LMFDB - Embedded newform 684.2.bb.b.677.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(293,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("684.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.bb (of order $6$, degree $2$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$38$
Relative dimension:	$19$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			677.9
Character	$\chi$	$=$	684.677
Dual form			684.2.bb.b.293.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.237467 - 1.71570i) q^{3} +(1.87333 + 1.08157i) q^{5} +(-0.579619 + 1.00393i) q^{7} +(-2.88722 + 0.814842i) q^{9} +O(q^{10})$	\(q+(-0.237467 - 1.71570i) q^{3} +(1.87333 + 1.08157i) q^{5} +(-0.579619 + 1.00393i) q^{7} +(-2.88722 + 0.814842i) q^{9} +(-4.75192 - 2.74352i) q^{11} -3.68846i q^{13} +(1.41079 - 3.47090i) q^{15} +(6.21370 - 3.58748i) q^{17} +(2.91036 - 3.24496i) q^{19} +(1.86008 + 0.756049i) q^{21} -7.99740i q^{23} +(-0.160423 - 0.277861i) q^{25} +(2.08364 + 4.76009i) q^{27} +(1.63790 + 2.83693i) q^{29} +(-3.80508 + 2.19686i) q^{31} +(-3.57862 + 8.80434i) q^{33} +(-2.17163 + 1.25379i) q^{35} -2.39332i q^{37} +(-6.32827 + 0.875888i) q^{39} +(1.98171 - 3.43243i) q^{41} +6.78029 q^{43} +(-6.29002 - 1.59625i) q^{45} +(-6.01605 + 3.47337i) q^{47} +(2.82808 + 4.89839i) q^{49} +(-7.63058 - 9.80891i) q^{51} +(2.23413 - 3.86962i) q^{53} +(-5.93461 - 10.2790i) q^{55} +(-6.25848 - 4.22272i) q^{57} +(1.20354 - 2.08459i) q^{59} +(1.52218 + 2.63649i) q^{61} +(0.855442 - 3.37086i) q^{63} +(3.98932 - 6.90970i) q^{65} +10.2069i q^{67} +(-13.7211 + 1.89912i) q^{69} +(-7.79143 - 13.4952i) q^{71} +(2.86726 + 4.96623i) q^{73} +(-0.438630 + 0.341220i) q^{75} +(5.50860 - 3.18039i) q^{77} +6.33541i q^{79} +(7.67206 - 4.70526i) q^{81} +(-0.385643 - 0.222651i) q^{83} +15.5204 q^{85} +(4.47836 - 3.48382i) q^{87} +(-5.64951 + 9.78524i) q^{89} +(3.70295 + 2.13790i) q^{91} +(4.67273 + 6.00667i) q^{93} +(8.96172 - 2.93113i) q^{95} +16.9639i q^{97} +(15.9554 + 4.04908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 3 q^{3} + 2 q^{7} - 5 q^{9}+O(q^{10}) $ 38 * q + 3 * q^3 + 2 * q^7 - 5 * q^9	$ 38 q + 3 q^{3} + 2 q^{7} - 5 q^{9} + 6 q^{11} - 3 q^{15} + 6 q^{17} + 7 q^{19} - 3 q^{21} + 25 q^{25} - 9 q^{27} - 3 q^{29} + 21 q^{31} + 24 q^{33} + 3 q^{41} + 10 q^{43} - 4 q^{45} + 18 q^{47} - 27 q^{49} + 3 q^{51} + 21 q^{53} - 33 q^{57} + 48 q^{59} + 5 q^{61} + 20 q^{63} + 6 q^{65} - 57 q^{69} + 6 q^{71} + 7 q^{73} - 6 q^{75} - 51 q^{77} - 41 q^{81} - 12 q^{83} + 54 q^{87} - 21 q^{89} - 15 q^{91} - 6 q^{93} - 24 q^{95} - 28 q^{99}+O(q^{100}) $ 38 * q + 3 * q^3 + 2 * q^7 - 5 * q^9 + 6 * q^11 - 3 * q^15 + 6 * q^17 + 7 * q^19 - 3 * q^21 + 25 * q^25 - 9 * q^27 - 3 * q^29 + 21 * q^31 + 24 * q^33 + 3 * q^41 + 10 * q^43 - 4 * q^45 + 18 * q^47 - 27 * q^49 + 3 * q^51 + 21 * q^53 - 33 * q^57 + 48 * q^59 + 5 * q^61 + 20 * q^63 + 6 * q^65 - 57 * q^69 + 6 * q^71 + 7 * q^73 - 6 * q^75 - 51 * q^77 - 41 * q^81 - 12 * q^83 + 54 * q^87 - 21 * q^89 - 15 * q^91 - 6 * q^93 - 24 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.237467	−	1.71570i	−0.137102	−	0.990557i
$3$	−0.237467	−	1.71570i	−0.137102	−	0.990557i
$4$		0			0
$5$	1.87333	+	1.08157i	0.837779	+	0.483692i	0.856509	−	0.516133i	$-0.172629\pi$
$5$	1.87333	+	1.08157i	0.837779	+	0.483692i	−0.0187299	+	0.999825i	$0.505962\pi$
$6$		0			0
$7$	−0.579619	+	1.00393i	−0.219075	+	0.379449i	−0.954526	−	0.298129i	$-0.903637\pi$
$7$	−0.579619	+	1.00393i	−0.219075	+	0.379449i	0.735450	+	0.677579i	$0.236971\pi$
$8$		0			0
$9$	−2.88722	+	0.814842i	−0.962406	+	0.271614i
$10$		0			0
$11$	−4.75192	−	2.74352i	−1.43276	−	0.827203i	−0.435427	−	0.900224i	$-0.643402\pi$
$11$	−4.75192	−	2.74352i	−1.43276	−	0.827203i	−0.997330	+	0.0730216i	$0.976736\pi$
$12$		0			0
$13$		−	3.68846i		−	1.02299i	−0.859285	−	0.511497i	$-0.829091\pi$
$13$		−	3.68846i		−	1.02299i	0.859285	−	0.511497i	$-0.170909\pi$
$14$		0			0
$15$	1.41079	−	3.47090i	0.364263	−	0.896182i
$16$		0			0
$17$	6.21370	−	3.58748i	1.50704	−	0.870092i	0.507078	−	0.861900i	$-0.330726\pi$
$17$	6.21370	−	3.58748i	1.50704	−	0.870092i	0.999966	−	0.00819208i	$-0.00260765\pi$
$18$		0			0
$19$	2.91036	−	3.24496i	0.667683	−	0.744446i
$19$	2.91036	−	3.24496i	0.667683	−	0.744446i
$20$		0			0
$21$	1.86008	+	0.756049i	0.405902	+	0.164983i
$22$		0			0
$23$		−	7.99740i		−	1.66757i	−0.552087	−	0.833787i	$-0.686168\pi$
$23$		−	7.99740i		−	1.66757i	0.552087	−	0.833787i	$-0.313832\pi$
$24$		0			0
$25$	−0.160423	−	0.277861i	−0.0320846	−	0.0555722i
$26$		0			0
$27$	2.08364	+	4.76009i	0.400997	+	0.916079i
$28$		0			0
$29$	1.63790	+	2.83693i	0.304151	+	0.526805i	0.977072	−	0.212909i	$-0.0682939\pi$
$29$	1.63790	+	2.83693i	0.304151	+	0.526805i	−0.672921	+	0.739714i	$0.734961\pi$
$30$		0			0
$31$	−3.80508	+	2.19686i	−0.683412	+	0.394568i	−0.801140	−	0.598478i	$-0.795773\pi$
$31$	−3.80508	+	2.19686i	−0.683412	+	0.394568i	0.117727	+	0.993046i	$0.462439\pi$
$32$		0			0
$33$	−3.57862	+	8.80434i	−0.622958	+	1.53264i
$34$		0			0
$35$	−2.17163	+	1.25379i	−0.367073	+	0.211930i
$36$		0			0
$37$		−	2.39332i		−	0.393459i	−0.980458	−	0.196729i	$-0.936968\pi$
$37$		−	2.39332i		−	0.393459i	0.980458	−	0.196729i	$-0.0630320\pi$
$38$		0			0
$39$	−6.32827	+	0.875888i	−1.01333	+	0.140254i
$40$		0			0
$41$	1.98171	−	3.43243i	0.309492	−	0.536056i	−0.668759	−	0.743479i	$-0.733174\pi$
$41$	1.98171	−	3.43243i	0.309492	−	0.536056i	0.978251	+	0.207423i	$0.0665077\pi$
$42$		0			0
$43$	6.78029			1.03398			0.516992	−	0.855990i	$-0.327052\pi$
$43$	6.78029			1.03398			0.516992	+	0.855990i	$0.327052\pi$
$44$		0			0
$45$	−6.29002	−	1.59625i	−0.937661	−	0.237955i
$46$		0			0
$47$	−6.01605	+	3.47337i	−0.877532	+	0.506643i	−0.869844	−	0.493327i	$-0.835780\pi$
$47$	−6.01605	+	3.47337i	−0.877532	+	0.506643i	−0.00768790	+	0.999970i	$0.502447\pi$
$48$		0			0
$49$	2.82808	+	4.89839i	0.404012	+	0.699769i
$50$		0			0
$51$	−7.63058	−	9.80891i	−1.06849	−	1.37352i
$52$		0			0
$53$	2.23413	−	3.86962i	0.306881	−	0.531533i	−0.670798	−	0.741640i	$-0.734048\pi$
$53$	2.23413	−	3.86962i	0.306881	−	0.531533i	0.977678	+	0.210107i	$0.0673814\pi$
$54$		0			0
$55$	−5.93461	−	10.2790i	−0.800222	−	1.38603i
$56$		0			0
$57$	−6.25848	−	4.22272i	−0.828956	−	0.559313i
$58$		0			0
$59$	1.20354	−	2.08459i	0.156687	−	0.271391i	−0.776985	−	0.629519i	$-0.783252\pi$
$59$	1.20354	−	2.08459i	0.156687	−	0.271391i	0.933672	+	0.358129i	$0.116585\pi$
$60$		0			0
$61$	1.52218	+	2.63649i	0.194895	+	0.337568i	0.946866	−	0.321628i	$-0.104230\pi$
$61$	1.52218	+	2.63649i	0.194895	+	0.337568i	−0.751971	+	0.659196i	$0.770897\pi$
$62$		0			0
$63$	0.855442	−	3.37086i	0.107776	−	0.424688i
$64$		0			0
$65$	3.98932	−	6.90970i	0.494814	−	0.857043i
$66$		0			0
