LMFDB - Embedded newform 765.2.be.b.406.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(406,765)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(765, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("765.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.be (of order $8$, degree $4$, 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:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			406.5
Character	$\chi$	$=$	765.406
Dual form			765.2.be.b.586.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.528855 + 0.528855i) q^{2} -1.44062i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.98655 + 1.23707i) q^{7} +(1.81959 - 1.81959i) q^{8} +O(q^{10})$	\(q+(0.528855 + 0.528855i) q^{2} -1.44062i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.98655 + 1.23707i) q^{7} +(1.81959 - 1.81959i) q^{8} +(0.690983 + 0.286214i) q^{10} +(-1.04667 + 2.52689i) q^{11} -4.31833i q^{13} +(0.925222 + 2.23368i) q^{14} -0.956646 q^{16} +(3.47152 + 2.22453i) q^{17} +(-0.897260 - 0.897260i) q^{19} +(-0.551303 - 1.33096i) q^{20} +(-1.88990 + 0.782821i) q^{22} +(0.188421 - 0.454888i) q^{23} +(0.707107 - 0.707107i) q^{25} +(2.28377 - 2.28377i) q^{26} +(1.78215 - 4.30250i) q^{28} +(0.410535 - 0.170049i) q^{29} +(-2.11561 - 5.10754i) q^{31} +(-4.14511 - 4.14511i) q^{32} +(0.659477 + 3.01239i) q^{34} +3.23262 q^{35} +(4.09469 + 9.88545i) q^{37} -0.949042i q^{38} +(0.984756 - 2.37741i) q^{40} +(2.00526 + 0.830608i) q^{41} +(1.52864 - 1.52864i) q^{43} +(3.64030 + 1.50786i) q^{44} +(0.340217 - 0.140922i) q^{46} -8.39597i q^{47} +(2.43940 + 2.43940i) q^{49} +0.747914 q^{50} -6.22109 q^{52} +(-1.28480 - 1.28480i) q^{53} +2.73509i q^{55} +(7.68527 - 3.18334i) q^{56} +(0.307045 + 0.127182i) q^{58} +(2.13537 - 2.13537i) q^{59} +(11.2928 + 4.67764i) q^{61} +(1.58230 - 3.82000i) q^{62} -2.47104i q^{64} +(-1.65255 - 3.98962i) q^{65} -4.21389 q^{67} +(3.20471 - 5.00116i) q^{68} +(1.70959 + 1.70959i) q^{70} +(1.48927 + 3.59542i) q^{71} +(-5.97807 + 2.47620i) q^{73} +(-3.06247 + 7.39347i) q^{74} +(-1.29261 + 1.29261i) q^{76} +(-6.25188 + 6.25188i) q^{77} +(-2.76355 + 6.67180i) q^{79} +(-0.883826 + 0.366093i) q^{80} +(0.621223 + 1.49977i) q^{82} +(-0.160866 - 0.160866i) q^{83} +(4.05856 + 0.726705i) q^{85} +1.61686 q^{86} +(2.69339 + 6.50243i) q^{88} +13.3408i q^{89} +(5.34208 - 12.8969i) q^{91} +(-0.655322 - 0.271443i) q^{92} +(4.44025 - 4.44025i) q^{94} +(-1.17233 - 0.485594i) q^{95} +(-13.6803 + 5.66657i) q^{97} +2.58018i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$1$

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 $

$2$	0.528855	+	0.528855i	0.373957	+	0.373957i	0.868916	−	0.494959i	$-0.164817\pi$
$2$	0.528855	+	0.528855i	0.373957	+	0.373957i	−0.494959	+	0.868916i	$0.664817\pi$
$3$		0			0
$3$		0			0
$4$		−	1.44062i		−	0.720312i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$5$	0.923880	−	0.382683i	0.413171	−	0.171141i
$6$		0			0
$7$	2.98655	+	1.23707i	1.12881	+	0.467569i	0.867376	−	0.497653i	$-0.165805\pi$
$7$	2.98655	+	1.23707i	1.12881	+	0.467569i	0.261434	+	0.965221i	$0.415805\pi$
$8$	1.81959	−	1.81959i	0.643323	−	0.643323i
$9$		0			0
$10$	0.690983	+	0.286214i	0.218508	+	0.0905089i
$11$	−1.04667	+	2.52689i	−0.315584	+	0.761886i	0.683894	+	0.729581i	$0.260285\pi$
$11$	−1.04667	+	2.52689i	−0.315584	+	0.761886i	−0.999478	+	0.0323052i	$0.989715\pi$
$12$		0			0
$13$		−	4.31833i		−	1.19769i	−0.800865	−	0.598845i	$-0.795627\pi$
$13$		−	4.31833i		−	1.19769i	0.800865	−	0.598845i	$-0.204373\pi$
$14$	0.925222	+	2.23368i	0.247276	+	0.596977i
$15$		0			0
$16$	−0.956646			−0.239162
$17$	3.47152	+	2.22453i	0.841968	+	0.539528i
$17$	3.47152	+	2.22453i	0.841968	+	0.539528i
$18$		0			0
$19$	−0.897260	−	0.897260i	−0.205846	−	0.205846i	0.596653	−	0.802499i	$-0.296497\pi$
$19$	−0.897260	−	0.897260i	−0.205846	−	0.205846i	−0.802499	+	0.596653i	$0.796497\pi$
$20$	−0.551303	−	1.33096i	−0.123275	−	0.297612i
$21$		0			0
$22$	−1.88990	+	0.782821i	−0.402928	+	0.166898i
$23$	0.188421	−	0.454888i	0.0392884	−	0.0948506i	−0.903017	−	0.429604i	$-0.858653\pi$
$23$	0.188421	−	0.454888i	0.0392884	−	0.0948506i	0.942306	+	0.334754i	$0.108653\pi$
$24$		0			0
$25$	0.707107	−	0.707107i	0.141421	−	0.141421i
$26$	2.28377	−	2.28377i	0.447884	−	0.447884i
$27$		0			0
$28$	1.78215	−	4.30250i	0.336795	−	0.813096i
$29$	0.410535	−	0.170049i	0.0762345	−	0.0315774i	−0.344240	−	0.938882i	$-0.611863\pi$
$29$	0.410535	−	0.170049i	0.0762345	−	0.0315774i	0.420475	+	0.907304i	$0.361863\pi$
$30$		0			0
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	−0.991969	−	0.126479i	$-0.959632\pi$
$31$	−2.11561	−	5.10754i	−0.379975	−	0.917342i	0.611994	−	0.790862i	$-0.290368\pi$
$32$	−4.14511	−	4.14511i	−0.732759	−	0.732759i
$33$		0			0
$34$	0.659477	+	3.01239i	0.113099	+	0.516620i
$35$	3.23262			0.546412
$36$		0			0
$37$	4.09469	+	9.88545i	0.673162	+	1.62516i	0.776205	+	0.630481i	$0.217142\pi$
$37$	4.09469	+	9.88545i	0.673162	+	1.62516i	−0.103043	+	0.994677i	$0.532858\pi$
$38$		−	0.949042i		−	0.153955i
$39$		0			0
$40$	0.984756	−	2.37741i	0.155704	−	0.375902i
$41$	2.00526	+	0.830608i	0.313170	+	0.129719i	0.533732	−	0.845654i	$-0.320789\pi$
$41$	2.00526	+	0.830608i	0.313170	+	0.129719i	−0.220562	+	0.975373i	$0.570789\pi$
$42$		0			0
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	−0.580876	−	0.813992i	$-0.697290\pi$
$43$	1.52864	−	1.52864i	0.233115	−	0.233115i	0.813992	+	0.580876i	$0.197290\pi$
$44$	3.64030	+	1.50786i	0.548796	+	0.227319i
$45$		0			0
$46$	0.340217	−	0.140922i	0.0501622	−	0.0207779i
$47$		−	8.39597i		−	1.22468i	−0.790595	−	0.612339i	$-0.790229\pi$
$47$		−	8.39597i		−	1.22468i	0.790595	−	0.612339i	$-0.209771\pi$
$48$		0			0
$49$	2.43940	+	2.43940i	0.348485	+	0.348485i
$50$	0.747914			0.105771
$51$		0			0
$52$	−6.22109			−0.862710
$53$	−1.28480	−	1.28480i	−0.176481	−	0.176481i	0.613339	−	0.789820i	$-0.289826\pi$
$53$	−1.28480	−	1.28480i	−0.176481	−	0.176481i	−0.789820	+	0.613339i	$0.789826\pi$
$54$		0			0
$55$			2.73509i			0.368799i
$56$	7.68527	−	3.18334i	1.02699	−	0.425392i
$57$		0			0
$58$	0.307045	+	0.127182i	0.0403170	+	0.0166999i
$59$	2.13537	−	2.13537i	0.278001	−	0.278001i	−0.554309	−	0.832311i	$-0.687018\pi$
$59$	2.13537	−	2.13537i	0.278001	−	0.278001i	0.832311	+	0.554309i	$0.187018\pi$
$60$		0			0
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.961220	−	0.275783i	$-0.0889371\pi$
$61$	11.2928	+	4.67764i	1.44590	+	0.598910i	0.484677	+	0.874693i	$0.338937\pi$
$62$	1.58230	−	3.82000i	0.200952	−	0.485141i
$63$		0			0
$64$		−	2.47104i		−	0.308880i
$65$	−1.65255	−	3.98962i	−0.204974	−	0.494851i
$66$		0			0
$67$	−4.21389			−0.514808			−0.257404	−	0.966304i	$-0.582867\pi$
$67$	−4.21389			−0.514808			−0.257404	+	0.966304i	$0.582867\pi$
$68$	3.20471	−	5.00116i	0.388629	−	0.606479i
$69$		0			0
$70$	1.70959	+	1.70959i	0.204335	+	0.204335i
$71$	1.48927	+	3.59542i	0.176744	+	0.426698i	0.987280	−	0.158991i	$-0.0508241\pi$
$71$	1.48927	+	3.59542i	0.176744	+	0.426698i	−0.810536	+	0.585689i	$0.800824\pi$
$72$		0			0
$73$	−5.97807	+	2.47620i	−0.699680	+	0.289817i	−0.704027	−	0.710173i	$-0.748617\pi$
$73$	−5.97807	+	2.47620i	−0.699680	+	0.289817i	0.00434632	+	0.999991i	$0.498617\pi$
$74$	−3.06247	+	7.39347i	−0.356005	+	0.859473i
$75$		0			0
$76$	−1.29261	+	1.29261i	−0.148273	+	0.148273i
$77$	−6.25188	+	6.25188i	−0.712468	+	0.712468i
$78$		0			0
$79$	−2.76355	+	6.67180i	−0.310923	+	0.750636i	0.688748	+	0.725001i	$0.258161\pi$
$79$	−2.76355	+	6.67180i	−0.310923	+	0.750636i	−0.999671	+	0.0256347i	$0.991839\pi$
