LMFDB - Embedded newform 784.2.bb.b.111.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(111,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 11]))

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

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

chi := DirichletCharacter("784.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.bb (of order $14$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.19
Character	$\chi$	$=$	784.111
Dual form			784.2.bb.b.671.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94065 + 2.43350i) q^{3} +(-2.10945 + 1.68223i) q^{5} +(1.58011 + 2.12208i) q^{7} +(-1.48823 + 6.52037i) q^{9} +O(q^{10})$	\(q+(1.94065 + 2.43350i) q^{3} +(-2.10945 + 1.68223i) q^{5} +(1.58011 + 2.12208i) q^{7} +(-1.48823 + 6.52037i) q^{9} +(3.26810 - 0.745923i) q^{11} +(2.27789 - 0.519914i) q^{13} +(-8.18742 - 1.86872i) q^{15} +(0.798533 - 1.65817i) q^{17} +2.04246 q^{19} +(-2.09764 + 7.96343i) q^{21} +(-2.42503 - 5.03562i) q^{23} +(0.507276 - 2.22252i) q^{25} +(-10.3425 + 4.98068i) q^{27} +(-7.15128 - 3.44388i) q^{29} -8.39595 q^{31} +(8.15745 + 6.50535i) q^{33} +(-6.90301 - 1.81831i) q^{35} +(7.74463 + 3.72962i) q^{37} +(5.68581 + 4.53428i) q^{39} +(3.65752 - 2.91677i) q^{41} +(-4.01452 - 3.20147i) q^{43} +(-7.82941 - 16.2579i) q^{45} +(2.35662 + 10.3250i) q^{47} +(-2.00648 + 6.70627i) q^{49} +(5.58483 - 1.27470i) q^{51} +(-1.71348 + 0.825167i) q^{53} +(-5.63908 + 7.07119i) q^{55} +(3.96370 + 4.97032i) q^{57} +(7.26876 - 9.11474i) q^{59} +(4.62760 - 9.60931i) q^{61} +(-16.1883 + 7.14478i) q^{63} +(-3.93048 + 4.92867i) q^{65} +6.97459i q^{67} +(7.54805 - 15.6737i) q^{69} +(-3.45857 - 7.18179i) q^{71} +(7.82301 + 1.78555i) q^{73} +(6.39295 - 3.07868i) q^{75} +(6.74688 + 5.75654i) q^{77} -9.68836i q^{79} +(-14.1145 - 6.79718i) q^{81} +(3.58252 - 15.6960i) q^{83} +(1.10496 + 4.84114i) q^{85} +(-5.49747 - 24.0860i) q^{87} +(11.3721 + 2.59562i) q^{89} +(4.70263 + 4.01235i) q^{91} +(-16.2936 - 20.4316i) q^{93} +(-4.30846 + 3.43588i) q^{95} +17.3194i q^{97} +22.4193i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 24 q^{9}+O(q^{10}) $ 120 * q - 24 * q^9	$ 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) $ 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{14}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.94065	+	2.43350i	1.12044	+	1.40498i	0.903390	+	0.428821i	$0.141071\pi$
$3$	1.94065	+	2.43350i	1.12044	+	1.40498i	0.217046	+	0.976161i	$0.430358\pi$
$4$		0			0
$5$	−2.10945	+	1.68223i	−0.943375	+	0.752316i	−0.968924	−	0.247357i	$-0.920438\pi$
$5$	−2.10945	+	1.68223i	−0.943375	+	0.752316i	0.0255496	+	0.999674i	$0.491866\pi$
$6$		0			0
$7$	1.58011	+	2.12208i	0.597227	+	0.802072i
$7$	1.58011	+	2.12208i	0.597227	+	0.802072i
$8$		0			0
$9$	−1.48823	+	6.52037i	−0.496077	+	2.17346i
$10$		0			0
$11$	3.26810	−	0.745923i	0.985370	−	0.224904i	0.300669	−	0.953729i	$-0.402790\pi$
$11$	3.26810	−	0.745923i	0.985370	−	0.224904i	0.684701	+	0.728824i	$0.259933\pi$
$12$		0			0
$13$	2.27789	−	0.519914i	0.631773	−	0.144198i	0.105370	−	0.994433i	$-0.466397\pi$
$13$	2.27789	−	0.519914i	0.631773	−	0.144198i	0.526403	+	0.850235i	$0.323540\pi$
$14$		0			0
$15$	−8.18742	−	1.86872i	−2.11398	−	0.482503i
$16$		0			0
$17$	0.798533	−	1.65817i	0.193673	−	0.402166i	−0.781407	−	0.624022i	$-0.785497\pi$
$17$	0.798533	−	1.65817i	0.193673	−	0.402166i	0.975079	+	0.221857i	$0.0712117\pi$
$18$		0			0
$19$	2.04246			0.468572			0.234286	−	0.972168i	$-0.424725\pi$
$19$	2.04246			0.468572			0.234286	+	0.972168i	$0.424725\pi$
$20$		0			0
$21$	−2.09764	+	7.96343i	−0.457743	+	1.73776i
$22$		0			0
$23$	−2.42503	−	5.03562i	−0.505653	−	1.05000i	−0.985029	−	0.172390i	$-0.944851\pi$
$23$	−2.42503	−	5.03562i	−0.505653	−	1.05000i	0.479376	−	0.877610i	$-0.340863\pi$
$24$		0			0
$25$	0.507276	−	2.22252i	0.101455	−	0.444504i
$26$		0			0
$27$	−10.3425	+	4.98068i	−1.99041	+	0.958533i
$28$		0			0
$29$	−7.15128	−	3.44388i	−1.32796	−	0.639512i	−0.370703	−	0.928751i	$-0.620883\pi$
$29$	−7.15128	−	3.44388i	−1.32796	−	0.639512i	−0.957257	+	0.289240i	$0.906598\pi$
$30$		0			0
$31$	−8.39595			−1.50796			−0.753979	−	0.656899i	$-0.771868\pi$
$31$	−8.39595			−1.50796			−0.753979	+	0.656899i	$0.771868\pi$
$32$		0			0
$33$	8.15745	+	6.50535i	1.42003	+	1.13244i
$34$		0			0
$35$	−6.90301	−	1.81831i	−1.16682	−	0.307351i
$36$		0			0
$37$	7.74463	+	3.72962i	1.27321	+	0.613145i	0.943636	−	0.330985i	$-0.107381\pi$
$37$	7.74463	+	3.72962i	1.27321	+	0.613145i	0.329573	+	0.944130i	$0.393095\pi$
$38$		0			0
$39$	5.68581	+	4.53428i	0.910458	+	0.726066i
$40$		0			0
$41$	3.65752	−	2.91677i	0.571208	−	0.455523i	−0.294796	−	0.955560i	$-0.595252\pi$
$41$	3.65752	−	2.91677i	0.571208	−	0.455523i	0.866004	+	0.500037i	$0.166680\pi$
$42$		0			0
$43$	−4.01452	−	3.20147i	−0.612209	−	0.488220i	0.267611	−	0.963527i	$-0.413766\pi$
$43$	−4.01452	−	3.20147i	−0.612209	−	0.488220i	−0.879820	+	0.475307i	$0.842337\pi$
$44$		0			0
$45$	−7.82941	−	16.2579i	−1.16714	−	2.42359i
$46$		0			0
$47$	2.35662	+	10.3250i	0.343748	+	1.50606i	0.791092	+	0.611697i	$0.209513\pi$
$47$	2.35662	+	10.3250i	0.343748	+	1.50606i	−0.447344	+	0.894362i	$0.647630\pi$
$48$		0			0
$49$	−2.00648	+	6.70627i	−0.286640	+	0.958038i
$50$		0			0
$51$	5.58483	−	1.27470i	0.782033	−	0.178494i
$52$		0			0
$53$	−1.71348	+	0.825167i	−0.235364	+	0.113345i	−0.547849	−	0.836577i	$-0.684553\pi$
$53$	−1.71348	+	0.825167i	−0.235364	+	0.113345i	0.312485	+	0.949923i	$0.398839\pi$
$54$		0			0
$55$	−5.63908	+	7.07119i	−0.760374	+	0.953479i
$56$		0			0
$57$	3.96370	+	4.97032i	0.525005	+	0.658335i
$58$		0			0
$59$	7.26876	−	9.11474i	0.946313	−	1.18664i	−0.0359928	−	0.999352i	$-0.511459\pi$
$59$	7.26876	−	9.11474i	0.946313	−	1.18664i	0.982305	−	0.187286i	$-0.0599692\pi$
$60$		0			0
$61$	4.62760	−	9.60931i	0.592503	−	1.23035i	−0.362009	−	0.932175i	$-0.617909\pi$
$61$	4.62760	−	9.60931i	0.592503	−	1.23035i	0.954512	−	0.298171i	$-0.0963766\pi$
$62$		0			0
$63$	−16.1883	+	7.14478i	−2.03954	+	0.900157i
$64$		0			0
$65$	−3.93048	+	4.92867i	−0.487516	+	0.611326i
$66$		0			0
$67$			6.97459i			0.852082i	0.904704	+	0.426041i	$0.140092\pi$
$67$			6.97459i			0.852082i	−0.904704	+	0.426041i	$0.859908\pi$
$68$		0			0
$69$	7.54805	−	15.6737i	0.908679	−	1.88689i
$70$		0			0
$71$	−3.45857	−	7.18179i	−0.410456	−	0.852322i	−0.999037	−	0.0438828i	$-0.986027\pi$
$71$	−3.45857	−	7.18179i	−0.410456	−	0.852322i	0.588580	−	0.808439i	$-0.299687\pi$
$72$		0			0
$73$	7.82301	+	1.78555i	0.915614	+	0.208983i	0.654268	−	0.756262i	$-0.272977\pi$
$73$	7.82301	+	1.78555i	0.915614	+	0.208983i	0.261346	+	0.965245i	$0.415834\pi$
$74$		0			0
$75$	6.39295	−	3.07868i	0.738195	−	0.355496i
$76$		0			0
$77$	6.74688	+	5.75654i	0.768879	+	0.656019i
$78$		0			0