$67$			10.2069i			1.24697i	0.781836	+	0.623484i	$0.214283\pi$
$67$			10.2069i			1.24697i	−0.781836	+	0.623484i	$0.785717\pi$
$68$		0			0
$69$	−13.7211	+	1.89912i	−1.65183	+	0.228627i
$70$		0			0
$71$	−7.79143	−	13.4952i	−0.924673	−	1.60158i	−0.792086	−	0.610410i	$-0.791005\pi$
$71$	−7.79143	−	13.4952i	−0.924673	−	1.60158i	−0.132587	−	0.991171i	$-0.542328\pi$
$72$		0			0
$73$	2.86726	+	4.96623i	0.335587	+	0.581254i	0.983597	−	0.180378i	$-0.0577320\pi$
$73$	2.86726	+	4.96623i	0.335587	+	0.581254i	−0.648010	+	0.761632i	$0.724399\pi$
$74$		0			0
$75$	−0.438630	+	0.341220i	−0.0506486	+	0.0394007i
$76$		0			0
$77$	5.50860	−	3.18039i	0.627763	−	0.362439i
$78$		0			0
$79$			6.33541i			0.712789i	0.934336	+	0.356395i	$0.115994\pi$
$79$			6.33541i			0.712789i	−0.934336	+	0.356395i	$0.884006\pi$
$80$		0			0
$81$	7.67206	−	4.70526i	0.852452	−	0.522806i
$82$		0			0
$83$	−0.385643	−	0.222651i	−0.0423298	−	0.0244391i	0.478686	−	0.877986i	$-0.341113\pi$
$83$	−0.385643	−	0.222651i	−0.0423298	−	0.0244391i	−0.521016	+	0.853547i	$0.674447\pi$
$84$		0			0
$85$	15.5204			1.68343
$86$		0			0
$87$	4.47836	−	3.48382i	0.480131	−	0.373505i
$88$		0			0
$89$	−5.64951	+	9.78524i	−0.598847	+	1.03723i	0.394144	+	0.919049i	$0.371041\pi$
$89$	−5.64951	+	9.78524i	−0.598847	+	1.03723i	−0.992992	+	0.118185i	$0.962292\pi$
$90$		0			0
$91$	3.70295	+	2.13790i	0.388175	+	0.224113i
$92$		0			0
$93$	4.67273	+	6.00667i	0.484539	+	0.622863i
$94$		0			0
$95$	8.96172	−	2.93113i	0.919453	−	0.300728i
$96$		0			0
$97$			16.9639i			1.72242i	0.508246	+	0.861212i	$0.330294\pi$
$97$			16.9639i			1.72242i	−0.508246	+	0.861212i	$0.669706\pi$
$98$		0			0
$99$	15.9554	+	4.04908i	1.60357	+	0.406948i
$100$		0			0
$101$	−12.1748	+	7.02910i	−1.21143	+	0.699422i	−0.963072	−	0.269245i	$-0.913226\pi$
$101$	−12.1748	+	7.02910i	−1.21143	+	0.699422i	−0.248363	+	0.968667i	$0.579893\pi$
$102$		0			0
$103$	−12.1652	+	7.02361i	−1.19868	+	0.692057i	−0.960260	−	0.279106i	$-0.909962\pi$
$103$	−12.1652	+	7.02361i	−1.19868	+	0.692057i	−0.238417	+	0.971163i	$0.576628\pi$
$104$		0			0
$105$	2.66682	+	3.42813i	0.260255	+	0.334551i
$106$		0			0
$107$	6.39088			0.617830			0.308915	−	0.951090i	$-0.400034\pi$
$107$	6.39088			0.617830			0.308915	+	0.951090i	$0.400034\pi$
$108$		0			0
$109$	−6.36562	+	3.67519i	−0.609716	+	0.352019i	−0.772854	−	0.634584i	$-0.781172\pi$
$109$	−6.36562	+	3.67519i	−0.609716	+	0.352019i	0.163139	+	0.986603i	$0.447838\pi$
$110$		0			0
$111$	−4.10620	+	0.568334i	−0.389743	+	0.0539439i
$112$		0			0
$113$	−8.45109	−	14.6377i	−0.795012	−	1.37700i	−0.922832	−	0.385204i	$-0.874131\pi$
$113$	−8.45109	−	14.6377i	−0.795012	−	1.37700i	0.127820	−	0.991797i	$-0.459202\pi$
$114$		0			0
$115$	8.64973	−	14.9818i	0.806592	−	1.39706i
$116$		0			0
$117$	3.00551	+	10.6494i	0.277860	+	0.984536i
$118$		0			0
$119$			8.31749i			0.762463i
$120$		0			0
$121$	9.55381	+	16.5477i	0.868528	+	1.50434i
$122$		0			0
$123$	−6.35960	−	2.58493i	−0.573425	−	0.233075i
$124$		0			0
$125$		−	11.5097i		−	1.02946i
$126$		0			0
$127$	11.0946	+	6.40550i	0.984490	+	0.568396i	0.903623	−	0.428329i	$-0.140898\pi$
$127$	11.0946	+	6.40550i	0.984490	+	0.568396i	0.0808675	+	0.996725i	$0.474231\pi$
$128$		0			0
$129$	−1.61010	−	11.6329i	−0.141761	−	1.02422i
$130$		0			0
$131$	0.917184	+	0.529537i	0.0801348	+	0.0462658i	0.539532	−	0.841965i	$-0.318601\pi$
$131$	0.917184	+	0.529537i	0.0801348	+	0.0462658i	−0.459397	+	0.888231i	$0.651935\pi$
$132$		0			0
$133$	1.57081	+	4.80264i	0.136207	+	0.416442i
$134$		0			0
$135$	−1.24501	+	11.1708i	−0.107153	+	0.961431i
$136$		0			0
$137$	7.72664	−	4.46098i	0.660131	−	0.381127i	−0.132196	−	0.991224i	$-0.542203\pi$
$137$	7.72664	−	4.46098i	0.660131	−	0.381127i	0.792327	+	0.610097i	$0.208869\pi$
$138$		0			0
$139$	21.2606			1.80330			0.901649	−	0.432468i	$-0.142357\pi$
$139$	21.2606			1.80330			0.901649	+	0.432468i	$0.142357\pi$
$140$		0			0
$141$	7.38786	+	9.49690i	0.622170	+	0.799783i
$142$		0			0
$143$	−10.1194	+	17.5273i	−0.846224	+	1.46570i
$144$		0			0
$145$			7.08601i			0.588461i
$146$		0			0
$147$	7.73256	−	6.01534i	0.637771	−	0.496137i
$148$		0			0
$149$	4.81487	+	2.77986i	0.394449	+	0.227735i	0.684086	−	0.729401i	$-0.260201\pi$
$149$	4.81487	+	2.77986i	0.394449	+	0.227735i	−0.289637	+	0.957137i	$0.593535\pi$
$150$		0			0
$151$	−18.0660	−	10.4304i	−1.47019	−	0.848817i	−0.470753	−	0.882265i	$-0.656018\pi$
$151$	−18.0660	−	10.4304i	−1.47019	−	0.848817i	−0.999440	+	0.0334479i	$0.989351\pi$
$152$		0			0
$153$	−15.0171	+	15.4210i	−1.21406	+	1.24672i
$154$		0			0
$155$	−9.50423			−0.763398
$156$		0			0
$157$	6.97253	−	12.0768i	0.556469	−	0.963832i	−0.441319	−	0.897350i	$-0.645489\pi$
$157$	6.97253	−	12.0768i	0.556469	−	0.963832i	0.997788	−	0.0664816i	$-0.0211774\pi$
$158$		0			0
$159$	−7.16962	−	2.91417i	−0.568588	−	0.231109i
$160$		0			0
$161$	8.02882	+	4.63544i	0.632760	+	0.365324i
$162$		0			0
$163$	16.7880			1.31494			0.657470	−	0.753481i	$-0.271627\pi$
$163$	16.7880			1.31494			0.657470	+	0.753481i	$0.271627\pi$
$164$		0			0
$165$	−16.2264	+	12.6229i	−1.26323	+	0.982692i
$166$		0			0
$167$	15.0537			1.16489			0.582444	−	0.812871i	$-0.302097\pi$
$167$	15.0537			1.16489			0.582444	+	0.812871i	$0.302097\pi$
$168$		0			0
$169$	−0.604728			−0.0465176
$170$		0			0
$171$	−5.75872	+	11.7404i	−0.440380	+	0.897811i
$172$		0			0
$173$	5.08326			0.386473			0.193237	−	0.981152i	$-0.438102\pi$
$173$	5.08326			0.386473			0.193237	+	0.981152i	$0.438102\pi$
$174$		0			0
$175$	0.371937			0.0281158
$176$		0			0
$177$	−3.86232	−	1.56988i	−0.290310	−	0.118000i
$178$		0			0
$179$	14.1795			1.05983			0.529914	−	0.848052i	$-0.322224\pi$
$179$	14.1795			1.05983			0.529914	+	0.848052i	$0.322224\pi$
$180$		0			0
$181$	−3.82724	−	2.20966i	−0.284476	−	0.164242i	0.350972	−	0.936386i	$-0.385851\pi$
$181$	−3.82724	−	2.20966i	−0.284476	−	0.164242i	−0.635448	+	0.772144i	$0.719185\pi$
$182$		0			0
$183$	4.16194	−	3.23767i	0.307660	−	0.239336i
$184$		0			0
$185$	2.58853	−	4.48347i	0.190313	−	0.329631i
$186$		0			0
$187$	−39.3693			−2.87897
$188$		0			0
$189$	−5.98651	−	0.667209i	−0.435454	−	0.0485323i
$190$		0			0
$191$	9.52964	+	5.50194i	0.689540	+	0.398106i	0.803440	−	0.595386i	$-0.203001\pi$
$191$	9.52964	+	5.50194i	0.689540	+	0.398106i	−0.113900	+	0.993492i	$0.536334\pi$
$192$		0			0
$193$	−16.1429	−	9.32009i	−1.16199	−	0.670875i	−0.210209	−	0.977656i	$-0.567415\pi$
$193$	−16.1429	−	9.32009i	−1.16199	−	0.670875i	−0.951780	+	0.306782i	$0.900748\pi$
$194$		0			0
$195$	−12.8023	−	5.20363i	−0.916790	−	0.372639i
$196$		0			0
$197$			9.51937i			0.678227i	0.940745	+	0.339114i	$0.110127\pi$
$197$			9.51937i			0.678227i	−0.940745	+	0.339114i	$0.889873\pi$
$198$		0			0
$199$	9.72606	−	16.8460i	0.689462	−	1.19418i	−0.282550	−	0.959253i	$-0.591180\pi$
