LMFDB - Embedded newform 552.2.q.d.265.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			265.1
Character	$\chi$	$=$	552.265
Dual form			552.2.q.d.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{3} +(-2.56277 + 0.752498i) q^{5} +(1.17327 + 1.35403i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{3} +(-2.56277 + 0.752498i) q^{5} +(1.17327 + 1.35403i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-2.42392 - 1.55776i) q^{11} +(-3.30631 + 3.81569i) q^{13} +(0.380118 + 2.64378i) q^{15} +(-0.712216 - 1.55954i) q^{17} +(-1.14997 + 2.51809i) q^{19} +(1.50722 - 0.968631i) q^{21} +(-3.93560 + 2.74063i) q^{23} +(1.79528 - 1.15376i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-1.36070 - 2.97953i) q^{29} +(1.48790 + 10.3486i) q^{31} +(-1.88687 + 2.17756i) q^{33} +(-4.02573 - 2.58718i) q^{35} +(-5.76631 - 1.69314i) q^{37} +(3.30631 + 3.81569i) q^{39} +(1.81150 - 0.531905i) q^{41} +(-0.668472 + 4.64933i) q^{43} +2.67097 q^{45} +2.78956 q^{47} +(0.539380 - 3.75147i) q^{49} +(-1.64502 + 0.483021i) q^{51} +(4.66539 + 5.38414i) q^{53} +(7.38418 + 2.16819i) q^{55} +(2.32880 + 1.49663i) q^{57} +(-4.37377 + 5.04760i) q^{59} +(-1.51384 - 10.5290i) q^{61} +(-0.744272 - 1.62973i) q^{63} +(5.60203 - 12.2667i) q^{65} +(2.48821 - 1.59907i) q^{67} +(2.15264 + 4.28557i) q^{69} +(-3.59643 + 2.31129i) q^{71} +(3.32454 - 7.27972i) q^{73} +(-0.886520 - 1.94121i) q^{75} +(-0.734669 - 5.10973i) q^{77} +(7.31852 - 8.44602i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-13.9612 - 4.09938i) q^{83} +(2.99879 + 3.46079i) q^{85} +(-3.14285 + 0.922823i) q^{87} +(0.245498 - 1.70747i) q^{89} -9.04575 q^{91} +10.4550 q^{93} +(1.05226 - 7.31864i) q^{95} +(-14.8335 + 4.35551i) q^{97} +(1.88687 + 2.17756i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	$ 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$		0			0
$5$	−2.56277	+	0.752498i	−1.14611	+	0.336527i	−0.799019	−	0.601305i	$-0.794648\pi$
$5$	−2.56277	+	0.752498i	−1.14611	+	0.336527i	−0.347088	+	0.937833i	$0.612829\pi$
$6$		0			0
$7$	1.17327	+	1.35403i	0.443455	+	0.511774i	0.932839	−	0.360294i	$-0.117324\pi$
$7$	1.17327	+	1.35403i	0.443455	+	0.511774i	−0.489384	+	0.872069i	$0.662778\pi$
$8$		0			0
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$		0			0
$11$	−2.42392	−	1.55776i	−0.730840	−	0.469683i	0.121552	−	0.992585i	$-0.461213\pi$
$11$	−2.42392	−	1.55776i	−0.730840	−	0.469683i	−0.852392	+	0.522903i	$0.824849\pi$
$12$		0			0
$13$	−3.30631	+	3.81569i	−0.917007	+	1.05828i	0.0810959	+	0.996706i	$0.474158\pi$
$13$	−3.30631	+	3.81569i	−0.917007	+	1.05828i	−0.998102	+	0.0615756i	$0.980387\pi$