$80$	−0.883826	+	0.366093i	−0.0988147	+	0.0409304i
$81$		0			0
$82$	0.621223	+	1.49977i	0.0686026	+	0.165621i
$83$	−0.160866	−	0.160866i	−0.0176574	−	0.0176574i	0.698223	−	0.715880i	$-0.253974\pi$
$83$	−0.160866	−	0.160866i	−0.0176574	−	0.0176574i	−0.715880	+	0.698223i	$0.753974\pi$
$84$		0			0
$85$	4.05856	+	0.726705i	0.440213	+	0.0788222i
$86$	1.61686			0.174350
$87$		0			0
$88$	2.69339	+	6.50243i	0.287117	+	0.693161i
$89$			13.3408i			1.41413i	0.707150	+	0.707064i	$0.249981\pi$
$89$			13.3408i			1.41413i	−0.707150	+	0.707064i	$0.750019\pi$
$90$		0			0
$91$	5.34208	−	12.8969i	0.560002	−	1.35196i
$92$	−0.655322	−	0.271443i	−0.0683220	−	0.0282999i
$93$		0			0
$94$	4.44025	−	4.44025i	0.457977	−	0.457977i
$95$	−1.17233	−	0.485594i	−0.120278	−	0.0498209i
$96$		0			0
$97$	−13.6803	+	5.66657i	−1.38902	+	0.575353i	−0.946879	−	0.321591i	$-0.895782\pi$
$97$	−13.6803	+	5.66657i	−1.38902	+	0.575353i	−0.442145	+	0.896943i	$0.645782\pi$
$98$			2.58018i			0.260637i
$99$		0			0
$100$	−1.01868	−	1.01868i	−0.101868	−	0.101868i
$101$	0.284213			0.0282803			0.0141401	−	0.999900i	$-0.495499\pi$
$101$	0.284213			0.0282803			0.0141401	+	0.999900i	$0.495499\pi$
$102$		0			0
$103$	−14.0842			−1.38775			−0.693877	−	0.720093i	$-0.744099\pi$
$103$	−14.0842			−1.38775			−0.693877	+	0.720093i	$0.744099\pi$
$104$	−7.85760	−	7.85760i	−0.770501	−	0.770501i
$105$		0			0
$106$		−	1.35894i		−	0.131992i
$107$	−17.2857	+	7.15995i	−1.67107	+	0.692179i	−0.998839	−	0.0481649i	$-0.984663\pi$
$107$	−17.2857	+	7.15995i	−1.67107	+	0.692179i	−0.672228	+	0.740344i	$0.734663\pi$
$108$		0			0
$109$	−3.26202	−	1.35117i	−0.312444	−	0.129419i	0.220951	−	0.975285i	$-0.429084\pi$
$109$	−3.26202	−	1.35117i	−0.312444	−	0.129419i	−0.533395	+	0.845866i	$0.679084\pi$
$110$	−1.44647	+	1.44647i	−0.137915	+	0.137915i
$111$		0			0
$112$	−2.85707	−	1.18344i	−0.269968	−	0.111824i
$113$	−1.08741	+	2.62525i	−0.102295	+	0.246963i	−0.966738	−	0.255769i	$-0.917671\pi$
$113$	−1.08741	+	2.62525i	−0.102295	+	0.246963i	0.864443	+	0.502731i	$0.167671\pi$
$114$		0			0
$115$		−	0.492367i		−	0.0459134i
$116$	−0.244977	−	0.591427i	−0.0227456	−	0.0549126i
$117$		0			0
$118$	2.25860			0.207921
$119$	7.61598	+	10.9382i	0.698155	+	1.00270i
$120$		0			0
$121$	2.48852	+	2.48852i	0.226229	+	0.226229i
$122$	3.49847	+	8.44606i	0.316737	+	0.764670i
$123$		0			0
$124$	−7.35805	+	3.04780i	−0.660772	+	0.273701i
$125$	0.382683	−	0.923880i	0.0342282	−	0.0826343i
$126$		0			0
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	−0.514548	−	0.857462i	$-0.672040\pi$
$127$	3.86444	−	3.86444i	0.342914	−	0.342914i	0.857462	+	0.514548i	$0.172040\pi$
$128$	−6.98340	+	6.98340i	−0.617251	+	0.617251i
$129$		0			0
$130$	1.23597	−	2.98389i	0.108402	−	0.261705i
$131$	−9.21986	+	3.81899i	−0.805543	+	0.333667i	−0.747174	−	0.664628i	$-0.768590\pi$
$131$	−9.21986	+	3.81899i	−0.805543	+	0.333667i	−0.0583689	+	0.998295i	$0.518590\pi$
$132$		0			0
$133$	−1.56974	−	3.78969i	−0.136114	−	0.328608i
$134$	−2.22854	−	2.22854i	−0.192516	−	0.192516i
$135$		0			0
$136$	10.3645	−	2.26901i	0.888748	−	0.194566i
$137$	3.07772			0.262947			0.131474	−	0.991320i	$-0.458029\pi$
$137$	3.07772			0.262947			0.131474	+	0.991320i	$0.458029\pi$
$138$		0			0
$139$	−2.56777	−	6.19915i	−0.217796	−	0.525805i	0.776786	−	0.629765i	$-0.216849\pi$
$139$	−2.56777	−	6.19915i	−0.217796	−	0.525805i	−0.994582	+	0.103960i	$0.966849\pi$
$140$		−	4.65699i		−	0.393587i
$141$		0			0
$142$	−1.11385	+	2.68907i	−0.0934720	+	0.225661i
$143$	10.9119	+	4.51988i	0.912503	+	0.377971i
$144$		0			0
$145$	0.314210	−	0.314210i	0.0260937	−	0.0260937i
$146$	−4.47109	−	1.85198i	−0.370030	−	0.153271i
$147$		0			0
$148$	14.2412	−	5.89890i	1.17062	−	0.484887i
$149$		−	22.9914i		−	1.88353i	−0.336276	−	0.941764i	$-0.609167\pi$
$149$		−	22.9914i		−	1.88353i	0.336276	−	0.941764i	$-0.390833\pi$
$150$		0			0
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	0.712716	−	0.701452i	$-0.247465\pi$
$151$	0.138411	+	0.138411i	0.0112638	+	0.0112638i	−0.701452	+	0.712716i	$0.747465\pi$
$152$	−3.26530			−0.264850
$153$		0			0
$154$	−6.61268			−0.532865
$155$	−3.90914	−	3.90914i	−0.313990	−	0.313990i
$156$		0			0
$157$			11.8582i			0.946391i	0.880957	+	0.473196i	$0.156900\pi$
$157$			11.8582i			0.946391i	−0.880957	+	0.473196i	$0.843100\pi$
$158$	−4.98993	+	2.06690i	−0.396978	+	0.164434i
$159$		0			0
$160$	−5.41585	−	2.24332i	−0.428161	−	0.177350i
$161$	1.12546	−	1.12546i	0.0886983	−	0.0886983i
$162$		0			0
$163$	−4.93787	−	2.04533i	−0.386764	−	0.160203i	0.180824	−	0.983515i	$-0.442123\pi$
$163$	−4.93787	−	2.04533i	−0.386764	−	0.160203i	−0.567588	+	0.823312i	$0.692123\pi$
$164$	1.19659	−	2.88883i	0.0934382	−	0.225580i
$165$		0			0
$166$		−	0.170150i		−	0.0132062i
$167$	4.43529	+	10.7077i	0.343213	+	0.828589i	0.997387	+	0.0722453i	$0.0230164\pi$
$167$	4.43529	+	10.7077i	0.343213	+	0.828589i	−0.654174	+	0.756344i	$0.726984\pi$
$168$		0			0
$169$	−5.64797			−0.434459
$170$	1.76207	+	2.53071i	0.135144	+	0.194097i
$171$		0			0
$172$	−2.20220	−	2.20220i	−0.167916	−	0.167916i
$173$	−4.21988	−	10.1877i	−0.320832	−	0.774556i	−0.999206	−	0.0398396i	$-0.987315\pi$
$173$	−4.21988	−	10.1877i	−0.320832	−	0.774556i	0.678375	−	0.734716i	$-0.262685\pi$
$174$		0			0
$175$	2.98655	−	1.23707i	0.225762	−	0.0935137i
$176$	1.00130	−	2.41734i	0.0754755	−	0.182214i
$177$		0			0
$178$	−7.05538	+	7.05538i	−0.528823	+	0.528823i
$179$	−14.9009	+	14.9009i	−1.11375	+	1.11375i	−0.121109	+	0.992639i	$0.538645\pi$
$179$	−14.9009	+	14.9009i	−1.11375	+	1.11375i	−0.992639	+	0.121109i	$0.961355\pi$
$180$		0			0
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	−0.175968	−	0.984396i	$-0.556305\pi$
$181$	8.67131	−	20.9344i	0.644533	−	1.55604i	0.820501	−	0.571645i	$-0.193695\pi$
$182$	9.64579	−	3.99542i	0.714993	−	0.296160i
$183$		0			0
$184$	−0.484861	−	1.17056i	−0.0357444	−	0.0862947i
$185$	7.56599	+	7.56599i	0.556263	+	0.556263i
$186$		0			0
$187$	−9.25469	+	6.44380i	−0.676770	+	0.471217i
$188$	−12.0954			−0.882150
$189$		0			0
$190$	−0.363182	−	0.876800i	−0.0263480	−	0.0636098i
$191$			3.50162i			0.253368i	0.991943	+	0.126684i	$0.0404335\pi$
$191$			3.50162i			0.253368i	−0.991943	+	0.126684i	$0.959567\pi$
$192$		0			0
$193$	−4.70480	+	11.3584i	−0.338659	+	0.817595i	0.659186	+	0.751980i	$0.270901\pi$
$193$	−4.70480	+	11.3584i	−0.338659	+	0.817595i	−0.997845	+	0.0656152i	$0.979099\pi$
$194$	−10.2317	−	4.23811i	−0.734593	−	0.304278i
$195$		0			0
$196$	3.51426	−	3.51426i	0.251018	−	0.251018i
$197$	−15.6835	−	6.49632i	−1.11740	−	0.462843i	−0.253922	−	0.967225i	$-0.581721\pi$
$197$	−15.6835	−	6.49632i	−1.11740	−	0.462843i	−0.863481	+	0.504381i	$0.831721\pi$
$198$		0			0
$199$	10.6966	−	4.43067i	0.758260	−	0.314082i	0.0301533	−	0.999545i	$-0.490400\pi$
$199$	10.6966	−	4.43067i	0.758260	−	0.314082i	0.728107	+	0.685464i	$0.240400\pi$
$200$		−	2.57329i		−	0.181959i
$201$		0			0
$202$	0.150308	+	0.150308i	0.0105756	+	0.0105756i
$203$	1.43645			0.100819
$204$		0			0
$205$	2.17048			0.151593
$206$	−7.44849	−	7.44849i	−0.518961	−	0.518961i
$207$		0			0
$208$			4.13111i			0.286441i
$209$	3.20642	−	1.32814i	0.221792	−	0.0918694i
$210$		0			0
$211$	6.15655	+	2.55013i	0.423834	+	0.175558i	0.584397	−	0.811468i	$-0.301331\pi$
$211$	6.15655	+	2.55013i	0.423834	+	0.175558i	−0.160563	+	0.987026i	$0.551331\pi$
$212$	−1.85091	+	1.85091i	−0.127121	+	0.127121i
$213$		0			0
$214$	−12.9282	−	5.35503i	−0.883753	−	0.366063i