$199$	9.72606	−	16.8460i	0.689462	−	1.19418i	0.972012	−	0.234931i	$-0.0754863\pi$
$200$		0			0
$201$	17.5119	−	2.42380i	1.23519	−	0.170961i
$202$		0			0
$203$	−3.79744			−0.266528
$204$		0			0
$205$	7.42481	−	4.28672i	0.518571	−	0.299397i
$206$		0			0
$207$	6.51662	+	23.0902i	0.452937	+	1.60488i
$208$		0			0
$209$	−22.7324	+	7.43515i	−1.57244	+	0.514300i
$210$		0			0
$211$	−3.11918	−	1.80086i	−0.214733	−	0.123976i	0.388776	−	0.921332i	$-0.372898\pi$
$211$	−3.11918	−	1.80086i	−0.214733	−	0.123976i	−0.603509	+	0.797356i	$0.706231\pi$
$212$		0			0
$213$	−21.3034	+	16.5724i	−1.45968	+	1.13552i
$214$		0			0
$215$	12.7017	+	7.33334i	0.866250	+	0.500130i
$216$		0			0
$217$		−	5.09337i		−	0.345761i
$218$		0			0
$219$	7.83967	−	6.09866i	0.529755	−	0.412109i
$220$		0			0
$221$	−13.2323	−	22.9190i	−0.890100	−	1.54170i
$222$		0			0
$223$			8.38312i			0.561375i	0.959799	+	0.280688i	$0.0905625\pi$
$223$			8.38312i			0.561375i	−0.959799	+	0.280688i	$0.909438\pi$
$224$		0			0
$225$	0.689590	+	0.671526i	0.0459726	+	0.0447684i
$226$		0			0
$227$	5.82775	−	10.0940i	0.386801	−	0.669959i	−0.605216	−	0.796061i	$-0.706913\pi$
$227$	5.82775	−	10.0940i	0.386801	−	0.669959i	0.992017	+	0.126102i	$0.0402466\pi$
$228$		0			0
$229$	6.12244	+	10.6044i	0.404582	+	0.700757i	0.994273	−	0.106873i	$-0.0340837\pi$
$229$	6.12244	+	10.6044i	0.404582	+	0.700757i	−0.589691	+	0.807629i	$0.700750\pi$
$230$		0			0
$231$	−6.76469	−	8.69584i	−0.445084	−	0.572144i
$232$		0			0
$233$	3.27873	−	1.89298i	0.214797	−	0.124013i	−0.388742	−	0.921347i	$-0.627090\pi$
$233$	3.27873	−	1.89298i	0.214797	−	0.124013i	0.603539	+	0.797334i	$0.293757\pi$
$234$		0			0
$235$	−15.0267			−0.980236
$236$		0			0
$237$	10.8696	−	1.50445i	0.706058	−	0.0977246i
$238$		0			0
$239$	−2.69508	+	1.55601i	−0.174330	+	0.100650i	−0.584626	−	0.811303i	$-0.698759\pi$
$239$	−2.69508	+	1.55601i	−0.174330	+	0.100650i	0.410296	+	0.911953i	$0.365425\pi$
$240$		0			0
$241$	14.5688	−	8.41130i	0.938458	−	0.541819i	0.0489817	−	0.998800i	$-0.484402\pi$
$241$	14.5688	−	8.41130i	0.938458	−	0.541819i	0.889477	+	0.456980i	$0.151069\pi$
$242$		0			0
$243$	−9.89465	−	12.0456i	−0.634742	−	0.772724i
$244$		0			0
$245$			12.2351i			0.781669i
$246$		0			0
$247$	−11.9689	−	10.7348i	−0.761564	−	0.683036i
$248$		0			0
$249$	−0.290424	+	0.714518i	−0.0184048	+	0.0452807i
$250$		0			0
$251$	−2.33836	−	1.35005i	−0.147596	−	0.0852147i	0.424383	−	0.905483i	$-0.360491\pi$
$251$	−2.33836	−	1.35005i	−0.147596	−	0.0852147i	−0.571979	+	0.820268i	$0.693824\pi$
$252$		0			0
$253$	−21.9410	+	38.0030i	−1.37942	+	2.38923i
$254$		0			0
$255$	−3.68559	−	26.6283i	−0.230801	−	1.66753i
$256$		0			0
$257$	−11.7641			−0.733822			−0.366911	−	0.930256i	$-0.619585\pi$
$257$	−11.7641			−0.733822			−0.366911	+	0.930256i	$0.619585\pi$
$258$		0			0
$259$	2.40272	+	1.38721i	0.149298	+	0.0861971i
$260$		0			0
$261$	−7.04064	−	6.85621i	−0.435805	−	0.424389i
$262$		0			0
$263$		−	8.04839i		−	0.496285i	−0.968724	−	0.248142i	$-0.920180\pi$
$263$		−	8.04839i		−	0.496285i	0.968724	−	0.248142i	$-0.0798201\pi$
$264$		0			0
$265$	8.37051	−	4.83272i	0.514196	−	0.296871i
$266$		0			0
$267$	18.1301	+	7.36917i	1.10954	+	0.450986i
$268$		0			0
$269$	9.45728	+	16.3805i	0.576621	+	0.998736i	0.995863	+	0.0908622i	$0.0289623\pi$
$269$	9.45728	+	16.3805i	0.576621	+	0.998736i	−0.419243	+	0.907874i	$0.637704\pi$
$270$		0			0
$271$	1.11047	+	1.92338i	0.0674560	+	0.116837i	0.897781	−	0.440443i	$-0.145178\pi$
$271$	1.11047	+	1.92338i	0.0674560	+	0.116837i	−0.830325	+	0.557280i	$0.811845\pi$
$272$		0			0
$273$	2.78865	−	6.86081i	0.168777	−	0.415235i
$274$		0			0
$275$			1.76050i			0.106162i
$276$		0			0
$277$	−5.25095	+	9.09491i	−0.315499	+	0.546460i	−0.979543	−	0.201233i	$-0.935505\pi$
$277$	−5.25095	+	9.09491i	−0.315499	+	0.546460i	0.664045	+	0.747693i	$0.268839\pi$
$278$		0			0
$279$	9.19600	−	9.44337i	0.550550	−	0.565360i
$280$		0			0
$281$	−6.26429	−	10.8501i	−0.373696	−	0.647261i	0.616435	−	0.787406i	$-0.288576\pi$
$281$	−6.26429	−	10.8501i	−0.373696	−	0.647261i	−0.990131	+	0.140145i	$0.955243\pi$
$282$		0			0
$283$	−6.65054	+	11.5191i	−0.395333	+	0.684738i	−0.993144	−	0.116900i	$-0.962704\pi$
$283$	−6.65054	+	11.5191i	−0.395333	+	0.684738i	0.597810	+	0.801638i	$0.296038\pi$
$284$		0			0
$285$	−7.15704	−	14.6795i	−0.423947	−	0.869540i
$286$		0			0
$287$	2.29728	+	3.97900i	0.135604	+	0.234873i
$288$		0			0
$289$	17.2401	−	29.8607i	1.01412	−	1.75651i
$290$		0			0
$291$	29.1049	−	4.02837i	1.70616	−	0.236147i
$292$		0			0
$293$	3.48707	+	6.03978i	0.203717	+	0.352848i	0.949723	−	0.313091i	$-0.101365\pi$
$293$	3.48707	+	6.03978i	0.203717	+	0.352848i	−0.746006	+	0.665939i	$0.768031\pi$
$294$		0			0
$295$	4.50925	−	2.60342i	0.262539	−	0.151577i
$296$		0			0
$297$	3.15811	−	28.3361i	0.183252	−	1.64422i
$298$		0			0
$299$	−29.4981			−1.70592
$300$		0			0
$301$	−3.92998	+	6.80693i	−0.226520	+	0.392345i
$302$		0			0
$303$	14.9509	+	19.2190i	0.858907	+	1.10410i
$304$		0			0
$305$			6.58535i			0.377076i
$306$		0			0
$307$	0.381923	−	0.220503i	0.0217975	−	0.0125848i	−0.489062	−	0.872249i	$-0.662661\pi$
$307$	0.381923	−	0.220503i	0.0217975	−	0.0125848i	0.510859	+	0.859664i	$0.329327\pi$
$308$		0			0
$309$	14.9392	+	19.2040i	0.849862	+	1.09248i
$310$		0			0
$311$	10.8678	−	6.27455i	0.616259	−	0.355797i	−0.159152	−	0.987254i	$-0.550876\pi$
$311$	10.8678	−	6.27455i	0.616259	−	0.355797i	0.775411	+	0.631457i	$0.217543\pi$
$312$		0			0
$313$	9.71764	+	16.8314i	0.549274	+	0.951370i	0.998325	+	0.0578635i	$0.0184288\pi$
$313$	9.71764	+	16.8314i	0.549274	+	0.951370i	−0.449051	+	0.893506i	$0.648238\pi$
$314$		0			0
$315$	5.24834	−	5.38951i	0.295710	−	0.303665i
$316$		0			0
$317$	1.37691	+	2.38488i	0.0773352	+	0.133948i	0.902099	−	0.431528i	$-0.142026\pi$
$317$	1.37691	+	2.38488i	0.0773352	+	0.133948i	−0.824764	+	0.565477i	$0.808692\pi$
$318$		0			0
$319$		−	17.9745i		−	1.00638i
$320$		0			0
$321$	−1.51762	−	10.9648i	−0.0847055	−	0.611996i
$322$		0			0
$323$	6.44288	−	30.6041i	0.358492	−	1.70286i
$324$		0			0
$325$	−1.02488	+	0.591714i	−0.0568501	+	0.0328224i
$326$		0			0
$327$	7.81713	+	10.0487i	0.432288	+	0.555696i
$328$		0			0
$329$		−	8.05292i		−	0.443972i
$330$		0			0
$331$	9.87049	+	5.69873i	0.542531	+	0.313230i	0.746104	−	0.665829i	$-0.231922\pi$
$331$	9.87049	+	5.69873i	0.542531	+	0.313230i	−0.203573	+	0.979060i	$0.565255\pi$
$332$		0			0
$333$	1.95018	+	6.91003i	0.106869	+	0.378667i
$334$		0			0
$335$	−11.0394	+	19.1208i	−0.603148	+	1.04468i
$336$		0			0
$337$	−9.03012	−	5.21354i	−0.491902	−	0.284000i	0.233461	−	0.972366i	$-0.424995\pi$
$337$	−9.03012	−	5.21354i	−0.491902	−	0.284000i	−0.725363	+	0.688366i	$0.758328\pi$
$338$		0			0
