LMFDB - Embedded newform 765.2.bh.b.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [765,2,Mod(19,765)]

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, 4, 7]))

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

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

chi := DirichletCharacter("765.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.bh (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			19.4
Character	$\chi$	$=$	765.19
Dual form			765.2.bh.b.604.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.352960 - 0.352960i) q^{2} +1.75084i q^{4} +(1.40760 - 1.73743i) q^{5} +(3.57820 + 1.48214i) q^{7} +(1.32390 + 1.32390i) q^{8} +O(q^{10})$	\(q+(0.352960 - 0.352960i) q^{2} +1.75084i q^{4} +(1.40760 - 1.73743i) q^{5} +(3.57820 + 1.48214i) q^{7} +(1.32390 + 1.32390i) q^{8} +(-0.116419 - 1.11007i) q^{10} +(2.71049 + 1.12272i) q^{11} -0.983677 q^{13} +(1.78610 - 0.739825i) q^{14} -2.56711 q^{16} +(-3.97002 + 1.11308i) q^{17} +(-1.81628 - 1.81628i) q^{19} +(3.04196 + 2.46447i) q^{20} +(1.35297 - 0.560418i) q^{22} +(-1.15054 + 2.77766i) q^{23} +(-1.03735 - 4.89121i) q^{25} +(-0.347198 + 0.347198i) q^{26} +(-2.59499 + 6.26485i) q^{28} +(-0.210302 - 0.507715i) q^{29} +(6.98112 - 2.89167i) q^{31} +(-3.55388 + 3.55388i) q^{32} +(-1.00838 + 1.79413i) q^{34} +(7.61178 - 4.13063i) q^{35} +(3.76666 + 9.09352i) q^{37} -1.28214 q^{38} +(4.16369 - 0.436669i) q^{40} +(2.83334 - 6.84028i) q^{41} +(-5.85161 - 5.85161i) q^{43} +(-1.96570 + 4.74563i) q^{44} +(0.574306 + 1.38650i) q^{46} +10.9492 q^{47} +(5.65702 + 5.65702i) q^{49} +(-2.09254 - 1.36026i) q^{50} -1.72226i q^{52} +(-2.53645 + 2.53645i) q^{53} +(5.76592 - 3.12895i) q^{55} +(2.77496 + 6.69936i) q^{56} +(-0.253431 - 0.104975i) q^{58} +(-0.216234 + 0.216234i) q^{59} +(-2.60281 + 6.28374i) q^{61} +(1.44341 - 3.48470i) q^{62} -2.62548i q^{64} +(-1.38462 + 1.70907i) q^{65} -5.09621i q^{67} +(-1.94883 - 6.95086i) q^{68} +(1.22870 - 4.14460i) q^{70} +(3.33246 - 1.38035i) q^{71} +(-4.62935 + 1.91754i) q^{73} +(4.53912 + 1.88017i) q^{74} +(3.18001 - 3.18001i) q^{76} +(8.03464 + 8.03464i) q^{77} +(-11.4965 - 4.76199i) q^{79} +(-3.61346 + 4.46019i) q^{80} +(-1.41429 - 3.41440i) q^{82} +(-5.74272 + 5.74272i) q^{83} +(-3.65428 + 8.46441i) q^{85} -4.13077 q^{86} +(2.10204 + 5.07477i) q^{88} -13.2723i q^{89} +(-3.51979 - 1.45795i) q^{91} +(-4.86323 - 2.01442i) q^{92} +(3.86462 - 3.86462i) q^{94} +(-5.71224 + 0.599074i) q^{95} +(-4.18163 + 1.73209i) q^{97} +3.99340 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50} - 24 q^{56} + 48 q^{59} + 16 q^{61} - 24 q^{65} + 32 q^{70} - 16 q^{71} + 64 q^{74} - 24 q^{76} - 72 q^{79} + 64 q^{80} - 24 q^{85} - 8 q^{91} - 40 q^{94} + 88 q^{95}+O(q^{100}) $ 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$

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 $

$2$	0.352960	−	0.352960i	0.249580	−	0.249580i	−0.571218	−	0.820798i	$-0.693529\pi$
$2$	0.352960	−	0.352960i	0.249580	−	0.249580i	0.820798	+	0.571218i	$0.193529\pi$
$3$		0			0
$3$		0			0
$4$			1.75084i			0.875419i
$5$	1.40760	−	1.73743i	0.629496	−	0.777004i
$5$	1.40760	−	1.73743i	0.629496	−	0.777004i
$6$		0			0
$7$	3.57820	+	1.48214i	1.35243	+	0.560196i	0.936968	−	0.349414i	$-0.113619\pi$
$7$	3.57820	+	1.48214i	1.35243	+	0.560196i	0.415464	+	0.909610i	$0.363619\pi$
$8$	1.32390	+	1.32390i	0.468068	+	0.468068i
$9$		0			0
$10$	−0.116419	−	1.11007i	−0.0368150	−	0.351035i
$11$	2.71049	+	1.12272i	0.817243	+	0.338513i	0.751840	−	0.659346i	$-0.229167\pi$
$11$	2.71049	+	1.12272i	0.817243	+	0.338513i	0.0654030	+	0.997859i	$0.479167\pi$
$12$		0			0
$13$	−0.983677			−0.272823			−0.136411	−	0.990652i	$-0.543557\pi$
$13$	−0.983677			−0.272823			−0.136411	+	0.990652i	$0.543557\pi$
$14$	1.78610	−	0.739825i	0.477354	−	0.197727i
$15$		0			0
$16$	−2.56711			−0.641779
$17$	−3.97002	+	1.11308i	−0.962871	+	0.269962i
$17$	−3.97002	+	1.11308i	−0.962871	+	0.269962i
$18$		0			0
$19$	−1.81628	−	1.81628i	−0.416682	−	0.416682i	0.467376	−	0.884058i	$-0.345199\pi$
$19$	−1.81628	−	1.81628i	−0.416682	−	0.416682i	−0.884058	+	0.467376i	$0.845199\pi$
$20$	3.04196	+	2.46447i	0.680204	+	0.551073i
$21$		0			0
$22$	1.35297	−	0.560418i	0.288454	−	0.119481i
$23$	−1.15054	+	2.77766i	−0.239905	+	0.579182i	−0.997273	−	0.0738068i	$-0.976485\pi$
$23$	−1.15054	+	2.77766i	−0.239905	+	0.579182i	0.757367	+	0.652989i	$0.226485\pi$
$24$		0			0
$25$	−1.03735	−	4.89121i	−0.207469	−	0.978242i
$26$	−0.347198	+	0.347198i	−0.0680912	+	0.0680912i
$27$		0			0
$28$	−2.59499	+	6.26485i	−0.490406	+	1.18395i
$29$	−0.210302	−	0.507715i	−0.0390521	−	0.0942802i	0.903150	−	0.429325i	$-0.141249\pi$
$29$	−0.210302	−	0.507715i	−0.0390521	−	0.0942802i	−0.942202	+	0.335045i	$0.891249\pi$
$30$		0			0
$31$	6.98112	−	2.89167i	1.25385	−	0.519360i	0.345831	−	0.938297i	$-0.387597\pi$
$31$	6.98112	−	2.89167i	1.25385	−	0.519360i	0.908015	+	0.418937i	$0.137597\pi$
$32$	−3.55388	+	3.55388i	−0.628243	+	0.628243i
$33$		0			0
$34$	−1.00838	+	1.79413i	−0.172936	+	0.307691i
$35$	7.61178	−	4.13063i	1.28662	−	0.698204i
$36$		0			0
$37$	3.76666	+	9.09352i	0.619235	+	1.49496i	0.852594	+	0.522574i	$0.175028\pi$
$37$	3.76666	+	9.09352i	0.619235	+	1.49496i	−0.233359	+	0.972391i	$0.574972\pi$
$38$	−1.28214			−0.207991
$39$		0			0
$40$	4.16369	−	0.436669i	0.658337	−	0.0690435i
$41$	2.83334	−	6.84028i	0.442493	−	1.06827i	−0.532578	−	0.846381i	$-0.678777\pi$
$41$	2.83334	−	6.84028i	0.442493	−	1.06827i	0.975071	−	0.221892i	$-0.0712232\pi$
$42$		0			0
$43$	−5.85161	−	5.85161i	−0.892363	−	0.892363i	0.102383	−	0.994745i	$-0.467353\pi$
$43$	−5.85161	−	5.85161i	−0.892363	−	0.892363i	−0.994745	+	0.102383i	$0.967353\pi$
$44$	−1.96570	+	4.74563i	−0.296341	+	0.715430i
$45$		0			0
$46$	0.574306	+	1.38650i	0.0846768	+	0.204428i
$47$	10.9492			1.59710			0.798551	−	0.601928i	$-0.205600\pi$
$47$	10.9492			1.59710			0.798551	+	0.601928i	$0.205600\pi$
$48$		0			0
$49$	5.65702	+	5.65702i	0.808146	+	0.808146i
$50$	−2.09254	−	1.36026i	−0.295930	−	0.192370i
$51$		0			0
$52$		−	1.72226i		−	0.238834i
$53$	−2.53645	+	2.53645i	−0.348408	+	0.348408i	−0.859516	−	0.511108i	$-0.829235\pi$
$53$	−2.53645	+	2.53645i	−0.348408	+	0.348408i	0.511108	+	0.859516i	$0.329235\pi$
$54$		0			0
$55$	5.76592	−	3.12895i	0.777477	−	0.421908i
$56$	2.77496	+	6.69936i	0.370820	+	0.895239i
$57$		0			0
$58$	−0.253431	−	0.104975i	−0.0332771	−	0.0137838i
$59$	−0.216234	+	0.216234i	−0.0281513	+	0.0281513i	−0.721042	−	0.692891i	$-0.756337\pi$
$59$	−0.216234	+	0.216234i	−0.0281513	+	0.0281513i	0.692891	+	0.721042i	$0.256337\pi$
$60$		0			0
$61$	−2.60281	+	6.28374i	−0.333256	+	0.804551i	0.665074	+	0.746778i	$0.268400\pi$
$61$	−2.60281	+	6.28374i	−0.333256	+	0.804551i	−0.998330	+	0.0577732i	$0.981600\pi$
$62$	1.44341	−	3.48470i	0.183313	−	0.442557i
$63$		0			0
$64$		−	2.62548i		−	0.328184i
$65$	−1.38462	+	1.70907i	−0.171741	+	0.211984i
$66$		0			0
$67$		−	5.09621i		−	0.622601i	−0.950312	−	0.311301i	$-0.899235\pi$
$67$		−	5.09621i		−	0.622601i	0.950312	−	0.311301i	$-0.100765\pi$
$68$	−1.94883	−	6.95086i	−0.236330	−	0.842916i
$69$		0			0
$70$	1.22870	−	4.14460i	0.146858	−	0.495374i
$71$	3.33246	−	1.38035i	0.395491	−	0.163818i	−0.176069	−	0.984378i	$-0.556338\pi$
$71$	3.33246	−	1.38035i	0.395491	−	0.163818i	0.571560	+	0.820560i	$0.306338\pi$
$72$		0			0
$73$	−4.62935	+	1.91754i	−0.541824	+	0.224431i	−0.636773	−	0.771051i	$-0.719731\pi$
$73$	−4.62935	+	1.91754i	−0.541824	+	0.224431i	0.0949491	+	0.995482i	$0.469731\pi$
$74$	4.53912	+	1.88017i	0.527662	+	0.218565i
$75$		0			0
$76$	3.18001	−	3.18001i	0.364772	−	0.364772i