$215$	0.827294	−	1.99726i	0.0564210	−	0.136212i
$216$		0			0
$217$		−	17.8711i		−	1.21317i
$218$	−1.01056	−	2.43971i	−0.0684438	−	0.165238i
$219$		0			0
$220$	3.94023			0.265650
$221$	9.60626	−	14.9912i	0.646187	−	1.00842i
$222$		0			0
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	0.939322	−	0.343037i	$-0.111456\pi$
$223$	8.90442	+	8.90442i	0.596284	+	0.596284i	−0.343037	+	0.939322i	$0.611456\pi$
$224$	−7.25180	−	17.5074i	−0.484531	−	1.16976i
$225$		0			0
$226$	−1.96346	+	0.813292i	−0.130607	+	0.0540994i
$227$	−3.07779	+	7.43044i	−0.204280	+	0.493176i	−0.992504	−	0.122213i	$-0.961001\pi$
$227$	−3.07779	+	7.43044i	−0.204280	+	0.493176i	0.788224	+	0.615389i	$0.211001\pi$
$228$		0			0
$229$	−15.2944	+	15.2944i	−1.01068	+	1.01068i	−0.0107373	+	0.999942i	$0.503418\pi$
$229$	−15.2944	+	15.2944i	−1.01068	+	1.01068i	−0.999942	+	0.0107373i	$0.996582\pi$
$230$	0.260391	−	0.260391i	0.0171697	−	0.0171697i
$231$		0			0
$232$	0.437587	−	1.05643i	0.0287290	−	0.0693579i
$233$	20.2797	−	8.40011i	1.32857	−	0.550310i	0.398320	−	0.917247i	$-0.369594\pi$
$233$	20.2797	−	8.40011i	1.32857	−	0.550310i	0.930246	+	0.366937i	$0.119594\pi$
$234$		0			0
$235$	−3.21300	−	7.75686i	−0.209593	−	0.506002i
$236$	−3.07626	−	3.07626i	−0.200248	−	0.200248i
$237$		0			0
$238$	−1.75697	+	9.81247i	−0.113888	+	0.636048i
$239$	−5.90132			−0.381725			−0.190862	−	0.981617i	$-0.561128\pi$
$239$	−5.90132			−0.381725			−0.190862	+	0.981617i	$0.561128\pi$
$240$		0			0
$241$	5.09407	+	12.2982i	0.328138	+	0.792195i	0.998731	+	0.0503696i	$0.0160399\pi$
$241$	5.09407	+	12.2982i	0.328138	+	0.792195i	−0.670593	+	0.741826i	$0.733960\pi$
$242$			2.63214i			0.169200i
$243$		0			0
$244$	6.73872	−	16.2687i	0.431402	−	1.04150i
$245$	3.18723	+	1.32019i	0.203624	+	0.0843440i
$246$		0			0
$247$	−3.87467	+	3.87467i	−0.246539	+	0.246539i
$248$	−13.1432	−	5.44409i	−0.834594	−	0.345700i
$249$		0			0
$250$	0.690983	−	0.286214i	0.0437016	−	0.0181018i
$251$			3.59367i			0.226831i	0.993548	+	0.113415i	$0.0361790\pi$
$251$			3.59367i			0.226831i	−0.993548	+	0.113415i	$0.963821\pi$
$252$		0			0
$253$	0.952236	+	0.952236i	0.0598666	+	0.0598666i
$254$	4.08746			0.256470
$255$		0			0
$256$	−12.3285			−0.770531
$257$	17.3588	+	17.3588i	1.08281	+	1.08281i	0.996246	+	0.0865680i	$0.0275900\pi$
$257$	17.3588	+	17.3588i	1.08281	+	1.08281i	0.0865680	+	0.996246i	$0.472410\pi$
$258$		0			0
$259$			34.5888i			2.14924i
$260$	−5.74754	+	2.38071i	−0.356447	+	0.147645i
$261$		0			0
$262$	−6.89567	−	2.85628i	−0.426016	−	0.176462i
$263$	−10.3521	+	10.3521i	−0.638340	+	0.638340i	−0.950146	−	0.311806i	$-0.899066\pi$
$263$	−10.3521	+	10.3521i	−0.638340	+	0.638340i	0.311806	+	0.950146i	$0.399066\pi$
$264$		0			0
$265$	−1.67867	−	0.695328i	−0.103120	−	0.0427136i
$266$	1.17403	−	2.83436i	0.0719845	−	0.173786i
$267$		0			0
$268$			6.07063i			0.370823i
$269$	7.17904	+	17.3317i	0.437714	+	1.05673i	0.976736	+	0.214443i	$0.0687936\pi$
$269$	7.17904	+	17.3317i	0.437714	+	1.05673i	−0.539023	+	0.842291i	$0.681206\pi$
$270$		0			0
$271$	5.76388			0.350131			0.175065	−	0.984557i	$-0.443986\pi$
$271$	5.76388			0.350131			0.175065	+	0.984557i	$0.443986\pi$
$272$	−3.32102	−	2.12809i	−0.201366	−	0.129034i
$273$		0			0
$274$	1.62767	+	1.62767i	0.0983311	+	0.0983311i
$275$	1.04667	+	2.52689i	0.0631167	+	0.152377i
$276$		0			0
$277$	0.113870	−	0.0471663i	0.00684176	−	0.00283395i	−0.379260	−	0.925290i	$-0.623821\pi$
$277$	0.113870	−	0.0471663i	0.00684176	−	0.00283395i	0.386102	+	0.922456i	$0.373821\pi$
$278$	1.92047	−	4.63643i	0.115182	−	0.278075i
$279$		0			0
$280$	5.88205	−	5.88205i	0.351520	−	0.351520i
$281$	1.28950	−	1.28950i	0.0769253	−	0.0769253i	−0.667597	−	0.744523i	$-0.732677\pi$
$281$	1.28950	−	1.28950i	0.0769253	−	0.0769253i	0.744523	+	0.667597i	$0.232677\pi$
$282$		0			0
$283$	10.9554	−	26.4486i	0.651229	−	1.57221i	−0.159767	−	0.987155i	$-0.551074\pi$
$283$	10.9554	−	26.4486i	0.651229	−	1.57221i	0.810996	−	0.585052i	$-0.198926\pi$
$284$	5.17965	−	2.14548i	0.307355	−	0.127311i
$285$		0			0
$286$	3.38048	+	8.16120i	0.199892	+	0.482582i
$287$	4.96130	+	4.96130i	0.292856	+	0.292856i
$288$		0			0
$289$	7.10292	+	15.4450i	0.417819	+	0.908530i
$290$	0.332343			0.0195159
$291$		0			0
$292$	3.56727	+	8.61216i	0.208759	+	0.503988i
$293$			1.41607i			0.0827278i	0.999144	+	0.0413639i	$0.0131703\pi$
$293$			1.41607i			0.0827278i	−0.999144	+	0.0413639i	$0.986830\pi$
$294$		0			0
$295$	1.15565	−	2.78999i	0.0672848	−	0.162440i
$296$	25.4381	+	10.5368i	1.47856	+	0.612440i
$297$		0			0
$298$	12.1591	−	12.1591i	0.704358	−	0.704358i
$299$	−1.96435	−	0.813662i	−0.113602	−	0.0470553i
$300$		0			0
$301$	6.45639	−	2.67433i	0.372140	−	0.154146i
$302$			0.146399i			0.00842433i
$303$		0			0
$304$	0.858361	+	0.858361i	0.0492304	+	0.0492304i
$305$	12.2233			0.699902
$306$		0			0
$307$	−21.7364			−1.24056			−0.620281	−	0.784379i	$-0.712982\pi$
$307$	−21.7364			−1.24056			−0.620281	+	0.784379i	$0.712982\pi$
$308$	9.00661	+	9.00661i	0.513199	+	0.513199i
$309$		0			0
$310$		−	4.13474i		−	0.234838i
$311$	−7.99250	+	3.31060i	−0.453213	+	0.187727i	−0.597600	−	0.801794i	$-0.703879\pi$
$311$	−7.99250	+	3.31060i	−0.453213	+	0.187727i	0.144387	+	0.989521i	$0.453879\pi$
$312$		0			0
$313$	9.49936	+	3.93476i	0.536936	+	0.222406i	0.634638	−	0.772810i	$-0.281149\pi$
$313$	9.49936	+	3.93476i	0.536936	+	0.222406i	−0.0977022	+	0.995216i	$0.531149\pi$
$314$	−6.27130	+	6.27130i	−0.353910	+	0.353910i
$315$		0			0
$316$	9.61155	+	3.98123i	0.540692	+	0.223962i
$317$	0.431538	−	1.04183i	0.0242376	−	0.0585147i	−0.911297	−	0.411749i	$-0.864918\pi$
$317$	0.431538	−	1.04183i	0.0242376	−	0.0585147i	0.935535	+	0.353234i	$0.114918\pi$
$318$		0			0
$319$			1.21536i			0.0680473i
$320$	−0.945625	−	2.28294i	−0.0528620	−	0.127620i
$321$		0			0
$322$	1.19041			0.0663387
$323$	−1.11887	−	5.11084i	−0.0622559	−	0.284375i
$324$		0			0
$325$	−3.05352	−	3.05352i	−0.169379	−	0.169379i
$326$	−1.52974	−	3.69311i	−0.0847242	−	0.204542i
$327$		0			0
$328$	5.16013	−	2.13740i	0.284921	−	0.118018i
$329$	10.3864	−	25.0750i	0.572621	−	1.38243i
$330$		0			0
$331$	−24.2254	+	24.2254i	−1.33155	+	1.33155i	−0.427567	+	0.903984i	$0.640629\pi$
$331$	−24.2254	+	24.2254i	−1.33155	+	1.33155i	−0.903984	+	0.427567i	$0.859371\pi$
$332$	−0.231748	+	0.231748i	−0.0127188	+	0.0127188i
$333$		0			0
$334$	−3.31722	+	8.00847i	−0.181510	+	0.438204i
$335$	−3.89312	+	1.61259i	−0.212704	+	0.0881049i
$336$		0			0
$337$	−5.26046	−	12.6999i	−0.286556	−	0.691807i	0.713404	−	0.700753i	$-0.247152\pi$
$337$	−5.26046	−	12.6999i	−0.286556	−	0.691807i	−0.999960	+	0.00894611i	$0.997152\pi$
$338$	−2.98696	−	2.98696i	−0.162469	−	0.162469i
$339$		0			0
$340$	1.04691	−	5.84686i	0.0567766	−	0.317090i
$341$	15.1206			0.818824
$342$		0			0
$343$	−4.39181	−	10.6028i	−0.237135	−	0.572495i
$344$		−	5.56300i		−	0.299937i
$345$		0			0
$346$	3.15611	−	7.61952i	0.169673	−	0.409628i
$347$	−17.4415	−	7.22453i	−0.936311	−	0.387833i	−0.138242	−	0.990398i	$-0.544145\pi$
$347$	−17.4415	−	7.22453i	−0.936311	−	0.387833i	−0.798069	+	0.602566i	$0.794145\pi$
$348$		0			0
$349$	4.98501	−	4.98501i	0.266842	−	0.266842i	−0.560985	−	0.827826i	$-0.689577\pi$
$349$	4.98501	−	4.98501i	0.266842	−	0.266842i	0.827826	+	0.560985i	$0.189577\pi$
$350$	2.23368	+	0.925222i	0.119395	+	0.0494552i
$351$		0			0
$352$	14.8128	−	6.13567i	0.789526	−	0.327032i
$353$			8.60779i			0.458146i	0.973409	+	0.229073i	$0.0735695\pi$
$353$			8.60779i			0.458146i	−0.973409	+	0.229073i	$0.926431\pi$
$354$		0			0
