LMFDB - Embedded newform 765.2.be.b.586.5

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			586.5
Character	$\chi$	$=$	765.586
Dual form			765.2.be.b.406.5

$q$-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 $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$	$1$

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	−0.494959	−	0.868916i	$-0.664817\pi$
$2$	0.528855	−	0.528855i	0.373957	−	0.373957i	0.868916	+	0.494959i	$0.164817\pi$
$3$		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	0.261434	−	0.965221i	$-0.415805\pi$
$7$	2.98655	−	1.23707i	1.12881	−	0.467569i	0.867376	+	0.497653i	$0.165805\pi$
$8$	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	−0.999478	−	0.0323052i	$-0.989715\pi$
$11$	−1.04667	−	2.52689i	−0.315584	−	0.761886i	0.683894	−	0.729581i	$-0.260285\pi$
$12$		0			0
$13$			4.31833i			1.19769i	0.800865	+	0.598845i	$0.204373\pi$
$13$			4.31833i			1.19769i	−0.800865	+	0.598845i	$0.795627\pi$
$14$	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	−0.802499	−	0.596653i	$-0.796497\pi$
$19$	−0.897260	+	0.897260i	−0.205846	+	0.205846i	0.596653	+	0.802499i	$0.296497\pi$
$20$	−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	0.942306	−	0.334754i	$-0.108653\pi$
$23$	0.188421	+	0.454888i	0.0392884	+	0.0948506i	−0.903017	+	0.429604i	$0.858653\pi$
$24$		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	0.420475	−	0.907304i	$-0.361863\pi$
$29$	0.410535	+	0.170049i	0.0762345	+	0.0315774i	−0.344240	+	0.938882i	$0.611863\pi$
$30$		0			0
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	0.611994	+	0.790862i	$0.290368\pi$
$31$	−2.11561	+	5.10754i	−0.379975	+	0.917342i	−0.991969	+	0.126479i	$0.959632\pi$
$32$	−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	−0.103043	−	0.994677i	$-0.532858\pi$
$37$	4.09469	−	9.88545i	0.673162	−	1.62516i	0.776205	−	0.630481i	$-0.217142\pi$
$38$			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	−0.220562	−	0.975373i	$-0.570789\pi$
$41$	2.00526	−	0.830608i	0.313170	−	0.129719i	0.533732	+	0.845654i	$0.320789\pi$
$42$		0			0
$43$	1.52864	+	1.52864i	0.233115	+	0.233115i	0.813992	−	0.580876i	$-0.197290\pi$
$43$	1.52864	+	1.52864i	0.233115	+	0.233115i	−0.580876	+	0.813992i	$0.697290\pi$
$44$	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	$0.209771\pi$
$47$			8.39597i			1.22468i	−0.790595	+	0.612339i	$0.790229\pi$
$48$		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	−0.789820	−	0.613339i	$-0.789826\pi$
$53$	−1.28480	+	1.28480i	−0.176481	+	0.176481i	0.613339	+	0.789820i	$0.289826\pi$
$54$		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	0.832311	−	0.554309i	$-0.187018\pi$
$59$	2.13537	+	2.13537i	0.278001	+	0.278001i	−0.554309	+	0.832311i	$0.687018\pi$
$60$		0			0
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.484677	−	0.874693i	$-0.338937\pi$
$61$	11.2928	−	4.67764i	1.44590	−	0.598910i	0.961220	+	0.275783i	$0.0889371\pi$
$62$	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	−0.810536	−	0.585689i	$-0.800824\pi$
$71$	1.48927	−	3.59542i	0.176744	−	0.426698i	0.987280	+	0.158991i	$0.0508241\pi$
$72$		0			0
$73$	−5.97807	−	2.47620i	−0.699680	−	0.289817i	0.00434632	−	0.999991i	$-0.498617\pi$
$73$	−5.97807	−	2.47620i	−0.699680	−	0.289817i	−0.704027	+	0.710173i	$0.748617\pi$
$74$	−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	−0.999671	−	0.0256347i	$-0.991839\pi$
$79$	−2.76355	−	6.67180i	−0.310923	−	0.750636i	0.688748	−	0.725001i	$-0.258161\pi$