$77$	8.03464	+	8.03464i	0.915632	+	0.915632i
$78$		0			0
$79$	−11.4965	−	4.76199i	−1.29345	−	0.535766i	−0.373441	−	0.927654i	$-0.621822\pi$
$79$	−11.4965	−	4.76199i	−1.29345	−	0.535766i	−0.920013	+	0.391888i	$0.871822\pi$
$80$	−3.61346	+	4.46019i	−0.403997	+	0.498664i
$81$		0			0
$82$	−1.41429	−	3.41440i	−0.156182	−	0.377057i
$83$	−5.74272	+	5.74272i	−0.630345	+	0.630345i	−0.948155	−	0.317809i	$-0.897053\pi$
$83$	−5.74272	+	5.74272i	−0.630345	+	0.630345i	0.317809	+	0.948155i	$0.397053\pi$
$84$		0			0
$85$	−3.65428	+	8.46441i	−0.396362	+	0.918094i
$86$	−4.13077			−0.445432
$87$		0			0
$88$	2.10204	+	5.07477i	0.224078	+	0.540972i
$89$		−	13.2723i		−	1.40687i	−0.710761	−	0.703433i	$-0.751649\pi$
$89$		−	13.2723i		−	1.40687i	0.710761	−	0.703433i	$-0.248351\pi$
$90$		0			0
$91$	−3.51979	−	1.45795i	−0.368974	−	0.152834i
$92$	−4.86323	−	2.01442i	−0.507027	−	0.210018i
$93$		0			0
$94$	3.86462	−	3.86462i	0.398605	−	0.398605i
$95$	−5.71224	+	0.599074i	−0.586063	+	0.0614637i
$96$		0			0
$97$	−4.18163	+	1.73209i	−0.424581	+	0.175867i	−0.584734	−	0.811225i	$-0.698801\pi$
$97$	−4.18163	+	1.73209i	−0.424581	+	0.175867i	0.160153	+	0.987092i	$0.448801\pi$
$98$	3.99340			0.403395
$99$		0			0
$100$	8.56372	−	1.81623i	0.856372	−	0.181623i
$101$	−2.62696			−0.261393			−0.130696	−	0.991422i	$-0.541721\pi$
$101$	−2.62696			−0.261393			−0.130696	+	0.991422i	$0.541721\pi$
$102$		0			0
$103$			9.21332i			0.907815i	0.891049	+	0.453908i	$0.149970\pi$
$103$			9.21332i			0.907815i	−0.891049	+	0.453908i	$0.850030\pi$
$104$	−1.30229	−	1.30229i	−0.127700	−	0.127700i
$105$		0			0
$106$			1.79053i			0.173911i
$107$	5.38760	−	2.23162i	0.520839	−	0.215739i	−0.106747	−	0.994286i	$-0.534043\pi$
$107$	5.38760	−	2.23162i	0.520839	−	0.215739i	0.627585	+	0.778548i	$0.284043\pi$
$108$		0			0
$109$	6.52084	−	15.7427i	0.624584	−	1.50788i	−0.221683	−	0.975119i	$-0.571155\pi$
$109$	6.52084	−	15.7427i	0.624584	−	1.50788i	0.846267	−	0.532759i	$-0.178845\pi$
$110$	0.930745	−	3.13953i	0.0887430	−	0.299343i
$111$		0			0
$112$	−9.18564	−	3.80482i	−0.867962	−	0.359522i
$113$	0.448023	−	1.08162i	0.0421464	−	0.101750i	−0.901404	−	0.432978i	$-0.857463\pi$
$113$	0.448023	−	1.08162i	0.0421464	−	0.101750i	0.943551	+	0.331228i	$0.107463\pi$
$114$		0			0
$115$	3.20650	+	5.90882i	0.299007	+	0.551000i
$116$	0.888926	−	0.368205i	0.0825347	−	0.0341870i
$117$		0			0
$118$			0.152644i			0.0140520i
$119$	−15.8553	−	1.90129i	−1.45345	−	0.174291i
$120$		0			0
$121$	−1.69193	−	1.69193i	−0.153812	−	0.153812i
$122$	1.29922	+	3.13660i	0.117626	+	0.283974i
$123$		0			0
$124$	5.06285	+	12.2228i	0.454658	+	1.09764i
$125$	−9.95831	−	5.08253i	−0.890698	−	0.454595i
$126$		0			0
$127$	−4.70813	−	4.70813i	−0.417779	−	0.417779i	0.466659	−	0.884437i	$-0.345458\pi$
$127$	−4.70813	−	4.70813i	−0.417779	−	0.417779i	−0.884437	+	0.466659i	$0.845458\pi$
$128$	−8.03444	−	8.03444i	−0.710151	−	0.710151i
$129$		0			0
$130$	0.114519	+	1.09195i	0.0100440	+	0.0957703i
$131$	−4.70084	−	11.3488i	−0.410715	−	0.991553i	−0.984946	−	0.172860i	$-0.944699\pi$
$131$	−4.70084	−	11.3488i	−0.410715	−	0.991553i	0.574232	−	0.818693i	$-0.305301\pi$
$132$		0			0
$133$	−3.80702	−	9.19097i	−0.330111	−	0.796958i
$134$	−1.79876	−	1.79876i	−0.155389	−	0.155389i
$135$		0			0
$136$	−6.72949	−	3.78228i	−0.577049	−	0.324328i
$137$		−	9.68972i		−	0.827848i	−0.910311	−	0.413924i	$-0.864158\pi$
$137$		−	9.68972i		−	0.827848i	0.910311	−	0.413924i	$-0.135842\pi$
$138$		0			0
$139$	−1.32180	+	0.547508i	−0.112114	+	0.0464390i	−0.438035	−	0.898958i	$-0.644325\pi$
$139$	−1.32180	+	0.547508i	−0.112114	+	0.0464390i	0.325922	+	0.945397i	$0.394325\pi$
$140$	7.23206	+	13.3270i	0.611221	+	1.12634i
$141$		0			0
$142$	0.689017	−	1.66343i	0.0578210	−	0.139592i
$143$	−2.66624	−	1.10439i	−0.222963	−	0.0923541i
$144$		0			0
$145$	−1.17814	−	0.349271i	−0.0978392	−	0.0290054i
$146$	−0.957159	+	2.31079i	−0.0792150	+	0.191242i
$147$		0			0
$148$	−15.9213	+	6.59481i	−1.30872	+	0.542090i
$149$			9.40983i			0.770884i	0.922732	+	0.385442i	$0.125951\pi$
$149$			9.40983i			0.770884i	−0.922732	+	0.385442i	$0.874049\pi$
$150$		0			0
$151$	−6.12505	−	6.12505i	−0.498450	−	0.498450i	0.412506	−	0.910955i	$-0.364654\pi$
$151$	−6.12505	−	6.12505i	−0.498450	−	0.498450i	−0.910955	+	0.412506i	$0.864654\pi$
$152$		−	4.80912i		−	0.390071i
$153$		0			0
$154$	5.67181			0.457047
$155$	4.80251	−	16.1995i	0.385747	−	1.30118i
$156$		0			0
$157$	17.7467			1.41634			0.708169	−	0.706043i	$-0.249521\pi$
$157$	17.7467			1.41634			0.708169	+	0.706043i	$0.249521\pi$
$158$	−5.73858	+	2.37700i	−0.456537	+	0.189104i
$159$		0			0
$160$	1.17220	+	11.1771i	0.0926705	+	0.883623i
$161$	−8.23375	+	8.23375i	−0.648911	+	0.648911i
$162$		0			0
$163$	2.12558	+	0.880443i	0.166488	+	0.0689616i	0.464371	−	0.885641i	$-0.346280\pi$
$163$	2.12558	+	0.880443i	0.166488	+	0.0689616i	−0.297883	+	0.954602i	$0.596280\pi$
$164$	11.9762	+	4.96072i	0.935187	+	0.387367i
$165$		0			0
$166$			4.05390i			0.314643i
$167$	−3.58287	−	8.64980i	−0.277251	−	0.669342i	0.722507	−	0.691364i	$-0.242990\pi$
$167$	−3.58287	−	8.64980i	−0.277251	−	0.669342i	−0.999757	+	0.0220216i	$0.992990\pi$
$168$		0			0
$169$	−12.0324			−0.925568
$170$	1.69778	+	4.27741i	0.130214	+	0.328062i
$171$		0			0
$172$	10.2452	−	10.2452i	0.781191	−	0.781191i
$173$	3.55891	+	8.59197i	0.270579	+	0.653235i	0.999508	−	0.0313536i	$-0.00998178\pi$
$173$	3.55891	+	8.59197i	0.270579	+	0.653235i	−0.728929	+	0.684589i	$0.759982\pi$
$174$		0			0
$175$	3.53762	−	19.0392i	0.267419	−	1.43923i
$176$	−6.95813	−	2.88215i	−0.524489	−	0.217250i
$177$		0			0
$178$	−4.68461	−	4.68461i	−0.351126	−	0.351126i
$179$	−1.37022	+	1.37022i	−0.102415	+	0.102415i	−0.756458	−	0.654043i	$-0.773072\pi$
$179$	−1.37022	+	1.37022i	−0.102415	+	0.102415i	0.654043	+	0.756458i	$0.273072\pi$
$180$		0			0
$181$	15.6158	+	6.46827i	1.16071	+	0.480782i	0.878112	−	0.478455i	$-0.158803\pi$
$181$	15.6158	+	6.46827i	1.16071	+	0.480782i	0.282600	+	0.959238i	$0.408803\pi$
$182$	−1.75694	+	0.727749i	−0.130233	+	0.0539443i
$183$		0			0
$184$	−5.20053	+	2.15413i	−0.383388	+	0.158805i
$185$	21.1013	+	6.25568i	1.55140	+	0.459927i
$186$		0			0
$187$	−12.0104	−	1.44023i	−0.878285	−	0.105320i
$188$			19.1702i			1.39813i
$189$		0			0
$190$	−1.80474	+	2.22764i	−0.130930	+	0.161610i
$191$			16.6593i			1.20543i	0.797958	+	0.602713i	$0.205914\pi$
$191$			16.6593i			1.20543i	−0.797958	+	0.602713i	$0.794086\pi$
$192$		0			0
$193$	−5.42062	+	13.0865i	−0.390185	+	0.941989i	0.599714	+	0.800214i	$0.295281\pi$
$193$	−5.42062	+	13.0865i	−0.390185	+	0.941989i	−0.989899	+	0.141775i	$0.954719\pi$
$194$	−0.864591	+	2.08731i	−0.0620740	+	0.149860i
$195$		0			0
$196$	−9.90454	+	9.90454i	−0.707467	+	0.707467i
$197$	−16.9050	−	7.00226i	−1.20443	−	0.498891i	−0.312001	−	0.950082i	$-0.600999\pi$
$197$	−16.9050	−	7.00226i	−1.20443	−	0.498891i	−0.892427	+	0.451191i	$0.850999\pi$
$198$		0			0
$199$	−2.08861	−	5.04236i	−0.148058	−	0.357443i	0.832399	−	0.554176i	$-0.186967\pi$
$199$	−2.08861	−	5.04236i	−0.148058	−	0.357443i	−0.980457	+	0.196733i	$0.936967\pi$
$200$	5.10211	−	7.84878i	0.360774	−	0.554993i
$201$		0			0
$202$	−0.927212	+	0.927212i	−0.0652384	+	0.0652384i
$203$		−	2.12840i		−	0.149384i
$204$		0			0
$205$	−7.89634	−	14.5511i	−0.551504	−	1.01629i
$206$	3.25193	+	3.25193i	0.226573	+	0.226573i
$207$		0			0
$208$	2.52521			0.175092
$209$	−2.88382	−	6.96216i	−0.199478	−	0.481583i
$210$		0			0
$211$	−2.10833	+	5.08995i	−0.145143	+	0.350407i	−0.979686	−	0.200536i	$-0.935732\pi$
$211$	−2.10833	+	5.08995i	−0.145143	+	0.350407i	0.834543	+	0.550943i	$0.185732\pi$