$79$		−	9.68836i		−	1.09003i	−0.838428	−	0.545013i	$-0.816525\pi$
$79$		−	9.68836i		−	1.09003i	0.838428	−	0.545013i	$-0.183475\pi$
$80$		0			0
$81$	−14.1145	−	6.79718i	−1.56828	−	0.755243i
$82$		0			0
$83$	3.58252	−	15.6960i	0.393232	−	1.72286i	−0.259913	−	0.965632i	$-0.583694\pi$
$83$	3.58252	−	15.6960i	0.393232	−	1.72286i	0.653146	−	0.757232i	$-0.273449\pi$
$84$		0			0
$85$	1.10496	+	4.84114i	0.119850	+	0.525096i
$86$		0			0
$87$	−5.49747	−	24.0860i	−0.589391	−	2.58229i
$88$		0			0
$89$	11.3721	+	2.59562i	1.20544	+	0.275135i	0.777624	−	0.628729i	$-0.216425\pi$
$89$	11.3721	+	2.59562i	1.20544	+	0.275135i	0.427820	+	0.903864i	$0.359282\pi$
$90$		0			0
$91$	4.70263	+	4.01235i	0.492970	+	0.420609i
$92$		0			0
$93$	−16.2936	−	20.4316i	−1.68957	−	2.11865i
$94$		0			0
$95$	−4.30846	+	3.43588i	−0.442039	+	0.352514i
$96$		0			0
$97$			17.3194i			1.75852i	0.476344	+	0.879259i	$0.341962\pi$
$97$			17.3194i			1.75852i	−0.476344	+	0.879259i	$0.658038\pi$
$98$		0			0
$99$			22.4193i			2.25323i
$100$		0			0
$101$	−2.65272	+	2.11547i	−0.263955	+	0.210497i	−0.746520	−	0.665363i	$-0.768277\pi$
$101$	−2.65272	+	2.11547i	−0.263955	+	0.210497i	0.482565	+	0.875860i	$0.339705\pi$
$102$		0			0
$103$	7.23745	+	9.07547i	0.713127	+	0.894233i	0.997927	−	0.0643540i	$-0.0204987\pi$
$103$	7.23745	+	9.07547i	0.713127	+	0.894233i	−0.284800	+	0.958587i	$0.591927\pi$
$104$		0			0
$105$	−8.97146	−	20.3272i	−0.875525	−	1.98373i
$106$		0			0
$107$	−2.03082	−	0.463521i	−0.196327	−	0.0448103i	0.123227	−	0.992379i	$-0.460676\pi$
$107$	−2.03082	−	0.463521i	−0.196327	−	0.0448103i	−0.319553	+	0.947568i	$0.603533\pi$
$108$		0			0
$109$	1.26467	+	5.54086i	0.121133	+	0.530718i	0.998686	+	0.0512393i	$0.0163171\pi$
$109$	1.26467	+	5.54086i	0.121133	+	0.530718i	−0.877553	+	0.479479i	$0.840826\pi$
$110$		0			0
$111$	5.95360	+	26.0844i	0.565091	+	2.47583i
$112$		0			0
$113$	−2.76489	+	12.1138i	−0.260099	+	1.13957i	0.661045	+	0.750346i	$0.270113\pi$
$113$	−2.76489	+	12.1138i	−0.260099	+	1.13957i	−0.921144	+	0.389222i	$0.872744\pi$
$114$		0			0
$115$	13.5865	+	6.54294i	1.26695	+	0.610132i
$116$		0			0
$117$			15.6265i			1.44467i
$118$		0			0
$119$	4.78055	−	0.925545i	0.438232	−	0.0848446i
$120$		0			0
$121$	0.213429	−	0.102782i	0.0194027	−	0.00934383i
$122$		0			0
$123$	14.1959	+	3.24013i	1.28000	+	0.292153i
$124$		0			0
$125$	−3.18456	−	6.61281i	−0.284836	−	0.591468i
$126$		0			0
$127$	3.69502	−	7.67278i	0.327880	−	0.680849i	−0.670240	−	0.742144i	$-0.733809\pi$
$127$	3.69502	−	7.67278i	0.327880	−	0.680849i	0.998120	+	0.0612951i	$0.0195231\pi$
$128$		0			0
$129$		−	15.9823i		−	1.40716i
$130$		0			0
$131$	4.63101	−	5.80710i	0.404613	−	0.507369i	−0.537224	−	0.843440i	$-0.680527\pi$
$131$	4.63101	−	5.80710i	0.404613	−	0.507369i	0.941837	+	0.336071i	$0.109098\pi$
$132$		0			0
$133$	3.22732	+	4.33427i	0.279844	+	0.375828i
$134$		0			0
$135$	13.4383	−	27.9050i	1.15659	−	2.40168i
$136$		0			0
$137$	−5.55628	+	6.96736i	−0.474705	+	0.595261i	−0.960316	−	0.278914i	$-0.910026\pi$
$137$	−5.55628	+	6.96736i	−0.474705	+	0.595261i	0.485611	+	0.874175i	$0.338597\pi$
$138$		0			0
$139$	−0.0777188	−	0.0974562i	−0.00659202	−	0.00826613i	0.778525	−	0.627614i	$-0.215968\pi$
$139$	−0.0777188	−	0.0974562i	−0.00659202	−	0.00826613i	−0.785117	+	0.619348i	$0.787397\pi$
$140$		0			0
$141$	−20.5526	+	25.7721i	−1.73084	+	2.17040i
$142$		0			0
$143$	7.05657	−	3.39826i	0.590100	−	0.284177i
$144$		0			0
$145$	20.8787	−	4.76542i	1.73388	−	0.395746i
$146$		0			0
$147$	−20.2136	+	8.13177i	−1.66719	+	0.670697i
$148$		0			0
$149$	−0.00979794	−	0.0429276i	−0.000802679	−	0.00351677i	0.974525	−	0.224279i	$-0.0720027\pi$
$149$	−0.00979794	−	0.0429276i	−0.000802679	−	0.00351677i	−0.975328	+	0.220762i	$0.929146\pi$
$150$		0			0
$151$	5.87865	+	12.2072i	0.478398	+	0.993404i	0.990885	+	0.134709i	$0.0430100\pi$
$151$	5.87865	+	12.2072i	0.478398	+	0.993404i	−0.512487	+	0.858695i	$0.671276\pi$
$152$		0			0
$153$	9.62349	+	7.67447i	0.778013	+	0.620444i
$154$		0			0
$155$	17.7108	−	14.1239i	1.42257	−	1.13446i
$156$		0			0
$157$	9.89054	+	7.88744i	0.789351	+	0.629486i	0.932891	−	0.360158i	$-0.117277\pi$
$157$	9.89054	+	7.88744i	0.789351	+	0.629486i	−0.143540	+	0.989644i	$0.545849\pi$
$158$		0			0
$159$	−5.33330	−	2.56838i	−0.422958	−	0.203686i
$160$		0			0
$161$	6.85419	−	13.1030i	0.540186	−	1.03266i
$162$		0			0
$163$	−13.4718	−	10.7434i	−1.05519	−	0.841485i	−0.0674692	−	0.997721i	$-0.521492\pi$
$163$	−13.4718	−	10.7434i	−1.05519	−	0.841485i	−0.987720	+	0.156236i	$0.950064\pi$
$164$		0			0
$165$	−28.1512			−2.19157
$166$		0			0
$167$	−3.46733	−	1.66978i	−0.268310	−	0.129211i	0.294892	−	0.955531i	$-0.404716\pi$
$167$	−3.46733	−	1.66978i	−0.268310	−	0.129211i	−0.563202	+	0.826319i	$0.690431\pi$
$168$		0			0
$169$	−6.79412	+	3.27187i	−0.522624	+	0.251683i
$170$		0			0
$171$	−3.03965	+	13.3176i	−0.232448	+	1.01842i
$172$		0			0
$173$	−1.23542	−	2.56538i	−0.0939274	−	0.195042i	0.848712	−	0.528856i	$-0.177379\pi$
$173$	−1.23542	−	2.56538i	−0.0939274	−	0.195042i	−0.942639	+	0.333813i	$0.891664\pi$
$174$		0			0
$175$	5.51793	−	2.43536i	0.417116	−	0.184096i
$176$		0			0
$177$	36.2869			2.72749
$178$		0			0
$179$	3.06888	−	6.37259i	0.229379	−	0.476310i	−0.754234	−	0.656606i	$-0.771991\pi$
$179$	3.06888	−	6.37259i	0.229379	−	0.476310i	0.983612	+	0.180296i	$0.0577057\pi$
$180$		0			0
$181$	0.318569	+	0.0727113i	0.0236790	+	0.00540459i	0.234344	−	0.972154i	$-0.424706\pi$
$181$	0.318569	+	0.0727113i	0.0236790	+	0.00540459i	−0.210665	+	0.977558i	$0.567563\pi$
$182$		0			0
$183$	32.3648	−	7.38706i	2.39248	−	0.546067i
$184$		0			0
$185$	−22.6110	+	5.16081i	−1.66239	+	0.379430i
$186$		0			0
$187$	1.37282	−	6.01471i	0.100390	−	0.439840i
$188$		0			0
$189$	−26.9118	−	14.0776i	−1.95754	−	1.02399i
$190$		0			0
$191$	−15.6726	+	12.4985i	−1.13403	+	0.904357i	−0.996286	−	0.0861113i	$-0.972556\pi$
$191$	−15.6726	+	12.4985i	−1.13403	+	0.904357i	−0.137742	+	0.990468i	$0.543985\pi$
$192$		0			0
$193$	−11.5441	−	14.4758i	−0.830963	−	1.04199i	−0.998424	−	0.0561156i	$-0.982128\pi$
$193$	−11.5441	−	14.4758i	−0.830963	−	1.04199i	0.167462	−	0.985879i	$-0.446443\pi$
$194$		0			0
$195$	−19.6216			−1.40513
$196$		0			0
$197$	10.5154			0.749190			0.374595	−	0.927189i	$-0.377782\pi$
$197$	10.5154			0.749190			0.374595	+	0.927189i	$0.377782\pi$
$198$		0			0
$199$	6.47227	+	8.11597i	0.458807	+	0.575326i	0.956391	−	0.292090i	$-0.0943507\pi$
$199$	6.47227	+	8.11597i	0.458807	+	0.575326i	−0.497584	+	0.867416i	$0.665779\pi$
$200$		0			0
$201$	−16.9727	+	13.5352i	−1.19716	+	0.954703i
$202$		0			0
$203$	−3.99165	−	20.6173i	−0.280159	−	1.44705i
$204$		0			0
$205$	−2.80867	+	12.3056i	−0.196166	+	0.859458i
$206$		0			0
$207$	36.4431	−	8.31791i	2.53297	−	0.578134i
$208$		0			0