$339$	−23.1070	+	17.9755i	−1.25500	+	0.976294i
$340$		0			0
$341$	24.1086			1.30555
$342$		0			0
$343$	−14.6715			−0.792187
$344$		0			0
$345$	−27.7582	−	11.2826i	−1.49445	−	0.607436i
$346$		0			0
$347$	2.51298	+	1.45087i	0.134904	+	0.0778866i	0.565933	−	0.824451i	$-0.308516\pi$
$347$	2.51298	+	1.45087i	0.134904	+	0.0778866i	−0.431029	+	0.902338i	$0.641849\pi$
$348$		0			0
$349$	10.5068	−	18.1983i	0.562416	−	0.974134i	−0.434869	−	0.900494i	$-0.643205\pi$
$349$	10.5068	−	18.1983i	0.562416	−	0.974134i	0.997285	−	0.0736397i	$-0.0234615\pi$
$350$		0			0
$351$	17.5574	−	7.68542i	0.937144	−	0.410218i
$352$		0			0
$353$	−10.5606	−	6.09714i	−0.562082	−	0.324518i	0.191899	−	0.981415i	$-0.438536\pi$
$353$	−10.5606	−	6.09714i	−0.562082	−	0.324518i	−0.753981	+	0.656896i	$0.771869\pi$
$354$		0			0
$355$		−	33.7079i		−	1.78903i
$356$		0			0
$357$	14.2703	−	1.97513i	0.755263	−	0.104535i
$358$		0			0
$359$	−15.3852	+	8.88267i	−0.812002	+	0.468809i	−0.847651	−	0.530555i	$-0.821984\pi$
$359$	−15.3852	+	8.88267i	−0.812002	+	0.468809i	0.0356488	+	0.999364i	$0.488650\pi$
$360$		0			0
$361$	−2.05957	−	18.8880i	−0.108398	−	0.994108i
$362$		0			0
$363$	26.1221	−	20.3210i	1.37105	−	1.06657i
$364$		0			0
$365$			12.4045i			0.649283i
$366$		0			0
$367$	−15.5385	−	26.9134i	−0.811101	−	1.40487i	−0.912094	−	0.409981i	$-0.865535\pi$
$367$	−15.5385	−	26.9134i	−0.811101	−	1.40487i	0.100993	−	0.994887i	$-0.467798\pi$
$368$		0			0
$369$	−2.92475	+	11.5250i	−0.152257	+	0.599966i
$370$		0			0
$371$	2.58988	+	4.48581i	0.134460	+	0.232891i
$372$		0			0
$373$	−12.7351	+	7.35259i	−0.659396	+	0.380703i	−0.792047	−	0.610460i	$-0.790985\pi$
$373$	−12.7351	+	7.35259i	−0.659396	+	0.380703i	0.132650	+	0.991163i	$0.457651\pi$
$374$		0			0
$375$	−19.7472	+	2.73318i	−1.01974	+	0.141141i
$376$		0			0
$377$	10.4639	−	6.04134i	0.538919	−	0.311145i
$378$		0			0
$379$			16.7552i			0.860658i	0.902672	+	0.430329i	$0.141602\pi$
$379$			16.7552i			0.860658i	−0.902672	+	0.430329i	$0.858398\pi$
$380$		0			0
$381$	8.35526	−	20.5561i	0.428053	−	1.05312i
$382$		0			0
$383$	−16.8463	+	29.1786i	−0.860804	+	1.49096i	0.0103496	+	0.999946i	$0.496706\pi$
$383$	−16.8463	+	29.1786i	−0.860804	+	1.49096i	−0.871154	+	0.491010i	$0.836628\pi$
$384$		0			0
$385$	13.7592			0.701235
$386$		0			0
$387$	−19.5762	+	5.52487i	−0.995114	+	0.280845i
$388$		0			0
$389$	15.0581	−	8.69377i	0.763474	−	0.440792i	−0.0670679	−	0.997748i	$-0.521364\pi$
$389$	15.0581	−	8.69377i	0.763474	−	0.440792i	0.830542	+	0.556957i	$0.188031\pi$
$390$		0			0
$391$	−28.6905	−	49.6935i	−1.45094	−	2.51311i
$392$		0			0
$393$	0.690722	−	1.69936i	0.0348423	−	0.0857212i
$394$		0			0
$395$	−6.85217	+	11.8683i	−0.344770	+	0.597160i
$396$		0			0
$397$	18.9136	+	32.7594i	0.949248	+	1.64415i	0.747013	+	0.664809i	$0.231487\pi$
$397$	18.9136	+	32.7594i	0.949248	+	1.64415i	0.202235	+	0.979337i	$0.435179\pi$
$398$		0			0
$399$	7.86685	−	3.83550i	0.393835	−	0.192015i
$400$		0			0
$401$	13.1196	−	22.7238i	0.655161	−	1.13477i	−0.326693	−	0.945131i	$-0.605934\pi$
$401$	13.1196	−	22.7238i	0.655161	−	1.13477i	0.981853	−	0.189641i	$-0.0607324\pi$
$402$		0			0
$403$	8.10304	+	14.0349i	0.403641	+	0.699127i
$404$		0			0
$405$	19.4614	−	0.516643i	0.967043	−	0.0256722i
$406$		0			0
$407$	−6.56611	+	11.3728i	−0.325470	+	0.563731i
$408$		0			0
$409$		−	15.9688i		−	0.789607i	−0.918766	−	0.394803i	$-0.870813\pi$
$409$		−	15.9688i		−	0.789607i	0.918766	−	0.394803i	$-0.129187\pi$
$410$		0			0
$411$	−9.48850	−	12.1972i	−0.468033	−	0.601645i
$412$		0			0
$413$	1.39519	+	2.41654i	0.0686527	+	0.118910i
$414$		0			0
$415$	−0.481624	−	0.834197i	−0.0236420	−	0.0409491i
$416$		0			0
$417$	−5.04869	−	36.4767i	−0.247235	−	1.78627i
$418$		0			0
$419$	−0.841342	+	0.485749i	−0.0411022	+	0.0237304i	−0.520410	−	0.853916i	$-0.674221\pi$
$419$	−0.841342	+	0.485749i	−0.0411022	+	0.0237304i	0.479308	+	0.877647i	$0.340888\pi$
$420$		0			0
$421$		−	29.6008i		−	1.44265i	−0.692594	−	0.721327i	$-0.743532\pi$
$421$		−	29.6008i		−	1.44265i	0.692594	−	0.721327i	$-0.256468\pi$
$422$		0			0
$423$	14.5394	−	14.9305i	0.706930	−	0.725947i
$424$		0			0
$425$	−1.99364	−	1.15103i	−0.0967059	−	0.0558332i
$426$		0			0
$427$	−3.52913			−0.170787
$428$		0			0
$429$	32.4744	+	13.1996i	1.56788	+	0.637282i
$430$		0			0
$431$	−9.67388	+	16.7557i	−0.465974	+	0.807092i	−0.999245	−	0.0388533i	$-0.987629\pi$
$431$	−9.67388	+	16.7557i	−0.465974	+	0.807092i	0.533270	+	0.845945i	$0.320963\pi$
$432$		0			0
$433$	−15.3014	−	8.83429i	−0.735340	−	0.424549i	0.0850324	−	0.996378i	$-0.472901\pi$
$433$	−15.3014	−	8.83429i	−0.735340	−	0.424549i	−0.820373	+	0.571829i	$0.806234\pi$
$434$		0			0
$435$	12.1574	−	1.68270i	0.582905	−	0.0806791i
$436$		0			0
$437$	−25.9513	−	23.2753i	−1.24142	−	1.11341i
$438$		0			0
$439$		−	11.3514i		−	0.541771i	−0.962612	−	0.270885i	$-0.912684\pi$
$439$		−	11.3514i		−	0.541771i	0.962612	−	0.270885i	$-0.0873164\pi$
$440$		0			0
$441$	−12.1567	−	11.8383i	−0.578891	−	0.563727i
$442$		0			0
$443$	−19.0510	+	10.9991i	−0.905140	+	0.522583i	−0.878864	−	0.477072i	$-0.841698\pi$
$443$	−19.0510	+	10.9991i	−0.905140	+	0.522583i	−0.0262756	+	0.999655i	$0.508365\pi$
$444$		0			0
$445$	−21.1668	+	12.2207i	−1.00340	+	0.579315i
$446$		0			0
$447$	3.62603	−	8.92097i	0.171505	−	0.421947i
$448$		0			0
$449$	−9.46823			−0.446833			−0.223417	−	0.974723i	$-0.571721\pi$
$449$	−9.46823			−0.446833			−0.223417	+	0.974723i	$0.571721\pi$
$450$		0			0
$451$	−18.8339	+	10.8738i	−0.886853	+	0.512025i
$452$		0			0
$453$	−13.6054	+	33.4727i	−0.639235	+	1.57269i
$454$		0			0
$455$	4.62457	+	8.00998i	0.216803	+	0.375514i
$456$		0			0
$457$	−3.48307	+	6.03286i	−0.162931	+	0.282205i	−0.935919	−	0.352216i	$-0.885428\pi$
$457$	−3.48307	+	6.03286i	−0.162931	+	0.282205i	0.772987	+	0.634421i	$0.218762\pi$
$458$		0			0
$459$	30.0239	+	22.1027i	1.40139	+	1.03167i
$460$		0			0
$461$		−	27.8282i		−	1.29609i	−0.761603	−	0.648044i	$-0.775587\pi$
$461$		−	27.8282i		−	1.29609i	0.761603	−	0.648044i	$-0.224413\pi$
$462$		0			0
$463$	1.63444	+	2.83094i	0.0759590	+	0.131565i	0.901503	−	0.432773i	$-0.142465\pi$
$463$	1.63444	+	2.83094i	0.0759590	+	0.131565i	−0.825544	+	0.564338i	$0.809132\pi$
$464$		0			0
$465$	2.25694	+	16.3064i	0.104663	+	0.756189i
$466$		0			0
$467$			37.8307i			1.75060i	0.483583	+	0.875299i	$0.339335\pi$
$467$			37.8307i			1.75060i	−0.483583	+	0.875299i	$0.660665\pi$
$468$		0			0
$469$	−10.2470	−	5.91609i	−0.473161	−	0.273180i
$470$		0			0
$471$	−22.3758	−	9.09490i	−1.03102	−	0.419071i
$472$		0			0
$473$	−32.2194	−	18.6019i	−1.48145	−	0.855315i
$474$		0			0
$475$	−1.36854	−	0.288109i	−0.0627928	−	0.0132194i
$476$		0			0
$477$	−3.29728	+	12.9929i	−0.150972	+	0.594904i
$478$		0			0