$14$		0			0
$15$	0.380118	+	2.64378i	0.0981461	+	0.682621i
$16$		0			0
$17$	−0.712216	−	1.55954i	−0.172738	−	0.378243i	0.803386	−	0.595459i	$-0.203030\pi$
$17$	−0.712216	−	1.55954i	−0.172738	−	0.378243i	−0.976124	+	0.217216i	$0.930302\pi$
$18$		0			0
$19$	−1.14997	+	2.51809i	−0.263822	+	0.577689i	−0.994465	−	0.105071i	$-0.966493\pi$
$19$	−1.14997	+	2.51809i	−0.263822	+	0.577689i	0.730643	+	0.682760i	$0.239220\pi$
$20$		0			0
$21$	1.50722	−	0.968631i	0.328902	−	0.211373i
$22$		0			0
$23$	−3.93560	+	2.74063i	−0.820629	+	0.571461i
$23$	−3.93560	+	2.74063i	−0.820629	+	0.571461i
$24$		0			0
$25$	1.79528	−	1.15376i	0.359057	−	0.230752i
$26$		0			0
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$		0			0
$29$	−1.36070	−	2.97953i	−0.252676	−	0.553284i	0.740206	−	0.672380i	$-0.234728\pi$
$29$	−1.36070	−	2.97953i	−0.252676	−	0.553284i	−0.992883	+	0.119096i	$0.962000\pi$
$30$		0			0
$31$	1.48790	+	10.3486i	0.267235	+	1.85866i	0.474336	+	0.880344i	$0.342688\pi$
$31$	1.48790	+	10.3486i	0.267235	+	1.85866i	−0.207101	+	0.978320i	$0.566403\pi$
$32$		0			0
$33$	−1.88687	+	2.17756i	−0.328461	+	0.379064i
$34$		0			0
$35$	−4.02573	−	2.58718i	−0.680473	−	0.437313i
$36$		0			0
$37$	−5.76631	−	1.69314i	−0.947976	−	0.278351i	−0.229032	−	0.973419i	$-0.573556\pi$
$37$	−5.76631	−	1.69314i	−0.947976	−	0.278351i	−0.718944	+	0.695068i	$0.755374\pi$
$38$		0			0
$39$	3.30631	+	3.81569i	0.529434	+	0.610999i
$40$		0			0
$41$	1.81150	−	0.531905i	0.282909	−	0.0830696i	−0.137200	−	0.990543i	$-0.543810\pi$
$41$	1.81150	−	0.531905i	0.282909	−	0.0830696i	0.420109	+	0.907474i	$0.361992\pi$
$42$		0			0
$43$	−0.668472	+	4.64933i	−0.101941	+	0.709016i	0.873189	+	0.487382i	$0.162048\pi$
$43$	−0.668472	+	4.64933i	−0.101941	+	0.709016i	−0.975130	+	0.221634i	$0.928861\pi$
$44$		0			0
$45$	2.67097			0.398164
$46$		0			0
$47$	2.78956			0.406899			0.203450	−	0.979085i	$-0.434785\pi$
$47$	2.78956			0.406899			0.203450	+	0.979085i	$0.434785\pi$
$48$		0			0
$49$	0.539380	−	3.75147i	0.0770542	−	0.535924i
$50$		0			0
$51$	−1.64502	+	0.483021i	−0.230349	+	0.0676365i
$52$		0			0
$53$	4.66539	+	5.38414i	0.640840	+	0.739569i	0.979523	−	0.201332i	$-0.0645269\pi$
$53$	4.66539	+	5.38414i	0.640840	+	0.739569i	−0.338683	+	0.940901i	$0.609981\pi$
$54$		0			0
$55$	7.38418	+	2.16819i	0.995682	+	0.292359i
$56$		0			0
$57$	2.32880	+	1.49663i	0.308457	+	0.198233i
$58$		0			0
$59$	−4.37377	+	5.04760i	−0.569417	+	0.657142i	−0.965295	−	0.261161i	$-0.915895\pi$
$59$	−4.37377	+	5.04760i	−0.569417	+	0.657142i	0.395879	+	0.918303i	$0.370440\pi$
$60$		0			0
$61$	−1.51384	−	10.5290i	−0.193828	−	1.34810i	−0.821761	−	0.569833i	$-0.807008\pi$