$209$	6.67496	−	1.52352i	0.461716	−	0.105384i
$210$		0			0
$211$	−7.88256	−	1.79914i	−0.542658	−	0.123858i	−0.0575992	−	0.998340i	$-0.518345\pi$
$211$	−7.88256	−	1.79914i	−0.542658	−	0.123858i	−0.485059	+	0.874482i	$0.661202\pi$
$212$		0			0
$213$	10.7650	−	22.3538i	0.737606	−	1.53166i
$214$		0			0
$215$	13.8541			0.944838
$216$		0			0
$217$	−13.2666	−	17.8169i	−0.900593	−	1.20949i
$218$		0			0
$219$	10.8366	+	22.5024i	0.732269	+	1.52057i
$220$		0			0
$221$	0.956866	−	4.19230i	0.0643657	−	0.282005i
$222$		0			0
$223$	19.3686	−	9.32742i	1.29702	−	0.624610i	0.347310	−	0.937750i	$-0.387095\pi$
$223$	19.3686	−	9.32742i	1.29702	−	0.624610i	0.949707	+	0.313140i	$0.101381\pi$
$224$		0			0
$225$	13.7367	+	6.61526i	0.915781	+	0.441017i
$226$		0			0
$227$	−24.4002			−1.61950			−0.809749	−	0.586776i	$-0.800397\pi$
$227$	−24.4002			−1.61950			−0.809749	+	0.586776i	$0.800397\pi$
$228$		0			0
$229$	−8.86853	−	7.07242i	−0.586049	−	0.467359i	0.285018	−	0.958522i	$-0.408000\pi$
$229$	−8.86853	−	7.07242i	−0.586049	−	0.467359i	−0.871067	+	0.491164i	$0.836572\pi$
$230$		0			0
$231$	−0.915193	+	27.5900i	−0.0602153	+	1.81529i
$232$		0			0
$233$	10.0862	+	4.85725i	0.660767	+	0.318209i	0.734043	−	0.679103i	$-0.237631\pi$
$233$	10.0862	+	4.85725i	0.660767	+	0.318209i	−0.0732756	+	0.997312i	$0.523345\pi$
$234$		0			0
$235$	−22.3402	−	17.8157i	−1.45732	−	1.16217i
$236$		0			0
$237$	23.5766	−	18.8017i	1.53147	−	1.22130i
$238$		0			0
$239$	−18.1186	−	14.4491i	−1.17200	−	0.934635i	−0.173258	−	0.984876i	$-0.555429\pi$
$239$	−18.1186	−	14.4491i	−1.17200	−	0.934635i	−0.998737	+	0.0502415i	$0.984001\pi$
$240$		0			0
$241$	−11.9844	−	24.8858i	−0.771982	−	1.60304i	−0.797468	−	0.603361i	$-0.793828\pi$
$241$	−11.9844	−	24.8858i	−0.771982	−	1.60304i	0.0254863	−	0.999675i	$-0.491887\pi$
$242$		0			0
$243$	−3.18722	−	13.9641i	−0.204460	−	0.895798i
$244$		0			0
$245$	−7.04892	−	17.5219i	−0.450339	−	1.11943i
$246$		0			0
$247$	4.65250	−	1.06190i	0.296031	−	0.0675672i
$248$		0			0
$249$	45.1487	−	21.7425i	2.86119	−	1.37787i
$250$		0			0
$251$	3.24612	−	4.07051i	0.204893	−	0.256928i	−0.668759	−	0.743480i	$-0.733174\pi$
$251$	3.24612	−	4.07051i	0.204893	−	0.256928i	0.873652	+	0.486552i	$0.161745\pi$
$252$		0			0
$253$	−11.6814	−	14.6480i	−0.734405	−	0.920914i
$254$		0			0
$255$	−9.63659	+	12.0839i	−0.603466	+	0.756723i
$256$		0			0
$257$	−2.09751	+	4.35552i	−0.130839	+	0.271690i	−0.956088	−	0.293079i	$-0.905320\pi$
$257$	−2.09751	+	4.35552i	−0.130839	+	0.271690i	0.825249	+	0.564768i	$0.191035\pi$
$258$		0			0
$259$	4.32284	+	22.3280i	0.268608	+	1.38739i
$260$		0			0
$261$	33.0981	−	41.5037i	2.04872	−	2.56902i
$262$		0			0
$263$			2.09570i			0.129226i	0.997910	+	0.0646132i	$0.0205814\pi$
$263$			2.09570i			0.129226i	−0.997910	+	0.0646132i	$0.979419\pi$
$264$		0			0
$265$	2.22637	−	4.62311i	0.136765	−	0.283995i
$266$		0			0
$267$	15.7529	+	32.7113i	0.964064	+	2.00190i
$268$		0			0
$269$	18.0800	+	4.12664i	1.10236	+	0.251606i	0.734725	−	0.678365i	$-0.237311\pi$
$269$	18.0800	+	4.12664i	1.10236	+	0.251606i	0.367633	+	0.929971i	$0.380168\pi$
$270$		0			0
$271$	5.24184	−	2.52434i	0.318419	−	0.153342i	−0.267846	−	0.963462i	$-0.586312\pi$
$271$	5.24184	−	2.52434i	0.318419	−	0.153342i	0.586265	+	0.810119i	$0.300598\pi$
$272$		0			0
$273$	−0.637897	+	19.2304i	−0.0386073	+	1.16388i
$274$		0			0
$275$		−	7.64181i		−	0.460819i
$276$		0			0
$277$	18.3142	+	8.81965i	1.10039	+	0.529921i	0.893782	−	0.448502i	$-0.148042\pi$
$277$	18.3142	+	8.81965i	1.10039	+	0.529921i	0.206611	+	0.978423i	$0.433757\pi$
$278$		0			0
$279$	12.4951	−	54.7447i	0.748064	−	3.27748i
$280$		0			0
$281$	−2.24729	−	9.84604i	−0.134062	−	0.587365i	−0.996674	−	0.0814979i	$-0.974030\pi$
$281$	−2.24729	−	9.84604i	−0.134062	−	0.587365i	0.862611	−	0.505867i	$-0.168828\pi$
$282$		0			0
$283$	2.71153	+	11.8800i	0.161184	+	0.706192i	0.989331	+	0.145682i	$0.0465377\pi$
$283$	2.71153	+	11.8800i	0.161184	+	0.706192i	−0.828148	+	0.560510i	$0.810605\pi$
$284$		0			0
$285$	−16.7224	−	3.81679i	−0.990552	−	0.226087i
$286$		0			0
$287$	11.9689	+	3.15272i	0.706503	+	0.186099i
$288$		0			0
$289$	8.48745	+	10.6429i	0.499262	+	0.626055i
$290$		0			0
$291$	−42.1468	+	33.6109i	−2.47069	+	1.97031i
$292$		0			0
$293$		−	7.50905i		−	0.438684i	−0.975648	−	0.219342i	$-0.929609\pi$
$293$		−	7.50905i		−	0.438684i	0.975648	−	0.219342i	$-0.0703910\pi$
$294$		0			0
$295$			31.4548i			1.83137i
$296$		0			0
$297$	−30.0851	+	23.9921i	−1.74572	+	1.39216i
$298$		0			0
$299$	−8.14204	−	10.2098i	−0.470866	−	0.590448i
$300$		0			0
$301$	0.450393	−	13.5778i	0.0259602	−	0.782614i
$302$		0			0
$303$	−10.2960	−	2.34999i	−0.591489	−	0.135004i
$304$		0			0
$305$	6.40338	+	28.0550i	0.366656	+	1.60643i
$306$		0			0
$307$	−3.64467	−	15.9683i	−0.208012	−	0.911361i	−0.965888	−	0.258961i	$-0.916620\pi$
$307$	−3.64467	−	15.9683i	−0.208012	−	0.911361i	0.757876	−	0.652399i	$-0.226237\pi$
$308$		0			0
$309$	−8.03980	+	35.2247i	−0.457368	+	2.00386i
$310$		0			0
$311$	−6.30559	−	3.03661i	−0.357557	−	0.172190i	0.246478	−	0.969148i	$-0.420727\pi$
$311$	−6.30559	−	3.03661i	−0.357557	−	0.172190i	−0.604035	+	0.796958i	$0.706441\pi$
$312$		0			0
$313$			23.8681i			1.34910i	0.738228	+	0.674551i	$0.235663\pi$
$313$			23.8681i			1.34910i	−0.738228	+	0.674551i	$0.764337\pi$
$314$		0			0
$315$	22.1294	−	42.3041i	1.24685	−	2.38356i
$316$		0			0
$317$	−9.70350	+	4.67296i	−0.545003	+	0.262459i	−0.686064	−	0.727541i	$-0.740663\pi$
$317$	−9.70350	+	4.67296i	−0.545003	+	0.262459i	0.141061	+	0.990001i	$0.454949\pi$
$318$		0			0
$319$	−25.9400	−	5.92063i	−1.45236	−	0.331492i
$320$		0			0
$321$	−2.81313	−	5.84153i	−0.157014	−	0.326042i
$322$		0			0
$323$	1.63097	−	3.38674i	0.0907496	−	0.188443i
$324$		0			0
$325$		−	5.32640i		−	0.295456i
$326$		0			0
$327$	−11.0294	+	13.8304i	−0.609928	+	0.764825i
$328$		0			0
$329$	−18.1868	+	21.3157i	−1.00267	+	1.17517i
$330$		0			0
$331$	1.24579	−	2.58692i	0.0684750	−	0.142190i	−0.863922	−	0.503626i	$-0.831999\pi$
$331$	1.24579	−	2.58692i	0.0684750	−	0.142190i	0.932397	+	0.361436i	$0.117713\pi$
$332$		0			0
$333$	−35.8443	+	44.9473i	−1.96425	+	2.46310i
$334$		0			0
$335$	−11.7329	−	14.7125i	−0.641035	−	0.803832i
$336$		0			0
$337$	17.5093	−	21.9560i	0.953793	−	1.19602i	−0.0267355	−	0.999643i	$-0.508511\pi$
$337$	17.5093	−	21.9560i	0.953793	−	1.19602i	0.980529	−	0.196376i	$-0.0629174\pi$
$338$		0			0
$339$	−34.8446	+	16.7803i	−1.89250	+	0.911378i
$340$		0			0
$341$	−27.4388	+	6.26273i	−1.48590	+	0.339146i
$342$		0			0
$343$	−17.4017	+	6.33876i	−0.939605	+	0.342261i
$344$		0			0
$345$	10.4445	+	45.7604i	0.562314	+	2.46366i
$346$		0			0
$347$	−1.04430	−	2.16852i	−0.0560612	−	0.116412i	0.871056	−	0.491183i	$-0.163436\pi$