$80$	−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	−0.715880	−	0.698223i	$-0.753974\pi$
$83$	−0.160866	+	0.160866i	−0.0176574	+	0.0176574i	0.698223	+	0.715880i	$0.253974\pi$
$84$		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	$-0.750019\pi$
$89$		−	13.3408i		−	1.41413i	0.707150	−	0.707064i	$-0.249981\pi$
$90$		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	−0.442145	−	0.896943i	$-0.645782\pi$
$97$	−13.6803	−	5.66657i	−1.38902	−	0.575353i	−0.946879	+	0.321591i	$0.895782\pi$
$98$		−	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	−0.672228	−	0.740344i	$-0.734663\pi$
$107$	−17.2857	−	7.15995i	−1.67107	−	0.692179i	−0.998839	+	0.0481649i	$0.984663\pi$
$108$		0			0
$109$	−3.26202	+	1.35117i	−0.312444	+	0.129419i	−0.533395	−	0.845866i	$-0.679084\pi$
$109$	−3.26202	+	1.35117i	−0.312444	+	0.129419i	0.220951	+	0.975285i	$0.429084\pi$
$110$	−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	0.864443	−	0.502731i	$-0.167671\pi$
$113$	−1.08741	−	2.62525i	−0.102295	−	0.246963i	−0.966738	+	0.255769i	$0.917671\pi$
$114$		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	0.857462	−	0.514548i	$-0.172040\pi$
$127$	3.86444	+	3.86444i	0.342914	+	0.342914i	−0.514548	+	0.857462i	$0.672040\pi$
$128$	−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	−0.0583689	−	0.998295i	$-0.518590\pi$
$131$	−9.21986	−	3.81899i	−0.805543	−	0.333667i	−0.747174	+	0.664628i	$0.768590\pi$
$132$		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	−0.994582	−	0.103960i	$-0.966849\pi$
$139$	−2.56777	+	6.19915i	−0.217796	+	0.525805i	0.776786	+	0.629765i	$0.216849\pi$
$140$			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	$0.390833\pi$
$149$			22.9914i			1.88353i	−0.336276	+	0.941764i	$0.609167\pi$
$150$		0			0
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	−0.701452	−	0.712716i	$-0.747465\pi$
$151$	0.138411	−	0.138411i	0.0112638	−	0.0112638i	0.712716	+	0.701452i	$0.247465\pi$
$152$	−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	$-0.843100\pi$
$157$		−	11.8582i		−	0.946391i	0.880957	−	0.473196i	$-0.156900\pi$
$158$	−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	−0.567588	−	0.823312i	$-0.692123\pi$
$163$	−4.93787	+	2.04533i	−0.386764	+	0.160203i	0.180824	+	0.983515i	$0.442123\pi$
$164$	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	−0.654174	−	0.756344i	$-0.726984\pi$
$167$	4.43529	−	10.7077i	0.343213	−	0.828589i	0.997387	−	0.0722453i	$-0.0230164\pi$
$168$		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	0.678375	+	0.734716i	$0.262685\pi$
$173$	−4.21988	+	10.1877i	−0.320832	+	0.774556i	−0.999206	+	0.0398396i	$0.987315\pi$
$174$		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	−0.992639	−	0.121109i	$-0.961355\pi$
$179$	−14.9009	−	14.9009i	−1.11375	−	1.11375i	−0.121109	−	0.992639i	$-0.538645\pi$
$180$		0			0
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	0.820501	+	0.571645i	$0.193695\pi$
$181$	8.67131	+	20.9344i	0.644533	+	1.55604i	−0.175968	+	0.984396i	$0.556305\pi$
$182$	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	$-0.959567\pi$
$191$		−	3.50162i		−	0.253368i	0.991943	−	0.126684i	$-0.0404335\pi$
$192$		0			0
$193$	−4.70480	−	11.3584i	−0.338659	−	0.817595i	−0.997845	−	0.0656152i	$-0.979099\pi$
$193$	−4.70480	−	11.3584i	−0.338659	−	0.817595i	0.659186	−	0.751980i	$-0.270901\pi$
$194$	−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	−0.863481	−	0.504381i	$-0.831721\pi$
$197$	−15.6835	+	6.49632i	−1.11740	+	0.462843i	−0.253922	+	0.967225i	$0.581721\pi$
