LMFDB - Embedded newform 1134.2.h.r.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1134.541
Dual form			1134.2.h.r.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} +1.00000 q^{8} +4.24264 q^{11} +(-3.12132 - 5.40629i) q^{13} +(-2.62132 + 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 - 3.67423i) q^{22} +7.24264 q^{23} -5.00000 q^{25} +(-3.12132 + 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(2.12132 - 3.67423i) q^{29} +(-0.378680 + 0.655892i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} +6.24264 q^{38} +(2.74264 + 4.75039i) q^{41} +(3.24264 - 5.61642i) q^{43} +(-2.12132 + 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} +(-6.62132 - 11.4685i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(2.50000 + 4.33013i) q^{50} +6.24264 q^{52} +(-2.12132 - 3.67423i) q^{53} +(1.00000 - 2.44949i) q^{56} -4.24264 q^{58} +(-3.12132 - 5.40629i) q^{61} +0.757359 q^{62} +1.00000 q^{64} +(4.12132 - 7.13834i) q^{67} -7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} -4.00000 q^{74} +(-3.12132 - 5.40629i) q^{76} +(4.24264 - 10.3923i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(2.74264 - 4.75039i) q^{82} +(-3.87868 + 6.71807i) q^{83} -6.48528 q^{86} +4.24264 q^{88} +(2.74264 - 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(-3.62132 + 6.27231i) q^{92} +(-6.62132 + 11.4685i) q^{94} +(6.24264 - 10.8126i) q^{97} +(-1.74264 + 6.77962i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{19} + 12 q^{23} - 20 q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} - 2 q^{32} + 8 q^{37} + 8 q^{38} - 6 q^{41} - 4 q^{43} - 6 q^{46}+ \cdots + 10 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^19 + 12 * q^23 - 20 * q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 - 2 * q^32 + 8 * q^37 + 8 * q^38 - 6 * q^41 - 4 * q^43 - 6 * q^46 - 18 * q^47 - 20 * q^49 + 10 * q^50 + 8 * q^52 + 4 * q^56 - 4 * q^61 + 20 * q^62 + 4 * q^64 + 8 * q^67 - 12 * q^71 + 14 * q^73 - 16 * q^74 - 4 * q^76 - 10 * q^79 - 6 * q^82 - 24 * q^83 + 8 * q^86 - 6 * q^89 - 40 * q^91 - 6 * q^92 - 18 * q^94 + 8 * q^97 + 10 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$7$	1.00000	−	2.44949i	0.377964	−	0.925820i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	4.24264			1.27920			0.639602	−	0.768706i	$-0.279099\pi$
$11$	4.24264			1.27920			0.639602	+	0.768706i	$0.279099\pi$
$12$		0			0
$13$	−3.12132	−	5.40629i	−0.865699	−	1.49943i	−0.866352	−	0.499434i	$-0.833541\pi$
$13$	−3.12132	−	5.40629i	−0.865699	−	1.49943i	0.000653431	−	1.00000i	$-0.499792\pi$
$14$	−2.62132	+	0.358719i	−0.700577	+	0.0958718i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	0.246462	+	0.969153i	$0.420732\pi$
$19$	−3.12132	+	5.40629i	−0.716080	+	1.24029i	−0.962542	+	0.271134i	$0.912601\pi$
$20$		0			0
$21$		0			0
$22$	−2.12132	−	3.67423i	−0.452267	−	0.783349i
$23$	7.24264			1.51019			0.755097	−	0.655613i	$-0.227590\pi$
$23$	7.24264			1.51019			0.755097	+	0.655613i	$0.227590\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	−3.12132	+	5.40629i	−0.612141	+	1.06026i
$27$		0			0
$28$	1.62132	+	2.09077i	0.306401	+	0.395118i
$29$	2.12132	−	3.67423i	0.393919	−	0.682288i	−0.599043	−	0.800717i	$-0.704452\pi$
$29$	2.12132	−	3.67423i	0.393919	−	0.682288i	0.992963	+	0.118428i	$0.0377856\pi$
$30$		0			0
$31$	−0.378680	+	0.655892i	−0.0680129	+	0.117802i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−0.378680	+	0.655892i	−0.0680129	+	0.117802i	0.830014	+	0.557743i	$0.188333\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	6.24264			1.01269
$39$		0			0
$40$		0			0
$41$	2.74264	+	4.75039i	0.428329	+	0.741887i	0.996725	−	0.0808682i	$-0.0257693\pi$
$41$	2.74264	+	4.75039i	0.428329	+	0.741887i	−0.568396	+	0.822755i	$0.692436\pi$
$42$		0			0
$43$	3.24264	−	5.61642i	0.494498	−	0.856496i	−0.505482	−	0.862837i	$-0.668685\pi$
$43$	3.24264	−	5.61642i	0.494498	−	0.856496i	0.999980	+	0.00634147i	$0.00201857\pi$
$44$	−2.12132	+	3.67423i	−0.319801	+	0.553912i
$45$		0			0
$46$	−3.62132	−	6.27231i	−0.533935	−	0.924802i
$47$	−6.62132	−	11.4685i	−0.965819	−	1.67285i	−0.707399	−	0.706815i	$-0.750131\pi$
$47$	−6.62132	−	11.4685i	−0.965819	−	1.67285i	−0.258420	−	0.966033i	$-0.583202\pi$
$48$		0			0
$49$	−5.00000	−	4.89898i	−0.714286	−	0.699854i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$		0			0
$52$	6.24264			0.865699
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	0.682752	−	0.730650i	$-0.260783\pi$
$53$	−2.12132	−	3.67423i	−0.291386	−	0.504695i	−0.974138	+	0.225955i	$0.927450\pi$
$54$		0			0
$55$		0			0
$56$	1.00000	−	2.44949i	0.133631	−	0.327327i
$57$		0			0
$58$	−4.24264			−0.557086
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	−3.12132	−	5.40629i	−0.399644	−	0.692204i	0.594038	−	0.804437i	$-0.297533\pi$
$61$	−3.12132	−	5.40629i	−0.399644	−	0.692204i	−0.993682	+	0.112233i	$0.964200\pi$
$62$	0.757359			0.0961847
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	4.12132	−	7.13834i	0.503499	−	0.872087i	−0.496492	−	0.868041i	$-0.665379\pi$
$67$	4.12132	−	7.13834i	0.503499	−	0.872087i	0.999992	−	0.00404550i	$-0.00128773\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.24264			−0.859543			−0.429772	−	0.902938i	$-0.641406\pi$
$71$	−7.24264			−0.859543			−0.429772	+	0.902938i	$0.641406\pi$
$72$		0			0
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−4.00000			−0.464991
$75$		0			0
$76$	−3.12132	−	5.40629i	−0.358040	−	0.620143i
$77$	4.24264	−	10.3923i	0.483494	−	1.18431i
$78$		0			0
$79$	−4.62132	−	8.00436i	−0.519939	−	0.900561i	−0.999731	−	0.0231789i	$-0.992621\pi$
$79$	−4.62132	−	8.00436i	−0.519939	−	0.900561i	0.479792	−	0.877382i	$-0.340712\pi$
$80$		0			0
$81$		0			0
$82$	2.74264	−	4.75039i	0.302874	−	0.524593i
$83$	−3.87868	+	6.71807i	−0.425740	+	0.737404i	−0.996489	−	0.0837207i	$-0.973320\pi$
$83$	−3.87868	+	6.71807i	−0.425740	+	0.737404i	0.570749	+	0.821125i	$0.306653\pi$
$84$		0			0
$85$		0			0
$86$	−6.48528			−0.699326
$87$		0			0
$88$	4.24264			0.452267
$89$	2.74264	−	4.75039i	0.290719	−	0.503541i	−0.683261	−	0.730175i	$-0.739439\pi$
$89$	2.74264	−	4.75039i	0.290719	−	0.503541i	0.973980	+	0.226634i	$0.0727721\pi$
$90$		0			0
$91$	−16.3640	+	2.23936i	−1.71541	+	0.234748i
$92$	−3.62132	+	6.27231i	−0.377549	+	0.653934i
$93$		0			0
$94$	−6.62132	+	11.4685i	−0.682937	+	1.18288i
$95$		0			0
$96$		0			0