$347$	−1.04430	−	2.16852i	−0.0560612	−	0.116412i	−0.927117	+	0.374771i	$0.877721\pi$
$348$		0			0
$349$	−7.41571	−	5.91383i	−0.396954	−	0.316560i	0.404588	−	0.914499i	$-0.367415\pi$
$349$	−7.41571	−	5.91383i	−0.396954	−	0.316560i	−0.801541	+	0.597939i	$0.795986\pi$
$350$		0			0
$351$	−20.9696	+	16.7227i	−1.11927	+	0.892590i
$352$		0			0
$353$	−19.6776	−	15.6923i	−1.04733	−	0.835219i	−0.0606950	−	0.998156i	$-0.519332\pi$
$353$	−19.6776	−	15.6923i	−1.04733	−	0.835219i	−0.986636	+	0.162937i	$0.947903\pi$
$354$		0			0
$355$	19.3771	+	9.33152i	1.02843	+	0.495266i
$356$		0			0
$357$	11.5297	+	9.83731i	0.610216	+	0.520646i
$358$		0			0
$359$	10.9605	+	8.74069i	0.578472	+	0.461316i	0.868491	−	0.495705i	$-0.165090\pi$
$359$	10.9605	+	8.74069i	0.578472	+	0.461316i	−0.290019	+	0.957021i	$0.593662\pi$
$360$		0			0
$361$	−14.8284			−0.780440
$362$		0			0
$363$	0.664312	+	0.319916i	0.0348674	+	0.0167912i
$364$		0			0
$365$	−19.5060	+	9.39357i	−1.02099	+	0.491682i
$366$		0			0
$367$	0.575515	−	2.52149i	0.0300416	−	0.131621i	−0.957683	−	0.287824i	$-0.907068\pi$
$367$	0.575515	−	2.52149i	0.0300416	−	0.131621i	0.987725	+	0.156203i	$0.0499254\pi$
$368$		0			0
$369$	13.5752	+	28.1892i	0.706697	+	1.46747i
$370$		0			0
$371$	−4.45856	−	2.33228i	−0.231477	−	0.121086i
$372$		0			0
$373$	15.7415			0.815063			0.407532	−	0.913191i	$-0.366390\pi$
$373$	15.7415			0.815063			0.407532	+	0.913191i	$0.366390\pi$
$374$		0			0
$375$	9.91215	−	20.5828i	0.511861	−	1.06289i
$376$		0			0
$377$	−18.0804	−	4.12673i	−0.931186	−	0.212537i
$378$		0			0
$379$	6.10862	−	1.39425i	0.313779	−	0.0716180i	−0.0627313	−	0.998030i	$-0.519981\pi$
$379$	6.10862	−	1.39425i	0.313779	−	0.0716180i	0.376510	+	0.926412i	$0.377124\pi$
$380$		0			0
$381$	25.8425	−	5.89837i	1.32395	−	0.302183i
$382$		0			0
$383$	1.48898	−	6.52366i	0.0760835	−	0.333343i	−0.922534	−	0.385917i	$-0.873885\pi$
$383$	1.48898	−	6.52366i	0.0760835	−	0.333343i	0.998617	+	0.0525733i	$0.0167423\pi$
$384$		0			0
$385$	−23.9160	−	0.793324i	−1.21887	−	0.0404315i
$386$		0			0
$387$	26.8493	−	21.4116i	1.36483	−	1.08841i
$388$		0			0
$389$	16.4265	+	20.5982i	0.832856	+	1.04437i	0.998308	+	0.0581507i	$0.0185204\pi$
$389$	16.4265	+	20.5982i	0.832856	+	1.04437i	−0.165452	+	0.986218i	$0.552908\pi$
$390$		0			0
$391$	−10.2864			−0.520205
$392$		0			0
$393$	23.1188			1.16619
$394$		0			0
$395$	16.2981	+	20.4371i	0.820044	+	1.02830i
$396$		0			0
$397$	22.7490	−	18.1417i	1.14174	−	0.910508i	0.144862	−	0.989452i	$-0.453726\pi$
$397$	22.7490	−	18.1417i	1.14174	−	0.910508i	0.996879	+	0.0789441i	$0.0251549\pi$
$398$		0			0
$399$	−4.28434	+	16.2650i	−0.214485	+	0.814267i
$400$		0			0
$401$	−0.312285	+	1.36821i	−0.0155948	+	0.0683251i	−0.982127	−	0.188222i	$-0.939728\pi$
$401$	−0.312285	+	1.36821i	−0.0155948	+	0.0683251i	0.966532	+	0.256547i	$0.0825848\pi$
$402$		0			0
$403$	−19.1251	+	4.36517i	−0.952688	+	0.217445i
$404$		0			0
$405$	41.2082	−	9.40551i	2.04765	−	0.467364i
$406$		0			0
$407$	28.0922	+	6.41187i	1.39248	+	0.317825i
$408$		0			0
$409$	−10.6844	+	22.1864i	−0.528309	+	1.09704i	0.450596	+	0.892728i	$0.351212\pi$
$409$	−10.6844	+	22.1864i	−0.528309	+	1.09704i	−0.978905	+	0.204317i	$0.934503\pi$
$410$		0			0
$411$	−27.7379			−1.36821
$412$		0			0
$413$	30.8277	+	1.02259i	1.51693	+	0.0503185i
$414$		0			0
$415$	18.8472	+	39.1366i	0.925173	+	1.92114i
$416$		0			0
$417$	0.0863348	−	0.378257i	0.00422783	−	0.0185233i
$418$		0			0
$419$	−17.0187	+	8.19576i	−0.831416	+	0.400389i	−0.800646	−	0.599138i	$-0.795510\pi$
$419$	−17.0187	+	8.19576i	−0.831416	+	0.400389i	−0.0307701	+	0.999526i	$0.509796\pi$
$420$		0			0
$421$	1.13138	+	0.544844i	0.0551401	+	0.0265541i	0.461251	−	0.887270i	$-0.347401\pi$
$421$	1.13138	+	0.544844i	0.0551401	+	0.0265541i	−0.406111	+	0.913824i	$0.633115\pi$
$422$		0			0
$423$	−70.8302			−3.44388
$424$		0			0
$425$	−3.28024	−	2.61591i	−0.159115	−	0.126890i
$426$		0			0
$427$	27.7039	−	5.36365i	1.34069	−	0.259565i
$428$		0			0
$429$	21.9640	+	10.5773i	1.06043	+	0.510677i
$430$		0			0
$431$	5.24022	+	4.17894i	0.252413	+	0.201292i	0.741519	−	0.670932i	$-0.234106\pi$
$431$	5.24022	+	4.17894i	0.252413	+	0.201292i	−0.489106	+	0.872224i	$0.662677\pi$
$432$		0			0
$433$	−17.7544	+	14.1587i	−0.853223	+	0.680423i	−0.949101	−	0.314970i	$-0.898005\pi$
$433$	−17.7544	+	14.1587i	−0.853223	+	0.680423i	0.0958785	+	0.995393i	$0.469434\pi$
$434$		0			0
$435$	52.1149	+	41.5602i	2.49872	+	1.99266i
$436$		0			0
$437$	−4.95301	−	10.2850i	−0.236935	−	0.492000i
$438$		0			0
$439$	−0.852535	−	3.73520i	−0.0406893	−	0.178271i	0.950500	−	0.310725i	$-0.100572\pi$
$439$	−0.852535	−	3.73520i	−0.0406893	−	0.178271i	−0.991189	+	0.132453i	$0.957715\pi$
$440$		0			0
$441$	−40.7413	−	23.0635i	−1.94006	−	1.09826i
$442$		0			0
$443$	−24.6839	+	5.63395i	−1.17277	+	0.267677i	−0.764157	−	0.645031i	$-0.776845\pi$
$443$	−24.6839	+	5.63395i	−1.17277	+	0.267677i	−0.408613	+	0.912708i	$0.633987\pi$
$444$		0			0
$445$	−28.3554	+	13.6552i	−1.34417	+	0.647320i
$446$		0			0
$447$	0.0854499	−	0.107151i	0.00404164	−	0.00506806i
$448$		0			0
$449$	−0.199514	−	0.250182i	−0.00941563	−	0.0118068i	0.777101	−	0.629375i	$-0.216689\pi$
$449$	−0.199514	−	0.250182i	−0.00941563	−	0.0118068i	−0.786517	+	0.617569i	$0.788118\pi$
$450$		0			0
$451$	9.77745	−	12.2605i	0.460402	−	0.577326i
$452$		0			0
$453$	−18.2977	+	37.9955i	−0.859700	+	1.78519i
$454$		0			0
$455$	−16.6697	−	0.552953i	−0.781486	−	0.0259228i
$456$		0			0
$457$	25.8613	−	32.4291i	1.20974	−	1.51697i	0.415235	−	0.909714i	$-0.363699\pi$
$457$	25.8613	−	32.4291i	1.20974	−	1.51697i	0.794507	−	0.607254i	$-0.207729\pi$
$458$		0			0
$459$			21.1269i			0.986118i
$460$		0			0
$461$	−9.68537	+	20.1119i	−0.451093	+	0.936703i	0.544124	+	0.839005i	$0.316862\pi$
$461$	−9.68537	+	20.1119i	−0.451093	+	0.936703i	−0.995216	+	0.0976982i	$0.968852\pi$
$462$		0			0
$463$	−13.0235	−	27.0435i	−0.605252	−	1.25682i	−0.948263	−	0.317487i	$-0.897161\pi$
$463$	−13.0235	−	27.0435i	−0.605252	−	1.25682i	0.343011	−	0.939331i	$-0.388553\pi$
$464$		0			0
$465$	68.7412	+	15.6897i	3.18779	+	0.727593i
$466$		0			0
$467$	17.5162	−	8.43536i	0.810553	−	0.390342i	0.0177674	−	0.999842i	$-0.494344\pi$
$467$	17.5162	−	8.43536i	0.810553	−	0.390342i	0.792786	+	0.609500i	$0.208630\pi$
$468$		0			0
$469$	−14.8007	+	11.0206i	−0.683431	+	0.508886i
$470$		0			0
$471$			39.3754i			1.81432i
$472$		0			0
$473$	−15.5079	−	7.46822i	−0.713055	−	0.343389i
$474$		0			0
$475$	1.03609	−	4.53941i	0.0475391	−	0.208282i
$476$		0			0
$477$	−2.83034	−	12.4005i	−0.129592	−	0.567782i
$478$		0			0
$479$	0.444748	+	1.94857i	0.0203211	+	0.0890324i	0.984072	−	0.177773i	$-0.0568892\pi$
$479$	0.444748	+	1.94857i	0.0203211	+	0.0890324i	−0.963751	+	0.266805i	$0.914032\pi$
$480$		0			0