$212$	−4.44091	−	4.44091i	−0.305003	−	0.305003i
$213$		0			0
$214$	1.11393	−	2.68928i	0.0761470	−	0.183835i
$215$	−18.4035	+	1.93008i	−1.25511	+	0.131630i
$216$		0			0
$217$	29.2657			1.98668
$218$	−3.25495	−	7.85814i	−0.220453	−	0.532220i
$219$		0			0
$220$	5.47829	+	10.0952i	0.369346	+	0.680618i
$221$	3.90522	−	1.09491i	0.262693	−	0.0736519i
$222$		0			0
$223$	−18.8220	+	18.8220i	−1.26042	+	1.26042i	−0.309525	+	0.950891i	$0.600170\pi$
$223$	−18.8220	+	18.8220i	−1.26042	+	1.26042i	−0.950891	+	0.309525i	$0.899830\pi$
$224$	−17.9838	+	7.44914i	−1.20159	+	0.497717i
$225$		0			0
$226$	−0.223635	−	0.539903i	−0.0148760	−	0.0359138i
$227$	−2.93516	+	7.08610i	−0.194813	+	0.470321i	−0.990857	−	0.134919i	$-0.956923\pi$
$227$	−2.93516	+	7.08610i	−0.194813	+	0.470321i	0.796043	+	0.605240i	$0.206923\pi$
$228$		0			0
$229$	−6.59984	+	6.59984i	−0.436130	+	0.436130i	−0.890707	−	0.454577i	$-0.849790\pi$
$229$	−6.59984	+	6.59984i	−0.436130	+	0.436130i	0.454577	+	0.890707i	$0.349790\pi$
$230$	3.21734	+	0.953811i	0.212145	+	0.0628924i
$231$		0			0
$232$	0.393743	−	0.950579i	0.0258505	−	0.0624086i
$233$	−3.60219	+	1.49207i	−0.235987	+	0.0977490i	−0.497543	−	0.867439i	$-0.665764\pi$
$233$	−3.60219	+	1.49207i	−0.235987	+	0.0977490i	0.261556	+	0.965188i	$0.415764\pi$
$234$		0			0
$235$	15.4120	−	19.0235i	1.00537	−	1.24095i
$236$	−0.378591	−	0.378591i	−0.0246442	−	0.0246442i
$237$		0			0
$238$	−6.26735	+	4.92519i	−0.406252	+	0.319253i
$239$	−22.6299			−1.46380			−0.731902	−	0.681410i	$-0.761367\pi$
$239$	−22.6299			−1.46380			−0.731902	+	0.681410i	$0.761367\pi$
$240$		0			0
$241$	2.67184	−	1.10671i	0.172108	−	0.0712896i	−0.294966	−	0.955508i	$-0.595308\pi$
$241$	2.67184	−	1.10671i	0.172108	−	0.0712896i	0.467074	+	0.884218i	$0.345308\pi$
$242$	−1.19437			−0.0767769
$243$		0			0
$244$	−11.0018	−	4.55710i	−0.704319	−	0.291739i
$245$	17.7915	−	1.86589i	1.13666	−	0.119208i
$246$		0			0
$247$	1.78663	+	1.78663i	0.113680	+	0.113680i
$248$	13.0705	+	5.41400i	0.829980	+	0.343789i
$249$		0			0
$250$	−5.30881	+	1.72096i	−0.335759	+	0.108843i
$251$		−	13.3749i		−	0.844213i	−0.906546	−	0.422107i	$-0.861291\pi$
$251$		−	13.3749i		−	0.844213i	0.906546	−	0.422107i	$-0.138709\pi$
$252$		0			0
$253$	−6.23707	+	6.23707i	−0.392121	+	0.392121i
$254$	−3.32356			−0.208539
$255$		0			0
$256$	−0.420720			−0.0262950
$257$	−5.18281	+	5.18281i	−0.323295	+	0.323295i	−0.850030	−	0.526735i	$-0.823416\pi$
$257$	−5.18281	+	5.18281i	−0.323295	+	0.323295i	0.526735	+	0.850030i	$0.323416\pi$
$258$		0			0
$259$			38.1211i			2.36873i
$260$	−2.99231	−	2.42425i	−0.185575	−	0.150345i
$261$		0			0
$262$	−5.66489	−	2.34648i	−0.349978	−	0.144966i
$263$	−17.0504	−	17.0504i	−1.05137	−	1.05137i	−0.998607	−	0.0527652i	$-0.983197\pi$
$263$	−17.0504	−	17.0504i	−1.05137	−	1.05137i	−0.0527652	−	0.998607i	$-0.516803\pi$
$264$		0			0
$265$	0.836614	+	7.97720i	0.0513928	+	0.490036i
$266$	−4.58777	−	1.90032i	−0.281294	−	0.116516i
$267$		0			0
$268$	8.92264			0.545037
$269$	23.2121	−	9.61475i	1.41526	−	0.586222i	0.461598	−	0.887089i	$-0.347276\pi$
$269$	23.2121	−	9.61475i	1.41526	−	0.586222i	0.953666	+	0.300868i	$0.0972762\pi$
$270$		0			0
$271$	14.0988			0.856440			0.428220	−	0.903674i	$-0.359141\pi$
$271$	14.0988			0.856440			0.428220	+	0.903674i	$0.359141\pi$
$272$	10.1915	−	2.85741i	0.617950	−	0.173256i
$273$		0			0
$274$	−3.42008	−	3.42008i	−0.206615	−	0.206615i
$275$	2.67975	−	14.4222i	0.161595	−	0.869692i
$276$		0			0
$277$	5.74838	−	2.38106i	0.345387	−	0.143064i	−0.203245	−	0.979128i	$-0.565149\pi$
$277$	5.74838	−	2.38106i	0.345387	−	0.143064i	0.548632	+	0.836064i	$0.315149\pi$
$278$	−0.273294	+	0.659790i	−0.0163911	+	0.0395716i
$279$		0			0
$280$	15.5457	+	4.60867i	0.929034	+	0.275421i
$281$	3.87369	−	3.87369i	0.231085	−	0.231085i	−0.582061	−	0.813145i	$-0.697753\pi$
$281$	3.87369	−	3.87369i	0.231085	−	0.231085i	0.813145	+	0.582061i	$0.197753\pi$
$282$		0			0
$283$	9.48690	−	22.9034i	0.563937	−	1.36147i	−0.342656	−	0.939461i	$-0.611327\pi$
$283$	9.48690	−	22.9034i	0.563937	−	1.36147i	0.906594	−	0.422005i	$-0.138673\pi$
$284$	2.41677	+	5.83461i	0.143409	+	0.346220i
$285$		0			0
$286$	−1.33088	+	0.551270i	−0.0786968	+	0.0325973i
$287$	20.2765	−	20.2765i	1.19688	−	1.19688i
$288$		0			0
$289$	14.5221	−	8.83792i	0.854241	−	0.519877i
$290$	−0.539115	+	0.292558i	−0.0316579	+	0.0171796i
$291$		0			0
$292$	−3.35730	−	8.10524i	−0.196471	−	0.474323i
$293$	24.3230			1.42096			0.710482	−	0.703715i	$-0.248477\pi$
$293$	24.3230			1.42096			0.710482	+	0.703715i	$0.248477\pi$
$294$		0			0
$295$	0.0713219	+	0.680062i	0.00415252	+	0.0395947i
$296$	−7.05220	+	17.0255i	−0.409901	+	0.989588i
$297$		0			0
$298$	3.32129	+	3.32129i	0.192397	+	0.192397i
$299$	1.13176	−	2.73232i	0.0654516	−	0.158014i
$300$		0			0
$301$	−12.2653	−	29.6111i	−0.706962	−	1.70676i
$302$	−4.32379			−0.248806
$303$		0			0
$304$	4.66259	+	4.66259i	0.267418	+	0.267418i
$305$	7.25387	+	13.3672i	0.415356	+	0.765403i
$306$		0			0
$307$		−	0.916042i		−	0.0522813i	−0.999658	−	0.0261406i	$-0.991678\pi$
$307$		−	0.916042i		−	0.0522813i	0.999658	−	0.0261406i	$-0.00832177\pi$
$308$	−14.0674	+	14.0674i	−0.801562	+	0.801562i
$309$		0			0
$310$	−4.02269	−	7.41288i	−0.228474	−	0.421023i
$311$	−3.26096	−	7.87266i	−0.184912	−	0.446418i	0.804054	−	0.594556i	$-0.202672\pi$
$311$	−3.26096	−	7.87266i	−0.184912	−	0.446418i	−0.988967	+	0.148138i	$0.952672\pi$
$312$		0			0
$313$	−15.6769	−	6.49359i	−0.886111	−	0.367039i	−0.107247	−	0.994232i	$-0.534204\pi$
$313$	−15.6769	−	6.49359i	−0.886111	−	0.367039i	−0.778864	+	0.627193i	$0.784204\pi$
$314$	6.26386	−	6.26386i	0.353490	−	0.353490i
$315$		0			0
$316$	8.33748	−	20.1285i	0.469020	−	1.13231i
$317$	−9.50873	+	22.9561i	−0.534064	+	1.28934i	0.394747	+	0.918790i	$0.370832\pi$
$317$	−9.50873	+	22.9561i	−0.534064	+	1.28934i	−0.928811	+	0.370554i	$0.879168\pi$
$318$		0			0
$319$		−	1.61226i		−	0.0902695i
$320$	−4.56159	−	3.69561i	−0.255001	−	0.206591i
$321$		0			0
$322$			5.81237i			0.323911i
$323$	9.23231	+	5.18898i	0.513699	+	0.288723i
$324$		0			0
$325$	1.02041	+	4.81137i	0.0566024	+	0.266887i
$326$	1.06100	−	0.439482i	0.0587636	−	0.0243407i
$327$		0			0
$328$	12.8069	−	5.30478i	0.707141	−	0.292907i
$329$	39.1783	+	16.2282i	2.15997	+	0.894689i
$330$		0			0
$331$	−19.7269	+	19.7269i	−1.08429	+	1.08429i	−0.0881836	+	0.996104i	$0.528106\pi$
$331$	−19.7269	+	19.7269i	−1.08429	+	1.08429i	−0.996104	+	0.0881836i	$0.971894\pi$
$332$	−10.0546	−	10.0546i	−0.551816	−	0.551816i
$333$		0			0
$334$	−4.31764	−	1.78843i	−0.236251	−	0.0978583i
$335$	−8.85432	−	7.17340i	−0.483763	−	0.391925i
$336$		0			0
$337$	−6.10377	−	14.7358i	−0.332493	−	0.802710i	−0.998393	−	0.0566688i	$-0.981952\pi$
$337$	−6.10377	−	14.7358i	−0.332493	−	0.802710i	0.665900	−	0.746041i	$-0.268048\pi$
$338$	−4.24695	+	4.24695i	−0.231003	+	0.231003i
$339$		0			0
$340$	−14.8198	−	6.39805i	−0.803718	−	0.346983i
$341$	22.1688			1.20051
$342$		0			0
$343$	1.48250	+	3.57906i	0.0800473	+	0.193251i
$344$		−	15.4938i		−	0.835372i
$345$		0			0
$346$	4.28877	+	1.77647i	0.230566	+	0.0955035i
$347$	24.0961	+	9.98091i	1.29354	+	0.535804i	0.920040	−	0.391825i	$-0.128156\pi$
$347$	24.0961	+	9.98091i	1.29354	+	0.535804i	0.373504	+	0.927628i	$0.378156\pi$
$348$		0			0
$349$	16.2233	−	16.2233i	0.868413	−	0.868413i	−0.123884	−	0.992297i	$-0.539535\pi$
$349$	16.2233	−	16.2233i	0.868413	−	0.868413i	0.992297	+	0.123884i	$0.0395349\pi$
$350$	−5.47144	−	7.96871i	−0.292461	−	0.425945i
$351$		0			0
$352$	−13.6228	+	5.64273i	−0.726095	+	0.300759i