$198$		0			0
$199$	10.6966	+	4.43067i	0.758260	+	0.314082i	0.728107	−	0.685464i	$-0.240400\pi$
$199$	10.6966	+	4.43067i	0.758260	+	0.314082i	0.0301533	+	0.999545i	$0.490400\pi$
$200$			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	−0.160563	−	0.987026i	$-0.551331\pi$
$211$	6.15655	−	2.55013i	0.423834	−	0.175558i	0.584397	+	0.811468i	$0.301331\pi$
$212$	−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	−0.343037	−	0.939322i	$-0.611456\pi$
$223$	8.90442	−	8.90442i	0.596284	−	0.596284i	0.939322	+	0.343037i	$0.111456\pi$
$224$	−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	0.788224	−	0.615389i	$-0.211001\pi$
$227$	−3.07779	−	7.43044i	−0.204280	−	0.493176i	−0.992504	+	0.122213i	$0.961001\pi$
$228$		0			0
$229$	−15.2944	−	15.2944i	−1.01068	−	1.01068i	−0.999942	−	0.0107373i	$-0.996582\pi$
$229$	−15.2944	−	15.2944i	−1.01068	−	1.01068i	−0.0107373	−	0.999942i	$-0.503418\pi$
$230$	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	0.930246	−	0.366937i	$-0.119594\pi$
$233$	20.2797	+	8.40011i	1.32857	+	0.550310i	0.398320	+	0.917247i	$0.369594\pi$
$234$		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	−0.670593	−	0.741826i	$-0.733960\pi$
$241$	5.09407	−	12.2982i	0.328138	−	0.792195i	0.998731	−	0.0503696i	$-0.0160399\pi$
$242$		−	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	$-0.963821\pi$
$251$		−	3.59367i		−	0.226831i	0.993548	−	0.113415i	$-0.0361790\pi$
$252$		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	0.0865680	−	0.996246i	$-0.472410\pi$
$257$	17.3588	−	17.3588i	1.08281	−	1.08281i	0.996246	−	0.0865680i	$-0.0275900\pi$
$258$		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	0.311806	−	0.950146i	$-0.399066\pi$
$263$	−10.3521	−	10.3521i	−0.638340	−	0.638340i	−0.950146	+	0.311806i	$0.899066\pi$
$264$		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	−0.539023	−	0.842291i	$-0.681206\pi$
$269$	7.17904	−	17.3317i	0.437714	−	1.05673i	0.976736	−	0.214443i	$-0.0687936\pi$
$270$		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	0.386102	−	0.922456i	$-0.373821\pi$
$277$	0.113870	+	0.0471663i	0.00684176	+	0.00283395i	−0.379260	+	0.925290i	$0.623821\pi$
$278$	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	0.744523	−	0.667597i	$-0.232677\pi$
$281$	1.28950	+	1.28950i	0.0769253	+	0.0769253i	−0.667597	+	0.744523i	$0.732677\pi$
$282$		0			0
$283$	10.9554	+	26.4486i	0.651229	+	1.57221i	0.810996	+	0.585052i	$0.198926\pi$
$283$	10.9554	+	26.4486i	0.651229	+	1.57221i	−0.159767	+	0.987155i	$0.551074\pi$
$284$	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	$-0.986830\pi$
$293$		−	1.41607i		−	0.0827278i	0.999144	−	0.0413639i	$-0.0131703\pi$
$294$		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	0.144387	−	0.989521i	$-0.453879\pi$
$311$	−7.99250	−	3.31060i	−0.453213	−	0.187727i	−0.597600	+	0.801794i	$0.703879\pi$
$312$		0			0
$313$	9.49936	−	3.93476i	0.536936	−	0.222406i	−0.0977022	−	0.995216i	$-0.531149\pi$
$313$	9.49936	−	3.93476i	0.536936	−	0.222406i	0.634638	+	0.772810i	$0.281149\pi$
$314$	−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	0.935535	−	0.353234i	$-0.114918\pi$
$317$	0.431538	+	1.04183i	0.0242376	+	0.0585147i	−0.911297	+	0.411749i	$0.864918\pi$
$318$		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	−0.903984	−	0.427567i	$-0.859371\pi$
$331$	−24.2254	−	24.2254i	−1.33155	−	1.33155i	−0.427567	−	0.903984i	$-0.640629\pi$
$332$	−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	−0.999960	−	0.00894611i	$-0.997152\pi$