$481$	19.5805	+	4.46912i	0.892794	+	0.203774i
$482$		0			0
$483$	45.1877	−	8.74863i	2.05611	−	0.398076i
$484$		0			0
$485$	−29.1352	−	36.5344i	−1.32296	−	1.65894i
$486$		0			0
$487$	−4.18823	+	3.34000i	−0.189787	+	0.151350i	−0.713774	−	0.700376i	$-0.753015\pi$
$487$	−4.18823	+	3.34000i	−0.189787	+	0.151350i	0.523987	+	0.851726i	$0.324444\pi$
$488$		0			0
$489$		−	53.6326i		−	2.42535i
$490$		0			0
$491$		−	14.7134i		−	0.664006i	−0.943278	−	0.332003i	$-0.892276\pi$
$491$		−	14.7134i		−	0.664006i	0.943278	−	0.332003i	$-0.107724\pi$
$492$		0			0
$493$	−11.4211	+	9.10800i	−0.514379	+	0.410204i
$494$		0			0
$495$	−37.7145	−	47.2925i	−1.69514	−	2.12564i
$496$		0			0
$497$	9.77543	−	18.6874i	0.438488	−	0.838245i
$498$		0			0
$499$	−14.4553	−	3.29932i	−0.647107	−	0.147698i	−0.113644	−	0.993522i	$-0.536252\pi$
$499$	−14.4553	−	3.29932i	−0.647107	−	0.147698i	−0.533463	+	0.845824i	$0.679110\pi$
$500$		0			0
$501$	−2.66548	−	11.6782i	−0.119085	−	0.521744i
$502$		0			0
$503$	−3.58085	−	15.6887i	−0.159662	−	0.699525i	−0.989859	−	0.142055i	$-0.954629\pi$
$503$	−3.58085	−	15.6887i	−0.159662	−	0.699525i	0.830197	−	0.557471i	$-0.188228\pi$
$504$		0			0
$505$	2.03706	−	8.92496i	0.0906481	−	0.397155i
$506$		0			0
$507$	−21.1471	−	10.1839i	−0.939177	−	0.452284i
$508$		0			0
$509$			6.22303i			0.275831i	0.990444	+	0.137916i	$0.0440403\pi$
$509$			6.22303i			0.275831i	−0.990444	+	0.137916i	$0.955960\pi$
$510$		0			0
$511$	8.57216	+	19.4225i	0.379210	+	0.859199i
$512$		0			0
$513$	−21.1241	+	10.1728i	−0.932652	+	0.449142i
$514$		0			0
$515$	−30.5341	−	6.96920i	−1.34549	−	0.307100i
$516$		0			0
$517$	15.4033	+	31.9854i	0.677438	+	1.40671i
$518$		0			0
$519$	3.84533	−	7.98491i	0.168791	−	0.350499i
$520$		0			0
$521$		−	29.9529i		−	1.31226i	−0.754649	−	0.656129i	$-0.772193\pi$
$521$		−	29.9529i		−	1.31226i	0.754649	−	0.656129i	$-0.227807\pi$
$522$		0			0
$523$	−5.79542	+	7.26722i	−0.253416	+	0.317773i	−0.892224	−	0.451592i	$-0.850856\pi$
$523$	−5.79542	+	7.26722i	−0.253416	+	0.317773i	0.638809	+	0.769366i	$0.279428\pi$
$524$		0			0
$525$	16.6348	+	8.70171i	0.726003	+	0.379774i
$526$		0			0
$527$	−6.70445	+	13.9219i	−0.292050	+	0.606449i
$528$		0			0
$529$	−5.13646	+	6.44092i	−0.223324	+	0.280040i
$530$		0			0
$531$	48.6139	+	60.9599i	2.10966	+	2.64543i
$532$		0			0
$533$	6.81496	−	8.54568i	0.295188	−	0.370155i
$534$		0			0
$535$	5.06366	−	2.43853i	0.218921	−	0.105427i
$536$		0			0
$537$	21.4633	−	4.89887i	0.926211	−	0.211402i
$538$		0			0
$539$	−1.55502	+	23.4134i	−0.0669792	+	1.00849i
$540$		0			0
$541$	6.69162	+	29.3179i	0.287695	+	1.26047i	0.887679	+	0.460463i	$0.152316\pi$
$541$	6.69162	+	29.3179i	0.287695	+	1.26047i	−0.599984	+	0.800012i	$0.704826\pi$
$542$		0			0
$543$	0.441288	+	0.916345i	0.0189375	+	0.0393241i
$544$		0			0
$545$	−11.9887	−	9.56071i	−0.513542	−	0.409536i
$546$		0			0
$547$	19.9080	−	15.8761i	0.851204	−	0.678812i	−0.0974115	−	0.995244i	$-0.531056\pi$
$547$	19.9080	−	15.8761i	0.851204	−	0.678812i	0.948615	+	0.316432i	$0.102485\pi$
$548$		0			0
$549$	55.7693	+	44.4745i	2.38018	+	1.89813i
$550$		0			0
$551$	−14.6062	−	7.03397i	−0.622244	−	0.299657i
$552$		0			0
$553$	20.5595	−	15.3087i	0.874279	−	0.650993i
$554$		0			0
$555$	−56.4389	−	45.0085i	−2.39570	−	1.91050i
$556$		0			0
$557$	−31.0420			−1.31529			−0.657646	−	0.753327i	$-0.728448\pi$
$557$	−31.0420			−1.31529			−0.657646	+	0.753327i	$0.728448\pi$
$558$		0			0
$559$	−10.8091	−	5.20541i	−0.457178	−	0.220165i
$560$		0			0
$561$	17.3010	−	8.33171i	0.730448	−	0.351765i
$562$		0			0
$563$	8.59238	−	37.6457i	0.362126	−	1.58658i	−0.385663	−	0.922640i	$-0.626027\pi$
$563$	8.59238	−	37.6457i	0.362126	−	1.58658i	0.747789	−	0.663937i	$-0.231116\pi$
$564$		0			0
$565$	−14.5458	−	30.2046i	−0.611945	−	1.27072i
$566$		0			0
$567$	−7.87832	−	40.6925i	−0.330859	−	1.70892i
$568$		0			0
$569$	−41.0058			−1.71905			−0.859527	−	0.511090i	$-0.829242\pi$
$569$	−41.0058			−1.71905			−0.859527	+	0.511090i	$0.829242\pi$
$570$		0			0
$571$	−0.0286532	+	0.0594989i	−0.00119910	+	0.00248995i	−0.901568	−	0.432638i	$-0.857583\pi$
$571$	−0.0286532	+	0.0594989i	−0.00119910	+	0.00248995i	0.900368	+	0.435128i	$0.143297\pi$
$572$		0			0
$573$	−60.8300	−	13.8841i	−2.54121	−	0.580015i
$574$		0			0
$575$	−12.4219	+	2.83523i	−0.518031	+	0.118237i
$576$		0			0
$577$	−5.68832	+	1.29832i	−0.236808	+	0.0540498i	−0.339278	−	0.940686i	$-0.610183\pi$
$577$	−5.68832	+	1.29832i	−0.236808	+	0.0540498i	0.102470	+	0.994736i	$0.467325\pi$
$578$		0			0
$579$	12.8239	−	56.1852i	0.532943	−	2.33498i
$580$		0			0
$581$	38.9691	−	17.1991i	1.61671	−	0.713540i
$582$		0			0
$583$	−4.98430	+	3.97485i	−0.206429	+	0.164621i
$584$		0			0
$585$	−26.2873	−	32.9632i	−1.08685	−	1.36286i
$586$		0			0
$587$	4.75708			0.196346			0.0981729	−	0.995169i	$-0.468700\pi$
$587$	4.75708			0.196346			0.0981729	+	0.995169i	$0.468700\pi$
$588$		0			0
$589$	−17.1484			−0.706586
$590$		0			0
$591$	20.4067	+	25.5892i	0.839419	+	1.05260i
$592$		0			0
$593$	−5.86180	+	4.67463i	−0.240715	+	0.191964i	−0.736415	−	0.676530i	$-0.763483\pi$
$593$	−5.86180	+	4.67463i	−0.240715	+	0.191964i	0.495700	+	0.868494i	$0.334912\pi$
$594$		0			0
$595$	−8.52735	+	9.99438i	−0.349587	+	0.409730i
$596$		0			0
$597$	−7.18980	+	31.5006i	−0.294259	+	1.28923i
$598$		0			0
$599$	−8.17514	+	1.86592i	−0.334027	+	0.0762395i	−0.386245	−	0.922396i	$-0.626228\pi$
$599$	−8.17514	+	1.86592i	−0.334027	+	0.0762395i	0.0522180	+	0.998636i	$0.483371\pi$
$600$		0			0
$601$	−12.3016	+	2.80776i	−0.501793	+	0.114531i	−0.465923	−	0.884825i	$-0.654277\pi$
$601$	−12.3016	+	2.80776i	−0.501793	+	0.114531i	−0.0358704	+	0.999356i	$0.511420\pi$
$602$		0			0
$603$	−45.4769	−	10.3798i	−1.85196	−	0.422698i
$604$		0			0
$605$	−0.277315	+	0.575851i	−0.0112745	+	0.0234117i
$606$		0			0
$607$	−32.6239			−1.32416			−0.662081	−	0.749432i	$-0.730327\pi$
$607$	−32.6239			−1.32416			−0.662081	+	0.749432i	$0.730327\pi$
$608$		0			0
$609$	42.4259	−	49.7248i	1.71918	−	2.01495i
$610$		0			0
$611$	10.7362	+	22.2940i	0.434342	+	0.901920i
$612$		0			0
$613$	10.2447	−	44.8849i	0.413779	−	1.81288i	−0.152063	−	0.988371i	$-0.548592\pi$
$613$	10.2447	−	44.8849i	0.413779	−	1.81288i	0.565842	−	0.824513i	$-0.308551\pi$
$614$		0			0
$615$	−35.3963	+	17.0459i	−1.42731	+	0.687358i
$616$		0			0
$617$	−33.3025	−	16.0377i	−1.34071	−	0.645652i	−0.380461	−	0.924797i	$-0.624235\pi$
$617$	−33.3025	−	16.0377i	−1.34071	−	0.645652i	−0.960249	+	0.279145i	$0.909949\pi$
$618$		0			0
$619$	36.3231			1.45995			0.729974	−	0.683475i	$-0.239532\pi$
$619$	36.3231			1.45995			0.729974	+	0.683475i	$0.239532\pi$
$620$		0			0
$621$	50.1617	+	40.0026i	2.01292	+	1.60525i
$622$		0			0
$623$	12.4612	+	28.2340i	0.499246	+	1.13117i
$624$		0			0
$625$	28.1115	+	13.5378i	1.12446	+	0.541512i