$61$	−1.51384	−	10.5290i	−0.193828	−	1.34810i	0.627933	−	0.778267i	$-0.283901\pi$
$62$		0			0
$63$	−0.744272	−	1.62973i	−0.0937695	−	0.205326i
$64$		0			0
$65$	5.60203	−	12.2667i	0.694847	−	1.52150i
$66$		0			0
$67$	2.48821	−	1.59907i	0.303983	−	0.195358i	−0.379752	−	0.925088i	$-0.623991\pi$
$67$	2.48821	−	1.59907i	0.303983	−	0.195358i	0.683735	+	0.729730i	$0.260354\pi$
$68$		0			0
$69$	2.15264	+	4.28557i	0.259148	+	0.515922i
$70$		0			0
$71$	−3.59643	+	2.31129i	−0.426818	+	0.274299i	−0.736364	−	0.676585i	$-0.763459\pi$
$71$	−3.59643	+	2.31129i	−0.426818	+	0.274299i	0.309547	+	0.950884i	$0.399823\pi$
$72$		0			0
$73$	3.32454	−	7.27972i	0.389108	−	0.852027i	−0.609152	−	0.793054i	$-0.708490\pi$
$73$	3.32454	−	7.27972i	0.389108	−	0.852027i	0.998260	−	0.0589733i	$-0.0187827\pi$
$74$		0			0
$75$	−0.886520	−	1.94121i	−0.102367	−	0.224151i
$76$		0			0
$77$	−0.734669	−	5.10973i	−0.0837233	−	0.582308i
$78$		0			0
$79$	7.31852	−	8.44602i	0.823398	−	0.950251i	−0.176020	−	0.984387i	$-0.556322\pi$
$79$	7.31852	−	8.44602i	0.823398	−	0.950251i	0.999417	+	0.0341352i	$0.0108677\pi$
$80$		0			0
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$		0			0
$83$	−13.9612	−	4.09938i	−1.53244	−	0.449965i	−0.596643	−	0.802506i	$-0.703499\pi$
$83$	−13.9612	−	4.09938i	−1.53244	−	0.449965i	−0.935796	+	0.352542i	$0.885318\pi$
$84$		0			0
$85$	2.99879	+	3.46079i	0.325265	+	0.375376i
$86$		0			0
$87$	−3.14285	+	0.922823i	−0.336949	+	0.0989370i
$88$		0			0
$89$	0.245498	−	1.70747i	0.0260227	−	0.180992i	−0.972665	−	0.232215i	$-0.925403\pi$
$89$	0.245498	−	1.70747i	0.0260227	−	0.180992i	0.998687	+	0.0512229i	$0.0163119\pi$
$90$		0			0
$91$	−9.04575			−0.948252
$92$		0			0
$93$	10.4550			1.08413
$94$		0			0
$95$	1.05226	−	7.31864i	0.107960	−	0.750876i
$96$		0			0
$97$	−14.8335	+	4.35551i	−1.50611	+	0.442235i	−0.927643	−	0.373468i	$-0.878169\pi$
$97$	−14.8335	+	4.35551i	−1.50611	+	0.442235i	−0.578471	+	0.815703i	$0.696350\pi$
$98$		0			0
$99$	1.88687	+	2.17756i	0.189637	+	0.218853i
$100$		0			0
$101$	−5.22857	−	1.53525i	−0.520262	−	0.152763i	0.0110500	−	0.999939i	$-0.496483\pi$
$101$	−5.22857	−	1.53525i	−0.520262	−	0.152763i	−0.531312	+	0.847176i	$0.678301\pi$
$102$		0			0
$103$	6.32309	+	4.06361i	0.623033	+	0.400399i	0.813724	−	0.581251i	$-0.197437\pi$
$103$	6.32309	+	4.06361i	0.623033	+	0.400399i	−0.190691	+	0.981650i	$0.561073\pi$
$104$		0			0
$105$	−3.13377	+	3.61656i	−0.305824	+	0.352940i
$106$		0			0
$107$	−1.92970	−	13.4213i	−0.186551	−	1.29749i	−0.840856	−	0.541259i	$-0.817948\pi$
$107$	−1.92970	−	13.4213i	−0.186551	−	1.29749i	0.654305	−	0.756230i	$-0.272961\pi$