$355$	2.75181	+	2.75181i	0.146051	+	0.146051i
$356$	19.2191			1.01861
$357$		0			0
$358$	−15.7609			−0.832988
$359$	6.49195	+	6.49195i	0.342632	+	0.342632i	0.857356	−	0.514724i	$-0.172106\pi$
$359$	6.49195	+	6.49195i	0.342632	+	0.342632i	−0.514724	+	0.857356i	$0.672106\pi$
$360$		0			0
$361$		−	17.3898i		−	0.915255i
$362$	15.6571	−	6.48540i	0.822921	−	0.340865i
$363$		0			0
$364$	−18.5796	−	7.69592i	−0.973836	−	0.403376i
$365$	−4.57542	+	4.57542i	−0.239488	+	0.239488i
$366$		0			0
$367$	−6.29722	−	2.60840i	−0.328712	−	0.136157i	0.212223	−	0.977221i	$-0.431930\pi$
$367$	−6.29722	−	2.60840i	−0.328712	−	0.136157i	−0.540935	+	0.841064i	$0.681930\pi$
$368$	−0.180252	+	0.435166i	−0.00939628	+	0.0226846i
$369$		0			0
$370$			8.00263i			0.416037i
$371$	−2.24773	−	5.42650i	−0.116696	−	0.281730i
$372$		0			0
$373$	10.4647			0.541841			0.270920	−	0.962602i	$-0.412672\pi$
$373$	10.4647			0.541841			0.270920	+	0.962602i	$0.412672\pi$
$374$	−8.30223	−	1.48656i	−0.429298	−	0.0768680i
$375$		0			0
$376$	−15.2772	−	15.2772i	−0.787863	−	0.787863i
$377$	−0.734329	−	1.77283i	−0.0378199	−	0.0913053i
$378$		0			0
$379$	23.4129	−	9.69794i	1.20264	−	0.498150i	0.310789	−	0.950479i	$-0.399407\pi$
$379$	23.4129	−	9.69794i	1.20264	−	0.498150i	0.891851	+	0.452330i	$0.149407\pi$
$380$	−0.699558	+	1.68888i	−0.0358866	+	0.0866378i
$381$		0			0
$382$	−1.85185	+	1.85185i	−0.0947489	+	0.0947489i
$383$	5.43799	−	5.43799i	0.277868	−	0.277868i	−0.554389	−	0.832258i	$-0.687048\pi$
$383$	5.43799	−	5.43799i	0.277868	−	0.277868i	0.832258	+	0.554389i	$0.187048\pi$
$384$		0			0
$385$	−3.38349	+	8.16848i	−0.172439	+	0.416304i
$386$	−8.49511	+	3.51879i	−0.432389	+	0.179102i
$387$		0			0
$388$	8.16339	+	19.7082i	0.414433	+	1.00053i
$389$	−11.1991	−	11.1991i	−0.567816	−	0.567816i	0.363700	−	0.931516i	$-0.381513\pi$
$389$	−11.1991	−	11.1991i	−0.567816	−	0.567816i	−0.931516	+	0.363700i	$0.881513\pi$
$390$		0			0
$391$	1.66602	−	1.16000i	0.0842541	−	0.0586639i
$392$	8.87742			0.448377
$393$		0			0
$394$	−4.85869	−	11.7299i	−0.244777	−	0.590944i
$395$			7.22150i			0.363353i
$396$		0			0
$397$	11.1606	−	26.9440i	0.560133	−	1.35228i	−0.349526	−	0.936927i	$-0.613657\pi$
$397$	11.1606	−	26.9440i	0.560133	−	1.35228i	0.909659	−	0.415355i	$-0.136343\pi$
$398$	8.00012	+	3.31376i	0.401010	+	0.166104i
$399$		0			0
$400$	−0.676451	+	0.676451i	−0.0338226	+	0.0338226i
$401$	15.1386	+	6.27060i	0.755984	+	0.313139i	0.727181	−	0.686446i	$-0.240830\pi$
$401$	15.1386	+	6.27060i	0.755984	+	0.313139i	0.0288034	+	0.999585i	$0.490830\pi$
$402$		0			0
$403$	−22.0561	+	9.13592i	−1.09869	+	0.455092i
$404$		−	0.409445i		−	0.0203706i
$405$		0			0
$406$	0.759673	+	0.759673i	0.0377019	+	0.0377019i
$407$	−29.2652			−1.45062
$408$		0			0
$409$	33.9971			1.68105			0.840525	−	0.541772i	$-0.182247\pi$
$409$	33.9971			1.68105			0.840525	+	0.541772i	$0.182247\pi$
$410$	1.14787	+	1.14787i	0.0566893	+	0.0566893i
$411$		0			0
$412$			20.2900i			0.999616i
$413$	9.01899	−	3.73579i	0.443796	−	0.183826i
$414$		0			0
$415$	−0.210182	−	0.0870601i	−0.0103174	−	0.00427361i
$416$	−17.9000	+	17.9000i	−0.877618	+	0.877618i
$417$		0			0
$418$	2.39812	+	0.993336i	0.117296	+	0.0485856i
$419$	−0.341711	+	0.824964i	−0.0166937	+	0.0403021i	−0.932007	−	0.362441i	$-0.881943\pi$
$419$	−0.341711	+	0.824964i	−0.0166937	+	0.0403021i	0.915313	+	0.402743i	$0.131943\pi$
$420$		0			0
$421$		−	33.6725i		−	1.64110i	−0.571575	−	0.820550i	$-0.693668\pi$
$421$		−	33.6725i		−	1.64110i	0.571575	−	0.820550i	$-0.306332\pi$
$422$	1.90728	+	4.60457i	0.0928448	+	0.224147i
$423$		0			0
$424$	−4.67562			−0.227068
$425$	4.02772	−	0.881755i	0.195373	−	0.0427714i
$426$		0			0
$427$	27.9400	+	27.9400i	1.35211	+	1.35211i
$428$	10.3148	+	24.9021i	0.498585	+	1.20369i
$429$		0			0
$430$	1.49378	−	0.618745i	0.0720366	−	0.0298385i
$431$	6.23658	−	15.0564i	0.300405	−	0.725243i	−0.699538	−	0.714595i	$-0.746611\pi$
$431$	6.23658	−	15.0564i	0.300405	−	0.725243i	0.999943	−	0.0106472i	$-0.00338917\pi$
$432$		0			0
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.211871	+	0.977298i	$0.567956\pi$
$433$	−24.7450	+	24.7450i	−1.18917	+	1.18917i	−0.977298	+	0.211871i	$0.932044\pi$
$434$	9.45122	−	9.45122i	0.453673	−	0.453673i
$435$		0			0
$436$	−1.94653	+	4.69934i	−0.0932219	+	0.225057i
$437$	−0.577215	+	0.239090i	−0.0276119	+	0.0114372i
$438$		0			0
$439$	8.52530	+	20.5819i	0.406891	+	0.982321i	0.985951	+	0.167036i	$0.0534196\pi$
$439$	8.52530	+	20.5819i	0.406891	+	0.982321i	−0.579060	+	0.815285i	$0.696580\pi$
$440$	4.97674	+	4.97674i	0.237257	+	0.237257i
$441$		0			0
$442$	13.0085	−	2.84784i	0.618750	−	0.135458i
$443$	8.79907			0.418056			0.209028	−	0.977910i	$-0.432970\pi$
$443$	8.79907			0.418056			0.209028	+	0.977910i	$0.432970\pi$
$444$		0			0
$445$	5.10532	+	12.3253i	0.242015	+	0.584277i
$446$			9.41830i			0.445970i
$447$		0			0
$448$	3.05685	−	7.37988i	0.144422	−	0.348666i
$449$	8.19189	+	3.39319i	0.386599	+	0.160135i	0.567513	−	0.823364i	$-0.307906\pi$
$449$	8.19189	+	3.39319i	0.386599	+	0.160135i	−0.180914	+	0.983499i	$0.557906\pi$
$450$		0			0
$451$	−4.19771	+	4.19771i	−0.197662	+	0.197662i
$452$	3.78200	+	1.56655i	0.177890	+	0.0736845i
$453$		0			0
$454$	−5.55733	+	2.30192i	−0.260819	+	0.108035i
$455$		−	13.9595i		−	0.654432i
$456$		0			0
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	0.332118	−	0.943238i	$-0.392237\pi$
$457$	−13.0643	−	13.0643i	−0.611120	−	0.611120i	−0.943238	+	0.332118i	$0.892237\pi$
$458$	−16.1770			−0.755902
$459$		0			0
$460$	−0.709315			−0.0330720
$461$	−17.3736	−	17.3736i	−0.809169	−	0.809169i	0.175339	−	0.984508i	$-0.443898\pi$
$461$	−17.3736	−	17.3736i	−0.809169	−	0.809169i	−0.984508	+	0.175339i	$0.943898\pi$
$462$		0			0
$463$		−	9.90931i		−	0.460525i	−0.973129	−	0.230262i	$-0.926042\pi$
$463$		−	9.90931i		−	0.460525i	0.973129	−	0.230262i	$-0.0739584\pi$
$464$	−0.392737	+	0.162677i	−0.0182324	+	0.00755209i
$465$		0			0
$466$	15.1675	+	6.28257i	0.702619	+	0.291034i
$467$	20.7918	−	20.7918i	0.962131	−	0.962131i	−0.0371777	−	0.999309i	$-0.511837\pi$
$467$	20.7918	−	20.7918i	0.962131	−	0.962131i	0.999309	+	0.0371777i	$0.0118367\pi$
$468$		0			0
$469$	−12.5850	−	5.21287i	−0.581121	−	0.240708i
$470$	2.40305	−	5.80147i	0.110844	−	0.267602i
$471$		0			0
$472$		−	7.77100i		−	0.357689i
$473$	2.26272	+	5.46269i	0.104040	+	0.251175i
$474$		0			0
$475$	−1.26892			−0.0582219
$476$	15.7578	−	10.9718i	0.722259	−	0.502890i
$477$		0			0
$478$	−3.12095	−	3.12095i	−0.142749	−	0.142749i
$479$	10.9449	+	26.4232i	0.500083	+	1.20731i	0.949438	+	0.313955i	$0.101654\pi$
$479$	10.9449	+	26.4232i	0.500083	+	1.20731i	−0.449354	+	0.893354i	$0.648346\pi$
$480$		0			0
$481$	42.6886	−	17.6822i	1.94643	−	0.806239i
$482$	−3.80993	+	9.19799i	−0.173538	+	0.418957i
$483$		0			0
$484$	3.58503	−	3.58503i	0.162956	−	0.162956i
$485$	−10.4704	+	10.4704i	−0.475439	+	0.475439i
$486$		0			0
$487$	−0.236454	+	0.570849i	−0.0107147	+	0.0258677i	−0.929146	−	0.369712i	$-0.879456\pi$
$487$	−0.236454	+	0.570849i	−0.0107147	+	0.0258677i	0.918432	+	0.395580i	$0.129456\pi$
$488$	29.0597	−	12.0369i	1.31547	−	0.544886i
$489$		0			0
$490$	0.987391	+	2.38377i	0.0446058	+	0.107688i
$491$	−18.0077	−	18.0077i	−0.812675	−	0.812675i	0.172359	−	0.985034i	$-0.444861\pi$
$491$	−18.0077	−	18.0077i	−0.812675	−	0.812675i	−0.985034	+	0.172359i	$0.944861\pi$
$492$		0			0
$493$	1.80346	+	0.322919i	0.0812239	+	0.0145435i
$494$	−4.09827			−0.184390
$495$		0			0
$496$	2.02389	+	4.88611i	0.0908755	+	0.219393i