$626$		0			0
$627$	16.6612	+	13.2869i	0.665386	+	0.530628i
$628$		0			0
$629$	12.3687	−	9.86370i	0.493172	−	0.393291i
$630$		0			0
$631$	11.1307	+	8.87645i	0.443107	+	0.353366i	0.819485	−	0.573100i	$-0.194259\pi$
$631$	11.1307	+	8.87645i	0.443107	+	0.353366i	−0.376379	+	0.926466i	$0.622831\pi$
$632$		0			0
$633$	−10.9191	−	22.6737i	−0.433995	−	0.901199i
$634$		0			0
$635$	5.11293	+	22.4012i	0.202901	+	0.888965i
$636$		0			0
$637$	−1.08386	+	16.3194i	−0.0429440	+	0.646596i
$638$		0			0
$639$	51.9751	−	11.8630i	2.05610	−	0.469292i
$640$		0			0
$641$	−23.8806	+	11.5003i	−0.943228	+	0.454234i	−0.841307	−	0.540558i	$-0.818213\pi$
$641$	−23.8806	+	11.5003i	−0.943228	+	0.454234i	−0.101921	+	0.994793i	$0.532499\pi$
$642$		0			0
$643$	3.52691	−	4.42261i	0.139088	−	0.174411i	−0.707409	−	0.706805i	$-0.750136\pi$
$643$	3.52691	−	4.42261i	0.139088	−	0.174411i	0.846497	+	0.532394i	$0.178707\pi$
$644$		0			0
$645$	26.8859	+	33.7138i	1.05863	+	1.32748i
$646$		0			0
$647$	1.77884	−	2.23060i	0.0699334	−	0.0876938i	−0.745634	−	0.666355i	$-0.767853\pi$
$647$	1.77884	−	2.23060i	0.0699334	−	0.0876938i	0.815568	+	0.578662i	$0.196425\pi$
$648$		0			0
$649$	16.9562	−	35.2098i	0.665588	−	1.38211i
$650$		0			0
$651$	17.6117	−	66.8606i	0.690256	−	2.62047i
$652$		0			0
$653$	20.3015	−	25.4572i	0.794457	−	0.996218i	−0.205389	−	0.978680i	$-0.565846\pi$
$653$	20.3015	−	25.4572i	0.794457	−	0.996218i	0.999846	−	0.0175375i	$-0.00558266\pi$
$654$		0			0
$655$			20.0402i			0.783036i
$656$		0			0
$657$	−23.2849	+	48.3516i	−0.908431	+	1.88638i
$658$		0			0
$659$	−3.66441	−	7.60923i	−0.142745	−	0.296413i	0.817323	−	0.576180i	$-0.195457\pi$
$659$	−3.66441	−	7.60923i	−0.142745	−	0.296413i	−0.960068	+	0.279766i	$0.909743\pi$
$660$		0			0
$661$	0.666613	+	0.152150i	0.0259282	+	0.00591795i	0.235465	−	0.971883i	$-0.424339\pi$
$661$	0.666613	+	0.152150i	0.0259282	+	0.00591795i	−0.209537	+	0.977801i	$0.567196\pi$
$662$		0			0
$663$	12.0589	−	5.80727i	0.468329	−	0.225536i
$664$		0			0
$665$	−14.0991	−	3.71383i	−0.546739	−	0.144016i
$666$		0			0
$667$			44.3626i			1.71773i
$668$		0			0
$669$	60.2860	+	29.0322i	2.33079	+	1.12245i
$670$		0			0
$671$	7.95566	−	34.8560i	0.307125	−	1.34560i
$672$		0			0
$673$	4.82873	+	21.1560i	0.186134	+	0.815505i	0.978630	+	0.205629i	$0.0659239\pi$
$673$	4.82873	+	21.1560i	0.186134	+	0.815505i	−0.792496	+	0.609877i	$0.791219\pi$
$674$		0			0
$675$	5.82318	+	25.5130i	0.224134	+	0.981996i
$676$		0			0
$677$	18.6667	+	4.26056i	0.717421	+	0.163747i	0.565622	−	0.824665i	$-0.308636\pi$
$677$	18.6667	+	4.26056i	0.717421	+	0.163747i	0.151799	+	0.988411i	$0.451493\pi$
$678$		0			0
$679$	−36.7532	+	27.3666i	−1.41046	+	1.05023i
$680$		0			0
$681$	−47.3523	−	59.3779i	−1.81454	−	2.27537i
$682$		0			0
$683$	8.64736	−	6.89604i	0.330882	−	0.263870i	−0.443930	−	0.896062i	$-0.646416\pi$
$683$	8.64736	−	6.89604i	0.330882	−	0.263870i	0.774812	+	0.632192i	$0.217845\pi$
$684$		0			0
$685$		−	24.0442i		−	0.918683i
$686$		0			0
$687$		−	35.3067i		−	1.34703i
$688$		0			0
$689$	−3.47410	+	2.77050i	−0.132353	+	0.105548i
$690$		0			0
$691$	7.70314	+	9.65943i	0.293041	+	0.367462i	0.906457	−	0.422298i	$-0.138776\pi$
$691$	7.70314	+	9.65943i	0.293041	+	0.367462i	−0.613416	+	0.789760i	$0.710205\pi$
$692$		0			0
$693$	−47.5757	+	35.4251i	−1.80725	+	1.34569i
$694$		0			0
$695$	0.327888	+	0.0748382i	0.0124375	+	0.00283878i
$696$		0			0
$697$	−1.91586	−	8.39393i	−0.0725683	−	0.317943i
$698$		0			0
$699$	7.75365	+	33.9709i	0.293270	+	1.28490i
$700$		0			0
$701$	8.29224	−	36.3307i	0.313193	−	1.37219i	−0.536049	−	0.844187i	$-0.680084\pi$
$701$	8.29224	−	36.3307i	0.313193	−	1.37219i	0.849242	−	0.528003i	$-0.177059\pi$
$702$		0			0
$703$	15.8181	+	7.61758i	0.596590	+	0.287303i
$704$		0			0
$705$		−	88.9391i		−	3.34964i
$706$		0			0
$707$	−8.68080	−	2.28660i	−0.326475	−	0.0859965i
$708$		0			0
$709$	−21.7611	+	10.4796i	−0.817254	+	0.393569i	−0.795319	−	0.606191i	$-0.792697\pi$
$709$	−21.7611	+	10.4796i	−0.817254	+	0.393569i	−0.0219343	+	0.999759i	$0.506982\pi$
$710$		0			0
$711$	63.1717	+	14.4185i	2.36912	+	0.540737i
$712$		0			0
$713$	20.3604	+	42.2788i	0.762504	+	1.58335i
$714$		0			0
$715$	−9.16881	+	19.0392i	−0.342894	+	0.712027i
$716$		0			0
$717$		−	72.1323i		−	2.69383i
$718$		0			0
$719$	16.5272	−	20.7245i	0.616362	−	0.772894i	−0.371465	−	0.928447i	$-0.621144\pi$
$719$	16.5272	−	20.7245i	0.616362	−	0.772894i	0.987828	+	0.155553i	$0.0497159\pi$
$720$		0			0
$721$	−7.82292	+	29.6988i	−0.291341	+	1.10604i
$722$		0			0
$723$	37.3021	−	77.4587i	1.38728	−	2.88072i
$724$		0			0
$725$	−11.2818	+	14.1469i	−0.418994	+	0.525402i
$726$		0			0
$727$	0.304715	+	0.382100i	0.0113013	+	0.0141713i	0.787450	−	0.616379i	$-0.211401\pi$
$727$	0.304715	+	0.382100i	0.0113013	+	0.0141713i	−0.776149	+	0.630550i	$0.782829\pi$
$728$		0			0
$729$	−1.50621	+	1.88872i	−0.0557854	+	0.0699527i
$730$		0			0
$731$	−8.51432	+	4.10028i	−0.314914	+	0.151654i
$732$		0			0
$733$	−29.2135	+	6.66778i	−1.07902	+	0.246280i	−0.724855	−	0.688901i	$-0.758093\pi$
$733$	−29.2135	+	6.66778i	−1.07902	+	0.246280i	−0.354169	+	0.935182i	$0.615236\pi$
$734$		0			0
$735$	28.9600	−	51.1575i	1.06821	−	1.88697i
$736$		0			0
$737$	5.20250	+	22.7937i	0.191637	+	0.839615i
$738$		0			0
$739$	−0.882819	−	1.83319i	−0.0324750	−	0.0674351i	0.884100	−	0.467297i	$-0.154772\pi$
$739$	−0.882819	−	1.83319i	−0.0324750	−	0.0674351i	−0.916575	+	0.399862i	$0.869058\pi$
$740$		0			0
$741$	11.6130	+	9.26107i	0.426615	+	0.340214i
$742$		0			0
$743$	−33.7365	+	26.9040i	−1.23767	+	0.987010i	−0.237795	+	0.971315i	$0.576425\pi$
$743$	−33.7365	+	26.9040i	−1.23767	+	0.987010i	−0.999877	+	0.0156948i	$0.995004\pi$
$744$		0			0
$745$	0.0928824	+	0.0740712i	0.00340295	+	0.00271376i
$746$		0			0
$747$	97.0124	+	46.7187i	3.54950	+	1.70935i
$748$		0			0
$749$	−2.22529	−	5.04198i	−0.0813105	−	0.184230i
$750$		0			0
$751$	−13.6989	−	10.9245i	−0.499880	−	0.398641i	0.340831	−	0.940124i	$-0.389292\pi$
$751$	−13.6989	−	10.9245i	−0.499880	−	0.398641i	−0.840712	+	0.541483i	$0.817863\pi$
$752$		0			0
$753$	16.2052			0.590549
$754$		0			0
$755$	−32.9360	−	15.8611i	−1.19866	−	0.577246i
$756$		0			0
$757$	1.32382	−	0.637518i	0.0481150	−	0.0231710i	−0.409672	−	0.912233i	$-0.634357\pi$
$757$	1.32382	−	0.637518i	0.0481150	−	0.0231710i	0.457787	+	0.889062i	$0.348642\pi$
$758$		0			0
$759$	12.9764	−	56.8535i	0.471015	−	2.06365i
$760$		0			0
$761$	16.6176	+	34.5069i	0.602389	+	1.25087i	0.949711	+	0.313128i	$0.101377\pi$
$761$	16.6176	+	34.5069i	0.602389	+	1.25087i	−0.347322	+	0.937746i	$0.612909\pi$
$762$		0			0
$763$	−9.75985	+	11.4389i	−0.353330	+	0.414117i
$764$		0			0
$765$	−33.2105			−1.20073
$766$		0			0
$767$	11.8186	−	24.5415i	0.426744	−	0.886143i