$479$	12.5210	−	7.22898i	0.572097	−	0.330300i	−0.185889	−	0.982571i	$-0.559517\pi$
$479$	12.5210	−	7.22898i	0.572097	−	0.330300i	0.757986	+	0.652270i	$0.226183\pi$
$480$		0			0
$481$	−8.82765			−0.402506
$482$		0			0
$483$	6.04642	−	14.8758i	0.275122	−	0.676871i
$484$		0			0
$485$	−18.3476	+	31.7790i	−0.833122	+	1.44301i
$486$		0			0
$487$			18.1127i			0.820764i	0.911914	+	0.410382i	$0.134605\pi$
$487$			18.1127i			0.820764i	−0.911914	+	0.410382i	$0.865395\pi$
$488$		0			0
$489$	−3.98661	−	28.8031i	−0.180281	−	1.30252i
$490$		0			0
$491$	12.6553	+	7.30655i	0.571126	+	0.329740i	0.757599	−	0.652720i	$-0.226372\pi$
$491$	12.6553	+	7.30655i	0.571126	+	0.329740i	−0.186473	+	0.982460i	$0.559706\pi$
$492$		0			0
$493$	20.3549	+	11.7519i	0.916738	+	0.529279i
$494$		0			0
$495$	25.5103	+	24.8421i	1.14660	+	1.11657i
$496$		0			0
$497$	18.0642			0.810292
$498$		0			0
$499$	−9.81329	+	16.9971i	−0.439303	+	0.760895i	−0.997636	−	0.0687217i	$-0.978108\pi$
$499$	−9.81329	+	16.9971i	−0.439303	+	0.760895i	0.558333	+	0.829617i	$0.311441\pi$
$500$		0			0
$501$	−3.57475	−	25.8275i	−0.159708	−	1.15389i
$502$		0			0
$503$	33.3905	+	19.2780i	1.48881	+	0.859564i	0.999918	−	0.0127813i	$-0.00406852\pi$
$503$	33.3905	+	19.2780i	1.48881	+	0.859564i	0.488890	+	0.872345i	$0.337402\pi$
$504$		0			0
$505$	−30.4098			−1.35322
$506$		0			0
$507$	0.143603	+	1.03753i	0.00637764	+	0.0460783i
$508$		0			0
$509$	22.3423			0.990304			0.495152	−	0.868806i	$-0.335112\pi$
$509$	22.3423			0.990304			0.495152	+	0.868806i	$0.335112\pi$
$510$		0			0
$511$	−6.64766			−0.294075
$512$		0			0
$513$	21.5105	+	7.09225i	0.949710	+	0.313130i
$514$		0			0
$515$	−30.3860			−1.33897
$516$		0			0
$517$	38.1171			1.67639
$518$		0			0
$519$	−1.20711	−	8.72132i	−0.0529861	−	0.382824i
$520$		0			0
$521$	28.2189			1.23629			0.618147	−	0.786063i	$-0.287884\pi$
$521$	28.2189			1.23629			0.618147	+	0.786063i	$0.287884\pi$
$522$		0			0
$523$	−1.57143	−	0.907267i	−0.0687139	−	0.0396720i	0.465249	−	0.885180i	$-0.345965\pi$
$523$	−1.57143	−	0.907267i	−0.0687139	−	0.0396720i	−0.533963	+	0.845508i	$0.679298\pi$
$524$		0			0
$525$	−0.0883228	−	0.638130i	−0.00385472	−	0.0278503i
$526$		0			0
$527$	−15.7624	+	27.3013i	−0.686622	+	1.18926i
$528$		0			0
$529$	−40.9584			−1.78080
$530$		0			0
$531$	−1.77627	+	6.99937i	−0.0770835	+	0.303747i
$532$		0			0
$533$	−12.6604	−	7.30947i	−0.548382	−	0.316608i
$534$		0			0
$535$	11.9722	+	6.91217i	0.517605	+	0.298839i
$536$		0			0
$537$	−3.36717	−	24.3277i	−0.145304	−	1.04982i
$538$		0			0
$539$		−	31.0356i		−	1.33680i
$540$		0			0
$541$	2.82744	−	4.89728i	0.121561	−	0.210550i	−0.798822	−	0.601567i	$-0.794543\pi$
$541$	2.82744	−	4.89728i	0.121561	−	0.210550i	0.920384	+	0.391017i	$0.127877\pi$
$542$		0			0
$543$	−2.88225	+	7.09109i	−0.123689	+	0.304308i
$544$		0			0
$545$	−15.8999			−0.681076
$546$		0			0
$547$	−5.72987	+	3.30814i	−0.244991	+	0.141446i	−0.617469	−	0.786595i	$-0.711842\pi$
$547$	−5.72987	+	3.30814i	−0.244991	+	0.141446i	0.372477	+	0.928041i	$0.378508\pi$
$548$		0			0
$549$	−6.54318	−	6.37178i	−0.279256	−	0.271941i
$550$		0			0
$551$	13.9726	+	2.94157i	0.595254	+	0.125315i
$552$		0			0
$553$	−6.36030	−	3.67212i	−0.270467	−	0.156154i
$554$		0			0
$555$	−8.30696	−	3.37646i	−0.352611	−	0.143323i
$556$		0			0
$557$	−4.57661	−	2.64231i	−0.193917	−	0.111958i	0.399898	−	0.916560i	$-0.369046\pi$
$557$	−4.57661	−	2.64231i	−0.193917	−	0.111958i	−0.593815	+	0.804602i	$0.702379\pi$
$558$		0			0
$559$		−	25.0088i		−	1.05776i
$560$		0			0
$561$	9.34892	+	67.5458i	0.394712	+	2.85178i
$562$		0			0
$563$	20.2665	+	35.1027i	0.854132	+	1.47940i	0.877448	+	0.479673i	$0.159245\pi$
$563$	20.2665	+	35.1027i	0.854132	+	1.47940i	−0.0233152	+	0.999728i	$0.507422\pi$
$564$		0			0
$565$		−	36.5617i		−	1.53816i
$566$		0			0
$567$	0.276872	+	10.4295i	0.0116275	+	0.437996i
$568$		0			0
$569$	−6.01566	+	10.4194i	−0.252190	+	0.436805i	−0.964128	−	0.265436i	$-0.914484\pi$
$569$	−6.01566	+	10.4194i	−0.252190	+	0.436805i	0.711939	+	0.702242i	$0.247817\pi$
$570$		0			0
$571$	20.7598	+	35.9570i	0.868769	+	1.50475i	0.863255	+	0.504768i	$0.168422\pi$
$571$	20.7598	+	35.9570i	0.868769	+	1.50475i	0.00551421	+	0.999985i	$0.498245\pi$
$572$		0			0
$573$	7.17667	−	17.6565i	0.299810	−	0.737610i
$574$		0			0
$575$	−2.22217	+	1.28297i	−0.0926707	+	0.0535035i
$576$		0			0
$577$	13.1000			0.545362			0.272681	−	0.962105i	$-0.412090\pi$
$577$	13.1000			0.545362			0.272681	+	0.962105i	$0.412090\pi$
$578$		0			0
$579$	−12.1570	+	29.9095i	−0.505229	+	1.24299i
$580$		0			0
$581$	0.447051	−	0.258105i	0.0185468	−	0.0107080i
$582$		0			0
$583$	−21.2328	+	12.2587i	−0.879371	+	0.507705i
$584$		0			0
$585$	−5.88771	+	23.2005i	−0.243427	+	0.959222i
$586$		0			0
$587$		−	12.2077i		−	0.503866i	−0.967745	−	0.251933i	$-0.918934\pi$
$587$		−	12.2077i		−	0.503866i	0.967745	−	0.251933i	$-0.0810663\pi$
$588$		0			0
$589$	−3.94542	+	18.7410i	−0.162568	+	0.772210i
$590$		0			0
$591$	16.3323	−	2.26054i	0.671823	−	0.0929861i
$592$		0			0
$593$	9.32150	+	5.38177i	0.382788	+	0.221003i	0.679031	−	0.734110i	$-0.262400\pi$
$593$	9.32150	+	5.38177i	0.382788	+	0.221003i	−0.296242	+	0.955113i	$0.595734\pi$
$594$		0			0
$595$	−8.99592	+	15.5814i	−0.368797	+	0.638775i
$596$		0			0
$597$	−31.2123	−	12.6866i	−1.27743	−	0.519227i
$598$		0			0
$599$	−10.4530			−0.427098			−0.213549	−	0.976932i	$-0.568502\pi$
$599$	−10.4530			−0.427098			−0.213549	+	0.976932i	$0.568502\pi$
$600$		0			0
$601$	3.63430	+	2.09826i	0.148246	+	0.0855899i	0.572288	−	0.820053i	$-0.306056\pi$
$601$	3.63430	+	2.09826i	0.148246	+	0.0855899i	−0.424042	+	0.905642i	$0.639389\pi$
$602$		0			0
$603$	−8.31699	−	29.4695i	−0.338694	−	1.20009i
$604$		0			0
$605$			41.3324i			1.68040i
$606$		0			0
$607$	31.8972	−	18.4159i	1.29467	−	0.747476i	0.315189	−	0.949029i	$-0.397932\pi$
$607$	31.8972	−	18.4159i	1.29467	−	0.747476i	0.979478	+	0.201553i	$0.0645987\pi$
$608$		0			0
$609$	0.901767	+	6.51524i	0.0365414	+	0.264011i
$610$		0			0
$611$	12.8114	+	22.1900i	0.518293	+	0.897710i
$612$		0			0
$613$	−1.22361	−	2.11935i	−0.0494209	−	0.0855996i	0.840257	−	0.542189i	$-0.182404\pi$
$613$	−1.22361	−	2.11935i	−0.0494209	−	0.0855996i	−0.889678	+	0.456589i	$0.849071\pi$
$614$		0			0
$615$	−9.11785	−	11.7208i	−0.367667	−	0.472627i
$616$		0			0
$617$		−	17.4247i		−	0.701491i	−0.936471	−	0.350746i	$-0.885928\pi$
$617$		−	17.4247i		−	0.701491i	0.936471	−	0.350746i	$-0.114072\pi$
$618$		0			0
$619$	5.45452	−	9.44751i	0.219236	−	0.379728i	−0.735339	−	0.677700i	$-0.762977\pi$
$619$	5.45452	−	9.44751i	0.219236	−	0.379728i	0.954575	+	0.297972i	$0.0963103\pi$
$620$		0			0
$621$	38.0683	−	16.6637i	1.52763	−	0.668692i
$622$		0			0
$623$	−6.54913	−	11.3434i	−0.262385	−	0.454464i
$624$		0			0
$625$	11.6464	−	20.1722i	0.465857	−	0.806887i