$497$			12.5802i			0.564301i
$498$		0			0
$499$	13.9527	−	33.6849i	0.624611	−	1.50794i	−0.221624	−	0.975132i	$-0.571136\pi$
$499$	13.9527	−	33.6849i	0.624611	−	1.50794i	0.846234	−	0.532811i	$-0.178864\pi$
$500$	−1.33096	−	0.551303i	−0.0595225	−	0.0246550i
$501$		0			0
$502$	−1.90053	+	1.90053i	−0.0848249	+	0.0848249i
$503$	−27.8902	−	11.5525i	−1.24356	−	0.515100i	−0.338736	−	0.940881i	$-0.609999\pi$
$503$	−27.8902	−	11.5525i	−1.24356	−	0.515100i	−0.904826	+	0.425781i	$0.859999\pi$
$504$		0			0
$505$	0.262579	−	0.108764i	0.0116846	−	0.00483992i
$506$			1.00719i			0.0447751i
$507$		0			0
$508$	−5.56721	−	5.56721i	−0.247005	−	0.247005i
$509$	40.1857			1.78120			0.890600	−	0.454787i	$-0.150285\pi$
$509$	40.1857			1.78120			0.890600	+	0.454787i	$0.150285\pi$
$510$		0			0
$511$	−20.9171			−0.925316
$512$	7.44682	+	7.44682i	0.329106	+	0.329106i
$513$		0			0
$514$			18.3606i			0.809852i
$515$	−13.0121	+	5.38978i	−0.573381	+	0.237502i
$516$		0			0
$517$	21.2157	+	8.78783i	0.933065	+	0.386488i
$518$	−18.2925	+	18.2925i	−0.803725	+	0.803725i
$519$		0			0
$520$	−10.2664	−	4.25250i	−0.450214	−	0.186485i
$521$	13.5302	−	32.6647i	0.592767	−	1.43107i	−0.288053	−	0.957614i	$-0.593008\pi$
$521$	13.5302	−	32.6647i	0.592767	−	1.43107i	0.880820	−	0.473451i	$-0.156992\pi$
$522$		0			0
$523$		−	24.5035i		−	1.07146i	−0.844388	−	0.535732i	$-0.820036\pi$
$523$		−	24.5035i		−	1.07146i	0.844388	−	0.535732i	$-0.179964\pi$
$524$	5.50173	+	13.2824i	0.240344	+	0.580243i
$525$		0			0
$526$	−10.9496			−0.477424
$527$	4.01749	−	22.4372i	0.175005	−	0.977379i
$528$		0			0
$529$	16.0920	+	16.0920i	0.699654	+	0.699654i
$530$	−0.520046	−	1.25550i	−0.0225893	−	0.0545355i
$531$		0			0
$532$	−5.45951	+	2.26140i	−0.236700	+	0.0980443i
$533$	3.58684	−	8.65939i	0.155363	−	0.375080i
$534$		0			0
$535$	−13.2299	+	13.2299i	−0.571977	+	0.571977i
$536$	−7.66756	+	7.66756i	−0.331188	+	0.331188i
$537$		0			0
$538$	−5.36930	+	12.9626i	−0.231487	+	0.558859i
$539$	−8.71734	+	3.61084i	−0.375483	+	0.155530i
$540$		0			0
$541$	9.77786	+	23.6058i	0.420383	+	1.01489i	0.982235	+	0.187657i	$0.0600892\pi$
$541$	9.77786	+	23.6058i	0.420383	+	1.01489i	−0.561852	+	0.827238i	$0.689911\pi$
$542$	3.04826	+	3.04826i	0.130934	+	0.130934i
$543$		0			0
$544$	−5.16891	−	23.6108i	−0.221615	−	1.01230i
$545$	−3.53078			−0.151242
$546$		0			0
$547$	−4.50103	−	10.8664i	−0.192450	−	0.464616i	0.797971	−	0.602696i	$-0.205907\pi$
$547$	−4.50103	−	10.8664i	−0.192450	−	0.464616i	−0.990421	+	0.138080i	$0.955907\pi$
$548$		−	4.43384i		−	0.189404i
$549$		0			0
$550$	−0.782821	+	1.88990i	−0.0333796	+	0.0805855i
$551$	−0.520936	−	0.215779i	−0.0221926	−	0.00919248i
$552$		0			0
$553$	−16.5070	+	16.5070i	−0.701947	+	0.701947i
$554$	0.0851647	+	0.0352764i	0.00361830	+	0.00149875i
$555$		0			0
$556$	−8.93065	+	3.69919i	−0.378744	+	0.156881i
$557$		−	35.6812i		−	1.51186i	−0.654651	−	0.755931i	$-0.727184\pi$
$557$		−	35.6812i		−	1.51186i	0.654651	−	0.755931i	$-0.272816\pi$
$558$		0			0
$559$	−6.60117	−	6.60117i	−0.279200	−	0.279200i
$560$	−3.09247			−0.130681
$561$		0			0
$562$	1.36392			0.0575335
$563$	21.3003	+	21.3003i	0.897702	+	0.897702i	0.995233	−	0.0975306i	$-0.0310944\pi$
$563$	21.3003	+	21.3003i	0.897702	+	0.897702i	−0.0975306	+	0.995233i	$0.531094\pi$
$564$		0			0
$565$			2.84155i			0.119545i
$566$	19.7813	−	8.19368i	0.831470	−	0.344406i
$567$		0			0
$568$	9.25206	+	3.83233i	0.388208	+	0.160801i
$569$	17.2524	−	17.2524i	0.723257	−	0.723257i	−0.246010	−	0.969267i	$-0.579120\pi$
$569$	17.2524	−	17.2524i	0.723257	−	0.723257i	0.969267	+	0.246010i	$0.0791197\pi$
$570$		0			0
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.368755	−	0.929527i	$-0.620216\pi$
$571$	−30.7483	−	12.7364i	−1.28678	−	0.533001i	−0.918024	+	0.396526i	$0.870216\pi$
$572$	6.51144	−	15.7200i	0.272257	−	0.657287i
$573$		0			0
$574$			5.24762i			0.219032i
$575$	−0.188421	−	0.454888i	−0.00785768	−	0.0189701i
$576$		0			0
$577$	−18.0611			−0.751895			−0.375947	−	0.926641i	$-0.622683\pi$
$577$	−18.0611			−0.751895			−0.375947	+	0.926641i	$0.622683\pi$
$578$	−4.41176	+	11.9246i	−0.183505	+	0.495998i
$579$		0			0
$580$	−0.452659	−	0.452659i	−0.0187956	−	0.0187956i
$581$	−0.281432	−	0.679438i	−0.0116758	−	0.0281878i
$582$		0			0
$583$	4.59131	−	1.90178i	0.190152	−	0.0787637i
$584$	−6.37198	+	15.3833i	−0.263675	+	0.636567i
$585$		0			0
$586$	−0.748897	+	0.748897i	−0.0309366	+	0.0309366i
$587$	29.5785	−	29.5785i	1.22084	−	1.22084i	0.253500	−	0.967335i	$-0.418418\pi$
$587$	29.5785	−	29.5785i	1.22084	−	1.22084i	0.967335	−	0.253500i	$-0.0815817\pi$
$588$		0			0
$589$	−2.68454	+	6.48105i	−0.110614	+	0.267047i
$590$	2.08668	−	0.864330i	0.0859071	−	0.0355839i
$591$		0			0
$592$	−3.91717	−	9.45688i	−0.160995	−	0.388675i
$593$	−14.6130	−	14.6130i	−0.600085	−	0.600085i	0.340250	−	0.940335i	$-0.389488\pi$
$593$	−14.6130	−	14.6130i	−0.600085	−	0.600085i	−0.940335	+	0.340250i	$0.889488\pi$
$594$		0			0
$595$	11.2221	+	7.19106i	0.460062	+	0.294805i
$596$	−33.1219			−1.35673
$597$		0			0
$598$	−0.608550	−	1.46917i	−0.0248854	−	0.0600788i
$599$		−	9.21817i		−	0.376644i	−0.982107	−	0.188322i	$-0.939695\pi$
$599$		−	9.21817i		−	0.376644i	0.982107	−	0.188322i	$-0.0603049\pi$
$600$		0			0
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	−0.936024	−	0.351936i	$-0.885524\pi$
$601$	−0.620216	+	1.49733i	−0.0252991	+	0.0610775i	0.910725	+	0.413013i	$0.135524\pi$
$602$	4.82883	+	2.00017i	0.196808	+	0.0815207i
$603$		0			0
$604$	0.199399	−	0.199399i	0.00811342	−	0.00811342i
$605$	3.25141	+	1.34678i	0.132189	+	0.0547543i
$606$		0			0
$607$	23.1115	−	9.57311i	0.938068	−	0.388560i	0.139334	−	0.990245i	$-0.455504\pi$
$607$	23.1115	−	9.57311i	0.938068	−	0.388560i	0.798733	+	0.601685i	$0.205504\pi$
$608$			7.43849i			0.301671i
$609$		0			0
$610$	6.46434	+	6.46434i	0.261733	+	0.261733i
$611$	−36.2566			−1.46678
$612$		0			0
$613$	4.83538			0.195299			0.0976495	−	0.995221i	$-0.468868\pi$
$613$	4.83538			0.195299			0.0976495	+	0.995221i	$0.468868\pi$
$614$	−11.4954	−	11.4954i	−0.463917	−	0.463917i
$615$		0			0
$616$			22.7517i			0.916694i
$617$	−15.5336	+	6.43422i	−0.625358	+	0.259032i	−0.672779	−	0.739843i	$-0.734900\pi$
$617$	−15.5336	+	6.43422i	−0.625358	+	0.259032i	0.0474212	+	0.998875i	$0.484900\pi$
$618$		0			0
$619$	11.7540	+	4.86865i	0.472431	+	0.195687i	0.606179	−	0.795328i	$-0.292701\pi$
$619$	11.7540	+	4.86865i	0.472431	+	0.195687i	−0.133748	+	0.991015i	$0.542701\pi$
$620$	−5.63161	+	5.63161i	−0.226171	+	0.226171i
$621$		0			0
$622$	−5.97771	−	2.47605i	−0.239684	−	0.0992804i
$623$	−16.5036	+	39.8431i	−0.661201	+	1.59628i
$624$		0			0
$625$		−	1.00000i		−	0.0400000i
$626$	2.94287	+	7.10471i	0.117621	+	0.283961i
$627$		0			0
$628$	17.0833			0.681697
$629$	−7.77569	+	43.4263i	−0.310037	+	1.73152i
$630$		0			0
$631$	−2.99812	−	2.99812i	−0.119353	−	0.119353i	0.644907	−	0.764261i	$-0.276896\pi$
$631$	−2.99812	−	2.99812i	−0.119353	−	0.119353i	−0.764261	+	0.644907i	$0.776896\pi$
$632$	7.11142	+	17.1685i	0.282877	+	0.682925i
$633$		0			0
$634$	0.779196	−	0.322754i	0.0309458	−	0.0128182i
$635$	2.09142	−	5.04914i	0.0829956	−	0.200369i
$636$		0			0
$637$	10.5341	−	10.5341i	0.417377	−	0.417377i
$638$	−0.642752	+	0.642752i	−0.0254468	+	0.0254468i
$639$		0			0
$640$	−3.77939	+	9.12426i	−0.149394	+	0.360668i
$641$	−19.6050	+	8.12065i	−0.774350	+	0.320746i	−0.734633	−	0.678465i	$-0.762646\pi$
$641$	−19.6050	+	8.12065i	−0.774350	+	0.320746i	−0.0397171	+	0.999211i	$0.512646\pi$
$642$		0			0