$768$		0			0
$769$	−26.2784	−	5.99788i	−0.947625	−	0.216289i	−0.279338	−	0.960193i	$-0.590115\pi$
$769$	−26.2784	−	5.99788i	−0.947625	−	0.216289i	−0.668287	+	0.743904i	$0.732972\pi$
$770$		0			0
$771$	−14.6697	+	3.34826i	−0.528316	+	0.120585i
$772$		0			0
$773$	−12.4613	+	2.84422i	−0.448203	+	0.102299i	−0.440664	−	0.897672i	$-0.645257\pi$
$773$	−12.4613	+	2.84422i	−0.448203	+	0.102299i	−0.00753908	+	0.999972i	$0.502400\pi$
$774$		0			0
$775$	−4.25907	+	18.6602i	−0.152990	+	0.670294i
$776$		0			0
$777$	−45.9460	+	53.8504i	−1.64830	+	1.93187i
$778$		0			0
$779$	7.47032	−	5.95738i	0.267652	−	0.213445i
$780$		0			0
$781$	−16.6600	−	20.8910i	−0.596142	−	0.747538i
$782$		0			0
$783$	91.1150			3.25618
$784$		0			0
$785$	−34.1321			−1.21823
$786$		0			0
$787$	−26.4485	−	33.1654i	−0.942787	−	1.18222i	−0.983107	−	0.183031i	$-0.941409\pi$
$787$	−26.4485	−	33.1654i	−0.942787	−	1.18222i	0.0403198	−	0.999187i	$-0.487162\pi$
$788$		0			0
$789$	−5.09989	+	4.06703i	−0.181561	+	0.144790i
$790$		0			0
$791$	−30.0753	+	13.2738i	−1.06935	+	0.471963i
$792$		0			0
$793$	5.54516	−	24.2949i	0.196914	−	0.862738i
$794$		0			0
$795$	15.5710	−	3.55397i	0.552245	−	0.126046i
$796$		0			0
$797$	10.6260	−	2.42531i	0.376391	−	0.0859089i	−0.0301400	−	0.999546i	$-0.509595\pi$
$797$	10.6260	−	2.42531i	0.376391	−	0.0859089i	0.406531	+	0.913637i	$0.366738\pi$
$798$		0			0
$799$	19.0025	+	4.33719i	0.672260	+	0.153439i
$800$		0			0
$801$	−33.8488	+	70.2877i	−1.19599	+	2.48349i
$802$		0			0
$803$	26.8983			0.949219
$804$		0			0
$805$	7.58364	+	39.1704i	0.267288	+	1.38057i
$806$		0			0
$807$	25.0448	+	52.0061i	0.881619	+	1.83070i
$808$		0			0
$809$	−0.209739	+	0.918926i	−0.00737403	+	0.0323077i	−0.978481	−	0.206337i	$-0.933846\pi$
$809$	−0.209739	+	0.918926i	−0.00737403	+	0.0323077i	0.971107	+	0.238644i	$0.0767030\pi$
$810$		0			0
$811$	−21.5547	+	10.3802i	−0.756888	+	0.364498i	−0.772196	−	0.635385i	$-0.780842\pi$
$811$	−21.5547	+	10.3802i	−0.756888	+	0.364498i	0.0153074	+	0.999883i	$0.495127\pi$
$812$		0			0
$813$	16.3156	+	7.85716i	0.572211	+	0.275562i
$814$		0			0
$815$	46.4908			1.62850
$816$		0			0
$817$	−8.19949	−	6.53887i	−0.286864	−	0.228766i
$818$		0			0
$819$	−33.1606	+	24.6916i	−1.15873	+	0.862794i
$820$		0			0
$821$	−0.983661	−	0.473706i	−0.0343300	−	0.0165325i	0.416640	−	0.909072i	$-0.363208\pi$
$821$	−0.983661	−	0.473706i	−0.0343300	−	0.0165325i	−0.450970	+	0.892539i	$0.648922\pi$
$822$		0			0
$823$	−6.85608	−	5.46754i	−0.238988	−	0.190586i	0.496671	−	0.867939i	$-0.334556\pi$
$823$	−6.85608	−	5.46754i	−0.238988	−	0.190586i	−0.735658	+	0.677353i	$0.763127\pi$
$824$		0			0
$825$	18.5964	−	14.8301i	0.647442	−	0.516318i
$826$		0			0
$827$	20.2294	+	16.1324i	0.703445	+	0.560979i	0.908558	−	0.417760i	$-0.137185\pi$
$827$	20.2294	+	16.1324i	0.703445	+	0.560979i	−0.205112	+	0.978738i	$0.565756\pi$
$828$		0			0
$829$	7.95986	+	16.5288i	0.276457	+	0.574070i	0.992252	−	0.124241i	$-0.0396496\pi$
$829$	7.95986	+	16.5288i	0.276457	+	0.574070i	−0.715795	+	0.698311i	$0.753935\pi$
$830$		0			0
$831$	14.0788	+	61.6834i	0.488390	+	2.13977i
$832$		0			0
$833$	9.51790	+	8.68226i	0.329776	+	0.300823i
$834$		0			0
$835$	10.1231	−	2.31054i	0.350325	−	0.0799594i
$836$		0			0
$837$	86.8351	−	41.8176i	3.00146	−	1.44543i
$838$		0			0
$839$	10.0799	−	12.6397i	0.347995	−	0.436372i	−0.576772	−	0.816905i	$-0.695688\pi$
$839$	10.0799	−	12.6397i	0.347995	−	0.436372i	0.924767	+	0.380533i	$0.124259\pi$
$840$		0			0
$841$	21.1993	+	26.5831i	0.731012	+	0.916660i
$842$		0			0
$843$	19.5991	−	24.5765i	0.675030	−	0.846460i
$844$		0			0
$845$	8.82780	−	18.3311i	0.303686	−	0.630610i
$846$		0			0
$847$	0.555355	+	0.290507i	0.0190822	+	0.00998195i
$848$		0			0
$849$	−23.6478	+	29.6534i	−0.811591	+	1.01770i
$850$		0			0
$851$		−	48.0434i		−	1.64691i
$852$		0			0
$853$	11.4555	−	23.7876i	0.392228	−	0.814470i	−0.607568	−	0.794268i	$-0.707855\pi$
$853$	11.4555	−	23.7876i	0.392228	−	0.814470i	0.999796	−	0.0202025i	$-0.00643109\pi$
$854$		0			0
$855$	−15.9912	−	33.2062i	−0.546889	−	1.13563i
$856$		0			0
$857$	−0.493556	−	0.112651i	−0.0168595	−	0.00384808i	0.214083	−	0.976816i	$-0.431324\pi$
$857$	−0.493556	−	0.112651i	−0.0168595	−	0.00384808i	−0.230942	+	0.972967i	$0.574181\pi$
$858$		0			0
$859$	−19.8700	+	9.56888i	−0.677955	+	0.326486i	−0.740981	−	0.671526i	$-0.765639\pi$
$859$	−19.8700	+	9.56888i	−0.677955	+	0.326486i	0.0630259	+	0.998012i	$0.479925\pi$
$860$		0			0
$861$	15.5554	+	35.2447i	0.530126	+	1.20114i
$862$		0			0
$863$			6.46151i			0.219952i	0.993934	+	0.109976i	$0.0350775\pi$
$863$			6.46151i			0.219952i	−0.993934	+	0.109976i	$0.964923\pi$
$864$		0			0
$865$	6.92162	+	3.33328i	0.235342	+	0.113335i
$866$		0			0
$867$	−9.42838	+	41.3084i	−0.320205	+	1.40291i
$868$		0			0
$869$	−7.22677	−	31.6625i	−0.245151	−	1.07408i
$870$		0			0
$871$	3.62619	+	15.8874i	0.122869	+	0.538323i
$872$		0			0
$873$	−112.929	−	25.7753i	−3.82206	−	0.872361i
$874$		0			0
$875$	9.00097	−	17.2069i	0.304288	−	0.581700i
$876$		0			0
$877$	15.3219	+	19.2130i	0.517383	+	0.648778i	0.970051	−	0.242901i	$-0.0780992\pi$
$877$	15.3219	+	19.2130i	0.517383	+	0.648778i	−0.452668	+	0.891679i	$0.649528\pi$
$878$		0			0
$879$	18.2733	−	14.5725i	0.616343	−	0.491517i
$880$		0			0
$881$		−	0.812446i		−	0.0273720i	−0.999906	−	0.0136860i	$-0.995643\pi$
$881$		−	0.812446i		−	0.0273720i	0.999906	−	0.0136860i	$-0.00435653\pi$
$882$		0			0
$883$		−	44.5313i		−	1.49860i	−0.662232	−	0.749298i	$-0.730391\pi$
$883$		−	44.5313i		−	1.49860i	0.662232	−	0.749298i	$-0.269609\pi$
$884$		0			0
$885$	−76.5453	+	61.0429i	−2.57304	+	2.05193i
$886$		0			0
$887$	30.3534	+	38.0620i	1.01917	+	1.27800i	0.960074	+	0.279745i	$0.0902499\pi$
$887$	30.3534	+	38.0620i	1.01917	+	1.27800i	0.0590944	+	0.998252i	$0.481179\pi$
$888$		0			0
$889$	22.1208	−	4.28274i	0.741909	−	0.143638i
$890$		0			0
$891$	−51.1978	−	11.6856i	−1.71519	−	0.391481i
$892$		0			0
$893$	4.81329	+	21.0884i	0.161071	+	0.705697i
$894$		0			0
$895$	4.24652	+	18.6052i	0.141946	+	0.621904i
$896$		0			0
$897$	9.04468	−	39.6273i	0.301993	−	1.32312i
$898$		0			0
$899$	60.0418	+	28.9146i	2.00251	+	0.964356i
$900$		0			0
$901$			3.50016i			0.116607i
$902$		0			0
$903$	33.9158	−	25.2538i	1.12865	−	0.840395i
$904$		0			0
$905$	−0.794322	+	0.382525i	−0.0264042	+	0.0127156i
$906$		0			0
$907$	−15.2120	−	3.47205i	−0.505107	−	0.115287i	−0.0376286	−	0.999292i	$-0.511980\pi$
$907$	−15.2120	−	3.47205i	−0.505107	−	0.115287i	−0.467479	+	0.884004i	$0.654838\pi$
$908$		0			0
$909$	−9.84579	−	20.4450i	−0.326564	−	0.678118i
$910$		0			0
$911$	8.52932	−	17.7113i	0.282589	−	0.586802i	−0.710563	−	0.703634i	$-0.751560\pi$
$911$	8.52932	−	17.7113i	0.282589	−	0.586802i	0.993152	+	0.116832i	$0.0372739\pi$