$97$	6.24264	−	10.8126i	0.633844	−	1.09785i	−0.352915	−	0.935656i	$-0.614809\pi$
$97$	6.24264	−	10.8126i	0.633844	−	1.09785i	0.986759	−	0.162195i	$-0.0518573\pi$
$98$	−1.74264	+	6.77962i	−0.176033	+	0.684845i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	7.75736			0.771886			0.385943	−	0.922523i	$-0.373876\pi$
$101$	7.75736			0.771886			0.385943	+	0.922523i	$0.373876\pi$
$102$		0			0
$103$	0.757359			0.0746248			0.0373124	−	0.999304i	$-0.488120\pi$
$103$	0.757359			0.0746248			0.0373124	+	0.999304i	$0.488120\pi$
$104$	−3.12132	−	5.40629i	−0.306071	−	0.530130i
$105$		0			0
$106$	−2.12132	+	3.67423i	−0.206041	+	0.356873i
$107$	1.24264	−	2.15232i	0.120131	−	0.208072i	−0.799688	−	0.600415i	$-0.795002\pi$
$107$	1.24264	−	2.15232i	0.120131	−	0.208072i	0.919819	+	0.392343i	$0.128335\pi$
$108$		0			0
$109$	1.12132	+	1.94218i	0.107403	+	0.186027i	0.914717	−	0.404094i	$-0.132413\pi$
$109$	1.12132	+	1.94218i	0.107403	+	0.186027i	−0.807314	+	0.590122i	$0.799080\pi$
$110$		0			0
$111$		0			0
$112$	−2.62132	+	0.358719i	−0.247691	+	0.0338958i
$113$	10.2426	+	17.7408i	0.963547	+	1.66891i	0.713470	+	0.700686i	$0.247122\pi$
$113$	10.2426	+	17.7408i	0.963547	+	1.66891i	0.250076	+	0.968226i	$0.419544\pi$
$114$		0			0
$115$		0			0
$116$	2.12132	+	3.67423i	0.196960	+	0.341144i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	7.00000			0.636364
$122$	−3.12132	+	5.40629i	−0.282591	+	0.489462i
$123$		0			0
$124$	−0.378680	−	0.655892i	−0.0340064	−	0.0589009i
$125$		0			0
$126$		0			0
$127$	6.75736			0.599619			0.299809	−	0.953999i	$-0.403077\pi$
$127$	6.75736			0.599619			0.299809	+	0.953999i	$0.403077\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−7.75736			−0.677764			−0.338882	−	0.940829i	$-0.610049\pi$
$131$	−7.75736			−0.677764			−0.338882	+	0.940829i	$0.610049\pi$
$132$		0			0
$133$	10.1213	+	13.0519i	0.877630	+	1.13175i
$134$	−8.24264			−0.712056
$135$		0			0
$136$		0			0
$137$	−19.9706			−1.70620			−0.853100	−	0.521747i	$-0.825280\pi$
$137$	−19.9706			−1.70620			−0.853100	+	0.521747i	$0.825280\pi$
$138$		0			0
$139$	2.36396	+	4.09450i	0.200509	+	0.347291i	0.948692	−	0.316200i	$-0.102407\pi$
$139$	2.36396	+	4.09450i	0.200509	+	0.347291i	−0.748184	+	0.663491i	$0.769074\pi$
$140$		0			0
$141$		0			0
$142$	3.62132	+	6.27231i	0.303894	+	0.526361i
$143$	−13.2426	−	22.9369i	−1.10741	−	1.91808i
$144$		0			0
$145$		0			0
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$		0			0
$148$	2.00000	+	3.46410i	0.164399	+	0.284747i
$149$	16.2426			1.33065			0.665324	−	0.746554i	$-0.268293\pi$
$149$	16.2426			1.33065			0.665324	+	0.746554i	$0.268293\pi$
$150$		0			0
$151$	−2.75736			−0.224391			−0.112195	−	0.993686i	$-0.535788\pi$
$151$	−2.75736			−0.224391			−0.112195	+	0.993686i	$0.535788\pi$
$152$	−3.12132	+	5.40629i	−0.253173	+	0.438508i
$153$		0			0
$154$	−11.1213	+	1.52192i	−0.896182	+	0.122640i
$155$		0			0
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−4.62132	+	8.00436i	−0.367653	+	0.636793i
$159$		0			0
$160$		0			0
$161$	7.24264	−	17.7408i	0.570800	−	1.39817i
$162$		0			0
$163$	5.87868	−	10.1822i	0.460454	−	0.797529i	−0.538530	−	0.842606i	$-0.681020\pi$
$163$	5.87868	−	10.1822i	0.460454	−	0.797529i	0.998984	+	0.0450772i	$0.0143534\pi$
$164$	−5.48528			−0.428329
$165$		0			0
$166$	7.75736			0.602088
$167$	−12.1066	−	20.9692i	−0.936837	−	1.62265i	−0.771325	−	0.636441i	$-0.780406\pi$
$167$	−12.1066	−	20.9692i	−0.936837	−	1.62265i	−0.165512	−	0.986208i	$-0.552928\pi$
$168$		0			0
$169$	−12.9853	+	22.4912i	−0.998868	+	1.73009i
$170$		0			0
$171$		0			0
$172$	3.24264	+	5.61642i	0.247249	+	0.428248i
$173$	5.48528	+	9.50079i	0.417038	+	0.722331i	0.995640	−	0.0932788i	$-0.0297348\pi$
$173$	5.48528	+	9.50079i	0.417038	+	0.722331i	−0.578602	+	0.815610i	$0.696401\pi$
$174$		0			0
$175$	−5.00000	+	12.2474i	−0.377964	+	0.925820i
$176$	−2.12132	−	3.67423i	−0.159901	−	0.276956i
$177$		0			0
$178$	−5.48528			−0.411139
$179$	8.12132	+	14.0665i	0.607016	+	1.05138i	0.991729	+	0.128346i	$0.0409669\pi$
$179$	8.12132	+	14.0665i	0.607016	+	1.05138i	−0.384713	+	0.923036i	$0.625700\pi$
$180$		0			0
$181$	−20.2426			−1.50462			−0.752312	−	0.658807i	$-0.771061\pi$
$181$	−20.2426			−1.50462			−0.752312	+	0.658807i	$0.771061\pi$
$182$	10.1213	+	13.0519i	0.750242	+	0.967473i
$183$		0			0
$184$	7.24264			0.533935
$185$		0			0
$186$		0			0
$187$		0			0
$188$	13.2426			0.965819
$189$		0			0
$190$		0			0
$191$	−4.24264	−	7.34847i	−0.306987	−	0.531717i	0.670715	−	0.741715i	$-0.265987\pi$
$191$	−4.24264	−	7.34847i	−0.306987	−	0.531717i	−0.977702	+	0.209999i	$0.932654\pi$
$192$		0			0
$193$	2.25736	−	3.90986i	0.162488	−	0.281438i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	2.25736	−	3.90986i	0.162488	−	0.281438i	0.935760	+	0.352636i	$0.114715\pi$
$194$	−12.4853			−0.896391
$195$		0			0
$196$	6.74264	−	1.88064i	0.481617	−	0.134331i
$197$	16.9706			1.20910			0.604551	−	0.796566i	$-0.293352\pi$
$197$	16.9706			1.20910			0.604551	+	0.796566i	$0.293352\pi$
$198$		0			0
$199$	7.37868	+	12.7802i	0.523061	+	0.905968i	0.999640	+	0.0268362i	$0.00854325\pi$
$199$	7.37868	+	12.7802i	0.523061	+	0.905968i	−0.476579	+	0.879132i	$0.658123\pi$
$200$	−5.00000			−0.353553
$201$		0			0
$202$	−3.87868	−	6.71807i	−0.272903	−	0.472682i
$203$	−6.87868	−	8.87039i	−0.482789	−	0.622579i
$204$		0			0
$205$		0			0
$206$	−0.378680	−	0.655892i	−0.0263839	−	0.0456982i
$207$		0			0
$208$	−3.12132	+	5.40629i	−0.216425	+	0.374858i
$209$	−13.2426	+	22.9369i	−0.916013	+	1.58658i
$210$		0			0
$211$	3.24264	+	5.61642i	0.223233	+	0.386650i	0.955788	−	0.294058i	$-0.0950057\pi$
$211$	3.24264	+	5.61642i	0.223233	+	0.386650i	−0.732555	+	0.680708i	$0.761672\pi$
$212$	4.24264			0.291386
$213$		0			0
$214$	−2.48528			−0.169890
$215$		0			0
$216$		0			0
$217$	1.22792	+	1.58346i	0.0833568	+	0.107493i
$218$	1.12132	−	1.94218i	0.0759454	−	0.131541i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	−0.992802	−	0.119767i	$-0.961785\pi$
$223$	−5.86396	+	10.1567i	−0.392680	+	0.680141i	0.600122	+	0.799908i	$0.295119\pi$
$224$	1.62132	+	2.09077i	0.108329	+	0.139695i
$225$		0			0
$226$	10.2426	−	17.7408i	0.681330	−	1.18010i
$227$	26.4853			1.75789			0.878945	−	0.476923i	$-0.158248\pi$
$227$	26.4853			1.75789			0.878945	+	0.476923i	$0.158248\pi$
$228$		0			0