$643$	−3.12525	−	7.54502i	−0.123248	−	0.297547i	0.850198	−	0.526462i	$-0.176482\pi$
$643$	−3.12525	−	7.54502i	−0.123248	−	0.297547i	−0.973446	+	0.228916i	$0.926482\pi$
$644$	−1.62136	−	1.62136i	−0.0638905	−	0.0638905i
$645$		0			0
$646$	2.11117	−	3.29462i	0.0830630	−	0.129625i
$647$	−23.4331			−0.921249			−0.460624	−	0.887595i	$-0.652374\pi$
$647$	−23.4331			−0.921249			−0.460624	+	0.887595i	$0.652374\pi$
$648$		0			0
$649$	3.16081	+	7.63088i	0.124073	+	0.299538i
$650$		−	3.22974i		−	0.126681i
$651$		0			0
$652$	−2.94656	+	7.11362i	−0.115396	+	0.278591i
$653$	−15.5279	−	6.43188i	−0.607655	−	0.251699i	0.0575706	−	0.998341i	$-0.481665\pi$
$653$	−15.5279	−	6.43188i	−0.607655	−	0.251699i	−0.665225	+	0.746643i	$0.731665\pi$
$654$		0			0
$655$	−7.05658	+	7.05658i	−0.275723	+	0.275723i
$656$	−1.91833	−	0.794598i	−0.0748981	−	0.0310238i
$657$		0			0
$658$	18.7539	−	7.76814i	0.731105	−	0.302833i
$659$			14.0972i			0.549150i	0.961566	+	0.274575i	$0.0885371\pi$
$659$			14.0972i			0.549150i	−0.961566	+	0.274575i	$0.911463\pi$
$660$		0			0
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	0.549630	−	0.835408i	$-0.314769\pi$
$661$	−7.34734	−	7.34734i	−0.285779	−	0.285779i	−0.835408	+	0.549630i	$0.814769\pi$
$662$	−25.6235			−0.995886
$663$		0			0
$664$	−0.585422			−0.0227188
$665$	−2.90050	−	2.90050i	−0.112477	−	0.112477i
$666$		0			0
$667$		−	0.218788i		−	0.00847151i
$668$	15.4258	−	6.38959i	0.596843	−	0.247220i
$669$		0			0
$670$	−2.91172	−	1.20608i	−0.112490	−	0.0465948i
$671$	−23.6398	+	23.6398i	−0.912603	+	0.912603i
$672$		0			0
$673$	−18.3153	−	7.58646i	−0.706005	−	0.292437i	0.000645530	−	1.00000i	$-0.499795\pi$
$673$	−18.3153	−	7.58646i	−0.706005	−	0.292437i	−0.706650	+	0.707563i	$0.749795\pi$
$674$	3.93438	−	9.49842i	0.151546	−	0.365866i
$675$		0			0
$676$			8.13660i			0.312946i
$677$	−1.28043	−	3.09124i	−0.0492111	−	0.118806i	0.897362	−	0.441295i	$-0.145481\pi$
$677$	−1.28043	−	3.09124i	−0.0492111	−	0.118806i	−0.946573	+	0.322489i	$0.895481\pi$
$678$		0			0
$679$	−47.8669			−1.83696
$680$	8.70723	−	6.06262i	0.333907	−	0.232491i
$681$		0			0
$682$	7.99658	+	7.99658i	0.306205	+	0.306205i
$683$	−19.2424	−	46.4553i	−0.736290	−	1.77756i	−0.620380	−	0.784302i	$-0.713022\pi$
$683$	−19.2424	−	46.4553i	−0.736290	−	1.77756i	−0.115910	−	0.993260i	$-0.536978\pi$
$684$		0			0
$685$	2.84344	−	1.17779i	0.108642	−	0.0450012i
$686$	3.28470	−	7.92996i	0.125410	−	0.302767i
$687$		0			0
$688$	−1.46237	+	1.46237i	−0.0557522	+	0.0557522i
$689$	−5.54818	+	5.54818i	−0.211369	+	0.211369i
$690$		0			0
$691$	−14.8926	+	35.9539i	−0.566540	+	1.36775i	0.337913	+	0.941177i	$0.390279\pi$
$691$	−14.8926	+	35.9539i	−0.566540	+	1.36775i	−0.904454	+	0.426572i	$0.859721\pi$
$692$	−14.6766	+	6.07926i	−0.557922	+	0.231099i
$693$		0			0
$694$	−5.40333	−	13.0448i	−0.205107	−	0.495173i
$695$	−4.74462	−	4.74462i	−0.179974	−	0.179974i
$696$		0			0
$697$	5.11360	+	7.34424i	0.193692	+	0.278183i
$698$	5.27270			0.199575
$699$		0			0
$700$	−1.78215	−	4.30250i	−0.0673590	−	0.162619i
$701$			37.5419i			1.41794i	0.705239	+	0.708969i	$0.250840\pi$
$701$			37.5419i			1.41794i	−0.705239	+	0.708969i	$0.749160\pi$
$702$		0			0
$703$	5.19582	−	12.5438i	0.195964	−	0.473099i
$704$	6.24404	+	2.58637i	0.235331	+	0.0974773i
$705$		0			0
$706$	−4.55227	+	4.55227i	−0.171327	+	0.171327i
$707$	0.848818	+	0.351592i	0.0319231	+	0.0132230i
$708$		0			0
$709$	12.7076	−	5.26367i	0.477245	−	0.197681i	−0.131076	−	0.991372i	$-0.541843\pi$
$709$	12.7076	−	5.26367i	0.477245	−	0.197681i	0.608321	+	0.793691i	$0.291843\pi$
$710$			2.91062i			0.109234i
$711$		0			0
$712$	24.2749	+	24.2749i	0.909741	+	0.909741i
$713$	−2.72198			−0.101939
$714$		0			0
$715$	11.8110			0.441707
$716$	21.4667	+	21.4667i	0.802246	+	0.802246i
$717$		0			0
$718$			6.86660i			0.256259i
$719$	0.488717	−	0.202433i	0.0182261	−	0.00754949i	−0.373552	−	0.927609i	$-0.621860\pi$
$719$	0.488717	−	0.202433i	0.0182261	−	0.00754949i	0.391778	+	0.920060i	$0.371860\pi$
$720$		0			0
$721$	−42.0631	−	17.4231i	−1.56651	−	0.648870i
$722$	9.19671	−	9.19671i	0.342266	−	0.342266i
$723$		0			0
$724$	−30.1586	−	12.4921i	−1.12084	−	0.464265i
$725$	0.170049	−	0.410535i	0.00631547	−	0.0152469i
$726$		0			0
$727$		−	26.7632i		−	0.992591i	−0.868154	−	0.496296i	$-0.834693\pi$
$727$		−	26.7632i		−	0.992591i	0.868154	−	0.496296i	$-0.165307\pi$
$728$	−13.7467	−	33.1875i	−0.509487	−	1.23001i
$729$		0			0
$730$	−4.83947			−0.179117
$731$	8.70721	−	1.90620i	0.322048	−	0.0705033i
$732$		0			0
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	0.443279	−	0.896384i	$-0.353815\pi$
$733$	−12.2673	−	12.2673i	−0.453105	−	0.453105i	−0.896384	+	0.443279i	$0.853815\pi$
$734$	−1.95086	−	4.70978i	−0.0720074	−	0.173841i
$735$		0			0
$736$	−2.66658	+	1.10454i	−0.0982916	+	0.0407137i
$737$	4.41056	−	10.6480i	0.162465	−	0.392225i
$738$		0			0
$739$	21.3876	−	21.3876i	0.786757	−	0.786757i	−0.194204	−	0.980961i	$-0.562212\pi$
$739$	21.3876	−	21.3876i	0.786757	−	0.786757i	0.980961	+	0.194204i	$0.0622124\pi$
$740$	10.8998	−	10.8998i	0.400683	−	0.400683i
$741$		0			0
$742$	1.68111	−	4.05856i	0.0617155	−	0.148994i
$743$	−6.63416	+	2.74796i	−0.243384	+	0.100813i	−0.501041	−	0.865424i	$-0.667049\pi$
$743$	−6.63416	+	2.74796i	−0.243384	+	0.100813i	0.257657	+	0.966236i	$0.417049\pi$
$744$		0			0
$745$	−8.79842	−	21.2413i	−0.322349	−	0.778220i
$746$	5.53430	+	5.53430i	0.202625	+	0.202625i
$747$		0			0
$748$	9.28309	+	13.3325i	0.339423	+	0.487486i
$749$	−60.4819			−2.20996
$750$		0			0
$751$	11.9767	+	28.9144i	0.437037	+	1.05510i	0.976967	+	0.213390i	$0.0684505\pi$
$751$	11.9767	+	28.9144i	0.437037	+	1.05510i	−0.539930	+	0.841710i	$0.681549\pi$
$752$			8.03197i			0.292896i
$753$		0			0
$754$	0.549215	−	1.32592i	0.0200012	−	0.0482873i
$755$	0.180843	+	0.0749077i	0.00658156	+	0.00272617i
$756$		0			0
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	−0.831885	−	0.554948i	$-0.812738\pi$
$757$	−7.61956	+	7.61956i	−0.276938	+	0.276938i	0.554948	+	0.831885i	$0.312738\pi$
$758$	17.5108	+	7.25323i	0.636022	+	0.263449i
$759$		0			0
$760$	−3.01674	+	1.24957i	−0.109429	+	0.0453268i
$761$			33.1409i			1.20136i	0.799491	+	0.600678i	$0.205102\pi$
$761$			33.1409i			1.20136i	−0.799491	+	0.600678i	$0.794898\pi$
$762$		0			0
$763$	−8.07068	−	8.07068i	−0.292178	−	0.292178i
$764$	5.04452			0.182504
$765$		0			0
$766$	5.75182			0.207822
$767$	−9.22123	−	9.22123i	−0.332959	−	0.332959i
$768$		0			0
$769$		−	11.4864i		−	0.414210i	−0.978319	−	0.207105i	$-0.933596\pi$
$769$		−	11.4864i		−	0.414210i	0.978319	−	0.207105i	$-0.0664042\pi$
$770$	−6.10932	+	2.53056i	−0.220165	+	0.0911952i
$771$		0			0
$772$	16.3632	+	6.77785i	0.588924	+	0.243940i
$773$	2.26913	−	2.26913i	0.0816149	−	0.0816149i	−0.665121	−	0.746736i	$-0.731620\pi$
$773$	2.26913	−	2.26913i	0.0816149	−	0.0816149i	0.746736	+	0.665121i	$0.231620\pi$
$774$		0			0
$775$	−5.10754	−	2.11561i	−0.183468	−	0.0759951i
$776$	−14.5817	+	35.2034i	−0.523454	+	1.26373i
$777$		0			0
$778$		−	11.8454i		−	0.424678i
$779$	−1.05397	−	2.54451i	−0.0377625	−	0.0911667i
$780$		0			0
$781$	−10.6440			−0.380873
$782$	1.49456	+	0.267608i	0.0534452	+	0.00956963i
$783$		0			0
$784$	−2.33364	−	2.33364i	−0.0833443	−	0.0833443i
$785$	4.53796	+	10.9556i	0.161967	+	0.391022i
$786$		0			0
$787$	3.11375	−	1.28976i	0.110993	−	0.0459748i	−0.326496	−	0.945199i	$-0.605868\pi$
$787$	3.11375	−	1.28976i	0.110993	−	0.0459748i	0.437489	+	0.899224i	$0.355868\pi$
$788$	−9.35875	+	22.5940i	−0.333392	+	0.804879i
$789$		0			0
