10.5105	+	3.82553i	−0.348997	+	0.127024i	−0.510570	−	0.859836i	$-0.670566\pi$
$907$	−10.5105	+	3.82553i	−0.348997	+	0.127024i	0.161573	+	0.986861i	$0.448343\pi$
$908$		0			0
$909$	7.41421	+	7.02367i	0.245914	+	0.232961i
$910$		0			0
$911$	−22.0930	+	8.04120i	−0.731975	+	0.266417i	−0.681000	−	0.732283i	$-0.738455\pi$
$911$	−22.0930	+	8.04120i	−0.731975	+	0.266417i	−0.0509742	+	0.998700i	$0.516233\pi$
$912$		0			0
$913$	4.76906	+	27.0467i	0.157833	+	0.895114i
$914$		0			0
$915$	−12.3988	−	7.66523i	−0.409893	−	0.253405i
$916$		0			0
$917$	7.90263	−	1.31118i	0.260968	−	0.0432991i
$918$		0			0
$919$	3.38455	+	5.86221i	0.111646	+	0.193376i	0.916434	−	0.400186i	$-0.131054\pi$
$919$	3.38455	+	5.86221i	0.111646	+	0.193376i	−0.804788	+	0.593562i	$0.797721\pi$
$920$		0			0
$921$	−25.6356	−	15.8485i	−0.844720	−	0.522225i
$922$		0			0
$923$	52.7132	−	44.2316i	1.73508	−	1.45590i
$924$		0			0
$925$	21.4225	−	7.79714i	0.704367	−	0.256368i
$926$		0			0
$927$	−0.514430	+	0.381346i	−0.0168961	+	0.0125250i
$928$		0			0
$929$	6.92948	−	39.2990i	0.227349	−	1.28936i	−0.630795	−	0.775949i	$-0.717271\pi$
$929$	6.92948	−	39.2990i	0.227349	−	1.28936i	0.858144	−	0.513409i	$-0.171618\pi$
$930$		0			0
$931$	51.9746	+	1.05142i	1.70340	+	0.0344590i
$932$		0			0
$933$	−21.0728	+	3.06470i	−0.689892	+	0.100334i
$934$		0			0
$935$	−53.4555			−1.74818
$936$		0			0
$937$	−9.25461	+	16.0295i	−0.302335	+	0.523660i	−0.976664	−	0.214771i	$-0.931099\pi$
$937$	−9.25461	+	16.0295i	−0.302335	+	0.523660i	0.674329	+	0.738431i	$0.264433\pi$
$938$		0			0
$939$	−17.1739	−	52.0061i	−0.560450	−	1.69715i
$940$		0			0
$941$	34.2838	−	28.7675i	1.11762	−	0.937794i	0.119138	−	0.992878i	$-0.461987\pi$
$941$	34.2838	−	28.7675i	1.11762	−	0.937794i	0.998482	+	0.0550837i	$0.0175426\pi$
$942$		0			0
$943$	−14.5686	+	5.30252i	−0.474418	+	0.172674i
$944$		0			0
$945$	−43.0507	−	20.7701i	−1.40044	−	0.675651i
$946$		0			0
$947$	−13.3123	+	4.84529i	−0.432592	+	0.157451i	−0.549133	−	0.835735i	$-0.685042\pi$
$947$	−13.3123	+	4.84529i	−0.432592	+	0.157451i	0.116540	+	0.993186i	$0.462820\pi$
$948$		0			0
$949$	12.2778	−	10.3023i	0.398554	−	0.334426i
$950$		0			0
$951$	16.2509	+	3.37288i	0.526973	+	0.109373i
$952$		0			0
$953$	−7.63802	+	13.2294i	−0.247420	+	0.428543i	−0.962809	−	0.270183i	$-0.912916\pi$
$953$	−7.63802	+	13.2294i	−0.247420	+	0.428543i	0.715390	+	0.698726i	$0.246249\pi$
$954$		0			0
$955$	−22.3259			−0.722448
$956$		0			0
$957$	−25.9357	−	32.8701i	−0.838381	−	1.06254i
$958$		0			0
$959$	12.0695	−	14.0919i	0.389744	−	0.455052i
$960$		0			0
$961$	4.36938	−	24.7800i	0.140948	−	0.799355i
$962$		0			0
$963$	−43.8962	−	2.64677i	−1.41454	−	0.0852911i
$964$		0			0
$965$	0.691804	−	0.251796i	0.0222700	−	0.00810560i
$966$		0			0
$967$	−9.10754	+	7.64213i	−0.292879	+	0.245754i	−0.777373	−	0.629040i	$-0.783448\pi$
$967$	−9.10754	+	7.64213i	−0.292879	+	0.245754i	0.484494	+	0.874795i	$0.339004\pi$
$968$		0			0
$969$	−49.7070	+	26.7362i	−1.59682	+	0.858890i
$970$		0			0
$971$	6.97589	+	12.0826i	0.223867	+	0.387749i	0.955979	−	0.293435i	$-0.0947985\pi$
$971$	6.97589	+	12.0826i	0.223867	+	0.387749i	−0.732112	+	0.681184i	$0.761465\pi$
$972$		0			0
$973$	−14.3897	+	38.3250i	−0.461313	+	1.22864i
$974$		0			0
$975$	2.21273	−	73.4620i	0.0708641	−	2.35267i
$976$		0			0