$229$	24.9706			1.65010			0.825051	−	0.565059i	$-0.191147\pi$
$229$	24.9706			1.65010			0.825051	+	0.565059i	$0.191147\pi$
$230$		0			0
$231$		0			0
$232$	2.12132	−	3.67423i	0.139272	−	0.241225i
$233$	−10.2426	+	17.7408i	−0.671018	+	1.16224i	0.306598	+	0.951839i	$0.400809\pi$
$233$	−10.2426	+	17.7408i	−0.671018	+	1.16224i	−0.977616	+	0.210398i	$0.932524\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.86396	−	3.22848i	−0.120570	−	0.208833i	0.799423	−	0.600769i	$-0.205139\pi$
$239$	−1.86396	−	3.22848i	−0.120570	−	0.208833i	−0.919992	+	0.391936i	$0.871805\pi$
$240$		0			0
$241$	8.51472			0.548481			0.274241	−	0.961661i	$-0.411574\pi$
$241$	8.51472			0.548481			0.274241	+	0.961661i	$0.411574\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	6.24264			0.399644
$245$		0			0
$246$		0			0
$247$	38.9706			2.47964
$248$	−0.378680	+	0.655892i	−0.0240462	+	0.0416492i
$249$		0			0
$250$		0			0
$251$	18.7279			1.18210			0.591048	−	0.806636i	$-0.298714\pi$
$251$	18.7279			1.18210			0.591048	+	0.806636i	$0.298714\pi$
$252$		0			0
$253$	30.7279			1.93185
$254$	−3.37868	−	5.85204i	−0.211997	−	0.367190i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.48528			0.342162			0.171081	−	0.985257i	$-0.445274\pi$
$257$	5.48528			0.342162			0.171081	+	0.985257i	$0.445274\pi$
$258$		0			0
$259$	−6.48528	−	8.36308i	−0.402976	−	0.519657i
$260$		0			0
$261$		0			0
$262$	3.87868	+	6.71807i	0.239626	+	0.415044i
$263$	22.9706			1.41643			0.708213	−	0.705999i	$-0.249502\pi$
$263$	22.9706			1.41643			0.708213	+	0.705999i	$0.249502\pi$
$264$		0			0
$265$		0			0
$266$	6.24264	−	15.2913i	0.382761	−	0.937569i
$267$		0			0
$268$	4.12132	+	7.13834i	0.251750	+	0.436043i
$269$	5.48528	+	9.50079i	0.334444	+	0.579273i	0.983378	−	0.181571i	$-0.0581183\pi$
$269$	5.48528	+	9.50079i	0.334444	+	0.579273i	−0.648934	+	0.760844i	$0.724785\pi$
$270$		0			0
$271$	6.24264	−	10.8126i	0.379213	−	0.656817i	−0.611735	−	0.791063i	$-0.709528\pi$
$271$	6.24264	−	10.8126i	0.379213	−	0.656817i	0.990948	+	0.134246i	$0.0428613\pi$
$272$		0			0
$273$		0			0
$274$	9.98528	+	17.2950i	0.603233	+	1.04483i
$275$	−21.2132			−1.27920
$276$		0			0
$277$	−19.2132			−1.15441			−0.577205	−	0.816599i	$-0.695857\pi$
$277$	−19.2132			−1.15441			−0.577205	+	0.816599i	$0.695857\pi$
$278$	2.36396	−	4.09450i	0.141781	−	0.245572i
$279$		0			0
$280$		0			0
$281$	−11.2279	+	19.4473i	−0.669802	+	1.16013i	0.308158	+	0.951335i	$0.400288\pi$
$281$	−11.2279	+	19.4473i	−0.669802	+	1.16013i	−0.977959	+	0.208795i	$0.933046\pi$
$282$		0			0
$283$	−12.4853	+	21.6251i	−0.742173	+	1.28548i	0.209331	+	0.977845i	$0.432871\pi$
$283$	−12.4853	+	21.6251i	−0.742173	+	1.28548i	−0.951504	+	0.307636i	$0.900462\pi$
$284$	3.62132	−	6.27231i	0.214886	−	0.372193i
$285$		0			0
$286$	−13.2426	+	22.9369i	−0.783054	+	1.35629i
$287$	14.3787	−	1.96768i	0.848747	−	0.116148i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$		0			0
$292$	−7.00000			−0.409644
$293$	5.48528	+	9.50079i	0.320454	+	0.555042i	0.980582	−	0.196111i	$-0.0628314\pi$
$293$	5.48528	+	9.50079i	0.320454	+	0.555042i	−0.660128	+	0.751153i	$0.729498\pi$
$294$		0			0
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$		0			0
$298$	−8.12132	−	14.0665i	−0.470455	−	0.814853i
$299$	−22.6066	−	39.1558i	−1.30737	−	2.26444i
$300$		0			0
$301$	−10.5147	−	13.5592i	−0.606058	−	0.781541i
$302$	1.37868	+	2.38794i	0.0793341	+	0.137411i
$303$		0			0
$304$	6.24264			0.358040
$305$		0			0
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	6.87868	+	8.87039i	0.391949	+	0.505437i
$309$		0			0
$310$		0			0
$311$	5.48528	−	9.50079i	0.311042	−	0.538740i	−0.667546	−	0.744568i	$-0.732655\pi$
$311$	5.48528	−	9.50079i	0.311042	−	0.538740i	0.978588	+	0.205828i	$0.0659888\pi$
$312$		0			0
$313$	8.98528	+	15.5630i	0.507878	+	0.879671i	0.999958	+	0.00912090i	$0.00290331\pi$
$313$	8.98528	+	15.5630i	0.507878	+	0.879671i	−0.492080	+	0.870550i	$0.663763\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	9.24264			0.519939
$317$	8.48528	+	14.6969i	0.476581	+	0.825462i	0.999640	−	0.0268342i	$-0.00854260\pi$
$317$	8.48528	+	14.6969i	0.476581	+	0.825462i	−0.523059	+	0.852296i	$0.675209\pi$
$318$		0			0
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$		0			0
$321$		0			0
$322$	−18.9853	+	2.59808i	−1.05801	+	0.144785i
$323$		0			0
$324$		0			0
$325$	15.6066	+	27.0314i	0.865699	+	1.49943i
$326$	−11.7574			−0.651180
$327$		0			0
$328$	2.74264	+	4.75039i	0.151437	+	0.262297i
$329$	−34.7132	+	4.75039i	−1.91380	+	0.261898i
$330$		0			0
$331$	9.24264	+	16.0087i	0.508021	+	0.879919i	0.999957	+	0.00928730i	$0.00295628\pi$
$331$	9.24264	+	16.0087i	0.508021	+	0.879919i	−0.491935	+	0.870632i	$0.663710\pi$
$332$	−3.87868	−	6.71807i	−0.212870	−	0.368702i
$333$		0			0
$334$	−12.1066	+	20.9692i	−0.662444	+	1.14739i
$335$		0			0
$336$		0			0
$337$	−2.24264	−	3.88437i	−0.122164	−	0.211595i	0.798457	−	0.602052i	$-0.205650\pi$
$337$	−2.24264	−	3.88437i	−0.122164	−	0.211595i	−0.920621	+	0.390457i	$0.872317\pi$
$338$	25.9706			1.41261
$339$		0			0
$340$		0			0
$341$	−1.60660	+	2.78272i	−0.0870024	+	0.150693i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	3.24264	−	5.61642i	0.174831	−	0.302817i
$345$		0			0
$346$	5.48528	−	9.50079i	0.294891	−	0.510765i
$347$	3.36396	−	5.82655i	0.180587	−	0.312786i	−0.761494	−	0.648172i	$-0.775534\pi$
$347$	3.36396	−	5.82655i	0.180587	−	0.312786i	0.942081	+	0.335387i	$0.108867\pi$
$348$		0			0
$349$	−12.4853	+	21.6251i	−0.668322	+	1.15757i	0.310051	+	0.950720i	$0.399654\pi$
$349$	−12.4853	+	21.6251i	−0.668322	+	1.15757i	−0.978373	+	0.206848i	$0.933680\pi$
$350$	13.1066	−	1.79360i	0.700577	−	0.0958718i
$351$		0			0
$352$	−2.12132	+	3.67423i	−0.113067	+	0.195837i
$353$	21.0000			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$353$	21.0000			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$354$		0			0
$355$		0			0
$356$	2.74264	+	4.75039i	0.145360	+	0.251770i
$357$		0			0
$358$	8.12132	−	14.0665i	0.429225	−	0.743440i
$359$	−5.37868	+	9.31615i	−0.283876	+	0.491687i	−0.972336	−	0.233587i	$-0.924954\pi$
$359$	−5.37868	+	9.31615i	−0.283876	+	0.491687i	0.688460	+	0.725274i	$0.258287\pi$
$360$		0			0
$361$	−9.98528	−	17.2950i	−0.525541	−	0.910264i
$362$	10.1213	+	17.5306i	0.531965	+	0.921390i
$363$		0			0
$364$	6.24264	−	15.2913i	0.327203	−	0.801481i