$337$	−5.26046	+	12.6999i	−0.286556	+	0.691807i	0.713404	+	0.700753i	$0.247152\pi$
$338$	−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	−0.798069	−	0.602566i	$-0.794145\pi$
$347$	−17.4415	+	7.22453i	−0.936311	+	0.387833i	−0.138242	+	0.990398i	$0.544145\pi$
$348$		0			0
$349$	4.98501	+	4.98501i	0.266842	+	0.266842i	0.827826	−	0.560985i	$-0.189577\pi$
$349$	4.98501	+	4.98501i	0.266842	+	0.266842i	−0.560985	+	0.827826i	$0.689577\pi$
$350$	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	$-0.926431\pi$
$353$		−	8.60779i		−	0.458146i	0.973409	−	0.229073i	$-0.0735695\pi$
$354$		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	−0.514724	−	0.857356i	$-0.672106\pi$
$359$	6.49195	−	6.49195i	0.342632	−	0.342632i	0.857356	+	0.514724i	$0.172106\pi$
$360$		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	−0.540935	−	0.841064i	$-0.681930\pi$
$367$	−6.29722	+	2.60840i	−0.328712	+	0.136157i	0.212223	+	0.977221i	$0.431930\pi$
$368$	−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	0.891851	−	0.452330i	$-0.149407\pi$
$379$	23.4129	+	9.69794i	1.20264	+	0.498150i	0.310789	+	0.950479i	$0.399407\pi$
$380$	−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	0.832258	−	0.554389i	$-0.187048\pi$
$383$	5.43799	+	5.43799i	0.277868	+	0.277868i	−0.554389	+	0.832258i	$0.687048\pi$
$384$		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	−0.931516	−	0.363700i	$-0.881513\pi$
$389$	−11.1991	+	11.1991i	−0.567816	+	0.567816i	0.363700	+	0.931516i	$0.381513\pi$
$390$		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	0.909659	+	0.415355i	$0.136343\pi$
$397$	11.1606	+	26.9440i	0.560133	+	1.35228i	−0.349526	+	0.936927i	$0.613657\pi$
$398$	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	0.0288034	−	0.999585i	$-0.490830\pi$
$401$	15.1386	−	6.27060i	0.755984	−	0.313139i	0.727181	+	0.686446i	$0.240830\pi$
$402$		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	0.915313	−	0.402743i	$-0.131943\pi$
$419$	−0.341711	−	0.824964i	−0.0166937	−	0.0403021i	−0.932007	+	0.362441i	$0.881943\pi$
$420$		0			0
$421$			33.6725i			1.64110i	0.571575	+	0.820550i	$0.306332\pi$
$421$			33.6725i			1.64110i	−0.571575	+	0.820550i	$0.693668\pi$
$422$	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	0.999943	+	0.0106472i	$0.00338917\pi$
$431$	6.23658	+	15.0564i	0.300405	+	0.725243i	−0.699538	+	0.714595i	$0.746611\pi$
$432$		0			0
$433$	−24.7450	−	24.7450i	−1.18917	−	1.18917i	−0.977298	−	0.211871i	$-0.932044\pi$
$433$	−24.7450	−	24.7450i	−1.18917	−	1.18917i	−0.211871	−	0.977298i	$-0.567956\pi$
$434$	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	−0.579060	−	0.815285i	$-0.696580\pi$
$439$	8.52530	−	20.5819i	0.406891	−	0.982321i	0.985951	−	0.167036i	$-0.0534196\pi$
$440$	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	−0.180914	−	0.983499i	$-0.557906\pi$
$449$	8.19189	−	3.39319i	0.386599	−	0.160135i	0.567513	+	0.823364i	$0.307906\pi$
$450$		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	−0.943238	−	0.332118i	$-0.892237\pi$
$457$	−13.0643	+	13.0643i	−0.611120	+	0.611120i	0.332118	+	0.943238i	$0.392237\pi$
$458$	−16.1770			−0.755902
$459$		0			0
$460$	−0.709315			−0.0330720
$461$	−17.3736	+	17.3736i	−0.809169	+	0.809169i	−0.984508	−	0.175339i	$-0.943898\pi$
$461$	−17.3736	+	17.3736i	−0.809169	+	0.809169i	0.175339	+	0.984508i	$0.443898\pi$
$462$		0			0
$463$			9.90931i			0.460525i	0.973129	+	0.230262i	$0.0739584\pi$
$463$			9.90931i			0.460525i	−0.973129	+	0.230262i	$0.926042\pi$