$108$		0			0
$109$	6.38722	+	13.9861i	0.611785	+	1.33962i	0.921346	+	0.388743i	$0.127091\pi$
$109$	6.38722	+	13.9861i	0.611785	+	1.33962i	−0.309561	+	0.950879i	$0.600182\pi$
$110$		0			0
$111$	−2.49654	+	5.46666i	−0.236961	+	0.518873i
$112$		0			0
$113$	−1.44103	+	0.926092i	−0.135560	+	0.0871194i	−0.606663	−	0.794959i	$-0.707492\pi$
$113$	−1.44103	+	0.926092i	−0.135560	+	0.0871194i	0.471103	+	0.882078i	$0.343856\pi$
$114$		0			0
$115$	8.02373	−	9.98515i	0.748217	−	0.931120i
$116$		0			0
$117$	4.24739	−	2.72963i	0.392671	−	0.252354i
$118$		0			0
$119$	1.27603	−	2.79412i	0.116974	−	0.256136i
$120$		0			0
$121$	−1.12078	−	2.45417i	−0.101889	−	0.223106i
$122$		0			0
$123$	−0.268687	−	1.86876i	−0.0242267	−	0.168500i
$124$		0			0
$125$	5.01285	−	5.78514i	0.448363	−	0.517438i
$126$		0			0
$127$	0.206415	+	0.132655i	0.0183164	+	0.0117712i	0.549767	−	0.835318i	$-0.314717\pi$
$127$	0.206415	+	0.132655i	0.0183164	+	0.0117712i	−0.531451	+	0.847089i	$0.678353\pi$
$128$		0			0
$129$	4.50687	+	1.32334i	0.396808	+	0.116513i
$130$		0			0
$131$	13.4899	+	15.5682i	1.17862	+	1.36020i	0.918890	+	0.394514i	$0.129087\pi$
$131$	13.4899	+	15.5682i	1.17862	+	1.36020i	0.259727	+	0.965682i	$0.416367\pi$
$132$		0			0
$133$	−4.75879	+	1.39731i	−0.412639	+	0.121162i
$134$		0			0
$135$	0.380118	−	2.64378i	0.0327154	−	0.227540i
$136$		0			0
$137$	−1.43108			−0.122266			−0.0611328	−	0.998130i	$-0.519471\pi$
$137$	−1.43108			−0.122266			−0.0611328	+	0.998130i	$0.519471\pi$
$138$		0			0
$139$	13.2995			1.12805			0.564026	−	0.825757i	$-0.309252\pi$
$139$	13.2995			1.12805			0.564026	+	0.825757i	$0.309252\pi$
$140$		0			0
$141$	0.396996	−	2.76117i	0.0334331	−	0.232532i
$142$		0			0
$143$	13.9582	−	4.09849i	1.16724	−	0.342733i
$144$		0			0
$145$	5.72926	+	6.61192i	0.475789	+	0.549090i
$146$		0			0
$147$	−3.63652	−	1.06778i	−0.299935	−	0.0880689i
$148$		0			0
$149$	−20.0168	−	12.8640i	−1.63984	−	1.05386i	−0.940905	−	0.338671i	$-0.890023\pi$
$149$	−20.0168	−	12.8640i	−1.63984	−	1.05386i	−0.698932	−	0.715188i	$-0.746341\pi$
$150$		0			0
$151$	2.12653	−	2.45415i	0.173055	−	0.199716i	−0.662596	−	0.748977i	$-0.730545\pi$
$151$	2.12653	−	2.45415i	0.173055	−	0.199716i	0.835651	+	0.549261i	$0.185091\pi$
$152$		0			0
$153$	0.243994	+	1.69702i	0.0197258	+	0.137196i
$154$		0			0
$155$	−11.6005	−	25.4015i	−0.931771	−	2.04029i
$156$		0			0
$157$	6.26764	−	13.7242i	0.500212	−	1.09531i	−0.476188	−	0.879343i	$-0.657982\pi$
$157$	6.26764	−	13.7242i	0.500212	−	1.09531i	0.976400	−	0.215968i	$-0.0692908\pi$
$158$		0			0
$159$	5.99329	−	3.85166i	0.475299	−	0.305456i
$160$		0			0