$626$		0			0
$627$	18.1547	+	37.2363i	0.725027	+	1.48708i
$628$		0			0
$629$	−8.58598	−	14.8714i	−0.342345	−	0.592960i
$630$		0			0
$631$	7.62241	−	13.2024i	0.303443	−	0.525579i	−0.673470	−	0.739214i	$-0.735197\pi$
$631$	7.62241	−	13.2024i	0.303443	−	0.525579i	0.976914	+	0.213635i	$0.0685303\pi$
$632$		0			0
$633$	−2.34902	+	5.77920i	−0.0933652	+	0.229703i
$634$		0			0
$635$	13.8560	+	23.9992i	0.549857	+	0.952380i
$636$		0			0
$637$	18.0675	−	10.4313i	0.715860	−	0.413302i
$638$		0			0
$639$	33.4920	+	32.6147i	1.32492	+	1.29022i
$640$		0			0
$641$	29.8538			1.17915			0.589576	−	0.807713i	$-0.299295\pi$
$641$	29.8538			1.17915			0.589576	+	0.807713i	$0.299295\pi$
$642$		0			0
$643$	−16.1427	+	27.9599i	−0.636605	+	1.10263i	0.349568	+	0.936911i	$0.386328\pi$
$643$	−16.1427	+	27.9599i	−0.636605	+	1.10263i	−0.986173	+	0.165721i	$0.947005\pi$
$644$		0			0
$645$	9.56554	−	23.5337i	0.376643	−	0.926639i
$646$		0			0
$647$			19.1495i			0.752843i	0.926449	+	0.376421i	$0.122845\pi$
$647$			19.1495i			0.752843i	−0.926449	+	0.376421i	$0.877155\pi$
$648$		0			0
$649$	−11.4382	+	6.60387i	−0.448990	+	0.259225i
$650$		0			0
$651$	−8.73867	+	1.20951i	−0.342496	+	0.0474044i
$652$		0			0
$653$	4.23728	−	2.44639i	0.165818	−	0.0957348i	−0.414795	−	0.909915i	$-0.636147\pi$
$653$	4.23728	−	2.44639i	0.165818	−	0.0957348i	0.580612	+	0.814180i	$0.302813\pi$
$654$		0			0
$655$	1.14546	+	1.98399i	0.0447568	+	0.0775211i
$656$		0			0
$657$	−12.3251	−	12.0022i	−0.480848	−	0.468252i
$658$		0			0
$659$	−4.57152	−	7.91811i	−0.178081	−	0.308446i	0.763142	−	0.646231i	$-0.223656\pi$
$659$	−4.57152	−	7.91811i	−0.178081	−	0.308446i	−0.941223	+	0.337785i	$0.890322\pi$
$660$		0			0
$661$			26.1088i			1.01552i	0.861500	+	0.507758i	$0.169526\pi$
$661$			26.1088i			1.01552i	−0.861500	+	0.507758i	$0.830474\pi$
$662$		0			0
$663$	−36.1798	+	28.1451i	−1.40511	+	1.09306i
$664$		0			0
$665$	−2.25173	+	10.6959i	−0.0873184	+	0.414768i
$666$		0			0
$667$	22.6881	−	13.0990i	0.878486	−	0.507194i
$668$		0			0
$669$	14.3829	−	1.99072i	0.556074	−	0.0769655i
$670$		0			0
$671$		−	16.7045i		−	0.644870i
$672$		0			0
$673$	14.5893	+	8.42315i	0.562377	+	0.324688i	0.754099	−	0.656761i	$-0.228074\pi$
$673$	14.5893	+	8.42315i	0.562377	+	0.324688i	−0.191722	+	0.981449i	$0.561407\pi$
$674$		0			0
$675$	0.988379	−	1.34259i	0.0380427	−	0.0516763i
$676$		0			0
$677$	−8.35434	+	14.4701i	−0.321083	+	0.556133i	−0.980712	−	0.195459i	$-0.937380\pi$
$677$	−8.35434	+	14.4701i	−0.321083	+	0.556133i	0.659628	+	0.751592i	$0.270714\pi$
$678$		0			0
$679$	−17.0306	−	9.83260i	−0.653573	−	0.377340i
$680$		0			0
$681$	−18.7020	−	7.60166i	−0.716664	−	0.291296i
$682$		0			0
$683$	20.8098			0.796265			0.398132	−	0.917328i	$-0.369658\pi$
$683$	20.8098			0.796265			0.398132	+	0.917328i	$0.369658\pi$
$684$		0			0
$685$	19.2994			0.737392
$686$		0			0
$687$	16.7400	−	13.0224i	0.638670	−	0.496836i
$688$		0			0
$689$	−14.2729	−	8.24048i	−0.543755	−	0.313937i
$690$		0			0
$691$	15.9769	−	27.6729i	0.607792	−	1.05273i	−0.383812	−	0.923411i	$-0.625389\pi$
$691$	15.9769	−	27.6729i	0.607792	−	1.05273i	0.991604	−	0.129315i	$-0.0412778\pi$
$692$		0			0
$693$	−13.3130	+	13.6711i	−0.505720	+	0.519323i
$694$		0			0
$695$	39.8281	+	22.9947i	1.51076	+	0.872240i
$696$		0			0
$697$		−	28.4375i		−	1.07715i
$698$		0			0
$699$	−4.02636	−	5.17578i	−0.152291	−	0.195766i
$700$		0			0
$701$	−34.2634	+	19.7820i	−1.29411	+	0.747156i	−0.979380	−	0.202025i	$-0.935248\pi$
$701$	−34.2634	+	19.7820i	−1.29411	+	0.747156i	−0.314731	+	0.949181i	$0.601914\pi$
$702$		0			0
$703$	−7.76622	−	6.96542i	−0.292909	−	0.262706i
$704$		0			0
$705$	3.56836	+	25.7813i	0.134392	+	0.970980i
$706$		0			0
$707$		−	16.2968i		−	0.612904i
$708$		0			0
$709$	4.83476	+	8.37404i	0.181573	+	0.314494i	0.942416	−	0.334442i	$-0.108548\pi$
$709$	4.83476	+	8.37404i	0.181573	+	0.314494i	−0.760843	+	0.648936i	$0.775214\pi$
$710$		0			0
$711$	−5.16236	−	18.2917i	−0.193604	−	0.685993i
$712$		0			0
$713$	17.5692	+	30.4308i	0.657972	+	1.13964i
$714$		0			0
$715$	−37.9138	+	21.8896i	−1.41790	+	0.818623i
$716$		0			0
$717$	3.30963	+	4.25444i	0.123600	+	0.158885i
$718$		0			0
$719$	−17.7233	+	10.2326i	−0.660969	+	0.381610i	−0.792646	−	0.609682i	$-0.791297\pi$
$719$	−17.7233	+	10.2326i	−0.660969	+	0.381610i	0.131677	+	0.991293i	$0.457964\pi$
$720$		0			0
$721$		−	16.2841i		−	0.606450i
$722$		0			0
$723$	−17.8908	−	22.9982i	−0.665367	−	0.855312i
$724$		0			0
$725$	0.525515	−	0.910219i	0.0195171	−	0.0338047i
$726$		0			0
$727$	−5.04707			−0.187186			−0.0935928	−	0.995611i	$-0.529835\pi$
$727$	−5.04707			−0.187186			−0.0935928	+	0.995611i	$0.529835\pi$
$728$		0			0
$729$	−18.3169	+	19.8366i	−0.678403	+	0.734690i
$730$		0			0
$731$	42.1307	−	24.3242i	1.55826	−	0.899662i
$732$		0			0
$733$	−15.8405	−	27.4366i	−0.585082	−	1.01339i	−0.994865	−	0.101209i	$-0.967729\pi$
$733$	−15.8405	−	27.4366i	−0.585082	−	1.01339i	0.409783	−	0.912183i	$-0.365604\pi$
$734$		0			0
$735$	20.9916	−	2.90542i	0.774288	−	0.107168i
$736$		0			0
$737$	28.0028	−	48.5022i	1.03150	−	1.78660i
$738$		0			0
$739$	−19.8400	−	34.3638i	−0.729825	−	1.26409i	−0.956957	−	0.290230i	$-0.906268\pi$
$739$	−19.8400	−	34.3638i	−0.729825	−	1.26409i	0.227132	−	0.973864i	$-0.427065\pi$
$740$		0			0
$741$	−15.5753	+	23.0842i	−0.572175	+	0.848018i
$742$		0			0
$743$	3.04017	−	5.26573i	0.111533	−	0.193181i	−0.804855	−	0.593471i	$-0.797757\pi$
$743$	3.04017	−	5.26573i	0.111533	−	0.193181i	0.916389	+	0.400290i	$0.131091\pi$
$744$		0			0
$745$	6.01322	+	10.4152i	0.220307	+	0.381584i
$746$		0			0
$747$	1.29486	+	0.328604i	0.0473765	+	0.0120230i
$748$		0			0
$749$	−3.70427	+	6.41599i	−0.135351	+	0.234435i
$750$		0			0
$751$			21.3874i			0.780436i	0.920722	+	0.390218i	$0.127600\pi$
$751$			21.3874i			0.780436i	−0.920722	+	0.390218i	$0.872400\pi$
$752$		0			0
$753$	−1.76100	+	4.33251i	−0.0641743	+	0.157885i
$754$		0			0
$755$	−22.5624	−	39.0793i	−0.821131	−	1.42224i
$756$		0			0
$757$	24.7787	+	42.9180i	0.900598	+	1.55988i	0.826719	+	0.562615i	$0.190205\pi$
$757$	24.7787	+	42.9180i	0.900598	+	1.55988i	0.0738793	+	0.997267i	$0.476462\pi$
$758$		0			0
$759$	70.4118	+	28.6197i	2.55579	+	1.03883i
$760$		0			0
$761$	−21.7860	+	12.5782i	−0.789744	+	0.455959i	−0.839872	−	0.542784i	$-0.817370\pi$
$761$	−21.7860	+	12.5782i	−0.789744	+	0.455959i	0.0501287	+	0.998743i	$0.484037\pi$
$762$		0			0
$763$		−	8.52084i		−	0.308475i
$764$		0			0
$765$	−44.8108	+	12.6467i	−1.62014	+	0.457242i
$766$		0			0
$767$	−7.68893	−	4.43920i	−0.277631	−	0.160290i
$768$		0			0
$769$	−31.4071			−1.13257			−0.566285	−	0.824210i	$-0.691620\pi$
$769$	−31.4071			−1.13257			−0.566285	+	0.824210i	$0.691620\pi$
$770$		0			0