$353$	−3.96701			−0.211142			−0.105571	−	0.994412i	$-0.533667\pi$
$353$	−3.96701			−0.211142			−0.105571	+	0.994412i	$0.533667\pi$
$354$		0			0
$355$	2.29250	−	7.73291i	0.121673	−	0.410420i
$356$	23.2377			1.23160
$357$		0			0
$358$			0.967265i			0.0511215i
$359$	13.2967	+	13.2967i	0.701773	+	0.701773i	0.964791	−	0.263018i	$-0.0847179\pi$
$359$	13.2967	+	13.2967i	0.701773	+	0.701773i	−0.263018	+	0.964791i	$0.584718\pi$
$360$		0			0
$361$		−	12.4023i		−	0.652752i
$362$	7.79478	−	3.22870i	0.409685	−	0.169697i
$363$		0			0
$364$	2.55263	−	6.16259i	0.133794	−	0.323007i
$365$	−3.18466	+	10.7423i	−0.166692	+	0.562277i
$366$		0			0
$367$	−6.93632	−	2.87312i	−0.362073	−	0.149976i	0.194228	−	0.980956i	$-0.437780\pi$
$367$	−6.93632	−	2.87312i	−0.362073	−	0.149976i	−0.556301	+	0.830981i	$0.687780\pi$
$368$	2.95358	−	7.13057i	0.153966	−	0.371707i
$369$		0			0
$370$	9.65592	−	5.23991i	0.501987	−	0.272410i
$371$	−12.8353	+	5.31655i	−0.666375	+	0.276021i
$372$		0			0
$373$			18.5763i			0.961844i	0.876763	+	0.480922i	$0.159698\pi$
$373$			18.5763i			0.961844i	−0.876763	+	0.480922i	$0.840302\pi$
$374$	−4.74752	+	3.73083i	−0.245488	+	0.192917i
$375$		0			0
$376$	14.4956	+	14.4956i	0.747551	+	0.747551i
$377$	0.206869	+	0.499427i	0.0106543	+	0.0257218i
$378$		0			0
$379$	5.62054	+	13.5692i	0.288708	+	0.697002i	0.999983	−	0.00591199i	$-0.00188186\pi$
$379$	5.62054	+	13.5692i	0.288708	+	0.697002i	−0.711275	+	0.702914i	$0.751882\pi$
$380$	−1.04888	−	10.0012i	−0.0538065	−	0.513051i
$381$		0			0
$382$	5.88007	+	5.88007i	0.300851	+	0.300851i
$383$	−15.0658	−	15.0658i	−0.769829	−	0.769829i	0.208248	−	0.978076i	$-0.433224\pi$
$383$	−15.0658	−	15.0658i	−0.769829	−	0.769829i	−0.978076	+	0.208248i	$0.933224\pi$
$384$		0			0
$385$	25.2692	−	2.65012i	1.28784	−	0.135063i
$386$	2.70576	+	6.53228i	0.137720	+	0.332484i
$387$		0			0
$388$	−3.03261	−	7.32137i	−0.153957	−	0.371686i
$389$	−3.37903	−	3.37903i	−0.171323	−	0.171323i	0.616237	−	0.787561i	$-0.288656\pi$
$389$	−3.37903	−	3.37903i	−0.171323	−	0.171323i	−0.787561	+	0.616237i	$0.788656\pi$
$390$		0			0
$391$	1.47592	−	12.3080i	0.0746404	−	0.622443i
$392$			14.9786i			0.756534i
$393$		0			0
$394$	−8.43829	+	3.49525i	−0.425115	+	0.176088i
$395$	−24.4560	+	13.2714i	−1.23052	+	0.667755i
$396$		0			0
$397$	−12.3580	+	29.8348i	−0.620228	+	1.49736i	0.231207	+	0.972904i	$0.425732\pi$
$397$	−12.3580	+	29.8348i	−0.620228	+	1.49736i	−0.851436	+	0.524459i	$0.824268\pi$
$398$	−2.51694	−	1.04255i	−0.126163	−	0.0522584i
$399$		0			0
$400$	2.66299	+	12.5563i	0.133149	+	0.627814i
$401$	9.50957	−	22.9581i	0.474885	−	1.14647i	−0.487093	−	0.873350i	$-0.661943\pi$
$401$	9.50957	−	22.9581i	0.474885	−	1.14647i	0.961979	−	0.273125i	$-0.0880572\pi$
$402$		0			0
$403$	−6.86717	+	2.84447i	−0.342078	+	0.141693i
$404$		−	4.59939i		−	0.228828i
$405$		0			0
$406$	−0.751240	−	0.751240i	−0.0372834	−	0.0372834i
$407$			28.8768i			1.43137i
$408$		0			0
$409$	18.4025			0.909945			0.454973	−	0.890505i	$-0.349649\pi$
$409$	18.4025			0.909945			0.454973	+	0.890505i	$0.349649\pi$
$410$	−7.92304	−	2.34886i	−0.391291	−	0.116002i
$411$		0			0
$412$	−16.1310			−0.794719
$413$	−1.09422	+	0.453239i	−0.0538429	+	0.0223024i
$414$		0			0
$415$	1.89416	+	18.0610i	0.0929806	+	0.886580i
$416$	3.49587	−	3.49587i	0.171399	−	0.171399i
$417$		0			0
$418$	−3.47524	−	1.43949i	−0.169979	−	0.0704078i
$419$	2.80373	+	1.16134i	0.136971	+	0.0567354i	0.450116	−	0.892970i	$-0.351383\pi$
$419$	2.80373	+	1.16134i	0.136971	+	0.0567354i	−0.313145	+	0.949705i	$0.601383\pi$
$420$		0			0
$421$			31.0514i			1.51335i	0.653788	+	0.756677i	$0.273179\pi$
$421$			31.0514i			1.51335i	−0.653788	+	0.756677i	$0.726821\pi$
$422$	1.05239	+	2.54070i	0.0512297	+	0.123679i
$423$		0			0
$424$	−6.71598			−0.326157
$425$	9.56260	+	18.2635i	0.463854	+	0.885912i
$426$		0			0
$427$	−18.6268	+	18.6268i	−0.901412	+	0.901412i
$428$	3.90720	+	9.43282i	0.188862	+	0.455952i
$429$		0			0
$430$	−5.81445	+	7.17693i	−0.280398	+	0.346102i
$431$	−32.8743	−	13.6170i	−1.58350	−	0.655907i	−0.594536	−	0.804069i	$-0.702664\pi$
$431$	−32.8743	−	13.6170i	−1.58350	−	0.655907i	−0.988963	+	0.148163i	$0.952664\pi$
$432$		0			0
$433$	2.33269	+	2.33269i	0.112102	+	0.112102i	0.760933	−	0.648831i	$-0.224742\pi$
$433$	2.33269	+	2.33269i	0.112102	+	0.112102i	−0.648831	+	0.760933i	$0.724742\pi$
$434$	10.3296	−	10.3296i	0.495837	−	0.495837i
$435$		0			0
$436$	27.5629	+	11.4169i	1.32003	+	0.546773i
$437$	7.13470	−	2.95529i	0.341299	−	0.141371i
$438$		0			0
$439$	−3.06718	+	1.27047i	−0.146389	+	0.0606362i	−0.454675	−	0.890657i	$-0.650245\pi$
$439$	−3.06718	+	1.27047i	−0.146389	+	0.0606362i	0.308286	+	0.951294i	$0.400245\pi$
$440$	11.7759	+	3.49107i	0.561393	+	0.166430i
$441$		0			0
$442$	0.991924	−	1.76484i	0.0471810	−	0.0839451i
$443$			5.62292i			0.267153i	0.991039	+	0.133577i	$0.0426462\pi$
$443$			5.62292i			0.267153i	−0.991039	+	0.133577i	$0.957354\pi$
$444$		0			0
$445$	−23.0598	−	18.6821i	−1.09314	−	0.885617i
$446$			13.2868i			0.629150i
$447$		0			0
$448$	3.89132	−	9.39447i	0.183848	−	0.443847i
$449$	−2.34670	+	5.66543i	−0.110748	+	0.267368i	−0.969530	−	0.244972i	$-0.921221\pi$
$449$	−2.34670	+	5.66543i	−0.110748	+	0.267368i	0.858783	+	0.512340i	$0.171221\pi$
$450$		0			0
$451$	15.3595	−	15.3595i	0.723249	−	0.723249i
$452$	1.89375	+	0.784416i	0.0890743	+	0.0368958i
$453$		0			0
$454$	1.46511	+	3.53710i	0.0687613	+	0.166004i
$455$	−7.48753	+	4.06320i	−0.351021	+	0.190486i
$456$		0			0
$457$	20.0771	−	20.0771i	0.939169	−	0.939169i	−0.0590836	−	0.998253i	$-0.518818\pi$
$457$	20.0771	−	20.0771i	0.939169	−	0.939169i	0.998253	+	0.0590836i	$0.0188178\pi$
$458$			4.65896i			0.217699i
$459$		0			0
$460$	−10.3454	+	5.61406i	−0.482356	+	0.261757i
$461$	14.7095	+	14.7095i	0.685090	+	0.685090i	0.961142	−	0.276053i	$-0.0890264\pi$
$461$	14.7095	+	14.7095i	0.685090	+	0.685090i	−0.276053	+	0.961142i	$0.589026\pi$
$462$		0			0
$463$	31.4596			1.46205			0.731025	−	0.682351i	$-0.239042\pi$
$463$	31.4596			1.46205			0.731025	+	0.682351i	$0.239042\pi$
$464$	0.539870	+	1.30336i	0.0250628	+	0.0605070i
$465$		0			0
$466$	−0.744785	+	1.79807i	−0.0345015	+	0.0832939i
$467$	−1.05068	−	1.05068i	−0.0486197	−	0.0486197i	0.682379	−	0.730999i	$-0.260945\pi$
$467$	−1.05068	−	1.05068i	−0.0486197	−	0.0486197i	−0.730999	+	0.682379i	$0.760945\pi$
$468$		0			0
$469$	7.55329	−	18.2352i	0.348778	−	0.842026i
$470$	−1.27469	−	12.1543i	−0.0587972	−	0.560638i
$471$		0			0
$472$	−0.572542			−0.0263534
$473$	−9.29100	−	22.4304i	−0.427200	−	1.03135i
$474$		0			0
$475$	−6.99967	+	10.7679i	−0.321167	+	0.494064i
$476$	3.32885	−	27.7600i	0.152577	−	1.27238i
$477$		0			0
$478$	−7.98743	+	7.98743i	−0.365337	+	0.365337i
$479$	−13.5193	+	5.59989i	−0.617714	+	0.255865i	−0.669523	−	0.742792i	$-0.733501\pi$
$479$	−13.5193	+	5.59989i	−0.617714	+	0.255865i	0.0518091	+	0.998657i	$0.483501\pi$
$480$		0			0
$481$	−3.70517	−	8.94508i	−0.168941	−	0.407861i
$482$	0.552427	−	1.33368i	0.0251623	−	0.0607473i
$483$		0			0
$484$	2.96230	−	2.96230i	0.134650	−	0.134650i
$485$	−2.87666	+	9.70339i	−0.130623	+	0.440608i
$486$		0			0
$487$	−1.29143	+	3.11780i	−0.0585204	+	0.141281i	−0.950435	−	0.310923i	$-0.899362\pi$
$487$	−1.29143	+	3.11780i	−0.0585204	+	0.141281i	0.891915	+	0.452204i	$0.149362\pi$
$488$	−11.7649	+	4.87317i	−0.532570	+	0.220598i
$489$		0			0
$490$	5.62110	−	6.93827i	0.253935	−	0.313439i
$491$	5.35772	+	5.35772i	0.241790	+	0.241790i	0.817590	−	0.575800i	$-0.195309\pi$
$491$	5.35772	+	5.35772i	0.241790	+	0.241790i	−0.575800	+	0.817590i	$0.695309\pi$
$492$		0			0
$493$	1.40003	+	1.78155i	0.0630543	+	0.0802371i