$365$		0			0
$366$		0			0
$367$	11.7279			0.612193			0.306096	−	0.952001i	$-0.400977\pi$
$367$	11.7279			0.612193			0.306096	+	0.952001i	$0.400977\pi$
$368$	−3.62132	−	6.27231i	−0.188774	−	0.326967i
$369$		0			0
$370$		0			0
$371$	−11.1213	+	1.52192i	−0.577390	+	0.0790140i
$372$		0			0
$373$	−7.21320			−0.373486			−0.186743	−	0.982409i	$-0.559793\pi$
$373$	−7.21320			−0.373486			−0.186743	+	0.982409i	$0.559793\pi$
$374$		0			0
$375$		0			0
$376$	−6.62132	−	11.4685i	−0.341469	−	0.591441i
$377$	−26.4853			−1.36406
$378$		0			0
$379$	1.27208			0.0653423			0.0326711	−	0.999466i	$-0.489599\pi$
$379$	1.27208			0.0653423			0.0326711	+	0.999466i	$0.489599\pi$
$380$		0			0
$381$		0			0
$382$	−4.24264	+	7.34847i	−0.217072	+	0.375980i
$383$	−24.2132			−1.23724			−0.618618	−	0.785692i	$-0.712307\pi$
$383$	−24.2132			−1.23724			−0.618618	+	0.785692i	$0.712307\pi$
$384$		0			0
$385$		0			0
$386$	−4.51472			−0.229793
$387$		0			0
$388$	6.24264	+	10.8126i	0.316922	+	0.548925i
$389$	10.2426			0.519322			0.259661	−	0.965700i	$-0.416389\pi$
$389$	10.2426			0.519322			0.259661	+	0.965700i	$0.416389\pi$
$390$		0			0
$391$		0			0
$392$	−5.00000	−	4.89898i	−0.252538	−	0.247436i
$393$		0			0
$394$	−8.48528	−	14.6969i	−0.427482	−	0.740421i
$395$		0			0
$396$		0			0
$397$	10.1213	−	17.5306i	0.507975	−	0.879838i	−0.491983	−	0.870605i	$-0.663728\pi$
$397$	10.1213	−	17.5306i	0.507975	−	0.879838i	0.999957	−	0.00923278i	$-0.00293893\pi$
$398$	7.37868	−	12.7802i	0.369860	−	0.640616i
$399$		0			0
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	29.4853			1.47242			0.736212	−	0.676751i	$-0.236612\pi$
$401$	29.4853			1.47242			0.736212	+	0.676751i	$0.236612\pi$
$402$		0			0
$403$	4.72792			0.235515
$404$	−3.87868	+	6.71807i	−0.192972	+	0.334236i
$405$		0			0
$406$	−4.24264	+	10.3923i	−0.210559	+	0.515761i
$407$	8.48528	−	14.6969i	0.420600	−	0.728500i
$408$		0			0
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	0.00141047	+	0.999999i	$0.499551\pi$
$409$	−17.5000	+	30.3109i	−0.865319	+	1.49878i	−0.866730	+	0.498778i	$0.833782\pi$
$410$		0			0
$411$		0			0
$412$	−0.378680	+	0.655892i	−0.0186562	+	0.0323135i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	6.24264			0.306071
$417$		0			0
$418$	26.4853			1.29544
$419$	3.87868	+	6.71807i	0.189486	+	0.328199i	0.945079	−	0.326842i	$-0.105985\pi$
$419$	3.87868	+	6.71807i	0.189486	+	0.328199i	−0.755593	+	0.655041i	$0.772651\pi$
$420$		0			0
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	−0.638656	−	0.769492i	$-0.720509\pi$
$421$	7.12132	−	12.3345i	0.347072	−	0.601146i	0.985728	+	0.168346i	$0.0538426\pi$
$422$	3.24264	−	5.61642i	0.157849	−	0.273403i
$423$		0			0
$424$	−2.12132	−	3.67423i	−0.103020	−	0.178437i
$425$		0			0
$426$		0			0
$427$	−16.3640	+	2.23936i	−0.791908	+	0.108370i
$428$	1.24264	+	2.15232i	0.0600653	+	0.104036i
$429$		0			0
$430$		0			0
$431$	18.6213	+	32.2531i	0.896957	+	1.55358i	0.831363	+	0.555729i	$0.187561\pi$
$431$	18.6213	+	32.2531i	0.896957	+	1.55358i	0.0655943	+	0.997846i	$0.479106\pi$
$432$		0			0
$433$	3.97056			0.190813			0.0954065	−	0.995438i	$-0.469585\pi$
$433$	3.97056			0.190813			0.0954065	+	0.995438i	$0.469585\pi$
$434$	0.757359	−	1.85514i	0.0363544	−	0.0890498i
$435$		0			0
$436$	−2.24264			−0.107403
$437$	−22.6066	+	39.1558i	−1.08142	+	1.87308i
$438$		0			0
$439$	−5.86396	−	10.1567i	−0.279872	−	0.484752i	0.691481	−	0.722395i	$-0.256959\pi$
$439$	−5.86396	−	10.1567i	−0.279872	−	0.484752i	−0.971353	+	0.237643i	$0.923625\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.75736	−	8.23999i	−0.226029	−	0.391494i	0.730599	−	0.682807i	$-0.239241\pi$
$443$	−4.75736	−	8.23999i	−0.226029	−	0.391494i	−0.956628	+	0.291313i	$0.905908\pi$
$444$		0			0
$445$		0			0
$446$	11.7279			0.555333
$447$		0			0
$448$	1.00000	−	2.44949i	0.0472456	−	0.115728i
$449$	−4.97056			−0.234575			−0.117288	−	0.993098i	$-0.537420\pi$
$449$	−4.97056			−0.234575			−0.117288	+	0.993098i	$0.537420\pi$
$450$		0			0
$451$	11.6360	+	20.1542i	0.547920	+	0.949025i
$452$	−20.4853			−0.963547
$453$		0			0
$454$	−13.2426	−	22.9369i	−0.621508	−	1.07648i
$455$		0			0
$456$		0			0
$457$	−5.75736	−	9.97204i	−0.269318	−	0.466472i	0.699368	−	0.714762i	$-0.253465\pi$
$457$	−5.75736	−	9.97204i	−0.269318	−	0.466472i	−0.968686	+	0.248290i	$0.920132\pi$
$458$	−12.4853	−	21.6251i	−0.583399	−	1.01048i
$459$		0			0
$460$		0			0
$461$	−17.1213	+	29.6550i	−0.797419	+	1.38117i	0.123872	+	0.992298i	$0.460469\pi$
$461$	−17.1213	+	29.6550i	−0.797419	+	1.38117i	−0.921291	+	0.388873i	$0.872865\pi$
$462$		0			0
$463$	4.37868	+	7.58410i	0.203495	+	0.352463i	0.949652	−	0.313307i	$-0.101437\pi$
$463$	4.37868	+	7.58410i	0.203495	+	0.352463i	−0.746158	+	0.665769i	$0.768103\pi$
$464$	−4.24264			−0.196960
$465$		0			0
$466$	20.4853			0.948962
$467$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$467$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$468$		0			0
$469$	−13.3640	−	17.2335i	−0.617090	−	0.795768i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	13.7574	−	23.8284i	0.632564	−	1.09563i
$474$		0			0
$475$	15.6066	−	27.0314i	0.716080	−	1.24029i
$476$		0			0
$477$		0			0
$478$	−1.86396	+	3.22848i	−0.0852556	+	0.147667i
$479$	−13.2426			−0.605072			−0.302536	−	0.953138i	$-0.597833\pi$
$479$	−13.2426			−0.605072			−0.302536	+	0.953138i	$0.597833\pi$
$480$		0			0
$481$	−24.9706			−1.13856
$482$	−4.25736	−	7.37396i	−0.193917	−	0.335875i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$		0			0
$486$		0			0
$487$	1.37868	+	2.38794i	0.0624739	+	0.108208i	0.895571	−	0.444919i	$-0.146768\pi$
$487$	1.37868	+	2.38794i	0.0624739	+	0.108208i	−0.833097	+	0.553127i	$0.813434\pi$
$488$	−3.12132	−	5.40629i	−0.141296	−	0.244731i
$489$		0			0
$490$		0			0
$491$	−3.36396	−	5.82655i	−0.151813	−	0.262949i	0.780081	−	0.625679i	$-0.215178\pi$
$491$	−3.36396	−	5.82655i	−0.151813	−	0.262949i	−0.931894	+	0.362730i	$0.881845\pi$
$492$		0			0
$493$		0			0
$494$	−19.4853	−	33.7495i	−0.876684	−	1.51846i
$495$		0			0
$496$	0.757359			0.0340064
$497$	−7.24264	+	17.7408i	−0.324877	+	0.795782i
$498$		0			0
$499$	−10.7279			−0.480248			−0.240124	−	0.970742i	$-0.577188\pi$
$499$	−10.7279			−0.480248			−0.240124	+	0.970742i	$0.577188\pi$
$500$		0			0
$501$		0			0
$502$	−9.36396	−	16.2189i	−0.417934	−	0.723883i