$464$	−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	0.999309	−	0.0371777i	$-0.0118367\pi$
$467$	20.7918	+	20.7918i	0.962131	+	0.962131i	−0.0371777	+	0.999309i	$0.511837\pi$
$468$		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	−0.449354	−	0.893354i	$-0.648346\pi$
$479$	10.9449	−	26.4232i	0.500083	−	1.20731i	0.949438	−	0.313955i	$-0.101654\pi$
$480$		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	0.918432	−	0.395580i	$-0.129456\pi$
$487$	−0.236454	−	0.570849i	−0.0107147	−	0.0258677i	−0.929146	+	0.369712i	$0.879456\pi$
$488$	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	−0.985034	−	0.172359i	$-0.944861\pi$
$491$	−18.0077	+	18.0077i	−0.812675	+	0.812675i	0.172359	+	0.985034i	$0.444861\pi$
$492$		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	0.846234	+	0.532811i	$0.178864\pi$
$499$	13.9527	+	33.6849i	0.624611	+	1.50794i	−0.221624	+	0.975132i	$0.571136\pi$
$500$	−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	−0.904826	−	0.425781i	$-0.859999\pi$
$503$	−27.8902	+	11.5525i	−1.24356	+	0.515100i	−0.338736	+	0.940881i	$0.609999\pi$
$504$		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	0.880820	+	0.473451i	$0.156992\pi$
$521$	13.5302	+	32.6647i	0.592767	+	1.43107i	−0.288053	+	0.957614i	$0.593008\pi$
$522$		0			0
$523$			24.5035i			1.07146i	0.844388	+	0.535732i	$0.179964\pi$
$523$			24.5035i			1.07146i	−0.844388	+	0.535732i	$0.820036\pi$
$524$	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	−0.561852	−	0.827238i	$-0.689911\pi$
$541$	9.77786	−	23.6058i	0.420383	−	1.01489i	0.982235	−	0.187657i	$-0.0600892\pi$
$542$	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	−0.990421	−	0.138080i	$-0.955907\pi$
$547$	−4.50103	+	10.8664i	−0.192450	+	0.464616i	0.797971	+	0.602696i	$0.205907\pi$
$548$			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	$0.272816\pi$
$557$			35.6812i			1.51186i	−0.654651	+	0.755931i	$0.727184\pi$
$558$		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	−0.0975306	−	0.995233i	$-0.531094\pi$
$563$	21.3003	−	21.3003i	0.897702	−	0.897702i	0.995233	+	0.0975306i	$0.0310944\pi$
$564$		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	0.969267	−	0.246010i	$-0.0791197\pi$
$569$	17.2524	+	17.2524i	0.723257	+	0.723257i	−0.246010	+	0.969267i	$0.579120\pi$
$570$		0			0
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.918024	−	0.396526i	$-0.870216\pi$
$571$	−30.7483	+	12.7364i	−1.28678	+	0.533001i	−0.368755	+	0.929527i	$0.620216\pi$
$572$	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	0.967335	+	0.253500i	$0.0815817\pi$
$587$	29.5785	+	29.5785i	1.22084	+	1.22084i	0.253500	+	0.967335i	$0.418418\pi$
$588$		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	−0.940335	−	0.340250i	$-0.889488\pi$
$593$	−14.6130	+	14.6130i	−0.600085	+	0.600085i	0.340250	+	0.940335i	$0.389488\pi$
$594$		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	$0.0603049\pi$
$599$			9.21817i			0.376644i	−0.982107	+	0.188322i	$0.939695\pi$
$600$		0			0
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	0.910725	−	0.413013i	$-0.135524\pi$
$601$	−0.620216	−	1.49733i	−0.0252991	−	0.0610775i	−0.936024	+	0.351936i	$0.885524\pi$
$602$	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	0.798733	−	0.601685i	$-0.205504\pi$
$607$	23.1115	+	9.57311i	0.938068	+	0.388560i	0.139334	+	0.990245i	$0.455504\pi$
$608$		−	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	0.0474212	−	0.998875i	$-0.484900\pi$