$912$		0			0
$913$		−	53.9685i		−	1.78610i
$914$		0			0
$915$	−55.8452	+	70.0277i	−1.84619	+	2.31504i
$916$		0			0
$917$	19.6407	+	0.651505i	0.648592	+	0.0215146i
$918$		0			0
$919$	24.3209	−	50.5029i	0.802273	−	1.66594i	0.0577592	−	0.998331i	$-0.481604\pi$
$919$	24.3209	−	50.5029i	0.802273	−	1.66594i	0.744514	−	0.667607i	$-0.232681\pi$
$920$		0			0
$921$	31.7859	−	39.8583i	1.04738	−	1.31337i
$922$		0			0
$923$	−11.6122	−	14.5612i	−0.382219	−	0.479287i
$924$		0			0
$925$	12.2178	−	15.3207i	0.401719	−	0.503740i
$926$		0			0
$927$	−69.9464	+	33.6844i	−2.29734	+	1.10634i
$928$		0			0
$929$	24.7624	−	5.65185i	0.812427	−	0.185431i	0.203928	−	0.978986i	$-0.434629\pi$
$929$	24.7624	−	5.65185i	0.812427	−	0.185431i	0.608499	+	0.793555i	$0.291772\pi$
$930$		0			0
$931$	−4.09815	+	13.6973i	−0.134311	+	0.448910i
$932$		0			0
$933$	−4.84735	−	21.2376i	−0.158695	−	0.695289i
$934$		0			0
$935$	7.22224	+	14.9971i	0.236193	+	0.490459i
$936$		0			0
$937$	32.2204	+	25.6949i	1.05260	+	0.839417i	0.987366	−	0.158453i	$-0.0506508\pi$
$937$	32.2204	+	25.6949i	1.05260	+	0.839417i	0.0652290	+	0.997870i	$0.479222\pi$
$938$		0			0
$939$	−58.0829	+	46.3196i	−1.89547	+	1.51158i
$940$		0			0
$941$	−14.0343	−	11.1920i	−0.457506	−	0.364849i	0.367453	−	0.930042i	$-0.380230\pi$
$941$	−14.0343	−	11.1920i	−0.457506	−	0.364849i	−0.824958	+	0.565194i	$0.808801\pi$
$942$		0			0
$943$	−23.5573	−	11.3446i	−0.767132	−	0.369432i
$944$		0			0
$945$	80.4508	−	15.5758i	2.61706	−	0.506680i
$946$		0			0
$947$	−24.8808	−	19.8418i	−0.808517	−	0.644771i	0.129415	−	0.991591i	$-0.458690\pi$
$947$	−24.8808	−	19.8418i	−0.808517	−	0.644771i	−0.937932	+	0.346820i	$0.887262\pi$
$948$		0			0
$949$	18.7483			0.608596
$950$		0			0
$951$	−30.2028	−	14.5449i	−0.979391	−	0.471650i
$952$		0			0
$953$	0.729014	−	0.351075i	0.0236151	−	0.0113724i	−0.422039	−	0.906578i	$-0.638685\pi$
$953$	0.729014	−	0.351075i	0.0236151	−	0.0113724i	0.445654	+	0.895205i	$0.352971\pi$
$954$		0			0
$955$	12.0352	−	52.7298i	0.389451	−	1.70629i
$956$		0			0
$957$	−35.9326	−	74.6148i	−1.16154	−	2.41196i
$958$		0			0
$959$	−23.5649	−	0.781675i	−0.760949	−	0.0252416i
$960$		0			0
$961$	39.4920			1.27394
$962$		0			0
$963$	6.04466	−	12.5519i	0.194786	−	0.404478i
$964$		0			0
$965$	48.7034	+	11.1162i	1.56782	+	0.357844i
$966$		0			0
$967$	−26.2688	+	5.99568i	−0.844747	+	0.192808i	−0.622927	−	0.782280i	$-0.714057\pi$
$967$	−26.2688	+	5.99568i	−0.844747	+	0.192808i	−0.221820	+	0.975088i	$0.571200\pi$
$968$		0			0
$969$	11.4068	−	2.60352i	0.366439	−	0.0836372i
$970$		0			0
$971$	−1.74501	+	7.64540i	−0.0560001	+	0.245352i	−0.995179	−	0.0980760i	$-0.968731\pi$
$971$	−1.74501	+	7.64540i	−0.0560001	+	0.245352i	0.939179	+	0.343429i	$0.111588\pi$
$972$		0			0
$973$	0.0840058	−	0.318918i	0.00269310	−	0.0102240i
$974$		0			0
$975$	12.9618	−	10.3367i	0.415110	−	0.331039i
$976$		0			0
$977$	24.9893	+	31.3356i	0.799478	+	1.00251i	0.999741	+	0.0227720i	$0.00724917\pi$
$977$	24.9893	+	31.3356i	0.799478	+	1.00251i	−0.200262	+	0.979742i	$0.564179\pi$
$978$		0			0
$979$	39.1014			1.24969
$980$		0			0
$981$	−38.0106			−1.21358
$982$		0			0
$983$	−7.80892	−	9.79207i	−0.249066	−	0.312319i	0.641545	−	0.767086i	$-0.278294\pi$
$983$	−7.80892	−	9.79207i	−0.249066	−	0.312319i	−0.890610	+	0.454767i	$0.849722\pi$
$984$		0			0
$985$	−22.1817	+	17.6893i	−0.706767	+	0.563627i
$986$		0			0
$987$	−87.1660	−	2.89140i	−2.77452	−	0.0920343i
$988$		0			0
$989$	−6.38609	+	27.9793i	−0.203066	+	0.889689i
$990$		0			0
$991$	34.1870	−	7.80295i	1.08599	−	0.247869i	0.358180	−	0.933653i	$-0.383398\pi$
$991$	34.1870	−	7.80295i	1.08599	−	0.247869i	0.727805	+	0.685784i	$0.240540\pi$
$992$		0			0
$993$	8.71291	−	1.98866i	0.276496	−	0.0631084i
$994$		0			0
$995$	−27.3059	−	6.23239i	−0.865654	−	0.197580i
$996$		0			0
$997$	−8.89687	+	18.4745i	−0.281767	+	0.585094i	−0.993034	−	0.117827i	$-0.962407\pi$
$997$	−8.89687	+	18.4745i	−0.281767	+	0.585094i	0.711268	+	0.702921i	$0.248121\pi$
$998$		0			0
$999$	−98.6748			−3.12193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.bb.b.111.19	yes	120
4.3	odd	2	inner	784.2.bb.b.111.2	✓	120
49.34	odd	14	inner	784.2.bb.b.671.2	yes	120
196.83	even	14	inner	784.2.bb.b.671.19	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.bb.b.111.2	✓	120	4.3	odd	2	inner
784.2.bb.b.111.19	yes	120	1.1	even	1	trivial
784.2.bb.b.671.2	yes	120	49.34	odd	14	inner
784.2.bb.b.671.19	yes	120	196.83	even	14	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.bb (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.94065 + 2.43350i) q^{3} +(-2.10945 + 1.68223i) q^{5} +(1.58011 + 2.12208i) q^{7} +(-1.48823 + 6.52037i) q^{9} +O(q^{10})\)	\(q+(1.94065 + 2.43350i) q^{3} +(-2.10945 + 1.68223i) q^{5} +(1.58011 + 2.12208i) q^{7} +(-1.48823 + 6.52037i) q^{9} +(3.26810 - 0.745923i) q^{11} +(2.27789 - 0.519914i) q^{13} +(-8.18742 - 1.86872i) q^{15} +(0.798533 - 1.65817i) q^{17} +2.04246 q^{19} +(-2.09764 + 7.96343i) q^{21} +(-2.42503 - 5.03562i) q^{23} +(0.507276 - 2.22252i) q^{25} +(-10.3425 + 4.98068i) q^{27} +(-7.15128 - 3.44388i) q^{29} -8.39595 q^{31} +(8.15745 + 6.50535i) q^{33} +(-6.90301 - 1.81831i) q^{35} +(7.74463 + 3.72962i) q^{37} +(5.68581 + 4.53428i) q^{39} +(3.65752 - 2.91677i) q^{41} +(-4.01452 - 3.20147i) q^{43} +(-7.82941 - 16.2579i) q^{45} +(2.35662 + 10.3250i) q^{47} +(-2.00648 + 6.70627i) q^{49} +(5.58483 - 1.27470i) q^{51} +(-1.71348 + 0.825167i) q^{53} +(-5.63908 + 7.07119i) q^{55} +(3.96370 + 4.97032i) q^{57} +(7.26876 - 9.11474i) q^{59} +(4.62760 - 9.60931i) q^{61} +(-16.1883 + 7.14478i) q^{63} +(-3.93048 + 4.92867i) q^{65} +6.97459i q^{67} +(7.54805 - 15.6737i) q^{69} +(-3.45857 - 7.18179i) q^{71} +(7.82301 + 1.78555i) q^{73} +(6.39295 - 3.07868i) q^{75} +(6.74688 + 5.75654i) q^{77} -9.68836i q^{79} +(-14.1145 - 6.79718i) q^{81} +(3.58252 - 15.6960i) q^{83} +(1.10496 + 4.84114i) q^{85} +(-5.49747 - 24.0860i) q^{87} +(11.3721 + 2.59562i) q^{89} +(4.70263 + 4.01235i) q^{91} +(-16.2936 - 20.4316i) q^{93} +(-4.30846 + 3.43588i) q^{95} +17.3194i q^{97} +22.4193i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 24 q^{9}+O(q^{10}) \) 120 * q - 24 * q^9	\( 120 q - 24 q^{9} - 14 q^{17} + 16 q^{21} + 40 q^{25} + 32 q^{29} - 62 q^{37} - 28 q^{41} - 60 q^{49} + 14 q^{53} - 34 q^{57} - 112 q^{61} - 32 q^{65} + 112 q^{69} + 42 q^{73} + 66 q^{77} - 44 q^{81} - 12 q^{85} + 28 q^{89} - 58 q^{93}+O(q^{100}) \) 120 * q - 24 * q^9 - 14 * q^17 + 16 * q^21 + 40 * q^25 + 32 * q^29 - 62 * q^37 - 28 * q^41 - 60 * q^49 + 14 * q^53 - 34 * q^57 - 112 * q^61 - 32 * q^65 + 112 * q^69 + 42 * q^73 + 66 * q^77 - 44 * q^81 - 12 * q^85 + 28 * q^89 - 58 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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