$503$	−24.2132			−1.07961			−0.539807	−	0.841789i	$-0.681503\pi$
$503$	−24.2132			−1.07961			−0.539807	+	0.841789i	$0.681503\pi$
$504$		0			0
$505$		0			0
$506$	−15.3640	−	26.6112i	−0.683011	−	1.18301i
$507$		0			0
$508$	−3.37868	+	5.85204i	−0.149905	+	0.259643i
$509$	7.75736			0.343839			0.171919	−	0.985111i	$-0.445003\pi$
$509$	7.75736			0.343839			0.171919	+	0.985111i	$0.445003\pi$
$510$		0			0
$511$	18.3492	−	2.51104i	0.811723	−	0.111082i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−2.74264	−	4.75039i	−0.120973	−	0.209531i
$515$		0			0
$516$		0			0
$517$	−28.0919	−	48.6566i	−1.23548	−	2.13991i
$518$	−4.00000	+	9.79796i	−0.175750	+	0.430498i
$519$		0			0
$520$		0			0
$521$	−8.22792	−	14.2512i	−0.360472	−	0.624355i	0.627567	−	0.778563i	$-0.284051\pi$
$521$	−8.22792	−	14.2512i	−0.360472	−	0.624355i	−0.988039	+	0.154207i	$0.950718\pi$
$522$		0			0
$523$	10.1213	−	17.5306i	0.442574	−	0.766561i	−0.555305	−	0.831647i	$-0.687399\pi$
$523$	10.1213	−	17.5306i	0.442574	−	0.766561i	0.997880	+	0.0650852i	$0.0207319\pi$
$524$	3.87868	−	6.71807i	0.169441	−	0.293480i
$525$		0			0
$526$	−11.4853	−	19.8931i	−0.500782	−	0.867380i
$527$		0			0
$528$		0			0
$529$	29.4558			1.28069
$530$		0			0
$531$		0			0
$532$	−16.3640	+	2.23936i	−0.709468	+	0.0970884i
$533$	17.1213	−	29.6550i	0.741607	−	1.28450i
$534$		0			0
$535$		0			0
$536$	4.12132	−	7.13834i	0.178014	−	0.308329i
$537$		0			0
$538$	5.48528	−	9.50079i	0.236487	−	0.409608i
$539$	−21.2132	−	20.7846i	−0.913717	−	0.895257i
$540$		0			0
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	−0.659046	−	0.752103i	$-0.729040\pi$
$541$	7.48528	−	12.9649i	0.321817	−	0.557404i	0.980863	+	0.194699i	$0.0623730\pi$
$542$	−12.4853			−0.536289
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	3.24264	−	5.61642i	0.138645	−	0.240141i	−0.788339	−	0.615241i	$-0.789059\pi$
$547$	3.24264	−	5.61642i	0.138645	−	0.240141i	0.926984	+	0.375101i	$0.122392\pi$
$548$	9.98528	−	17.2950i	0.426550	−	0.738806i
$549$		0			0
$550$	10.6066	+	18.3712i	0.452267	+	0.783349i
$551$	13.2426	+	22.9369i	0.564155	+	0.977146i
$552$		0			0
$553$	−24.2279	+	3.31552i	−1.03028	+	0.140990i
$554$	9.60660	+	16.6391i	0.408145	+	0.706929i
$555$		0			0
$556$	−4.72792			−0.200509
$557$	20.4853	+	35.4815i	0.867989	+	1.50340i	0.864048	+	0.503409i	$0.167921\pi$
$557$	20.4853	+	35.4815i	0.867989	+	1.50340i	0.00394110	+	0.999992i	$0.498746\pi$
$558$		0			0
$559$	−40.4853			−1.71234
$560$		0			0
$561$		0			0
$562$	22.4558			0.947243
$563$	−9.36396	+	16.2189i	−0.394644	+	0.683543i	−0.993056	−	0.117645i	$-0.962465\pi$
$563$	−9.36396	+	16.2189i	−0.394644	+	0.683543i	0.598412	+	0.801189i	$0.295799\pi$
$564$		0			0
$565$		0			0
$566$	24.9706			1.04959
$567$		0			0
$568$	−7.24264			−0.303894
$569$	−12.4706	−	21.5996i	−0.522793	−	0.905504i	−0.999648	−	0.0265224i	$-0.991557\pi$
$569$	−12.4706	−	21.5996i	−0.522793	−	0.905504i	0.476855	−	0.878982i	$-0.341777\pi$
$570$		0			0
$571$	10.4853	−	18.1610i	0.438795	−	0.760016i	−0.558801	−	0.829301i	$-0.688739\pi$
$571$	10.4853	−	18.1610i	0.438795	−	0.760016i	0.997597	+	0.0692856i	$0.0220720\pi$
$572$	26.4853			1.10741
$573$		0			0
$574$	−8.89340	−	11.4685i	−0.371203	−	0.478684i
$575$	−36.2132			−1.51019
$576$		0			0
$577$	−17.9706	−	31.1259i	−0.748124	−	1.29579i	−0.948721	−	0.316115i	$-0.897621\pi$
$577$	−17.9706	−	31.1259i	−0.748124	−	1.29579i	0.200596	−	0.979674i	$-0.435712\pi$
$578$	−17.0000			−0.707107
$579$		0			0
$580$		0			0
$581$	12.5772	+	16.2189i	0.521789	+	0.672872i
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	3.50000	+	6.06218i	0.144831	+	0.250855i
$585$		0			0
$586$	5.48528	−	9.50079i	0.226595	−	0.392474i
$587$	1.60660	−	2.78272i	0.0663115	−	0.114855i	−0.830963	−	0.556327i	$-0.812210\pi$
$587$	1.60660	−	2.78272i	0.0663115	−	0.114855i	0.897275	+	0.441472i	$0.145544\pi$
$588$		0			0
$589$	−2.36396	−	4.09450i	−0.0974053	−	0.168711i
$590$		0			0
$591$		0			0
$592$	−4.00000			−0.164399
$593$	2.74264	−	4.75039i	0.112627	−	0.195075i	−0.804202	−	0.594356i	$-0.797407\pi$
$593$	2.74264	−	4.75039i	0.112627	−	0.195075i	0.916829	+	0.399281i	$0.130740\pi$
$594$		0			0
$595$		0			0
$596$	−8.12132	+	14.0665i	−0.332662	+	0.576188i
$597$		0			0
$598$	−22.6066	+	39.1558i	−0.924453	+	1.60120i
$599$	−11.4853	+	19.8931i	−0.469276	+	0.812810i	−0.999383	−	0.0351210i	$-0.988818\pi$
$599$	−11.4853	+	19.8931i	−0.469276	+	0.812810i	0.530107	+	0.847931i	$0.322152\pi$
$600$		0			0
$601$	8.98528	−	15.5630i	0.366517	−	0.634827i	−0.622501	−	0.782619i	$-0.713883\pi$
$601$	8.98528	−	15.5630i	0.366517	−	0.634827i	0.989018	+	0.147792i	$0.0472167\pi$
$602$	−6.48528	+	15.8856i	−0.264320	+	0.647450i
$603$		0			0
$604$	1.37868	−	2.38794i	0.0560977	−	0.0971640i
$605$		0			0
$606$		0			0
$607$	−38.9706			−1.58177			−0.790883	−	0.611967i	$-0.790378\pi$
$607$	−38.9706			−1.58177			−0.790883	+	0.611967i	$0.790378\pi$
$608$	−3.12132	−	5.40629i	−0.126586	−	0.219254i
$609$		0			0
$610$		0			0
$611$	−41.3345	+	71.5935i	−1.67222	+	2.89636i
$612$		0			0
$613$	18.9706	+	32.8580i	0.766214	+	1.32712i	0.939602	+	0.342268i	$0.111195\pi$
$613$	18.9706	+	32.8580i	0.766214	+	1.32712i	−0.173389	+	0.984853i	$0.555472\pi$
$614$	14.0000	+	24.2487i	0.564994	+	0.978598i
$615$		0			0
$616$	4.24264	−	10.3923i	0.170941	−	0.418718i
$617$	14.2279	+	24.6435i	0.572795	+	0.992109i	0.996277	+	0.0862052i	$0.0274741\pi$
$617$	14.2279	+	24.6435i	0.572795	+	0.992109i	−0.423483	+	0.905904i	$0.639193\pi$
$618$		0			0
$619$	−1.51472			−0.0608817			−0.0304408	−	0.999537i	$-0.509691\pi$
$619$	−1.51472			−0.0608817			−0.0304408	+	0.999537i	$0.509691\pi$
$620$		0			0
$621$		0			0
$622$	−10.9706			−0.439879
$623$	−8.89340	−	11.4685i	−0.356306	−	0.459474i
$624$		0			0
$625$	25.0000			1.00000
$626$	8.98528	−	15.5630i	0.359124	−	0.622021i
$627$		0			0
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$		0			0
$630$		0			0
$631$	−24.4853			−0.974744			−0.487372	−	0.873195i	$-0.662044\pi$
$631$	−24.4853			−0.974744			−0.487372	+	0.873195i	$0.662044\pi$
$632$	−4.62132	−	8.00436i	−0.183826	−	0.318396i
$633$		0			0
$634$	8.48528	−	14.6969i	0.336994	−	0.583690i
$635$		0			0
$636$		0			0
$637$	−10.8787	+	42.3227i	−0.431029	+	1.67689i
$638$	−18.0000			−0.712627
$639$		0			0
$640$		0			0
$641$	−4.45584			−0.175995			−0.0879976	−	0.996121i	$-0.528047\pi$