$771$	2.79358	+	20.1835i	0.100608	+	0.726892i
$772$		0			0
$773$	15.7143	−	27.2179i	0.565203	−	0.978960i	−0.431828	−	0.901956i	$-0.642131\pi$
$773$	15.7143	−	27.2179i	0.565203	−	0.978960i	0.997031	−	0.0770042i	$-0.0245355\pi$
$774$		0			0
$775$	1.22085	+	0.704856i	0.0438541	+	0.0253192i
$776$		0			0
$777$	1.80946	−	4.45175i	0.0649141	−	0.159706i
$778$		0			0
$779$	−5.37060	−	16.4202i	−0.192422	−	0.588315i
$780$		0			0
$781$			85.5039i			3.05957i
$782$		0			0
$783$	−10.0912	+	13.7077i	−0.360632	+	0.489874i
$784$		0			0
$785$	26.1237	−	15.0825i	0.932395	−	0.538318i
$786$		0			0
$787$	−41.5260	+	23.9750i	−1.48024	+	0.854618i	−0.999750	−	0.0223812i	$-0.992875\pi$
$787$	−41.5260	+	23.9750i	−1.48024	+	0.854618i	−0.480492	+	0.876999i	$0.659542\pi$
$788$		0			0
$789$	−13.8086	+	1.91123i	−0.491598	+	0.0680415i
$790$		0			0
$791$	19.5936			0.696670
$792$		0			0
$793$	9.72458	−	5.61449i	0.345330	−	0.199376i
$794$		0			0
$795$	−10.2792	−	13.2136i	−0.364565	−	0.468639i
$796$		0			0
$797$	1.56147	+	2.70454i	0.0553100	+	0.0957997i	0.892355	−	0.451335i	$-0.149052\pi$
$797$	1.56147	+	2.70454i	0.0553100	+	0.0957997i	−0.837045	+	0.547134i	$0.815719\pi$
$798$		0			0
$799$	−24.9213	+	43.1650i	−0.881653	+	1.52707i
$800$		0			0
$801$	8.33795	−	32.8556i	0.294607	−	1.16090i
$802$		0			0
$803$		−	31.4655i		−	1.11039i
$804$		0			0
$805$	10.0271	+	17.3674i	0.353408	+	0.612121i
$806$		0			0
$807$	25.8581	−	20.1156i	0.910250	−	0.708104i
$808$		0			0
$809$			7.58237i			0.266582i	0.991077	+	0.133291i	$0.0425545\pi$
$809$			7.58237i			0.266582i	−0.991077	+	0.133291i	$0.957445\pi$
$810$		0			0
$811$	20.3579	+	11.7536i	0.714862	+	0.412726i	0.812859	−	0.582461i	$-0.197910\pi$
$811$	20.3579	+	11.7536i	0.714862	+	0.412726i	−0.0979965	+	0.995187i	$0.531243\pi$
$812$		0			0
$813$	3.03624	−	2.36196i	0.106486	−	0.0828376i
$814$		0			0
$815$	31.4495	+	18.1574i	1.10163	+	0.636026i
$816$		0			0
$817$	19.7331	−	22.0018i	0.690374	−	0.769745i
$818$		0			0
$819$	−12.4333	−	3.15526i	−0.434454	−	0.110254i
$820$		0			0
$821$	−9.52100	+	5.49695i	−0.332285	+	0.191845i	−0.656855	−	0.754017i	$-0.728114\pi$
$821$	−9.52100	+	5.49695i	−0.332285	+	0.191845i	0.324570	+	0.945862i	$0.394780\pi$
$822$		0			0
$823$	7.61812			0.265551			0.132775	−	0.991146i	$-0.457611\pi$
$823$	7.61812			0.265551			0.132775	+	0.991146i	$0.457611\pi$
$824$		0			0
$825$	3.02048	−	0.418060i	0.105159	−	0.0145550i
$826$		0			0
$827$	−17.1257	+	29.6627i	−0.595521	+	1.03147i	0.397953	+	0.917406i	$0.369721\pi$
$827$	−17.1257	+	29.6627i	−0.595521	+	1.03147i	−0.993473	+	0.114066i	$0.963613\pi$
$828$		0			0
$829$		−	19.6742i		−	0.683313i	−0.939825	−	0.341656i	$-0.889012\pi$
$829$		−	19.6742i		−	0.683313i	0.939825	−	0.341656i	$-0.110988\pi$
$830$		0			0
$831$	16.8510	+	6.84928i	0.584555	+	0.237599i
$832$		0			0
$833$	35.1458	+	20.2914i	1.21773	+	0.703056i
$834$		0			0
$835$	28.2005	+	16.2816i	0.975918	+	0.563446i
$836$		0			0
$837$	−18.3857	−	13.5350i	−0.635502	−	0.467839i
$838$		0			0
$839$	−43.9921			−1.51878			−0.759388	−	0.650639i	$-0.774501\pi$
$839$	−43.9921			−1.51878			−0.759388	+	0.650639i	$0.774501\pi$
$840$		0			0
$841$	9.13454	−	15.8215i	0.314984	−	0.545569i
$842$		0			0
$843$	−17.1278	+	13.3241i	−0.589914	+	0.458908i
$844$		0			0
$845$	−1.13286	−	0.654054i	−0.0389714	−	0.0225002i
$846$		0			0
$847$	−22.1503			−0.761092
$848$		0			0
$849$	21.3425	+	8.67489i	0.732472	+	0.297722i
$850$		0			0
$851$	−19.1403			−0.656121
$852$		0			0
$853$	−21.0941			−0.722247			−0.361124	−	0.932518i	$-0.617607\pi$
$853$	−21.0941			−0.722247			−0.361124	+	0.932518i	$0.617607\pi$
$854$		0			0
$855$	−23.4860	+	15.7652i	−0.803205	+	0.539159i
$856$		0			0
$857$	−29.2090			−0.997761			−0.498880	−	0.866671i	$-0.666255\pi$
$857$	−29.2090			−0.997761			−0.498880	+	0.866671i	$0.666255\pi$
$858$		0			0
$859$	49.2891			1.68172			0.840862	−	0.541250i	$-0.182049\pi$
$859$	49.2891			1.68172			0.840862	+	0.541250i	$0.182049\pi$
$860$		0			0
$861$	6.28122	−	4.88631i	0.214064	−	0.166525i
$862$		0			0
$863$	−35.1023			−1.19490			−0.597448	−	0.801908i	$-0.703819\pi$
$863$	−35.1023			−1.19490			−0.597448	+	0.801908i	$0.703819\pi$
$864$		0			0
$865$	9.52262	+	5.49789i	0.323779	+	0.186934i
$866$		0			0
$867$	−55.3258	−	22.4878i	−1.87896	−	0.763725i
$868$		0			0
$869$	17.3813	−	30.1053i	0.589621	−	1.02125i
$870$		0			0
$871$	37.6476			1.27564
$872$		0			0
$873$	−13.8229	−	48.9785i	−0.467835	−	1.65767i
$874$		0			0
$875$	11.5549	+	6.67124i	0.390628	+	0.225529i
$876$		0			0
$877$	1.80498	+	1.04211i	0.0609499	+	0.0351895i	0.530165	−	0.847894i	$-0.322130\pi$
$877$	1.80498	+	1.04211i	0.0609499	+	0.0351895i	−0.469215	+	0.883084i	$0.655463\pi$
$878$		0			0
$879$	9.53435	−	7.41699i	0.321586	−	0.250169i
$880$		0			0
$881$		−	28.6918i		−	0.966653i	−0.875440	−	0.483326i	$-0.839428\pi$
$881$		−	28.6918i		−	0.966653i	0.875440	−	0.483326i	$-0.160572\pi$
$882$		0			0
$883$	10.5198	−	18.2208i	0.354018	−	0.613178i	−0.632931	−	0.774208i	$-0.718148\pi$
$883$	10.5198	−	18.2208i	0.354018	−	0.613178i	0.986949	+	0.161030i	$0.0514817\pi$
$884$		0			0
$885$	−5.53747	−	7.11828i	−0.186140	−	0.239278i
$886$		0			0
$887$	−3.25471			−0.109282			−0.0546412	−	0.998506i	$-0.517402\pi$
$887$	−3.25471			−0.109282			−0.0546412	+	0.998506i	$0.517402\pi$
$888$		0			0
$889$	−12.8613	+	7.42549i	−0.431355	+	0.249043i
$890$		0			0
$891$	−49.3660	+	1.31053i	−1.65382	+	0.0439043i
$892$		0			0
$893$	−6.23794	+	29.6306i	−0.208745	+	0.991552i
$894$		0			0
$895$	26.5629	+	15.3361i	0.887901	+	0.512630i
$896$		0			0
$897$	7.00483	+	50.6097i	0.233884	+	1.68981i
$898$		0			0
$899$	−12.4647	−	7.19650i	−0.415721	−	0.240017i
$900$		0			0
$901$		−	32.0595i		−	1.06806i
$902$		0			0
$903$	12.6119	+	5.12623i	0.419696	+	0.170590i
$904$		0			0
$905$	−4.77978	−	8.27883i	−0.158885	−	0.275198i
$906$		0			0
$907$			20.6635i			0.686120i	0.939314	+	0.343060i	$0.111463\pi$
$907$			20.6635i			0.686120i	−0.939314	+	0.343060i	$0.888537\pi$
$908$		0			0
$909$	29.4236	−	30.2151i	0.975919	−	1.00217i
$910$		0			0
$911$	1.86088	−	3.22314i	0.0616536	−	0.106787i	−0.833551	−	0.552442i	$-0.813696\pi$
$911$	1.86088	−	3.22314i	0.0616536	−	0.106787i	0.895205	+	0.445655i	$0.147029\pi$
$912$		0			0
$913$	1.22169	+	2.11604i	0.0404322	+	0.0700306i
$914$		0			0
$915$	11.2985	−	1.56380i	0.373515	−	0.0516978i
$916$		0			0
$917$	−1.06323	+	0.613859i	−0.0351111	+	0.0202714i
$918$		0			0
$919$	12.9790			0.428136			0.214068	−	0.976819i	$-0.431329\pi$
$919$	12.9790			0.428136			0.214068	+	0.976819i	$0.431329\pi$
$920$		0			0
$921$	−0.469010	−	0.602900i	−0.0154544	−	0.0198662i
$922$		0			0
$923$	−49.7763	+	28.7384i	−1.63841	+	0.945935i
$924$		0			0
$925$	−0.665009	+	0.383943i	−0.0218654	+	0.0126240i
$926$		0			0
$927$	29.4006	−	30.1914i	0.965642	−	0.991617i