$790$	−3.81913	+	3.81913i	−0.135878	+	0.135878i
$791$	−6.49523	+	6.49523i	−0.230944	+	0.230944i
$792$		0			0
$793$	20.1996	−	48.7661i	0.717308	−	1.73174i
$794$	20.1518	−	8.34716i	0.715161	−	0.296230i
$795$		0			0
$796$	−6.38293	−	15.4097i	−0.226237	−	0.546184i
$797$	15.0966	+	15.0966i	0.534747	+	0.534747i	0.921981	−	0.387234i	$-0.126569\pi$
$797$	15.0966	+	15.0966i	0.534747	+	0.534747i	−0.387234	+	0.921981i	$0.626569\pi$
$798$		0			0
$799$	18.6771	−	29.1468i	0.660748	−	1.03114i
$800$	−5.86207			−0.207256
$801$		0			0
$802$	4.68987	+	11.3224i	0.165605	+	0.399806i
$803$		−	17.6977i		−	0.624538i
$804$		0			0
$805$	0.609092	−	1.47048i	0.0214677	−	0.0518276i
$806$	−16.4960	−	6.83288i	−0.581048	−	0.240678i
$807$		0			0
$808$	0.517153	−	0.517153i	0.0181934	−	0.0181934i
$809$	2.52190	+	1.04460i	0.0886652	+	0.0367263i	0.426575	−	0.904452i	$-0.359720\pi$
$809$	2.52190	+	1.04460i	0.0886652	+	0.0367263i	−0.337910	+	0.941178i	$0.609720\pi$
$810$		0			0
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.894609	−	0.446849i	$-0.852546\pi$
$811$	−34.4933	+	14.2876i	−1.21122	+	0.501705i	−0.316614	+	0.948554i	$0.602546\pi$
$812$		−	2.06938i		−	0.0726211i
$813$		0			0
$814$	−15.4771	−	15.4771i	−0.542471	−	0.542471i
$815$	−5.34472			−0.187217
$816$		0			0
$817$	−2.74317			−0.0959715
$818$	17.9796	+	17.9796i	0.628641	+	0.628641i
$819$		0			0
$820$		−	3.12685i		−	0.109194i
$821$	39.0148	−	16.1605i	1.36163	−	0.564004i	0.422121	−	0.906540i	$-0.361286\pi$
$821$	39.0148	−	16.1605i	1.36163	−	0.564004i	0.939505	+	0.342536i	$0.111286\pi$
$822$		0			0
$823$	19.1803	+	7.94473i	0.668582	+	0.276936i	0.691045	−	0.722812i	$-0.257151\pi$
$823$	19.1803	+	7.94473i	0.668582	+	0.276936i	−0.0224627	+	0.999748i	$0.507151\pi$
$824$	−25.6275	+	25.6275i	−0.892775	+	0.892775i
$825$		0			0
$826$	6.74543	+	2.79405i	0.234704	+	0.0972174i
$827$	4.40367	−	10.6314i	0.153131	−	0.369690i	−0.828634	−	0.559791i	$-0.810881\pi$
$827$	4.40367	−	10.6314i	0.153131	−	0.369690i	0.981765	+	0.190101i	$0.0608815\pi$
$828$		0			0
$829$			11.7508i			0.408121i	0.978958	+	0.204060i	$0.0654139\pi$
$829$			11.7508i			0.408121i	−0.978958	+	0.204060i	$0.934586\pi$
$830$	−0.0651135	−	0.157198i	−0.00226012	−	0.00545642i
$831$		0			0
$832$	−10.6708			−0.369942
$833$	3.04191	+	13.8949i	0.105396	+	0.481431i
$834$		0			0
$835$	8.19535	+	8.19535i	0.283612	+	0.283612i
$836$	−1.91335	−	4.61924i	−0.0661747	−	0.159760i
$837$		0			0
$838$	−0.617003	+	0.255571i	−0.0213140	+	0.00882855i
$839$	14.0060	−	33.8134i	0.483540	−	1.16737i	−0.474377	−	0.880322i	$-0.657327\pi$
$839$	14.0060	−	33.8134i	0.483540	−	1.16737i	0.957917	−	0.287046i	$-0.0926733\pi$
$840$		0			0
$841$	−20.3665	+	20.3665i	−0.702292	+	0.702292i
$842$	17.8079	−	17.8079i	0.613701	−	0.613701i
$843$		0			0
$844$	3.67377	−	8.86927i	0.126457	−	0.305293i
$845$	−5.21805	+	2.16139i	−0.179506	+	0.0743539i
$846$		0			0
$847$	4.35362	+	10.5106i	0.149592	+	0.361148i
$848$	1.22910	+	1.22910i	0.0422074	+	0.0422074i
$849$		0			0
$850$	2.59640	+	1.66376i	0.0890558	+	0.0570665i
$851$	5.26829			0.180595
$852$		0			0
$853$	14.5715	+	35.1787i	0.498918	+	1.20450i	0.950067	+	0.312046i	$0.101014\pi$
$853$	14.5715	+	35.1787i	0.498918	+	1.20450i	−0.451149	+	0.892449i	$0.648986\pi$
$854$			29.5524i			1.01126i
$855$		0			0
$856$	−18.4247	+	44.4811i	−0.629742	+	1.52033i
$857$	18.6880	+	7.74080i	0.638368	+	0.264421i	0.678304	−	0.734781i	$-0.262715\pi$
$857$	18.6880	+	7.74080i	0.638368	+	0.264421i	−0.0399356	+	0.999202i	$0.512715\pi$
$858$		0			0
$859$	1.84360	−	1.84360i	0.0629028	−	0.0629028i	−0.674956	−	0.737858i	$-0.735837\pi$
$859$	1.84360	−	1.84360i	0.0629028	−	0.0629028i	0.737858	+	0.674956i	$0.235837\pi$
$860$	−2.87731	−	1.19182i	−0.0981153	−	0.0406407i
$861$		0			0
$862$	11.2609	−	4.66443i	0.383548	−	0.158871i
$863$			11.2563i			0.383169i	0.981476	+	0.191584i	$0.0613626\pi$
$863$			11.2563i			0.383169i	−0.981476	+	0.191584i	$0.938637\pi$
$864$		0			0
$865$	−7.79732	−	7.79732i	−0.265117	−	0.265117i
$866$	−26.1730			−0.889396
$867$		0			0
$868$	−25.7455			−0.873860
$869$	−13.9664	−	13.9664i	−0.473777	−	0.473777i
$870$		0			0
$871$			18.1970i			0.616580i
$872$	−8.39412	+	3.47696i	−0.284261	+	0.117745i
$873$		0			0
$874$	−0.431707	−	0.178819i	−0.0146027	−	0.00604864i
$875$	2.28581	−	2.28581i	0.0772744	−	0.0772744i
$876$		0			0
$877$	−5.54426	−	2.29651i	−0.187216	−	0.0775476i	0.287106	−	0.957899i	$-0.407307\pi$
$877$	−5.54426	−	2.29651i	−0.187216	−	0.0775476i	−0.474322	+	0.880351i	$0.657307\pi$
$878$	−6.37620	+	15.3935i	−0.215186	+	0.519506i
$879$		0			0
$880$		−	2.61651i		−	0.0882025i
$881$	−13.1380	−	31.7181i	−0.442632	−	1.06861i	−0.975022	−	0.222109i	$-0.928706\pi$
$881$	−13.1380	−	31.7181i	−0.442632	−	1.06861i	0.532390	−	0.846499i	$-0.321294\pi$
$882$		0			0
$883$	−11.8244			−0.397921			−0.198961	−	0.980007i	$-0.563757\pi$
$883$	−11.8244			−0.397921			−0.198961	+	0.980007i	$0.563757\pi$
$884$	−21.5966	−	13.8390i	−0.726374	−	0.465456i
$885$		0			0
$886$	4.65343	+	4.65343i	0.156335	+	0.156335i
$887$	9.27440	+	22.3904i	0.311404	+	0.751796i	0.999654	+	0.0263216i	$0.00837938\pi$
$887$	9.27440	+	22.3904i	0.311404	+	0.751796i	−0.688250	+	0.725474i	$0.741621\pi$
$888$		0			0
$889$	16.3220	−	6.76077i	0.547421	−	0.226749i
$890$	−3.81834	+	9.21830i	−0.127991	+	0.308998i
$891$		0			0
$892$	12.8279	−	12.8279i	0.429511	−	0.429511i
$893$	−7.53337	+	7.53337i	−0.252095	+	0.252095i
$894$		0			0
$895$	−8.06433	+	19.4690i	−0.269561	+	0.650777i
$896$	−29.4952	+	12.2173i	−0.985367	+	0.408152i
$897$		0			0
$898$	2.53782	+	6.12683i	0.0846880	+	0.204455i
$899$	−1.73707	−	1.73707i	−0.0579345	−	0.0579345i
$900$		0			0
$901$	−1.60213	−	7.31828i	−0.0533747	−	0.243807i
$902$	−4.43996			−0.147835
$903$		0			0
$904$	2.79823	+	6.75553i	0.0930678	+	0.224686i
$905$		−	22.6592i		−	0.753218i
$906$		0			0
$907$	−17.1364	+	41.3709i	−0.569005	+	1.37370i	0.333390	+	0.942789i	$0.391808\pi$
$907$	−17.1364	+	41.3709i	−0.569005	+	1.37370i	−0.902395	+	0.430910i	$0.858192\pi$
$908$	10.7045	+	4.43394i	0.355240	+	0.147145i
$909$		0			0
$910$	7.38256	−	7.38256i	0.244730	−	0.244730i
$911$	−9.19129	−	3.80716i	−0.304521	−	0.126137i	0.225190	−	0.974315i	$-0.427700\pi$
$911$	−9.19129	−	3.80716i	−0.304521	−	0.126137i	−0.529711	+	0.848178i	$0.677700\pi$
$912$		0			0
$913$	0.574865	−	0.238117i	0.0190253	−	0.00788052i
$914$		−	13.8182i		−	0.457066i
$915$		0			0
$916$	22.0334	+	22.0334i	0.728005	+	0.728005i
$917$	−32.2600			−1.06532
$918$		0			0
$919$	−33.3601			−1.10045			−0.550224	−	0.835017i	$-0.685458\pi$
$919$	−33.3601			−1.10045			−0.550224	+	0.835017i	$0.685458\pi$
$920$	−0.895907	−	0.895907i	−0.0295372	−	0.0295372i
$921$		0			0
$922$		−	18.3762i		−	0.605189i
$923$	15.5262	−	6.43116i	0.511051	−	0.211684i
$924$		0			0
$925$	9.88545	+	4.09469i	0.325032	+	0.134632i
$926$	5.24059	−	5.24059i	0.172217	−	0.172217i
$927$		0			0
$928$	−2.40659	−	0.996842i	−0.0790001	−	0.0327229i
$929$	9.52731	−	23.0010i	0.312581	−	0.754637i	−0.687027	−	0.726632i	$-0.741085\pi$
$929$	9.52731	−	23.0010i	0.312581	−	0.754637i	0.999608	−	0.0280049i	$-0.00891541\pi$
$930$		0			0
$931$		−	4.37755i		−	0.143468i
$932$	−12.1014	−	29.2154i	−0.396395	−	0.956982i
$933$		0			0
$934$	21.9917			0.719592
$935$	−6.08429	+	9.49491i	−0.198977	+	0.310517i
$936$		0			0
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	0.247181	−	0.968969i	$-0.420496\pi$
$937$	−22.0943	−	22.0943i	−0.721788	−	0.721788i	−0.968969	+	0.247181i	$0.920496\pi$
$938$	−3.89878	−	9.41250i	−0.127300	−	0.307329i