$641$	−4.45584			−0.175995			−0.0879976	+	0.996121i	$0.528047\pi$
$642$		0			0
$643$	23.3640	+	40.4676i	0.921385	+	1.59589i	0.797275	+	0.603617i	$0.206274\pi$
$643$	23.3640	+	40.4676i	0.921385	+	1.59589i	0.124110	+	0.992268i	$0.460392\pi$
$644$	11.7426	+	15.1427i	0.462725	+	0.596706i
$645$		0			0
$646$		0			0
$647$	−1.13604	−	1.96768i	−0.0446623	−	0.0773574i	0.842830	−	0.538180i	$-0.180888\pi$
$647$	−1.13604	−	1.96768i	−0.0446623	−	0.0773574i	−0.887492	+	0.460822i	$0.847555\pi$
$648$		0			0
$649$		0			0
$650$	15.6066	−	27.0314i	0.612141	−	1.06026i
$651$		0			0
$652$	5.87868	+	10.1822i	0.230227	+	0.398765i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$		0			0
$655$		0			0
$656$	2.74264	−	4.75039i	0.107082	−	0.185472i
$657$		0			0
$658$	21.4706	+	27.6873i	0.837010	+	1.07936i
$659$	19.6066	−	33.9596i	0.763765	−	1.32288i	−0.177132	−	0.984187i	$-0.556682\pi$
$659$	19.6066	−	33.9596i	0.763765	−	1.32288i	0.940897	−	0.338692i	$-0.109985\pi$
$660$		0			0
$661$	21.0919	−	36.5322i	0.820379	−	1.42094i	−0.0850210	−	0.996379i	$-0.527096\pi$
$661$	21.0919	−	36.5322i	0.820379	−	1.42094i	0.905400	−	0.424559i	$-0.139571\pi$
$662$	9.24264	−	16.0087i	0.359225	−	0.622197i
$663$		0			0
$664$	−3.87868	+	6.71807i	−0.150522	+	0.260712i
$665$		0			0
$666$		0			0
$667$	15.3640	−	26.6112i	0.594895	−	1.03039i
$668$	24.2132			0.936837
$669$		0			0
$670$		0			0
$671$	−13.2426	−	22.9369i	−0.511226	−	0.885470i
$672$		0			0
$673$	13.7426	−	23.8030i	0.529740	−	0.917536i	−0.469658	−	0.882848i	$-0.655623\pi$
$673$	13.7426	−	23.8030i	0.529740	−	0.917536i	0.999398	−	0.0346881i	$-0.0110438\pi$
$674$	−2.24264	+	3.88437i	−0.0863833	+	0.149620i
$675$		0			0
$676$	−12.9853	−	22.4912i	−0.499434	−	0.865045i
$677$	−17.1213	−	29.6550i	−0.658026	−	1.13973i	−0.981126	−	0.193369i	$-0.938058\pi$
$677$	−17.1213	−	29.6550i	−0.658026	−	1.13973i	0.323100	−	0.946365i	$-0.395275\pi$
$678$		0			0
$679$	−20.2426	−	26.1039i	−0.776841	−	1.00177i
$680$		0			0
$681$		0			0
$682$	3.21320			0.123040
$683$	−20.8492	−	36.1119i	−0.797774	−	1.38179i	−0.921063	−	0.389414i	$-0.872677\pi$
$683$	−20.8492	−	36.1119i	−0.797774	−	1.38179i	0.123289	−	0.992371i	$-0.460656\pi$
$684$		0			0
$685$		0			0
$686$	14.8640	+	11.0482i	0.567509	+	0.421822i
$687$		0			0
$688$	−6.48528			−0.247249
$689$	−13.2426	+	22.9369i	−0.504504	+	0.873827i
$690$		0			0
$691$	−3.12132	−	5.40629i	−0.118741	−	0.205665i	0.800528	−	0.599295i	$-0.204552\pi$
$691$	−3.12132	−	5.40629i	−0.118741	−	0.205665i	−0.919269	+	0.393630i	$0.871219\pi$
$692$	−10.9706			−0.417038
$693$		0			0
$694$	−6.72792			−0.255388
$695$		0			0
$696$		0			0
$697$		0			0
$698$	24.9706			0.945150
$699$		0			0
$700$	−8.10660	−	10.4539i	−0.306401	−	0.395118i
$701$	13.7574			0.519608			0.259804	−	0.965661i	$-0.416342\pi$
$701$	13.7574			0.519608			0.259804	+	0.965661i	$0.416342\pi$
$702$		0			0
$703$	12.4853	+	21.6251i	0.470891	+	0.815608i
$704$	4.24264			0.159901
$705$		0			0
$706$	−10.5000	−	18.1865i	−0.395173	−	0.684459i
$707$	7.75736	−	19.0016i	0.291746	−	0.714628i
$708$		0			0
$709$	−12.8492	−	22.2555i	−0.482563	−	0.835824i	0.517236	−	0.855843i	$-0.326961\pi$
$709$	−12.8492	−	22.2555i	−0.482563	−	0.835824i	−0.999800	+	0.0200183i	$0.993628\pi$
$710$		0			0
$711$		0			0
$712$	2.74264	−	4.75039i	0.102785	−	0.178029i
$713$	−2.74264	+	4.75039i	−0.102713	+	0.177904i
$714$		0			0
$715$		0			0
$716$	−16.2426			−0.607016
$717$		0			0
$718$	10.7574			0.401461
$719$	1.13604	−	1.96768i	0.0423671	−	0.0733820i	−0.844064	−	0.536242i	$-0.819843\pi$
$719$	1.13604	−	1.96768i	0.0423671	−	0.0733820i	0.886431	+	0.462860i	$0.153177\pi$
$720$		0			0
$721$	0.757359	−	1.85514i	0.0282055	−	0.0690892i
$722$	−9.98528	+	17.2950i	−0.371614	+	0.643654i
$723$		0			0
$724$	10.1213	−	17.5306i	0.376156	−	0.651521i
$725$	−10.6066	+	18.3712i	−0.393919	+	0.682288i
$726$		0			0
$727$	12.8640	−	22.2810i	0.477098	−	0.826358i	−0.522558	−	0.852604i	$-0.675022\pi$
$727$	12.8640	−	22.2810i	0.477098	−	0.826358i	0.999656	+	0.0262462i	$0.00835537\pi$
$728$	−16.3640	+	2.23936i	−0.606489	+	0.0829961i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−38.9706			−1.43941			−0.719705	−	0.694280i	$-0.755723\pi$
$733$	−38.9706			−1.43941			−0.719705	+	0.694280i	$0.755723\pi$
$734$	−5.86396	−	10.1567i	−0.216443	−	0.374890i
$735$		0			0
$736$	−3.62132	+	6.27231i	−0.133484	+	0.231200i
$737$	17.4853	−	30.2854i	0.644079	−	1.11558i
$738$		0			0
$739$	−5.24264	−	9.08052i	−0.192854	−	0.334032i	0.753341	−	0.657630i	$-0.228441\pi$
$739$	−5.24264	−	9.08052i	−0.192854	−	0.334032i	−0.946195	+	0.323598i	$0.895108\pi$
$740$		0			0
$741$		0			0
$742$	6.87868	+	8.87039i	0.252524	+	0.325642i
$743$	−17.3787	−	30.1008i	−0.637562	−	1.10429i	−0.985966	−	0.166945i	$-0.946610\pi$
$743$	−17.3787	−	30.1008i	−0.637562	−	1.10429i	0.348404	−	0.937344i	$-0.386724\pi$
$744$		0			0
$745$		0			0
$746$	3.60660	+	6.24682i	0.132047	+	0.228712i
$747$		0			0
$748$		0			0
$749$	−4.02944	−	5.19615i	−0.147232	−	0.189863i
$750$		0			0
$751$	−17.2426			−0.629193			−0.314596	−	0.949226i	$-0.601869\pi$
$751$	−17.2426			−0.629193			−0.314596	+	0.949226i	$0.601869\pi$
$752$	−6.62132	+	11.4685i	−0.241455	+	0.418212i
$753$		0			0
$754$	13.2426	+	22.9369i	0.482269	+	0.835314i
$755$		0			0
$756$		0			0
$757$	12.9706			0.471423			0.235712	−	0.971823i	$-0.424258\pi$
$757$	12.9706			0.471423			0.235712	+	0.971823i	$0.424258\pi$
$758$	−0.636039	−	1.10165i	−0.0231020	−	0.0400138i
$759$		0			0
$760$		0			0
$761$	21.0000			0.761249			0.380625	−	0.924730i	$-0.375709\pi$
$761$	21.0000			0.761249			0.380625	+	0.924730i	$0.375709\pi$
$762$		0			0
$763$	5.87868	−	0.804479i	0.212822	−	0.0291241i
$764$	8.48528			0.306987
$765$		0			0
$766$	12.1066	+	20.9692i	0.437429	+	0.757650i
$767$		0			0
$768$		0			0
$769$	6.24264	+	10.8126i	0.225115	+	0.389911i	0.956354	−	0.292210i	$-0.0943908\pi$
$769$	6.24264	+	10.8126i	0.225115	+	0.389911i	−0.731239	+	0.682122i	$0.761057\pi$
$770$		0			0
$771$		0			0
$772$	2.25736	+	3.90986i	0.0812441	+	0.140719i
$773$	22.6066	+	39.1558i	0.813103	+	1.40834i	0.910682	+	0.413108i	$0.135557\pi$
$773$	22.6066	+	39.1558i	0.813103	+	1.40834i	−0.0975792	+	0.995228i	$0.531110\pi$
$774$		0			0
$775$	1.89340	−	3.27946i	0.0680129	−	0.117802i
$776$	6.24264	−	10.8126i	0.224098	−	0.388149i
$777$		0			0
$778$	−5.12132	−	8.87039i	−0.183608	−	0.318019i