$494$	1.26122			0.0567448
$495$		0			0
$496$	−17.9213	+	7.42326i	−0.804691	+	0.333314i
$497$	13.9701			0.626644
$498$		0			0
$499$	−7.88006	−	3.26403i	−0.352760	−	0.146118i	0.199265	−	0.979946i	$-0.436145\pi$
$499$	−7.88006	−	3.26403i	−0.352760	−	0.146118i	−0.552025	+	0.833828i	$0.686145\pi$
$500$	8.89868	−	17.4354i	0.397961	−	0.779735i
$501$		0			0
$502$	−4.72078	−	4.72078i	−0.210699	−	0.210699i
$503$	17.7646	+	7.35832i	0.792082	+	0.328091i	0.741780	−	0.670643i	$-0.233982\pi$
$503$	17.7646	+	7.35832i	0.792082	+	0.328091i	0.0503018	+	0.998734i	$0.483982\pi$
$504$		0			0
$505$	−3.69770	+	4.56417i	−0.164546	+	0.203103i
$506$			4.40287i			0.195732i
$507$		0			0
$508$	8.24317	−	8.24317i	0.365732	−	0.365732i
$509$	5.89076			0.261104			0.130552	−	0.991441i	$-0.458325\pi$
$509$	5.89076			0.261104			0.130552	+	0.991441i	$0.458325\pi$
$510$		0			0
$511$	−19.4068			−0.858505
$512$	15.9204	−	15.9204i	0.703589	−	0.703589i
$513$		0			0
$514$			3.65864i			0.161376i
$515$	16.0075	+	12.9686i	0.705376	+	0.571466i
$516$		0			0
$517$	29.6776	+	12.2929i	1.30522	+	0.540640i
$518$	13.4552	+	13.4552i	0.591188	+	0.591188i
$519$		0			0
$520$	−4.09573	+	0.429542i	−0.179609	+	0.0188366i
$521$	23.8279	+	9.86983i	1.04392	+	0.432405i	0.837717	−	0.546104i	$-0.183890\pi$
$521$	23.8279	+	9.86983i	1.04392	+	0.432405i	0.206202	+	0.978510i	$0.433890\pi$
$522$		0			0
$523$	23.1957			1.01428			0.507138	−	0.861865i	$-0.330703\pi$
$523$	23.1957			1.01428			0.507138	+	0.861865i	$0.330703\pi$
$524$	19.8700	−	8.23042i	0.868025	−	0.359548i
$525$		0			0
$526$	−12.0362			−0.524803
$527$	−24.4965	+	19.2506i	−1.06708	+	0.838568i
$528$		0			0
$529$	9.87182	+	9.87182i	0.429209	+	0.429209i
$530$	3.11092	+	2.52034i	0.135130	+	0.109477i
$531$		0			0
$532$	16.0919	−	6.66548i	0.697672	−	0.288985i
$533$	−2.78709	+	6.72863i	−0.120722	+	0.291449i
$534$		0			0
$535$	3.70628	−	12.5018i	0.160236	−	0.540500i
$536$	6.74685	−	6.74685i	0.291419	−	0.291419i
$537$		0			0
$538$	4.79930	−	11.5865i	0.206913	−	0.499531i
$539$	8.98204	+	21.6846i	0.386884	+	0.934020i
$540$		0			0
$541$	0.294727	−	0.122080i	0.0126713	−	0.00524863i	−0.376339	−	0.926482i	$-0.622817\pi$
$541$	0.294727	−	0.122080i	0.0126713	−	0.00524863i	0.389010	+	0.921233i	$0.372817\pi$
$542$	4.97631	−	4.97631i	0.213751	−	0.213751i
$543$		0			0
$544$	10.1532	−	18.0647i	0.435315	−	0.774519i
$545$	−18.1732	−	33.4889i	−0.778454	−	1.43451i
$546$		0			0
$547$	11.1988	+	27.0363i	0.478826	+	1.15599i	0.960160	+	0.279450i	$0.0901523\pi$
$547$	11.1988	+	27.0363i	0.478826	+	1.15599i	−0.481334	+	0.876537i	$0.659848\pi$
$548$	16.9651			0.724714
$549$		0			0
$550$	−4.14462	−	6.03630i	−0.176727	−	0.257389i
$551$	−0.540183	+	1.30412i	−0.0230126	+	0.0555572i
$552$		0			0
$553$	−34.0787	−	34.0787i	−1.44917	−	1.44917i
$554$	1.18853	−	2.86936i	0.0504958	−	0.121908i
$555$		0			0
$556$	−0.958597	−	2.31426i	−0.0406536	−	0.0981464i
$557$	4.51904			0.191478			0.0957390	−	0.995406i	$-0.469479\pi$
$557$	4.51904			0.191478			0.0957390	+	0.995406i	$0.469479\pi$
$558$		0			0
$559$	5.75610	+	5.75610i	0.243457	+	0.243457i
$560$	−19.5403	+	10.6038i	−0.825728	+	0.448092i
$561$		0			0
$562$		−	2.73451i		−	0.115348i
$563$	−17.3320	+	17.3320i	−0.730457	+	0.730457i	−0.970710	−	0.240253i	$-0.922770\pi$
$563$	−17.3320	+	17.3320i	−0.730457	+	0.730457i	0.240253	+	0.970710i	$0.422770\pi$
$564$		0			0
$565$	−1.24861	−	2.30090i	−0.0525295	−	0.0967995i
$566$	−4.73548	−	11.4325i	−0.199047	−	0.480543i
$567$		0			0
$568$	6.23928	+	2.58439i	0.261794	+	0.108439i
$569$	−4.33415	+	4.33415i	−0.181697	+	0.181697i	−0.792095	−	0.610398i	$-0.791010\pi$
$569$	−4.33415	+	4.33415i	−0.181697	+	0.181697i	0.610398	+	0.792095i	$0.291010\pi$
$570$		0			0
$571$	0.200684	−	0.484495i	0.00839837	−	0.0202755i	−0.919625	−	0.392798i	$-0.871507\pi$
$571$	0.200684	−	0.484495i	0.00839837	−	0.0202755i	0.928023	+	0.372523i	$0.121507\pi$
$572$	1.93362	−	4.66816i	0.0808486	−	0.195186i
$573$		0			0
$574$		−	14.3136i		−	0.597437i
$575$	14.7796	+	2.74616i	0.616353	+	0.114523i
$576$		0			0
$577$			39.5403i			1.64608i	0.567982	+	0.823041i	$0.307724\pi$
$577$			39.5403i			1.64608i	−0.567982	+	0.823041i	$0.692276\pi$
$578$	2.00629	−	8.24514i	0.0834505	−	0.342953i
$579$		0			0
$580$	0.611517	−	2.06273i	0.0253919	−	0.0856504i
$581$	−29.0601	+	12.0371i	−1.20562	+	0.499382i
$582$		0			0
$583$	−9.72273	+	4.02729i	−0.402674	+	0.166793i
$584$	−8.66739	−	3.59015i	−0.358659	−	0.148561i
$585$		0			0
$586$	8.58504	−	8.58504i	0.354645	−	0.354645i
$587$	−7.73398	−	7.73398i	−0.319216	−	0.319216i	0.529250	−	0.848466i	$-0.322473\pi$
$587$	−7.73398	−	7.73398i	−0.319216	−	0.319216i	−0.848466	+	0.529250i	$0.822473\pi$
$588$		0			0
$589$	−17.9317	−	7.42756i	−0.738863	−	0.306047i
$590$	0.265208	+	0.214861i	0.0109185	+	0.00884568i
$591$		0			0
$592$	−9.66944	−	23.3441i	−0.397412	−	0.959436i
$593$	2.72059	−	2.72059i	0.111721	−	0.111721i	−0.649036	−	0.760757i	$-0.724828\pi$
$593$	2.72059	−	2.72059i	0.111721	−	0.111721i	0.760757	+	0.649036i	$0.224828\pi$
$594$		0			0
$595$	−25.6212	+	24.8712i	−1.05037	+	1.01962i
$596$	−16.4751			−0.674847
$597$		0			0
$598$	−0.564932	−	1.36387i	−0.0231018	−	0.0557726i
$599$		−	35.5384i		−	1.45206i	−0.687663	−	0.726030i	$-0.741363\pi$
$599$		−	35.5384i		−	1.45206i	0.687663	−	0.726030i	$-0.258637\pi$
$600$		0			0
$601$	−17.3881	−	7.20238i	−0.709275	−	0.293791i	−0.00127033	−	0.999999i	$-0.500404\pi$
$601$	−17.3881	−	7.20238i	−0.709275	−	0.293791i	−0.708004	+	0.706208i	$0.750404\pi$
$602$	−14.7807	−	6.12237i	−0.602417	−	0.249529i
$603$		0			0
$604$	10.7240	−	10.7240i	0.436352	−	0.436352i
$605$	−5.32118	+	0.558062i	−0.216337	+	0.0226884i
$606$		0			0
$607$	26.1113	−	10.8157i	1.05983	−	0.438994i	0.216437	−	0.976297i	$-0.430557\pi$
$607$	26.1113	−	10.8157i	1.05983	−	0.438994i	0.843390	+	0.537302i	$0.180557\pi$
$608$	12.9096			0.523555
$609$		0			0
$610$	7.27840	+	2.15775i	0.294694	+	0.0873648i
$611$	−10.7705			−0.435726
$612$		0			0
$613$			15.7155i			0.634743i	0.948301	+	0.317371i	$0.102800\pi$
$613$			15.7155i			0.634743i	−0.948301	+	0.317371i	$0.897200\pi$
$614$	−0.323326	−	0.323326i	−0.0130484	−	0.0130484i
$615$		0			0
$616$			21.2740i			0.857155i
$617$	−25.2794	+	10.4711i	−1.01771	+	0.421550i	−0.828262	−	0.560341i	$-0.810670\pi$
$617$	−25.2794	+	10.4711i	−1.01771	+	0.421550i	−0.189449	+	0.981891i	$0.560670\pi$
$618$		0			0
$619$	2.89443	−	6.98778i	0.116337	−	0.280863i	−0.854976	−	0.518668i	$-0.826428\pi$
$619$	2.89443	−	6.98778i	0.116337	−	0.280863i	0.971313	+	0.237805i	$0.0764281\pi$
$620$	28.3628	+	8.40841i	1.13908	+	0.337690i
$621$		0			0
$622$	−3.92972	−	1.62774i	−0.157568	−	0.0652666i
$623$	19.6715	−	47.4911i	0.788120	−	1.90269i
$624$		0			0
$625$	−22.8478	+	10.1478i	−0.913913	+	0.405910i
$626$	−7.82529	+	3.24134i	−0.312762	+	0.129550i
$627$		0			0
$628$			31.0716i			1.23989i
$629$	−25.0755	−	31.9088i	−0.999827	−	1.27229i
$630$		0			0
$631$	−7.18142	−	7.18142i	−0.285888	−	0.285888i	0.549564	−	0.835452i	$-0.314794\pi$
$631$	−7.18142	−	7.18142i	−0.285888	−	0.285888i	−0.835452	+	0.549564i	$0.814794\pi$
$632$	−8.91574	−	21.5245i	−0.354649	−	0.856198i
$633$		0			0
$634$	4.74638	+	11.4588i	0.188503	+	0.455087i
$635$	−14.8072	+	1.55291i	−0.587606	+	0.0616255i
$636$		0			0
$637$	−5.56469	−	5.56469i	−0.220481	−	0.220481i
$638$	−0.569065	−	0.569065i	−0.0225295	−	0.0225295i
$639$		0			0
$640$	−25.2686	+	2.65006i	−0.998828	+	0.104753i
$641$	−12.2267	−	29.5179i	−0.482925	−	1.16589i	−0.958213	−	0.286055i	$-0.907656\pi$
$641$	−12.2267	−	29.5179i	−0.482925	−	1.16589i	0.475288	−	0.879830i	$-0.342344\pi$
$642$		0			0