$617$	−15.5336	−	6.43422i	−0.625358	−	0.259032i	−0.672779	+	0.739843i	$0.734900\pi$
$618$		0			0
$619$	11.7540	−	4.86865i	0.472431	−	0.195687i	−0.133748	−	0.991015i	$-0.542701\pi$
$619$	11.7540	−	4.86865i	0.472431	−	0.195687i	0.606179	+	0.795328i	$0.292701\pi$
$620$	−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	−0.764261	−	0.644907i	$-0.776896\pi$
$631$	−2.99812	+	2.99812i	−0.119353	+	0.119353i	0.644907	+	0.764261i	$0.276896\pi$
$632$	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	−0.0397171	−	0.999211i	$-0.512646\pi$
$641$	−19.6050	−	8.12065i	−0.774350	−	0.320746i	−0.734633	+	0.678465i	$0.762646\pi$
$642$		0			0
$643$	−3.12525	+	7.54502i	−0.123248	+	0.297547i	−0.973446	−	0.228916i	$-0.926482\pi$
$643$	−3.12525	+	7.54502i	−0.123248	+	0.297547i	0.850198	+	0.526462i	$0.176482\pi$
$644$	−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	−0.665225	−	0.746643i	$-0.731665\pi$
$653$	−15.5279	+	6.43188i	−0.607655	+	0.251699i	0.0575706	+	0.998341i	$0.481665\pi$
$654$		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	$-0.911463\pi$
$659$		−	14.0972i		−	0.549150i	0.961566	−	0.274575i	$-0.0885371\pi$
$660$		0			0
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	−0.835408	−	0.549630i	$-0.814769\pi$
$661$	−7.34734	+	7.34734i	−0.285779	+	0.285779i	0.549630	+	0.835408i	$0.314769\pi$
$662$	−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	−0.706650	−	0.707563i	$-0.749795\pi$
$673$	−18.3153	+	7.58646i	−0.706005	+	0.292437i	0.000645530		1.00000i	$0.499795\pi$
$674$	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	−0.946573	−	0.322489i	$-0.895481\pi$
$677$	−1.28043	+	3.09124i	−0.0492111	+	0.118806i	0.897362	+	0.441295i	$0.145481\pi$
$678$		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	−0.115910	+	0.993260i	$0.536978\pi$
$683$	−19.2424	+	46.4553i	−0.736290	+	1.77756i	−0.620380	+	0.784302i	$0.713022\pi$
$684$		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	−0.904454	−	0.426572i	$-0.859721\pi$
$691$	−14.8926	−	35.9539i	−0.566540	−	1.36775i	0.337913	−	0.941177i	$-0.390279\pi$
$692$	−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	$-0.749160\pi$
$701$		−	37.5419i		−	1.41794i	0.705239	−	0.708969i	$-0.250840\pi$
$702$		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	0.608321	−	0.793691i	$-0.291843\pi$
$709$	12.7076	+	5.26367i	0.477245	+	0.197681i	−0.131076	+	0.991372i	$0.541843\pi$
$710$		−	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	0.391778	−	0.920060i	$-0.371860\pi$
$719$	0.488717	+	0.202433i	0.0182261	+	0.00754949i	−0.373552	+	0.927609i	$0.621860\pi$
$720$		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	$0.165307\pi$
$727$			26.7632i			0.992591i	−0.868154	+	0.496296i	$0.834693\pi$
$728$	−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	−0.896384	−	0.443279i	$-0.853815\pi$
$733$	−12.2673	+	12.2673i	−0.453105	+	0.453105i	0.443279	+	0.896384i	$0.353815\pi$
$734$	−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	0.980961	−	0.194204i	$-0.0622124\pi$
$739$	21.3876	+	21.3876i	0.786757	+	0.786757i	−0.194204	+	0.980961i	$0.562212\pi$
$740$	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	0.257657	−	0.966236i	$-0.417049\pi$
$743$	−6.63416	−	2.74796i	−0.243384	−	0.100813i	−0.501041	+	0.865424i	$0.667049\pi$
$744$		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	−0.539930	−	0.841710i	$-0.681549\pi$
$751$	11.9767	−	28.9144i	0.437037	−	1.05510i	0.976967	−	0.213390i	$-0.0684505\pi$
$752$		−	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	0.554948	−	0.831885i	$-0.312738\pi$