$977$	−3.17255	−	17.9924i	−0.101499	−	0.575629i	−0.992561	−	0.121748i	$-0.961150\pi$
$977$	−3.17255	−	17.9924i	−0.101499	−	0.575629i	0.891062	−	0.453881i	$-0.149961\pi$
$978$		0			0
$979$	25.2019	−	9.17276i	0.805458	−	0.293163i
$980$		0			0
$981$	−22.3105	−	44.6514i	−0.712320	−	1.42561i
$982$		0			0
$983$	−26.9837	+	9.82128i	−0.860648	+	0.313250i	−0.734374	−	0.678745i	$-0.762524\pi$
$983$	−26.9837	+	9.82128i	−0.860648	+	0.313250i	−0.126274	+	0.991995i	$0.540302\pi$
$984$		0			0
$985$	43.7317	−	36.6952i	1.39341	−	1.16921i
$986$		0			0
$987$	1.26334	−	5.79189i	0.0402125	−	0.184358i
$988$		0			0
$989$	22.2251	−	38.4951i	0.706718	−	1.22407i
$990$		0			0
$991$	20.9917	+	36.3586i	0.666822	+	1.15497i	0.978788	+	0.204876i	$0.0656792\pi$
$991$	20.9917	+	36.3586i	0.666822	+	1.15497i	−0.311966	+	0.950093i	$0.600987\pi$
$992$		0			0
$993$	5.74532	+	1.19244i	0.182322	+	0.0378410i
$994$		0			0
$995$	−33.2112	−	12.0879i	−1.05286	−	0.383211i
$996$		0			0
$997$	−0.805043	−	0.675511i	−0.0254960	−	0.0213936i	0.629951	−	0.776635i	$-0.283075\pi$
$997$	−0.805043	−	0.675511i	−0.0254960	−	0.0213936i	−0.655447	+	0.755242i	$0.727520\pi$
$998$		0			0
$999$	−13.6593	−	9.62693i	−0.432161	−	0.304583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.20	yes	144
7.2	even	3		756.2.bp.a.457.14	yes	144
27.13	even	9		756.2.bp.a.445.14	✓	144
189.121	even	9	inner	756.2.bq.a.121.20	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.14	✓	144	27.13	even	9
756.2.bp.a.457.14	yes	144	7.2	even	3
756.2.bq.a.25.20	yes	144	1.1	even	1	trivial
756.2.bq.a.121.20	yes	144	189.121	even	9	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.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52539 - 0.820472i) q^{3} +(-3.26720 - 1.18916i) q^{5} +(-0.0267571 + 2.64562i) q^{7} +(1.65365 - 2.50309i) q^{9} +O(q^{10})\)	\(q+(1.52539 - 0.820472i) q^{3} +(-3.26720 - 1.18916i) q^{5} +(-0.0267571 + 2.64562i) q^{7} +(1.65365 - 2.50309i) q^{9} +(3.29257 - 1.19840i) q^{11} +(-1.03945 - 5.89501i) q^{13} +(-5.95944 + 0.866704i) q^{15} +4.38787 q^{17} -7.42646 q^{19} +(2.12984 + 4.05756i) q^{21} +(-1.34542 - 7.63027i) q^{23} +(5.43025 + 4.55652i) q^{25} +(0.468756 - 5.17497i) q^{27} +(1.19802 - 6.79431i) q^{29} +(-5.74085 + 4.81715i) q^{31} +(4.03921 - 4.52949i) q^{33} +(3.23349 - 8.61193i) q^{35} +(1.60801 - 2.78515i) q^{37} +(-6.42226 - 8.13937i) q^{39} +(-0.347466 - 1.97058i) q^{41} +(4.39481 + 3.68768i) q^{43} +(-8.37938 + 6.21162i) q^{45} +(-0.990964 - 0.831517i) q^{47} +(-6.99857 - 0.141578i) q^{49} +(6.69323 - 3.60012i) q^{51} +(1.46375 - 2.53528i) q^{53} -12.1826 q^{55} +(-11.3283 + 6.09320i) q^{57} +(0.292690 + 1.65993i) q^{59} +(1.85426 + 1.55590i) q^{61} +(6.57796 + 4.44190i) q^{63} +(-3.61404 + 20.4962i) q^{65} +(8.99190 + 3.27278i) q^{67} +(-8.31272 - 10.5353i) q^{69} +(5.74781 + 9.95550i) q^{71} +(1.33876 + 2.31880i) q^{73} +(12.0218 + 2.49512i) q^{75} +(3.08240 + 8.74294i) q^{77} +(-3.00314 + 1.09305i) q^{79} +(-3.53088 - 8.27846i) q^{81} +(-1.36108 + 7.71907i) q^{83} +(-14.3360 - 5.21789i) q^{85} +(-3.74709 - 11.3469i) q^{87} +7.65419 q^{89} +(15.6237 - 2.59225i) q^{91} +(-4.80472 + 12.0583i) q^{93} +(24.2637 + 8.83127i) q^{95} +(7.06016 + 5.92418i) q^{97} +(2.44507 - 10.2233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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