$643$	−13.4924	−	32.5735i	−0.532088	−	1.28457i	−0.930138	−	0.367211i	$-0.880313\pi$
$643$	−13.4924	−	32.5735i	−0.532088	−	1.28457i	0.398050	−	0.917364i	$-0.369687\pi$
$644$	−14.4160	−	14.4160i	−0.568069	−	0.568069i
$645$		0			0
$646$	5.09014	−	1.42713i	0.200269	−	0.0561498i
$647$		−	7.97446i		−	0.313508i	−0.987638	−	0.156754i	$-0.949897\pi$
$647$		−	7.97446i		−	0.313508i	0.987638	−	0.156754i	$-0.0501031\pi$
$648$		0			0
$649$	−0.828870	+	0.343329i	−0.0325360	+	0.0134768i
$650$	2.05838	+	1.33805i	0.0807365	+	0.0524828i
$651$		0			0
$652$	−1.54151	+	3.72154i	−0.0603703	+	0.145747i
$653$	−12.9322	−	5.35670i	−0.506077	−	0.209624i	0.115012	−	0.993364i	$-0.463309\pi$
$653$	−12.9322	−	5.35670i	−0.506077	−	0.209624i	−0.621089	+	0.783740i	$0.713309\pi$
$654$		0			0
$655$	−26.3347	−	7.80718i	−1.02898	−	0.305052i
$656$	−7.27350	+	17.5598i	−0.283983	+	0.685595i
$657$		0			0
$658$	19.5563	−	8.10047i	0.762383	−	0.315789i
$659$			50.5377i			1.96867i	0.176309	+	0.984335i	$0.443584\pi$
$659$			50.5377i			1.96867i	−0.176309	+	0.984335i	$0.556416\pi$
$660$		0			0
$661$	23.9149	+	23.9149i	0.930181	+	0.930181i	0.997717	−	0.0675357i	$-0.0215137\pi$
$661$	23.9149	+	23.9149i	0.930181	+	0.930181i	−0.0675357	+	0.997717i	$0.521514\pi$
$662$			13.9256i			0.541234i
$663$		0			0
$664$	−15.2055			−0.590088
$665$	−21.3274	−	6.32272i	−0.827042	−	0.245185i
$666$		0			0
$667$	1.65222			0.0639742
$668$	15.1444	−	6.27302i	0.585955	−	0.242710i
$669$		0			0
$670$	−5.65714	+	0.593296i	−0.218554	+	0.0229210i
$671$	−14.1098	+	14.1098i	−0.544702	+	0.544702i
$672$		0			0
$673$	−0.237676	−	0.0984487i	−0.00916174	−	0.00379492i	0.378098	−	0.925766i	$-0.376578\pi$
$673$	−0.237676	−	0.0984487i	−0.00916174	−	0.00379492i	−0.387260	+	0.921971i	$0.626578\pi$
$674$	−7.35553	−	3.04676i	−0.283324	−	0.117357i
$675$		0			0
$676$		−	21.0668i		−	0.810260i
$677$	1.34830	+	3.25509i	0.0518195	+	0.125103i	0.947669	−	0.319254i	$-0.103432\pi$
$677$	1.34830	+	3.25509i	0.0518195	+	0.125103i	−0.895850	+	0.444357i	$0.853432\pi$
$678$		0			0
$679$	−17.5299			−0.672737
$680$	−16.0439	+	6.36811i	−0.615254	+	0.244206i
$681$		0			0
$682$	7.82469	−	7.82469i	0.299623	−	0.299623i
$683$	−6.21032	−	14.9930i	−0.237631	−	0.573693i	0.759406	−	0.650618i	$-0.225490\pi$
$683$	−6.21032	−	14.9930i	−0.237631	−	0.573693i	−0.997037	+	0.0769247i	$0.975490\pi$
$684$		0			0
$685$	−16.8352	−	13.6392i	−0.643241	−	0.521127i
$686$	1.78653	+	0.740004i	0.0682099	+	0.0282535i
$687$		0			0
$688$	15.0218	+	15.0218i	0.572699	+	0.572699i
$689$	2.49505	−	2.49505i	0.0950537	−	0.0950537i
$690$		0			0
$691$	−12.6973	−	5.25938i	−0.483027	−	0.200076i	0.127863	−	0.991792i	$-0.459188\pi$
$691$	−12.6973	−	5.25938i	−0.483027	−	0.200076i	−0.610890	+	0.791716i	$0.709188\pi$
$692$	−15.0432	+	6.23108i	−0.571855	+	0.236870i
$693$		0			0
$694$	12.0278	−	4.98208i	0.456569	−	0.189117i
$695$	−0.909303	+	3.06721i	−0.0344918	+	0.116346i
$696$		0			0
$697$	−3.63461	+	30.3098i	−0.137671	+	1.14807i
$698$		−	11.4523i		−	0.433478i
$699$		0			0
$700$	33.3346	+	6.19380i	1.25993	+	0.234103i
$701$			15.8410i			0.598305i	0.954205	+	0.299153i	$0.0967040\pi$
$701$			15.8410i			0.598305i	−0.954205	+	0.299153i	$0.903296\pi$
$702$		0			0
$703$	9.67504	−	23.3576i	0.364901	−	0.880949i
$704$	2.94768	−	7.11632i	0.111095	−	0.268206i
$705$		0			0
$706$	−1.40019	+	1.40019i	−0.0526970	+	0.0526970i
$707$	−9.39979	−	3.89352i	−0.353516	−	0.146431i
$708$		0			0
$709$	10.0675	+	24.3050i	0.378092	+	0.912795i	0.992324	+	0.123669i	$0.0394661\pi$
$709$	10.0675	+	24.3050i	0.378092	+	0.912795i	−0.614232	+	0.789126i	$0.710534\pi$
$710$	−1.92025	−	3.53857i	−0.0720656	−	0.132800i
$711$		0			0
$712$	17.5712	−	17.5712i	0.658509	−	0.658509i
$713$			22.7182i			0.850802i
$714$		0			0
$715$	−5.67181	+	3.07788i	−0.212114	+	0.115106i
$716$	−2.39903	−	2.39903i	−0.0896561	−	0.0896561i
$717$		0			0
$718$	9.38640			0.350297
$719$	10.9009	+	26.3171i	0.406535	+	0.981463i	0.986042	+	0.166496i	$0.0532452\pi$
$719$	10.9009	+	26.3171i	0.406535	+	0.981463i	−0.579507	+	0.814967i	$0.696755\pi$
$720$		0			0
$721$	−13.6554	+	32.9671i	−0.508554	+	1.22776i
$722$	−4.37751	−	4.37751i	−0.162914	−	0.162914i
$723$		0			0
$724$	−11.3249	+	27.3407i	−0.420886	+	1.01611i
$725$	−2.26518	+	1.55531i	−0.0841267	+	0.0577627i
$726$		0			0
$727$	−4.70692			−0.174570			−0.0872850	−	0.996183i	$-0.527819\pi$
$727$	−4.70692			−0.174570			−0.0872850	+	0.996183i	$0.527819\pi$
$728$	−2.72967	−	6.59000i	−0.101168	−	0.244242i
$729$		0			0
$730$	2.66754	+	4.91565i	0.0987302	+	0.181937i
$731$	29.7443	+	16.7177i	1.10013	+	0.618326i
$732$		0			0
$733$	18.9410	−	18.9410i	0.699601	−	0.699601i	−0.264723	−	0.964324i	$-0.585281\pi$
$733$	18.9410	−	18.9410i	0.699601	−	0.699601i	0.964324	+	0.264723i	$0.0852806\pi$
$734$	−3.46234	+	1.43415i	−0.127797	+	0.0529353i
$735$		0			0
$736$	−5.78257	−	13.9604i	−0.213148	−	0.514586i
$737$	5.72162	−	13.8132i	0.210759	−	0.508816i
$738$		0			0
$739$	−17.3148	+	17.3148i	−0.636935	+	0.636935i	−0.949798	−	0.312863i	$-0.898712\pi$
$739$	−17.3148	+	17.3148i	−0.636935	+	0.636935i	0.312863	+	0.949798i	$0.398712\pi$
$740$	−10.9527	+	36.9450i	−0.402629	+	1.35812i
$741$		0			0
$742$	−2.65381	+	6.40687i	−0.0974244	+	0.235203i
$743$	27.1524	−	11.2469i	0.996126	−	0.412609i	0.175751	−	0.984435i	$-0.443765\pi$
$743$	27.1524	−	11.2469i	0.996126	−	0.412609i	0.820375	+	0.571826i	$0.193765\pi$
$744$		0			0
$745$	16.3490	+	13.2452i	0.598979	+	0.485268i
$746$	6.55668	+	6.55668i	0.240057	+	0.240057i
$747$		0			0
$748$	2.52160	−	21.0282i	0.0921990	−	0.768868i
$749$	22.5855			0.825255
$750$		0			0
$751$	−10.6558	+	4.41379i	−0.388837	+	0.161062i	−0.568533	−	0.822661i	$-0.692489\pi$
$751$	−10.6558	+	4.41379i	−0.388837	+	0.161062i	0.179696	+	0.983722i	$0.442489\pi$
$752$	−28.1078			−1.02499
$753$		0			0
$754$	0.249294	+	0.103261i	0.00907876	+	0.00376055i
$755$	−19.2635	+	2.02027i	−0.701069	+	0.0735250i
$756$		0			0
$757$	−18.1908	−	18.1908i	−0.661157	−	0.661157i	0.294496	−	0.955653i	$-0.404848\pi$
$757$	−18.1908	−	18.1908i	−0.661157	−	0.661157i	−0.955653	+	0.294496i	$0.904848\pi$
$758$	6.77320	+	2.80555i	0.246014	+	0.101902i
$759$		0			0
$760$	−8.35552	−	6.76929i	−0.303086	−	0.245548i
$761$			19.0450i			0.690379i	0.938533	+	0.345190i	$0.112185\pi$
$761$			19.0450i			0.690379i	−0.938533	+	0.345190i	$0.887815\pi$
$762$		0			0
$763$	46.6657	−	46.6657i	1.68941	−	1.68941i
$764$	−29.1678			−1.05525
$765$		0			0
$766$	−10.6353			−0.384268
$767$	0.212704	−	0.212704i	0.00768031	−	0.00768031i
$768$		0			0
$769$		−	23.2434i		−	0.838178i	−0.907945	−	0.419089i	$-0.862349\pi$
$769$		−	23.2434i		−	0.838178i	0.907945	−	0.419089i	$-0.137651\pi$
$770$	7.98361	−	9.85438i	0.287709	−	0.355127i
$771$		0			0
$772$	−22.9124	−	9.49063i	−0.824636	−	0.341575i
$773$	27.6253	+	27.6253i	0.993611	+	0.993611i	0.999980	−	0.00636835i	$-0.00202712\pi$
$773$	27.6253	+	27.6253i	0.993611	+	0.993611i	−0.00636835	+	0.999980i	$0.502027\pi$
$774$		0			0
$775$	−21.3856	−	31.1464i	−0.768194	−	1.11881i
$776$	−7.82915	−	3.24294i	−0.281050	−	0.116415i
$777$		0			0
$778$	−2.38532			−0.0855179
$779$	−17.5700	+	7.27772i	−0.629509	+	0.260751i
$780$		0			0
$781$	10.5824			0.378666
$782$	−3.82329	−	4.86517i	−0.136721	−	0.173978i
$783$		0			0
$784$	−14.5222	−	14.5222i	−0.518651	−	0.518651i
$785$	24.9801	−	30.8337i	0.891580	−	1.10050i
$786$		0			0
$787$	−38.7192	+	16.0380i	−1.38019	+	0.571694i	−0.944533	−	0.328417i	$-0.893485\pi$
$787$	−38.7192	+	16.0380i	−1.38019	+	0.571694i	−0.435659	+	0.900112i	$0.643485\pi$
$788$	12.2598	−	29.5979i	0.436738	−	1.05438i
$789$		0			0