$757$	−7.61956	−	7.61956i	−0.276938	−	0.276938i	−0.831885	+	0.554948i	$0.812738\pi$
$758$	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	$-0.794898\pi$
$761$		−	33.1409i		−	1.20136i	0.799491	−	0.600678i	$-0.205102\pi$
$762$		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	$0.0664042\pi$
$769$			11.4864i			0.414210i	−0.978319	+	0.207105i	$0.933596\pi$
$770$	−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	0.746736	−	0.665121i	$-0.231620\pi$
$773$	2.26913	+	2.26913i	0.0816149	+	0.0816149i	−0.665121	+	0.746736i	$0.731620\pi$
$774$		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	0.437489	−	0.899224i	$-0.355868\pi$
$787$	3.11375	+	1.28976i	0.110993	+	0.0459748i	−0.326496	+	0.945199i	$0.605868\pi$
$788$	−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	−0.387234	−	0.921981i	$-0.626569\pi$
$797$	15.0966	−	15.0966i	0.534747	−	0.534747i	0.921981	+	0.387234i	$0.126569\pi$
$798$		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	−0.337910	−	0.941178i	$-0.609720\pi$
$809$	2.52190	−	1.04460i	0.0886652	−	0.0367263i	0.426575	+	0.904452i	$0.359720\pi$
$810$		0			0
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.316614	−	0.948554i	$-0.602546\pi$
$811$	−34.4933	−	14.2876i	−1.21122	−	0.501705i	−0.894609	+	0.446849i	$0.852546\pi$
$812$			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	0.939505	−	0.342536i	$-0.111286\pi$
$821$	39.0148	+	16.1605i	1.36163	+	0.564004i	0.422121	+	0.906540i	$0.361286\pi$
$822$		0			0
$823$	19.1803	−	7.94473i	0.668582	−	0.276936i	−0.0224627	−	0.999748i	$-0.507151\pi$
$823$	19.1803	−	7.94473i	0.668582	−	0.276936i	0.691045	+	0.722812i	$0.257151\pi$
$824$	−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	0.981765	−	0.190101i	$-0.0608815\pi$
$827$	4.40367	+	10.6314i	0.153131	+	0.369690i	−0.828634	+	0.559791i	$0.810881\pi$
$828$		0			0
$829$		−	11.7508i		−	0.408121i	−0.978958	−	0.204060i	$-0.934586\pi$
$829$		−	11.7508i		−	0.408121i	0.978958	−	0.204060i	$-0.0654139\pi$
$830$	−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	0.957917	+	0.287046i	$0.0926733\pi$
$839$	14.0060	+	33.8134i	0.483540	+	1.16737i	−0.474377	+	0.880322i	$0.657327\pi$
$840$		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	−0.451149	−	0.892449i	$-0.648986\pi$
$853$	14.5715	−	35.1787i	0.498918	−	1.20450i	0.950067	−	0.312046i	$-0.101014\pi$
$854$		−	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	−0.0399356	−	0.999202i	$-0.512715\pi$
$857$	18.6880	−	7.74080i	0.638368	−	0.264421i	0.678304	+	0.734781i	$0.262715\pi$
$858$		0			0
$859$	1.84360	+	1.84360i	0.0629028	+	0.0629028i	0.737858	−	0.674956i	$-0.235837\pi$
$859$	1.84360	+	1.84360i	0.0629028	+	0.0629028i	−0.674956	+	0.737858i	$0.735837\pi$
$860$	−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	$-0.938637\pi$
$863$		−	11.2563i		−	0.383169i	0.981476	−	0.191584i	$-0.0613626\pi$
$864$		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	−0.474322	−	0.880351i	$-0.657307\pi$
$877$	−5.54426	+	2.29651i	−0.187216	+	0.0775476i	0.287106	+	0.957899i	$0.407307\pi$
$878$	−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	0.532390	+	0.846499i	$0.321294\pi$
$881$	−13.1380	+	31.7181i	−0.442632	+	1.06861i	−0.975022	+	0.222109i	$0.928706\pi$
$882$		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	−0.688250	−	0.725474i	$-0.741621\pi$
$887$	9.27440	−	22.3904i	0.311404	−	0.751796i	0.999654	−	0.0263216i	$-0.00837938\pi$