$779$	−34.2426			−1.22687
$780$		0			0
$781$	−30.7279			−1.09953
$782$		0			0
$783$		0			0
$784$	−1.74264	+	6.77962i	−0.0622372	+	0.242129i
$785$		0			0
$786$		0			0
$787$	15.6066	−	27.0314i	0.556315	−	0.963566i	−0.441485	−	0.897269i	$-0.645548\pi$
$787$	15.6066	−	27.0314i	0.556315	−	0.963566i	0.997800	−	0.0662975i	$-0.0211186\pi$
$788$	−8.48528	+	14.6969i	−0.302276	+	0.523557i
$789$		0			0
$790$		0			0
$791$	53.6985	−	7.34847i	1.90930	−	0.261281i
$792$		0			0
$793$	−19.4853	+	33.7495i	−0.691943	+	1.19848i
$794$	−20.2426			−0.718384
$795$		0			0
$796$	−14.7574			−0.523061
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$		0			0
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	−14.7426	−	25.5350i	−0.520581	−	0.901672i
$803$	14.8492	+	25.7196i	0.524018	+	0.907626i
$804$		0			0
$805$		0			0
$806$	−2.36396	−	4.09450i	−0.0832670	−	0.144223i
$807$		0			0
$808$	7.75736			0.272903
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$		0			0
$811$	−23.4558			−0.823646			−0.411823	−	0.911264i	$-0.635108\pi$
$811$	−23.4558			−0.823646			−0.411823	+	0.911264i	$0.635108\pi$
$812$	11.1213	−	1.52192i	0.390282	−	0.0534088i
$813$		0			0
$814$	−16.9706			−0.594818
$815$		0			0
$816$		0			0
$817$	20.2426	+	35.0613i	0.708200	+	1.22664i
$818$	35.0000			1.22375
$819$		0			0
$820$		0			0
$821$	16.0919	+	27.8720i	0.561611	+	0.972738i	0.997356	+	0.0726682i	$0.0231514\pi$
$821$	16.0919	+	27.8720i	0.561611	+	0.972738i	−0.435746	+	0.900070i	$0.643515\pi$
$822$		0			0
$823$	−20.3492	+	35.2459i	−0.709330	+	1.22860i	0.255776	+	0.966736i	$0.417669\pi$
$823$	−20.3492	+	35.2459i	−0.709330	+	1.22860i	−0.965106	+	0.261860i	$0.915664\pi$
$824$	0.757359			0.0263839
$825$		0			0
$826$		0			0
$827$	16.9706			0.590124			0.295062	−	0.955478i	$-0.404660\pi$
$827$	16.9706			0.590124			0.295062	+	0.955478i	$0.404660\pi$
$828$		0			0
$829$	24.9706	+	43.2503i	0.867263	+	1.50214i	0.864782	+	0.502148i	$0.167457\pi$
$829$	24.9706	+	43.2503i	0.867263	+	1.50214i	0.00248151	+	0.999997i	$0.499210\pi$
$830$		0			0
$831$		0			0
$832$	−3.12132	−	5.40629i	−0.108212	−	0.187429i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	−13.2426	−	22.9369i	−0.458006	−	0.793290i
$837$		0			0
$838$	3.87868	−	6.71807i	0.133987	−	0.232072i
$839$	−7.75736	+	13.4361i	−0.267814	+	0.463867i	−0.968297	−	0.249802i	$-0.919635\pi$
$839$	−7.75736	+	13.4361i	−0.267814	+	0.463867i	0.700483	+	0.713669i	$0.252968\pi$
$840$		0			0
$841$	5.50000	+	9.52628i	0.189655	+	0.328492i
$842$	−14.2426			−0.490834
$843$		0			0
$844$	−6.48528			−0.223233
$845$		0			0
$846$		0			0
$847$	7.00000	−	17.1464i	0.240523	−	0.589158i
$848$	−2.12132	+	3.67423i	−0.0728464	+	0.126174i
$849$		0			0
$850$		0			0
$851$	14.4853	−	25.0892i	0.496549	−	0.860048i
$852$		0			0
$853$	−14.0919	+	24.4079i	−0.482497	+	0.835709i	−0.999798	−	0.0200943i	$-0.993603\pi$
$853$	−14.0919	+	24.4079i	−0.482497	+	0.835709i	0.517301	+	0.855803i	$0.326937\pi$
$854$	10.1213	+	13.0519i	0.346344	+	0.446628i
$855$		0			0
$856$	1.24264	−	2.15232i	0.0424726	−	0.0735647i
$857$	−5.48528			−0.187374			−0.0936868	−	0.995602i	$-0.529865\pi$
$857$	−5.48528			−0.187374			−0.0936868	+	0.995602i	$0.529865\pi$
$858$		0			0
$859$	43.6985			1.49097			0.745487	−	0.666521i	$-0.232217\pi$
$859$	43.6985			1.49097			0.745487	+	0.666521i	$0.232217\pi$
$860$		0			0
$861$		0			0
$862$	18.6213	−	32.2531i	0.634245	−	1.09854i
$863$	0.106602	−	0.184640i	0.00362876	−	0.00628520i	−0.864205	−	0.503139i	$-0.832178\pi$
$863$	0.106602	−	0.184640i	0.00362876	−	0.00628520i	0.867834	+	0.496854i	$0.165512\pi$
$864$		0			0
$865$		0			0
$866$	−1.98528	−	3.43861i	−0.0674626	−	0.116849i
$867$		0			0
$868$	−1.98528	+	0.271680i	−0.0673848	+	0.00922140i
$869$	−19.6066	−	33.9596i	−0.665108	−	1.15200i
$870$		0			0
$871$	−51.4558			−1.74351
$872$	1.12132	+	1.94218i	0.0379727	+	0.0657706i
$873$		0			0
$874$	45.2132			1.52936
$875$		0			0
$876$		0			0
$877$	25.6985			0.867776			0.433888	−	0.900967i	$-0.357141\pi$
$877$	25.6985			0.867776			0.433888	+	0.900967i	$0.357141\pi$
$878$	−5.86396	+	10.1567i	−0.197899	+	0.342771i
$879$		0			0
$880$		0			0
$881$	−36.5147			−1.23021			−0.615106	−	0.788444i	$-0.710887\pi$
$881$	−36.5147			−1.23021			−0.615106	+	0.788444i	$0.710887\pi$
$882$		0			0
$883$	49.6985			1.67249			0.836244	−	0.548358i	$-0.184747\pi$
$883$	49.6985			1.67249			0.836244	+	0.548358i	$0.184747\pi$
$884$		0			0
$885$		0			0
$886$	−4.75736	+	8.23999i	−0.159827	+	0.276828i
$887$	39.7279			1.33393			0.666967	−	0.745088i	$-0.267592\pi$
$887$	39.7279			1.33393			0.666967	+	0.745088i	$0.267592\pi$
$888$		0			0
$889$	6.75736	−	16.5521i	0.226635	−	0.555139i
$890$		0			0
$891$		0			0
$892$	−5.86396	−	10.1567i	−0.196340	−	0.340071i
$893$	82.6690			2.76641
$894$		0			0
$895$		0			0
$896$	−2.62132	+	0.358719i	−0.0875722	+	0.0119840i
$897$		0			0
$898$	2.48528	+	4.30463i	0.0829349	+	0.143647i
$899$	1.60660	+	2.78272i	0.0535832	+	0.0928088i
$900$		0			0
$901$		0			0
$902$	11.6360	−	20.1542i	0.387438	−	0.671062i
$903$		0			0
$904$	10.2426	+	17.7408i	0.340665	+	0.590049i
$905$		0			0
$906$		0			0
$907$	−37.9411			−1.25981			−0.629907	−	0.776670i	$-0.716907\pi$
$907$	−37.9411			−1.25981			−0.629907	+	0.776670i	$0.716907\pi$
$908$	−13.2426	+	22.9369i	−0.439472	+	0.761189i
$909$		0			0
$910$		0			0
$911$	7.13604	−	12.3600i	0.236428	−	0.409504i	−0.723259	−	0.690577i	$-0.757357\pi$
$911$	7.13604	−	12.3600i	0.236428	−	0.409504i	0.959687	+	0.281072i	$0.0906901\pi$
$912$		0			0
$913$	−16.4558	+	28.5024i	−0.544609	+	0.943290i
$914$	−5.75736	+	9.97204i	−0.190437	+	0.329846i
$915$		0			0
$916$	−12.4853	+	21.6251i	−0.412525	+	0.714515i
$917$	−7.75736	+	19.0016i	−0.256171	+	0.627487i
$918$		0			0
$919$	−16.7279	+	28.9736i	−0.551803	+	0.955751i	0.446341	+	0.894863i	$0.352727\pi$
$919$	−16.7279	+	28.9736i	−0.551803	+	0.955751i	−0.998145	+	0.0608884i	$0.980607\pi$
$920$		0			0
$921$		0			0
$922$	34.2426			1.12772
$923$	22.6066	+	39.1558i	0.744105	+	1.28883i
$924$		0			0
$925$	−10.0000	+	17.3205i	−0.328798	+	0.569495i
$926$	4.37868	−	7.58410i	0.143892	−	0.249229i
$927$		0			0
$928$	2.12132	+	3.67423i	0.0696358	+	0.120613i
$929$	5.01472	+	8.68575i	0.164528	+	0.284970i	0.936487	−	0.350701i	$-0.114057\pi$
$929$	5.01472	+	8.68575i	0.164528	+	0.284970i	−0.771960	+	0.635671i	$0.780723\pi$