$928$		0			0
$929$		−	1.77927i		−	0.0583759i	−0.999574	−	0.0291880i	$-0.990708\pi$
$929$		−	1.77927i		−	0.0583759i	0.999574	−	0.0291880i	$-0.00929213\pi$
$930$		0			0
$931$	24.1258	+	5.07905i	0.790692	+	0.166459i
$932$		0			0
$933$	−13.3460	−	17.1559i	−0.436928	−	0.561659i
$934$		0			0
$935$	−73.7518	−	42.5806i	−2.41194	−	1.39253i
$936$		0			0
$937$	15.6494	−	27.1056i	0.511244	−	0.885501i	−0.488671	−	0.872468i	$-0.662518\pi$
$937$	15.6494	−	27.1056i	0.511244	−	0.885501i	0.999915	−	0.0130328i	$-0.00414859\pi$
$938$		0			0
$939$	26.5700	−	20.6694i	0.867079	−	0.674521i
$940$		0			0
$941$	−34.1103			−1.11196			−0.555982	−	0.831194i	$-0.687658\pi$
$941$	−34.1103			−1.11196			−0.555982	+	0.831194i	$0.687658\pi$
$942$		0			0
$943$	−27.4505	−	15.8486i	−0.893912	−	0.516100i
$944$		0			0
$945$	−10.4931	−	7.72471i	−0.341340	−	0.251285i
$946$		0			0
$947$		−	37.9421i		−	1.23295i	−0.787374	−	0.616476i	$-0.788560\pi$
$947$		−	37.9421i		−	1.23295i	0.787374	−	0.616476i	$-0.211440\pi$
$948$		0			0
$949$	18.3178	−	10.5758i	0.594619	−	0.343304i
$950$		0			0
$951$	3.76476	−	2.92870i	0.122081	−	0.0949695i
$952$		0			0
$953$	−17.5320	−	30.3663i	−0.567917	−	0.983661i	−0.996772	−	0.0802879i	$-0.974416\pi$
$953$	−17.5320	−	30.3663i	−0.567917	−	0.983661i	0.428855	−	0.903374i	$-0.358917\pi$
$954$		0			0
$955$	11.9014	+	20.6139i	0.385121	+	0.667050i
$956$		0			0
$957$	−30.8387	+	4.26835i	−0.996875	+	0.137976i
$958$		0			0
$959$			10.3427i			0.333982i
$960$		0			0
$961$	−5.84758	+	10.1283i	−0.188632	+	0.326720i
$962$		0			0
$963$	−18.4519	+	5.20756i	−0.594603	+	0.167811i
$964$		0			0
$965$	−20.1606	−	34.9192i	−0.648993	−	1.12409i
$966$		0			0
$967$	13.8467	−	23.9831i	0.445279	−	0.771246i	−0.552793	−	0.833319i	$-0.686438\pi$
$967$	13.8467	−	23.9831i	0.445279	−	0.771246i	0.998072	+	0.0620732i	$0.0197712\pi$
$968$		0			0
$969$	−54.0373	−	3.78655i	−1.73593	−	0.121642i
$970$		0			0
$971$	−10.1329	−	17.5507i	−0.325181	−	0.563230i	0.656368	−	0.754441i	$-0.272092\pi$
$971$	−10.1329	−	17.5507i	−0.325181	−	0.563230i	−0.981549	+	0.191211i	$0.938759\pi$
$972$		0			0
$973$	−12.3230	+	21.3441i	−0.395058	+	0.684260i
$974$		0			0
$975$	1.25858	+	1.61787i	0.0403067	+	0.0518132i
$976$		0			0
$977$	22.6922	+	39.3040i	0.725987	+	1.25745i	0.958566	+	0.284869i	$0.0919502\pi$
$977$	22.6922	+	39.3040i	0.725987	+	1.25745i	−0.232579	+	0.972577i	$0.574716\pi$
$978$		0			0
$979$	53.6920	−	30.9991i	1.71600	−	0.990736i
$980$		0			0
$981$	15.3842	−	15.7981i	0.491181	−	0.504393i
$982$		0			0
$983$	12.5508			0.400309			0.200155	−	0.979764i	$-0.435856\pi$
$983$	12.5508			0.400309			0.200155	+	0.979764i	$0.435856\pi$
$984$		0			0
$985$	−10.2958	+	17.8329i	−0.328053	+	0.568204i
$986$		0			0
$987$	−13.8164	+	1.91230i	−0.439779	+	0.0608693i
$988$		0			0
$989$		−	54.2247i		−	1.72425i
$990$		0			0
$991$	−33.6309	+	19.4168i	−1.06832	+	0.616796i	−0.927722	−	0.373271i	$-0.878236\pi$
$991$	−33.6309	+	19.4168i	−1.06832	+	0.616796i	−0.140599	+	0.990067i	$0.544903\pi$
$992$		0			0
$993$	7.43336	−	18.2880i	0.235891	−	0.580352i
$994$		0			0
$995$	36.4402	−	21.0388i	1.15523	−	0.666974i
$996$		0			0
$997$	−12.9658	−	22.4574i	−0.410631	−	0.711235i	0.584327	−	0.811518i	$-0.301358\pi$
$997$	−12.9658	−	22.4574i	−0.410631	−	0.711235i	−0.994959	+	0.100283i	$0.968025\pi$
$998$		0			0
$999$	11.3924	−	4.98681i	0.360439	−	0.157776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.bb.b.677.9	yes	38
3.2	odd	2		2052.2.bb.b.1817.6		38
9.4	even	3		2052.2.n.b.449.6		38
9.5	odd	6		684.2.n.b.221.15	yes	38
19.8	odd	6		684.2.n.b.65.15	✓	38
57.8	even	6		2052.2.n.b.521.14		38
171.103	odd	6		2052.2.bb.b.1205.6		38
171.122	even	6	inner	684.2.bb.b.293.9	yes	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.n.b.65.15	✓	38	19.8	odd	6
684.2.n.b.221.15	yes	38	9.5	odd	6
684.2.bb.b.293.9	yes	38	171.122	even	6	inner
684.2.bb.b.677.9	yes	38	1.1	even	1	trivial
2052.2.n.b.449.6		38	9.4	even	3
2052.2.n.b.521.14		38	57.8	even	6
2052.2.bb.b.1205.6		38	171.103	odd	6
2052.2.bb.b.1817.6		38	3.2	odd	2

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.237467 - 1.71570i) q^{3} +(1.87333 + 1.08157i) q^{5} +(-0.579619 + 1.00393i) q^{7} +(-2.88722 + 0.814842i) q^{9} +O(q^{10})\)	\(q+(-0.237467 - 1.71570i) q^{3} +(1.87333 + 1.08157i) q^{5} +(-0.579619 + 1.00393i) q^{7} +(-2.88722 + 0.814842i) q^{9} +(-4.75192 - 2.74352i) q^{11} -3.68846i q^{13} +(1.41079 - 3.47090i) q^{15} +(6.21370 - 3.58748i) q^{17} +(2.91036 - 3.24496i) q^{19} +(1.86008 + 0.756049i) q^{21} -7.99740i q^{23} +(-0.160423 - 0.277861i) q^{25} +(2.08364 + 4.76009i) q^{27} +(1.63790 + 2.83693i) q^{29} +(-3.80508 + 2.19686i) q^{31} +(-3.57862 + 8.80434i) q^{33} +(-2.17163 + 1.25379i) q^{35} -2.39332i q^{37} +(-6.32827 + 0.875888i) q^{39} +(1.98171 - 3.43243i) q^{41} +6.78029 q^{43} +(-6.29002 - 1.59625i) q^{45} +(-6.01605 + 3.47337i) q^{47} +(2.82808 + 4.89839i) q^{49} +(-7.63058 - 9.80891i) q^{51} +(2.23413 - 3.86962i) q^{53} +(-5.93461 - 10.2790i) q^{55} +(-6.25848 - 4.22272i) q^{57} +(1.20354 - 2.08459i) q^{59} +(1.52218 + 2.63649i) q^{61} +(0.855442 - 3.37086i) q^{63} +(3.98932 - 6.90970i) q^{65} +10.2069i q^{67} +(-13.7211 + 1.89912i) q^{69} +(-7.79143 - 13.4952i) q^{71} +(2.86726 + 4.96623i) q^{73} +(-0.438630 + 0.341220i) q^{75} +(5.50860 - 3.18039i) q^{77} +6.33541i q^{79} +(7.67206 - 4.70526i) q^{81} +(-0.385643 - 0.222651i) q^{83} +15.5204 q^{85} +(4.47836 - 3.48382i) q^{87} +(-5.64951 + 9.78524i) q^{89} +(3.70295 + 2.13790i) q^{91} +(4.67273 + 6.00667i) q^{93} +(8.96172 - 2.93113i) q^{95} +16.9639i q^{97} +(15.9554 + 4.04908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 3 q^{3} + 2 q^{7} - 5 q^{9}+O(q^{10}) \) 38 * q + 3 * q^3 + 2 * q^7 - 5 * q^9	\( 38 q + 3 q^{3} + 2 q^{7} - 5 q^{9} + 6 q^{11} - 3 q^{15} + 6 q^{17} + 7 q^{19} - 3 q^{21} + 25 q^{25} - 9 q^{27} - 3 q^{29} + 21 q^{31} + 24 q^{33} + 3 q^{41} + 10 q^{43} - 4 q^{45} + 18 q^{47} - 27 q^{49} + 3 q^{51} + 21 q^{53} - 33 q^{57} + 48 q^{59} + 5 q^{61} + 20 q^{63} + 6 q^{65} - 57 q^{69} + 6 q^{71} + 7 q^{73} - 6 q^{75} - 51 q^{77} - 41 q^{81} - 12 q^{83} + 54 q^{87} - 21 q^{89} - 15 q^{91} - 6 q^{93} - 24 q^{95} - 28 q^{99}+O(q^{100}) \) 38 * q + 3 * q^3 + 2 * q^7 - 5 * q^9 + 6 * q^11 - 3 * q^15 + 6 * q^17 + 7 * q^19 - 3 * q^21 + 25 * q^25 - 9 * q^27 - 3 * q^29 + 21 * q^31 + 24 * q^33 + 3 * q^41 + 10 * q^43 - 4 * q^45 + 18 * q^47 - 27 * q^49 + 3 * q^51 + 21 * q^53 - 33 * q^57 + 48 * q^59 + 5 * q^61 + 20 * q^63 + 6 * q^65 - 57 * q^69 + 6 * q^71 + 7 * q^73 - 6 * q^75 - 51 * q^77 - 41 * q^81 - 12 * q^83 + 54 * q^87 - 21 * q^89 - 15 * q^91 - 6 * q^93 - 24 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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