$888$		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	−0.902395	−	0.430910i	$-0.858192\pi$
$907$	−17.1364	−	41.3709i	−0.569005	−	1.37370i	0.333390	−	0.942789i	$-0.391808\pi$
$908$	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	−0.529711	−	0.848178i	$-0.677700\pi$
$911$	−9.19129	+	3.80716i	−0.304521	+	0.126137i	0.225190	+	0.974315i	$0.427700\pi$
$912$		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	0.999608	+	0.0280049i	$0.00891541\pi$
$929$	9.52731	+	23.0010i	0.312581	+	0.754637i	−0.687027	+	0.726632i	$0.741085\pi$
$930$		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	−0.968969	−	0.247181i	$-0.920496\pi$
$937$	−22.0943	+	22.0943i	−0.721788	+	0.721788i	0.247181	+	0.968969i	$0.420496\pi$
$938$	−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	0.934325	−	0.356423i	$-0.116004\pi$
$941$	0.663467	+	1.60175i	0.0216284	+	0.0522156i	−0.912696	+	0.408638i	$0.866004\pi$
$942$		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	0.213800	−	0.976877i	$-0.431416\pi$
$947$	−10.0253	−	4.15260i	−0.325777	−	0.134941i	−0.539577	+	0.841936i	$0.681416\pi$
$948$		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	−0.256324	−	0.966591i	$-0.582511\pi$
$967$	22.0869	−	22.0869i	0.710267	−	0.710267i	0.966591	+	0.256324i	$0.0825115\pi$
$968$	9.05619			0.291077
$969$		0			0
$970$	−11.0747			−0.355587
$971$	12.2957	−	12.2957i	0.394589	−	0.394589i	−0.481731	−	0.876319i	$-0.659992\pi$
$971$	12.2957	−	12.2957i	0.394589	−	0.394589i	0.876319	+	0.481731i	$0.159992\pi$
$972$		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	0.803214	−	0.595691i	$-0.203122\pi$
$977$	6.48656	+	6.48656i	0.207523	+	0.207523i	−0.595691	+	0.803214i	$0.703122\pi$
$978$		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	0.515070	+	0.857148i	$0.327766\pi$
$983$	−14.2729	+	34.4578i	−0.455235	+	1.09903i	−0.970305	+	0.241886i	$0.922234\pi$
$984$		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	−0.196765	−	0.980451i	$-0.563044\pi$
$991$	−32.3988	−	13.4200i	−1.02918	−	0.426301i	−0.832417	+	0.554149i	$0.813044\pi$
$992$	−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	0.971267	+	0.237991i	$0.0764889\pi$
$997$	14.2961	+	34.5139i	0.452763	+	1.09307i	−0.518505	+	0.855075i	$0.673511\pi$
$998$	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.586.5		24
3.2	odd	2		85.2.l.a.76.2	yes	24
15.2	even	4		425.2.n.f.399.2		24
15.8	even	4		425.2.n.c.399.5		24
15.14	odd	2		425.2.m.b.76.5		24
17.15	even	8	inner	765.2.be.b.406.5		24
51.11	even	16		1445.2.d.j.866.7		24
51.23	even	16		1445.2.d.j.866.8		24
51.32	odd	8		85.2.l.a.66.2	✓	24
51.41	even	16		1445.2.a.p.1.9		12
51.44	even	16		1445.2.a.q.1.9		12
255.32	even	8		425.2.n.c.49.5		24
255.44	even	16		7225.2.a.bq.1.4		12
255.83	even	8		425.2.n.f.49.2		24
255.134	odd	8		425.2.m.b.151.5		24
255.194	even	16		7225.2.a.bs.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.2	✓	24	51.32	odd	8
85.2.l.a.76.2	yes	24	3.2	odd	2
425.2.m.b.76.5		24	15.14	odd	2
425.2.m.b.151.5		24	255.134	odd	8
425.2.n.c.49.5		24	255.32	even	8
425.2.n.c.399.5		24	15.8	even	4
425.2.n.f.49.2		24	255.83	even	8
425.2.n.f.399.2		24	15.2	even	4
765.2.be.b.406.5		24	17.15	even	8	inner
765.2.be.b.586.5		24	1.1	even	1	trivial
1445.2.a.p.1.9		12	51.41	even	16
1445.2.a.q.1.9		12	51.44	even	16
1445.2.d.j.866.7		24	51.11	even	16
1445.2.d.j.866.8		24	51.23	even	16
7225.2.a.bq.1.4		12	255.44	even	16
7225.2.a.bs.1.4		12	255.194	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

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