$930$		0			0
$931$	42.0919	−	11.7401i	1.37951	−	0.384768i
$932$	−10.2426	−	17.7408i	−0.335509	−	0.581118i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$	30.4558			0.994949			0.497475	−	0.867479i	$-0.334261\pi$
$937$	30.4558			0.994949			0.497475	+	0.867479i	$0.334261\pi$
$938$	−8.24264	+	20.1903i	−0.269132	+	0.659235i
$939$		0			0
$940$		0			0
$941$	20.3345	−	35.2204i	0.662887	−	1.14815i	−0.316967	−	0.948437i	$-0.602665\pi$
$941$	20.3345	−	35.2204i	0.662887	−	1.14815i	0.979854	−	0.199717i	$-0.0640022\pi$
$942$		0			0
$943$	19.8640	+	34.4054i	0.646860	+	1.12039i
$944$		0			0
$945$		0			0
$946$	−27.5147			−0.894581
$947$	10.7574	+	18.6323i	0.349567	+	0.605468i	0.986173	−	0.165722i	$-0.0529953\pi$
$947$	10.7574	+	18.6323i	0.349567	+	0.605468i	−0.636605	+	0.771190i	$0.719662\pi$
$948$		0			0
$949$	21.8492	−	37.8440i	0.709256	−	1.22847i
$950$	−31.2132			−1.01269
$951$		0			0
$952$		0			0
$953$	−6.51472			−0.211032			−0.105516	−	0.994418i	$-0.533649\pi$
$953$	−6.51472			−0.211032			−0.105516	+	0.994418i	$0.533649\pi$
$954$		0			0
$955$		0			0
$956$	3.72792			0.120570
$957$		0			0
$958$	6.62132	+	11.4685i	0.213925	+	0.370529i
$959$	−19.9706	+	48.9177i	−0.644883	+	1.57963i
$960$		0			0
$961$	15.2132	+	26.3500i	0.490748	+	0.850001i
$962$	12.4853	+	21.6251i	0.402542	+	0.697223i
$963$		0			0
$964$	−4.25736	+	7.37396i	−0.137120	+	0.237499i
$965$		0			0
$966$		0			0
$967$	3.34924	+	5.80106i	0.107704	+	0.186549i	0.914840	−	0.403817i	$-0.132317\pi$
$967$	3.34924	+	5.80106i	0.107704	+	0.186549i	−0.807136	+	0.590366i	$0.798983\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$		0			0
$971$	13.2426	−	22.9369i	0.424977	−	0.736081i	−0.571442	−	0.820643i	$-0.693616\pi$
$971$	13.2426	−	22.9369i	0.424977	−	0.736081i	0.996418	+	0.0845617i	$0.0269490\pi$
$972$		0			0
$973$	12.3934	−	1.69600i	0.397314	−	0.0543712i
$974$	1.37868	−	2.38794i	0.0441757	−	0.0765146i
$975$		0			0
$976$	−3.12132	+	5.40629i	−0.0999110	+	0.173051i
$977$	6.98528	−	12.0989i	0.223479	−	0.387077i	−0.732383	−	0.680893i	$-0.761592\pi$
$977$	6.98528	−	12.0989i	0.223479	−	0.387077i	0.955862	+	0.293816i	$0.0949253\pi$
$978$		0			0
$979$	11.6360	−	20.1542i	0.371889	−	0.644131i
$980$		0			0
$981$		0			0
$982$	−3.36396	+	5.82655i	−0.107348	+	0.185933i
$983$	−15.5147			−0.494843			−0.247421	−	0.968908i	$-0.579583\pi$
$983$	−15.5147			−0.494843			−0.247421	+	0.968908i	$0.579583\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−19.4853	+	33.7495i	−0.619909	+	1.07371i
$989$	23.4853	−	40.6777i	0.746789	−	1.29348i
$990$		0			0
$991$	−25.1066	−	43.4859i	−0.797537	−	1.38138i	−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−25.1066	−	43.4859i	−0.797537	−	1.38138i	0.123678	−	0.992322i	$-0.460531\pi$
$992$	−0.378680	−	0.655892i	−0.0120231	−	0.0208246i
$993$		0			0
$994$	18.9853	−	2.59808i	0.602177	−	0.0824060i
$995$		0			0
$996$		0			0
$997$	14.0000			0.443384			0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000			0.443384			0.221692	+	0.975117i	$0.428842\pi$
$998$	5.36396	+	9.29065i	0.169793	+	0.294090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.r.541.1		4
3.2	odd	2		1134.2.h.s.541.1		4
7.4	even	3		1134.2.e.s.865.2		4
9.2	odd	6		1134.2.g.j.163.1	yes	4
9.4	even	3		1134.2.e.s.919.2		4
9.5	odd	6		1134.2.e.r.919.2		4
9.7	even	3		1134.2.g.i.163.1	✓	4
21.11	odd	6		1134.2.e.r.865.2		4
63.2	odd	6		7938.2.a.bk.1.1		2
63.4	even	3	inner	1134.2.h.r.109.2		4
63.11	odd	6		1134.2.g.j.487.1	yes	4
63.16	even	3		7938.2.a.bq.1.2		2
63.25	even	3		1134.2.g.i.487.1	yes	4
63.32	odd	6		1134.2.h.s.109.2		4
63.47	even	6		7938.2.a.bj.1.1		2
63.61	odd	6		7938.2.a.bp.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.r.865.2		4	21.11	odd	6
1134.2.e.r.919.2		4	9.5	odd	6
1134.2.e.s.865.2		4	7.4	even	3
1134.2.e.s.919.2		4	9.4	even	3
1134.2.g.i.163.1	✓	4	9.7	even	3
1134.2.g.i.487.1	yes	4	63.25	even	3
1134.2.g.j.163.1	yes	4	9.2	odd	6
1134.2.g.j.487.1	yes	4	63.11	odd	6
1134.2.h.r.109.2		4	63.4	even	3	inner
1134.2.h.r.541.1		4	1.1	even	1	trivial
1134.2.h.s.109.2		4	63.32	odd	6
1134.2.h.s.541.1		4	3.2	odd	2
7938.2.a.bj.1.1		2	63.47	even	6
7938.2.a.bk.1.1		2	63.2	odd	6
7938.2.a.bp.1.2		2	63.61	odd	6
7938.2.a.bq.1.2		2	63.16	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 - 2.44949i) q^{7} +1.00000 q^{8} +4.24264 q^{11} +(-3.12132 - 5.40629i) q^{13} +(-2.62132 + 0.358719i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.12132 + 5.40629i) q^{19} +(-2.12132 - 3.67423i) q^{22} +7.24264 q^{23} -5.00000 q^{25} +(-3.12132 + 5.40629i) q^{26} +(1.62132 + 2.09077i) q^{28} +(2.12132 - 3.67423i) q^{29} +(-0.378680 + 0.655892i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{37} +6.24264 q^{38} +(2.74264 + 4.75039i) q^{41} +(3.24264 - 5.61642i) q^{43} +(-2.12132 + 3.67423i) q^{44} +(-3.62132 - 6.27231i) q^{46} +(-6.62132 - 11.4685i) q^{47} +(-5.00000 - 4.89898i) q^{49} +(2.50000 + 4.33013i) q^{50} +6.24264 q^{52} +(-2.12132 - 3.67423i) q^{53} +(1.00000 - 2.44949i) q^{56} -4.24264 q^{58} +(-3.12132 - 5.40629i) q^{61} +0.757359 q^{62} +1.00000 q^{64} +(4.12132 - 7.13834i) q^{67} -7.24264 q^{71} +(3.50000 + 6.06218i) q^{73} -4.00000 q^{74} +(-3.12132 - 5.40629i) q^{76} +(4.24264 - 10.3923i) q^{77} +(-4.62132 - 8.00436i) q^{79} +(2.74264 - 4.75039i) q^{82} +(-3.87868 + 6.71807i) q^{83} -6.48528 q^{86} +4.24264 q^{88} +(2.74264 - 4.75039i) q^{89} +(-16.3640 + 2.23936i) q^{91} +(-3.62132 + 6.27231i) q^{92} +(-6.62132 + 11.4685i) q^{94} +(6.24264 - 10.8126i) q^{97} +(-1.74264 + 6.77962i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{7} + 4 q^{8} - 4 q^{13} - 2 q^{14} - 2 q^{16} - 4 q^{19} + 12 q^{23} - 20 q^{25} - 4 q^{26} - 2 q^{28} - 10 q^{31} - 2 q^{32} + 8 q^{37} + 8 q^{38} - 6 q^{41} - 4 q^{43} - 6 q^{46}+ \cdots + 10 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^7 + 4 * q^8 - 4 * q^13 - 2 * q^14 - 2 * q^16 - 4 * q^19 + 12 * q^23 - 20 * q^25 - 4 * q^26 - 2 * q^28 - 10 * q^31 - 2 * q^32 + 8 * q^37 + 8 * q^38 - 6 * q^41 - 4 * q^43 - 6 * q^46 - 18 * q^47 - 20 * q^49 + 10 * q^50 + 8 * q^52 + 4 * q^56 - 4 * q^61 + 20 * q^62 + 4 * q^64 + 8 * q^67 - 12 * q^71 + 14 * q^73 - 16 * q^74 - 4 * q^76 - 10 * q^79 - 6 * q^82 - 24 * q^83 + 8 * q^86 - 6 * q^89 - 40 * q^91 - 6 * q^92 - 18 * q^94 + 8 * q^97 + 10 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more