$790$	−3.94773	+	13.3163i	−0.140454	+	0.473771i
$791$	3.20623	−	3.20623i	0.114000	−	0.114000i
$792$		0			0
$793$	2.56033	−	6.18117i	0.0909198	−	0.219500i
$794$	6.16861	+	14.8923i	0.218916	+	0.528509i
$795$		0			0
$796$	8.82835	−	3.65682i	0.312913	−	0.129613i
$797$	−28.5463	+	28.5463i	−1.01116	+	1.01116i	−0.0112235	+	0.999937i	$0.503573\pi$
$797$	−28.5463	+	28.5463i	−1.01116	+	1.01116i	−0.999937	+	0.0112235i	$0.996427\pi$
$798$		0			0
$799$	−43.4684	+	12.1873i	−1.53780	+	0.431157i
$800$	21.0694	+	13.6962i	0.744914	+	0.484232i
$801$		0			0
$802$	−4.74680	−	11.4598i	−0.167615	−	0.404659i
$803$	−14.7006			−0.518774
$804$		0			0
$805$	2.71579	+	25.8954i	0.0957192	+	0.912693i
$806$	−1.41985	+	3.42782i	−0.0500120	+	0.120740i
$807$		0			0
$808$	−3.47782	−	3.47782i	−0.122349	−	0.122349i
$809$	−10.0781	+	24.3308i	−0.354329	+	0.855425i	0.641747	+	0.766917i	$0.278210\pi$
$809$	−10.0781	+	24.3308i	−0.354329	+	0.855425i	−0.996075	+	0.0885086i	$0.971790\pi$
$810$		0			0
$811$	6.77328	+	16.3522i	0.237842	+	0.574202i	0.997059	−	0.0766358i	$-0.0244179\pi$
$811$	6.77328	+	16.3522i	0.237842	+	0.574202i	−0.759217	+	0.650838i	$0.774418\pi$
$812$	3.72649			0.130774
$813$		0			0
$814$	10.1923	+	10.1923i	0.357241	+	0.357241i
$815$	4.52166	−	2.45374i	0.158387	−	0.0859507i
$816$		0			0
$817$			21.2563i			0.743663i
$818$	6.49534	−	6.49534i	0.227104	−	0.227104i
$819$		0			0
$820$	25.4766	−	13.8252i	0.889682	−	0.482797i
$821$	−7.26680	−	17.5436i	−0.253613	−	0.612276i	0.744877	−	0.667201i	$-0.232508\pi$
$821$	−7.26680	−	17.5436i	−0.253613	−	0.612276i	−0.998490	+	0.0549252i	$0.982508\pi$
$822$		0			0
$823$	35.4556	+	14.6862i	1.23591	+	0.511929i	0.902433	−	0.430831i	$-0.141780\pi$
$823$	35.4556	+	14.6862i	1.23591	+	0.511929i	0.333473	+	0.942760i	$0.391780\pi$
$824$	−12.1975	+	12.1975i	−0.424919	+	0.424919i
$825$		0			0
$826$	−0.226239	+	0.546190i	−0.00787187	+	0.0190044i
$827$	18.6234	−	44.9609i	0.647599	−	1.56344i	−0.168608	−	0.985683i	$-0.553927\pi$
$827$	18.6234	−	44.9609i	0.647599	−	1.56344i	0.816207	−	0.577759i	$-0.196073\pi$
$828$		0			0
$829$			51.7088i			1.79592i	0.440076	+	0.897960i	$0.354951\pi$
$829$			51.7088i			1.79592i	−0.440076	+	0.897960i	$0.645049\pi$
$830$	7.04337	+	5.70625i	0.244479	+	0.198067i
$831$		0			0
$832$			2.58262i			0.0895362i
$833$	−28.7552	−	16.1618i	−0.996310	−	0.559972i
$834$		0			0
$835$	−20.0717	−	5.95044i	−0.694609	−	0.205924i
$836$	12.1896	−	5.04911i	0.421587	−	0.174627i
$837$		0			0
$838$	1.39951	−	0.579697i	0.0483454	−	0.0200253i
$839$	−33.6766	−	13.9493i	−1.16265	−	0.481584i	−0.283891	−	0.958857i	$-0.591625\pi$
$839$	−33.6766	−	13.9493i	−1.16265	−	0.481584i	−0.878755	+	0.477273i	$0.841625\pi$
$840$		0			0
$841$	20.2925	−	20.2925i	0.699743	−	0.699743i
$842$	10.9599	+	10.9599i	0.377703	+	0.377703i
$843$		0			0
$844$	−8.91168	−	3.69134i	−0.306753	−	0.127061i
$845$	−16.9367	+	20.9055i	−0.582641	+	0.719169i
$846$		0			0
$847$	−3.54639	−	8.56175i	−0.121856	−	0.294185i
$848$	6.51135	−	6.51135i	0.223601	−	0.223601i
$849$		0			0
$850$	9.82151	+	3.07108i	0.336875	+	0.105337i
$851$	−29.5924			−1.01441
$852$		0			0
$853$	0.358129	+	0.864600i	0.0122621	+	0.0296033i	0.929892	−	0.367833i	$-0.119900\pi$
$853$	0.358129	+	0.864600i	0.0122621	+	0.0296033i	−0.917630	+	0.397436i	$0.869900\pi$
$854$			13.1490i			0.449949i
$855$		0			0
$856$	10.0870	+	4.17819i	0.344768	+	0.142808i
$857$	28.1526	+	11.6612i	0.961676	+	0.398339i	0.807607	−	0.589721i	$-0.200762\pi$
$857$	28.1526	+	11.6612i	0.961676	+	0.398339i	0.154069	+	0.988060i	$0.450762\pi$
$858$		0			0
$859$	0.697980	−	0.697980i	0.0238148	−	0.0238148i	−0.695099	−	0.718914i	$-0.744640\pi$
$859$	0.697980	−	0.697980i	0.0238148	−	0.0238148i	0.718914	+	0.695099i	$0.244640\pi$
$860$	−3.37925	−	32.2215i	−0.115232	−	1.09875i
$861$		0			0
$862$	−16.4095	+	6.79706i	−0.558911	+	0.231509i
$863$	26.0032			0.885159			0.442580	−	0.896729i	$-0.354063\pi$
$863$	26.0032			0.885159			0.442580	+	0.896729i	$0.354063\pi$
$864$		0			0
$865$	19.9375	+	5.91065i	0.677895	+	0.200968i
$866$	1.64669			0.0559568
$867$		0			0
$868$			51.2395i			1.73918i
$869$	−25.8146	−	25.8146i	−0.875702	−	0.875702i
$870$		0			0
$871$			5.01302i			0.169860i
$872$	29.4746	−	12.2088i	0.998136	−	0.413442i
$873$		0			0
$874$	1.47516	−	3.56136i	0.0498982	−	0.120465i
$875$	−28.0998	−	32.9459i	−0.949947	−	1.11377i
$876$		0			0
$877$	−31.2380	−	12.9392i	−1.05483	−	0.436925i	−0.213217	−	0.977005i	$-0.568394\pi$
$877$	−31.2380	−	12.9392i	−1.05483	−	0.436925i	−0.841614	+	0.540080i	$0.818394\pi$
$878$	−0.634168	+	1.53102i	−0.0214021	+	0.0516693i
$879$		0			0
$880$	−14.8018	+	8.03238i	−0.498968	+	0.270771i
$881$	−17.5111	+	7.25334i	−0.589965	+	0.244371i	−0.657635	−	0.753336i	$-0.728443\pi$
$881$	−17.5111	+	7.25334i	−0.589965	+	0.244371i	0.0676708	+	0.997708i	$0.478443\pi$
$882$		0			0
$883$		−	38.1002i		−	1.28217i	−0.767468	−	0.641087i	$-0.778484\pi$
$883$		−	38.1002i		−	1.28217i	0.767468	−	0.641087i	$-0.221516\pi$
$884$	1.91702	+	6.83740i	0.0644763	+	0.229967i
$885$		0			0
$886$	1.98466	+	1.98466i	0.0666761	+	0.0666761i
$887$	16.5026	+	39.8409i	0.554104	+	1.33773i	0.914371	+	0.404876i	$0.132685\pi$
$887$	16.5026	+	39.8409i	0.554104	+	1.33773i	−0.360267	+	0.932849i	$0.617315\pi$
$888$		0			0
$889$	−9.86852	−	23.8247i	−0.330980	−	0.799055i
$890$	−14.7332	+	1.54516i	−0.493859	+	0.0517937i
$891$		0			0
$892$	−32.9543	−	32.9543i	−1.10339	−	1.10339i
$893$	−19.8867	−	19.8867i	−0.665483	−	0.665483i
$894$		0			0
$895$	0.451949	+	4.30938i	0.0151070	+	0.144047i
$896$	−16.8407	−	40.6570i	−0.562608	−	1.35825i
$897$		0			0
$898$	1.17138	+	2.82796i	0.0390894	+	0.0943702i
$899$	−2.93629	−	2.93629i	−0.0979307	−	0.0979307i
$900$		0			0
$901$	7.24647	−	12.8930i	0.241415	−	0.429529i
$902$		−	10.8425i		−	0.361017i
$903$		0			0
$904$	2.02509	−	0.838820i	0.0673535	−	0.0278987i
$905$	33.2189	−	18.0267i	1.10423	−	0.599226i
$906$		0			0
$907$	5.81633	−	14.0419i	0.193128	−	0.466253i	−0.797419	−	0.603426i	$-0.793802\pi$
$907$	5.81633	−	14.0419i	0.193128	−	0.466253i	0.990547	+	0.137174i	$0.0438018\pi$
$908$	−12.4066	−	5.13899i	−0.411728	−	0.170543i
$909$		0			0
$910$	−1.20865	+	4.07694i	−0.0400663	+	0.135149i
$911$	8.93184	−	21.5634i	0.295925	−	0.714426i	−0.704066	−	0.710135i	$-0.748634\pi$
$911$	8.93184	−	21.5634i	0.295925	−	0.714426i	0.999991	−	0.00429141i	$-0.00136600\pi$
$912$		0			0
$913$	−22.0130	+	9.11810i	−0.728525	+	0.301765i
$914$		−	14.1729i		−	0.468796i
$915$		0			0
$916$	−11.5553	−	11.5553i	−0.381797	−	0.381797i
$917$		−	47.5757i		−	1.57109i
$918$		0			0
$919$	11.1867			0.369017			0.184508	−	0.982831i	$-0.440931\pi$
$919$	11.1867			0.369017			0.184508	+	0.982831i	$0.440931\pi$
$920$	−3.57759	+	12.0677i	−0.117950	+	0.397861i
$921$		0			0
$922$	10.3837			0.341970
$923$	−3.27807	+	1.35782i	−0.107899	+	0.0446932i
$924$		0			0
$925$	40.5709	−	27.8566i	1.33396	−	0.915920i
$926$	11.1040	−	11.1040i	0.364899	−	0.364899i
$927$		0			0
$928$	2.55174	+	1.05697i	0.0837651	+	0.0346966i
$929$	−0.819025	−	0.339251i	−0.0268713	−	0.0111305i	0.369207	−	0.929347i	$-0.379629\pi$
$929$	−0.819025	−	0.339251i	−0.0268713	−	0.0111305i	−0.396079	+	0.918217i	$0.629629\pi$
$930$		0			0
$931$		−	20.5494i		−	0.673480i
$932$	−2.61238	−	6.30685i	−0.0855714	−	0.206588i
$933$		0			0
$934$	−0.741696			−0.0242690
$935$	−19.4080	+	18.8400i	−0.634711	+	0.616132i
$936$		0			0
$937$	5.65400	−	5.65400i	0.184708	−	0.184708i	−0.608696	−	0.793404i	$-0.708307\pi$
$937$	5.65400	−	5.65400i	0.184708	−	0.184708i	0.793404	+	0.608696i	$0.208307\pi$
$938$	−3.77030	−	9.10232i	−0.123105	−	0.297201i
$939$		0			0