$939$		0			0
$940$	−11.1747	+	4.62872i	−0.364479	+	0.150972i
$941$	0.663467	−	1.60175i	0.0216284	−	0.0522156i	−0.912696	−	0.408638i	$-0.866004\pi$
$941$	0.663467	−	1.60175i	0.0216284	−	0.0522156i	0.934325	+	0.356423i	$0.116004\pi$
$942$		0			0
$943$	0.755666	−	0.755666i	0.0246079	−	0.0246079i
$944$	−2.04279	+	2.04279i	−0.0664873	+	0.0664873i
$945$		0			0
$946$	−1.69232	+	4.08562i	−0.0550221	+	0.132835i
$947$	−10.0253	+	4.15260i	−0.325777	+	0.134941i	−0.539577	−	0.841936i	$-0.681416\pi$
$947$	−10.0253	+	4.15260i	−0.325777	+	0.134941i	0.213800	+	0.976877i	$0.431416\pi$
$948$		0			0
$949$	10.6930	+	25.8153i	0.347111	+	0.838000i
$950$	−0.671074	−	0.671074i	−0.0217725	−	0.0217725i
$951$		0			0
$952$	33.7610	+	6.04508i	1.09420	+	0.195922i
$953$	16.9007			0.547466			0.273733	−	0.961806i	$-0.411742\pi$
$953$	16.9007			0.547466			0.273733	+	0.961806i	$0.411742\pi$
$954$		0			0
$955$	1.34001	+	3.23508i	0.0433618	+	0.104685i
$956$			8.50159i			0.274961i
$957$		0			0
$958$	−8.18582	+	19.7623i	−0.264472	+	0.638491i
$959$	9.19177	+	3.80736i	0.296818	+	0.122946i
$960$		0			0
$961$	0.309144	−	0.309144i	0.00997239	−	0.00997239i
$962$	31.9274	+	13.2248i	1.02938	+	0.426384i
$963$		0			0
$964$	17.7171	−	7.33864i	0.570628	−	0.236362i
$965$			12.2942i			0.395765i
$966$		0			0
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	0.966591	−	0.256324i	$-0.0825115\pi$
$967$	22.0869	+	22.0869i	0.710267	+	0.710267i	−0.256324	+	0.966591i	$0.582511\pi$
$968$	9.05619			0.291077
$969$		0			0
$970$	−11.0747			−0.355587
$971$	12.2957	+	12.2957i	0.394589	+	0.394589i	0.876319	−	0.481731i	$-0.159992\pi$
$971$	12.2957	+	12.2957i	0.394589	+	0.394589i	−0.481731	+	0.876319i	$0.659992\pi$
$972$		0			0
$973$		−	21.6906i		−	0.695368i
$974$	−0.426947	+	0.176847i	−0.0136802	+	0.00566654i
$975$		0			0
$976$	−10.8032	−	4.47485i	−0.345803	−	0.143236i
$977$	6.48656	−	6.48656i	0.207523	−	0.207523i	−0.595691	−	0.803214i	$-0.703122\pi$
$977$	6.48656	−	6.48656i	0.207523	−	0.207523i	0.803214	+	0.595691i	$0.203122\pi$
$978$		0			0
$979$	−33.7109	−	13.9635i	−1.07740	−	0.446275i
$980$	1.90190	−	4.59160i	0.0607540	−	0.146673i
$981$		0			0
$982$		−	19.0469i		−	0.607811i
$983$	−14.2729	−	34.4578i	−0.455235	−	1.09903i	−0.970305	−	0.241886i	$-0.922234\pi$
$983$	−14.2729	−	34.4578i	−0.455235	−	1.09903i	0.515070	−	0.857148i	$-0.327766\pi$
$984$		0			0
$985$	−16.9757			−0.540891
$986$	0.782993	+	1.12455i	0.0249356	+	0.0358129i
$987$		0			0
$988$	5.58194	+	5.58194i	0.177585	+	0.177585i
$989$	−0.407332	−	0.983386i	−0.0129524	−	0.0312699i
$990$		0			0
$991$	−32.3988	+	13.4200i	−1.02918	+	0.426301i	−0.832417	−	0.554149i	$-0.813044\pi$
$991$	−32.3988	+	13.4200i	−1.02918	+	0.426301i	−0.196765	+	0.980451i	$0.563044\pi$
$992$	−12.4019	+	29.9408i	−0.393760	+	0.950621i
$993$		0			0
$994$	−6.65312	+	6.65312i	−0.211024	+	0.211024i
$995$	8.18680	−	8.18680i	0.259539	−	0.259539i
$996$		0			0
$997$	14.2961	−	34.5139i	0.452763	−	1.09307i	−0.518505	−	0.855075i	$-0.673511\pi$
$997$	14.2961	−	34.5139i	0.452763	−	1.09307i	0.971267	−	0.237991i	$-0.0764889\pi$
$998$	25.1934	−	10.4355i	0.797484	−	0.330329i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.be.b.406.5		24
3.2	odd	2		85.2.l.a.66.2	✓	24
15.2	even	4		425.2.n.c.49.5		24
15.8	even	4		425.2.n.f.49.2		24
15.14	odd	2		425.2.m.b.151.5		24
17.8	even	8	inner	765.2.be.b.586.5		24
51.5	even	16		1445.2.a.p.1.9		12
51.8	odd	8		85.2.l.a.76.2	yes	24
51.14	even	16		1445.2.d.j.866.8		24
51.20	even	16		1445.2.d.j.866.7		24
51.29	even	16		1445.2.a.q.1.9		12
255.8	even	8		425.2.n.c.399.5		24
255.29	even	16		7225.2.a.bq.1.4		12
255.59	odd	8		425.2.m.b.76.5		24
255.209	even	16		7225.2.a.bs.1.4		12
255.212	even	8		425.2.n.f.399.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	3.2	odd	2
85.2.l.a.76.2	yes	24	51.8	odd	8
425.2.m.b.76.5		24	255.59	odd	8
425.2.m.b.151.5		24	15.14	odd	2
425.2.n.c.49.5		24	15.2	even	4
425.2.n.c.399.5		24	255.8	even	8
425.2.n.f.49.2		24	15.8	even	4
425.2.n.f.399.2		24	255.212	even	8
765.2.be.b.406.5		24	1.1	even	1	trivial
765.2.be.b.586.5		24	17.8	even	8	inner
1445.2.a.p.1.9		12	51.5	even	16
1445.2.a.q.1.9		12	51.29	even	16
1445.2.d.j.866.7		24	51.20	even	16
1445.2.d.j.866.8		24	51.14	even	16
7225.2.a.bq.1.4		12	255.29	even	16
7225.2.a.bs.1.4		12	255.209	even	16

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.be (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.528855 + 0.528855i) q^{2} -1.44062i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.98655 + 1.23707i) q^{7} +(1.81959 - 1.81959i) q^{8} +O(q^{10})\)	\(q+(0.528855 + 0.528855i) q^{2} -1.44062i q^{4} +(0.923880 - 0.382683i) q^{5} +(2.98655 + 1.23707i) q^{7} +(1.81959 - 1.81959i) q^{8} +(0.690983 + 0.286214i) q^{10} +(-1.04667 + 2.52689i) q^{11} -4.31833i q^{13} +(0.925222 + 2.23368i) q^{14} -0.956646 q^{16} +(3.47152 + 2.22453i) q^{17} +(-0.897260 - 0.897260i) q^{19} +(-0.551303 - 1.33096i) q^{20} +(-1.88990 + 0.782821i) q^{22} +(0.188421 - 0.454888i) q^{23} +(0.707107 - 0.707107i) q^{25} +(2.28377 - 2.28377i) q^{26} +(1.78215 - 4.30250i) q^{28} +(0.410535 - 0.170049i) q^{29} +(-2.11561 - 5.10754i) q^{31} +(-4.14511 - 4.14511i) q^{32} +(0.659477 + 3.01239i) q^{34} +3.23262 q^{35} +(4.09469 + 9.88545i) q^{37} -0.949042i q^{38} +(0.984756 - 2.37741i) q^{40} +(2.00526 + 0.830608i) q^{41} +(1.52864 - 1.52864i) q^{43} +(3.64030 + 1.50786i) q^{44} +(0.340217 - 0.140922i) q^{46} -8.39597i q^{47} +(2.43940 + 2.43940i) q^{49} +0.747914 q^{50} -6.22109 q^{52} +(-1.28480 - 1.28480i) q^{53} +2.73509i q^{55} +(7.68527 - 3.18334i) q^{56} +(0.307045 + 0.127182i) q^{58} +(2.13537 - 2.13537i) q^{59} +(11.2928 + 4.67764i) q^{61} +(1.58230 - 3.82000i) q^{62} -2.47104i q^{64} +(-1.65255 - 3.98962i) q^{65} -4.21389 q^{67} +(3.20471 - 5.00116i) q^{68} +(1.70959 + 1.70959i) q^{70} +(1.48927 + 3.59542i) q^{71} +(-5.97807 + 2.47620i) q^{73} +(-3.06247 + 7.39347i) q^{74} +(-1.29261 + 1.29261i) q^{76} +(-6.25188 + 6.25188i) q^{77} +(-2.76355 + 6.67180i) q^{79} +(-0.883826 + 0.366093i) q^{80} +(0.621223 + 1.49977i) q^{82} +(-0.160866 - 0.160866i) q^{83} +(4.05856 + 0.726705i) q^{85} +1.61686 q^{86} +(2.69339 + 6.50243i) q^{88} +13.3408i q^{89} +(5.34208 - 12.8969i) q^{91} +(-0.655322 - 0.271443i) q^{92} +(4.44025 - 4.44025i) q^{94} +(-1.17233 - 0.485594i) q^{95} +(-13.6803 + 5.66657i) q^{97} +2.58018i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 8 q^{11} - 24 q^{16} + 8 q^{17} - 8 q^{19} - 32 q^{22} + 16 q^{23} - 16 q^{26} + 48 q^{28} + 8 q^{29} + 16 q^{34} + 32 q^{35} + 24 q^{37} + 16 q^{40} - 16 q^{41} + 8 q^{43} - 16 q^{44} + 8 q^{46} - 8 q^{50} - 48 q^{52} - 24 q^{53} - 64 q^{56} - 64 q^{58} - 32 q^{59} + 32 q^{61} + 32 q^{62} - 8 q^{65} + 16 q^{67} + 40 q^{68} + 24 q^{71} + 64 q^{74} - 8 q^{76} - 24 q^{77} + 32 q^{80} - 80 q^{82} + 96 q^{83} + 16 q^{86} - 8 q^{88} - 24 q^{91} - 80 q^{92} + 56 q^{94} + 16 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 8 * q^11 - 24 * q^16 + 8 * q^17 - 8 * q^19 - 32 * q^22 + 16 * q^23 - 16 * q^26 + 48 * q^28 + 8 * q^29 + 16 * q^34 + 32 * q^35 + 24 * q^37 + 16 * q^40 - 16 * q^41 + 8 * q^43 - 16 * q^44 + 8 * q^46 - 8 * q^50 - 48 * q^52 - 24 * q^53 - 64 * q^56 - 64 * q^58 - 32 * q^59 + 32 * q^61 + 32 * q^62 - 8 * q^65 + 16 * q^67 + 40 * q^68 + 24 * q^71 + 64 * q^74 - 8 * q^76 - 24 * q^77 + 32 * q^80 - 80 * q^82 + 96 * q^83 + 16 * q^86 - 8 * q^88 - 24 * q^91 - 80 * q^92 + 56 * q^94 + 16 * q^95 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more