$940$	33.3070	+	26.9840i	1.08635	+	0.880119i
$941$	42.8352	+	17.7429i	1.39639	+	0.578403i	0.948812	−	0.315842i	$-0.102287\pi$
$941$	42.8352	+	17.7429i	1.39639	+	0.578403i	0.447577	+	0.894245i	$0.352287\pi$
$942$		0			0
$943$	15.7401	+	15.7401i	0.512568	+	0.512568i
$944$	0.555097	−	0.555097i	0.0180669	−	0.0180669i
$945$		0			0
$946$	−11.1964	−	4.63770i	−0.364026	−	0.150785i
$947$	−29.0189	+	12.0200i	−0.942987	+	0.390598i	−0.800591	−	0.599212i	$-0.795481\pi$
$947$	−29.0189	+	12.0200i	−0.942987	+	0.390598i	−0.142396	+	0.989810i	$0.545481\pi$
$948$		0			0
$949$	4.55378	−	1.88624i	0.147822	−	0.0612299i
$950$	1.33003	+	6.27123i	0.0431518	+	0.203466i
$951$		0			0
$952$	−18.4736	−	23.5078i	−0.598733	−	0.761892i
$953$			53.1529i			1.72179i	0.508781	+	0.860896i	$0.330096\pi$
$953$			53.1529i			1.72179i	−0.508781	+	0.860896i	$0.669904\pi$
$954$		0			0
$955$	28.9445	+	23.4496i	0.936621	+	0.758811i
$956$		−	39.6212i		−	1.28144i
$957$		0			0
$958$	−2.79524	+	6.74831i	−0.0903102	+	0.218028i
$959$	14.3615	−	34.6717i	0.463757	−	1.11961i
$960$		0			0
$961$	18.4539	−	18.4539i	0.595288	−	0.595288i
$962$	−4.46503	−	1.84948i	−0.143958	−	0.0596295i
$963$		0			0
$964$	1.93767	+	4.67796i	0.0624083	+	0.150667i
$965$	15.1069	+	27.8385i	0.486309	+	0.896154i
$966$		0			0
$967$	−20.7371	+	20.7371i	−0.666860	+	0.666860i	−0.956988	−	0.290128i	$-0.906302\pi$
$967$	−20.7371	+	20.7371i	−0.666860	+	0.666860i	0.290128	+	0.956988i	$0.406302\pi$
$968$		−	4.47988i		−	0.143989i
$969$		0			0
$970$	2.40956	+	4.44025i	0.0773663	+	0.142568i
$971$	23.8303	+	23.8303i	0.764751	+	0.764751i	0.977177	−	0.212426i	$-0.0681365\pi$
$971$	23.8303	+	23.8303i	0.764751	+	0.764751i	−0.212426	+	0.977177i	$0.568136\pi$
$972$		0			0
$973$	−5.54115			−0.177641
$974$	0.644633	+	1.55628i	0.0206554	+	0.0498665i
$975$		0			0
$976$	6.68171	−	16.1311i	0.213876	−	0.516343i
$977$	40.9965	+	40.9965i	1.31160	+	1.31160i	0.920239	+	0.391356i	$0.127994\pi$
$977$	40.9965	+	40.9965i	1.31160	+	1.31160i	0.391356	+	0.920239i	$0.372006\pi$
$978$		0			0
$979$	14.9011	−	35.9745i	0.476243	−	1.14975i
$980$	3.26688	+	31.1501i	0.104357	+	0.995052i
$981$		0			0
$982$	3.78212			0.120692
$983$	7.84974	+	18.9510i	0.250368	+	0.604441i	0.998234	−	0.0594084i	$-0.0189214\pi$
$983$	7.84974	+	18.9510i	0.250368	+	0.604441i	−0.747866	+	0.663850i	$0.768921\pi$
$984$		0			0
$985$	−35.9613	+	19.5149i	−1.14582	+	0.621795i
$986$	1.12297	+	0.134661i	0.0357627	+	0.00428849i
$987$		0			0
$988$	−3.12810	+	3.12810i	−0.0995181	+	0.0995181i
$989$	22.9863	−	9.52125i	0.730923	−	0.302758i
$990$		0			0
$991$	11.7383	+	28.3388i	0.372881	+	0.900213i	0.993260	+	0.115911i	$0.0369788\pi$
$991$	11.7383	+	28.3388i	0.372881	+	0.900213i	−0.620379	+	0.784302i	$0.713021\pi$
$992$	−14.5334	+	35.0867i	−0.461436	+	1.11400i
$993$		0			0
$994$	4.93088	−	4.93088i	0.156398	−	0.156398i
$995$	−11.7007	−	3.46878i	−0.370936	−	0.109968i
$996$		0			0
$997$	−1.88809	+	4.55826i	−0.0597965	+	0.144361i	−0.950954	−	0.309333i	$-0.899894\pi$
$997$	−1.88809	+	4.55826i	−0.0597965	+	0.144361i	0.891157	+	0.453694i	$0.149894\pi$
$998$	−3.93341	+	1.62927i	−0.124510	+	0.0515738i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.bh.b.19.4		24
3.2	odd	2		85.2.m.a.19.3	yes	24
5.4	even	2	inner	765.2.bh.b.19.3		24
15.2	even	4		425.2.m.e.376.3		24
15.8	even	4		425.2.m.e.376.4		24
15.14	odd	2		85.2.m.a.19.4	yes	24
17.9	even	8	inner	765.2.bh.b.604.3		24
51.14	even	16		1445.2.b.i.579.16		24
51.20	even	16		1445.2.b.i.579.15		24
51.26	odd	8		85.2.m.a.9.4	yes	24
85.9	even	8	inner	765.2.bh.b.604.4		24
255.14	even	16		1445.2.b.i.579.9		24
255.77	even	8		425.2.m.e.26.3		24
255.122	odd	16		7225.2.a.by.1.9		24
255.128	even	8		425.2.m.e.26.4		24
255.167	odd	16		7225.2.a.by.1.10		24
255.173	odd	16		7225.2.a.by.1.16		24
255.179	odd	8		85.2.m.a.9.3	✓	24
255.218	odd	16		7225.2.a.by.1.15		24
255.224	even	16		1445.2.b.i.579.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.m.a.9.3	✓	24	255.179	odd	8
85.2.m.a.9.4	yes	24	51.26	odd	8
85.2.m.a.19.3	yes	24	3.2	odd	2
85.2.m.a.19.4	yes	24	15.14	odd	2
425.2.m.e.26.3		24	255.77	even	8
425.2.m.e.26.4		24	255.128	even	8
425.2.m.e.376.3		24	15.2	even	4
425.2.m.e.376.4		24	15.8	even	4
765.2.bh.b.19.3		24	5.4	even	2	inner
765.2.bh.b.19.4		24	1.1	even	1	trivial
765.2.bh.b.604.3		24	17.9	even	8	inner
765.2.bh.b.604.4		24	85.9	even	8	inner
1445.2.b.i.579.9		24	255.14	even	16
1445.2.b.i.579.10		24	255.224	even	16
1445.2.b.i.579.15		24	51.20	even	16
1445.2.b.i.579.16		24	51.14	even	16
7225.2.a.by.1.9		24	255.122	odd	16
7225.2.a.by.1.10		24	255.167	odd	16
7225.2.a.by.1.15		24	255.218	odd	16
7225.2.a.by.1.16		24	255.173	odd	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.bh (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.352960 - 0.352960i) q^{2} +1.75084i q^{4} +(1.40760 - 1.73743i) q^{5} +(3.57820 + 1.48214i) q^{7} +(1.32390 + 1.32390i) q^{8} +O(q^{10})\)	\(q+(0.352960 - 0.352960i) q^{2} +1.75084i q^{4} +(1.40760 - 1.73743i) q^{5} +(3.57820 + 1.48214i) q^{7} +(1.32390 + 1.32390i) q^{8} +(-0.116419 - 1.11007i) q^{10} +(2.71049 + 1.12272i) q^{11} -0.983677 q^{13} +(1.78610 - 0.739825i) q^{14} -2.56711 q^{16} +(-3.97002 + 1.11308i) q^{17} +(-1.81628 - 1.81628i) q^{19} +(3.04196 + 2.46447i) q^{20} +(1.35297 - 0.560418i) q^{22} +(-1.15054 + 2.77766i) q^{23} +(-1.03735 - 4.89121i) q^{25} +(-0.347198 + 0.347198i) q^{26} +(-2.59499 + 6.26485i) q^{28} +(-0.210302 - 0.507715i) q^{29} +(6.98112 - 2.89167i) q^{31} +(-3.55388 + 3.55388i) q^{32} +(-1.00838 + 1.79413i) q^{34} +(7.61178 - 4.13063i) q^{35} +(3.76666 + 9.09352i) q^{37} -1.28214 q^{38} +(4.16369 - 0.436669i) q^{40} +(2.83334 - 6.84028i) q^{41} +(-5.85161 - 5.85161i) q^{43} +(-1.96570 + 4.74563i) q^{44} +(0.574306 + 1.38650i) q^{46} +10.9492 q^{47} +(5.65702 + 5.65702i) q^{49} +(-2.09254 - 1.36026i) q^{50} -1.72226i q^{52} +(-2.53645 + 2.53645i) q^{53} +(5.76592 - 3.12895i) q^{55} +(2.77496 + 6.69936i) q^{56} +(-0.253431 - 0.104975i) q^{58} +(-0.216234 + 0.216234i) q^{59} +(-2.60281 + 6.28374i) q^{61} +(1.44341 - 3.48470i) q^{62} -2.62548i q^{64} +(-1.38462 + 1.70907i) q^{65} -5.09621i q^{67} +(-1.94883 - 6.95086i) q^{68} +(1.22870 - 4.14460i) q^{70} +(3.33246 - 1.38035i) q^{71} +(-4.62935 + 1.91754i) q^{73} +(4.53912 + 1.88017i) q^{74} +(3.18001 - 3.18001i) q^{76} +(8.03464 + 8.03464i) q^{77} +(-11.4965 - 4.76199i) q^{79} +(-3.61346 + 4.46019i) q^{80} +(-1.41429 - 3.41440i) q^{82} +(-5.74272 + 5.74272i) q^{83} +(-3.65428 + 8.46441i) q^{85} -4.13077 q^{86} +(2.10204 + 5.07477i) q^{88} -13.2723i q^{89} +(-3.51979 - 1.45795i) q^{91} +(-4.86323 - 2.01442i) q^{92} +(3.86462 - 3.86462i) q^{94} +(-5.71224 + 0.599074i) q^{95} +(-4.18163 + 1.73209i) q^{97} +3.99340 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 16 q^{10} + 24 q^{14} + 8 q^{16} - 24 q^{19} + 8 q^{20} + 16 q^{25} + 16 q^{26} - 24 q^{29} - 24 q^{31} + 8 q^{34} - 8 q^{35} + 16 q^{40} + 48 q^{41} - 72 q^{44} - 16 q^{46} + 48 q^{49} - 16 q^{50} - 24 q^{56} + 48 q^{59} + 16 q^{61} - 24 q^{65} + 32 q^{70} - 16 q^{71} + 64 q^{74} - 24 q^{76} - 72 q^{79} + 64 q^{80} - 24 q^{85} - 8 q^{91} - 40 q^{94} + 88 q^{95}+O(q^{100}) \) 24 * q - 16 * q^10 + 24 * q^14 + 8 * q^16 - 24 * q^19 + 8 * q^20 + 16 * q^25 + 16 * q^26 - 24 * q^29 - 24 * q^31 + 8 * q^34 - 8 * q^35 + 16 * q^40 + 48 * q^41 - 72 * q^44 - 16 * q^46 + 48 * q^49 - 16 * q^50 - 24 * q^56 + 48 * q^59 + 16 * q^61 - 24 * q^65 + 32 * q^70 - 16 * q^71 + 64 * q^74 - 24 * q^76 - 72 * q^79 + 64 * q^80 - 24 * q^85 - 8 * q^91 - 40 * q^94 + 88 * q^95

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