$161$	−8.32841	−	2.11341i	−0.656371	−	0.166560i
$162$		0			0
$163$	1.79080	−	1.15088i	0.140266	−	0.0901437i	−0.468626	−	0.883397i	$-0.655251\pi$
$163$	1.79080	−	1.15088i	0.140266	−	0.0901437i	0.608892	+	0.793253i	$0.291614\pi$
$164$		0			0
$165$	3.19700	−	7.00045i	0.248886	−	0.544984i
$166$		0			0
$167$	7.86096	+	17.2131i	0.608299	+	1.33199i	0.923731	+	0.383042i	$0.125123\pi$
$167$	7.86096	+	17.2131i	0.608299	+	1.33199i	−0.315432	+	0.948948i	$0.602149\pi$
$168$		0			0
$169$	−1.77768	−	12.3641i	−0.136745	−	0.951081i
$170$		0			0
$171$	1.81282	−	2.09210i	0.138630	−	0.159987i
$172$		0			0
$173$	17.3787	+	11.1686i	1.32128	+	0.849133i	0.995356	−	0.0962635i	$-0.0306891\pi$
$173$	17.3787	+	11.1686i	1.32128	+	0.849133i	0.325921	+	0.945397i	$0.394325\pi$
$174$		0			0
$175$	3.66858	+	1.07719i	0.277318	+	0.0814280i
$176$		0			0
$177$	4.37377	+	5.04760i	0.328753	+	0.379401i
$178$		0			0
$179$	0.173077	−	0.0508199i	0.0129363	−	0.00379845i	−0.275258	−	0.961370i	$-0.588763\pi$
$179$	0.173077	−	0.0508199i	0.0129363	−	0.00379845i	0.288194	+	0.957572i	$0.406945\pi$
$180$		0			0
$181$	−2.32103	+	16.1431i	−0.172520	+	1.19991i	0.701015	+	0.713146i	$0.252730\pi$
$181$	−2.32103	+	16.1431i	−0.172520	+	1.19991i	−0.873536	+	0.486760i	$0.838179\pi$
$182$		0			0
$183$	−10.6373			−0.786330
$184$		0			0
$185$	16.0518			1.18015
$186$		0			0
$187$	−0.703026	+	4.88965i	−0.0514104	+	0.357567i
$188$		0			0
$189$	−1.71906	+	0.504762i	−0.125043	+	0.0367160i
$190$		0			0
$191$	2.02141	+	2.33283i	0.146264	+	0.168798i	0.824154	−	0.566366i	$-0.191651\pi$
$191$	2.02141	+	2.33283i	0.146264	+	0.168798i	−0.677890	+	0.735163i	$0.737106\pi$
$192$		0			0
$193$	11.4672	+	3.36706i	0.825424	+	0.242366i	0.667050	−	0.745013i	$-0.267557\pi$
$193$	11.4672	+	3.36706i	0.825424	+	0.242366i	0.158374	+	0.987379i	$0.449375\pi$
$194$		0			0
$195$	−11.3446	−	7.29075i	−0.812406	−	0.522102i
$196$		0			0
$197$	−13.7850	+	15.9087i	−0.982140	+	1.13345i	0.00890968	+	0.999960i	$0.497164\pi$
$197$	−13.7850	+	15.9087i	−0.982140	+	1.13345i	−0.991050	+	0.133490i	$0.957382\pi$
$198$		0			0
$199$	−0.715176	−	4.97416i	−0.0506975	−	0.352609i	−0.999342	−	0.0362652i	$-0.988454\pi$
$199$	−0.715176	−	4.97416i	−0.0506975	−	0.352609i	0.948645	−	0.316343i	$-0.102455\pi$
$200$		0			0
$201$	−1.22869	−	2.69045i	−0.0866650	−	0.189770i
$202$		0			0
$203$	2.43788	−	5.33822i	0.171106	−	0.374670i
$204$		0			0
$205$	−4.24221	+	2.72630i	−0.296289	+	0.190413i
$206$		0			0
$207$	4.54830	−	1.52083i	0.316129	−	0.105705i
$208$		0			0
$209$	6.71002	−	4.31227i	0.464142	−	0.298286i
$210$		0			0
$211$	−3.33774	+	7.30863i	−0.229779	+	0.503147i	−0.989041	−	0.147638i	$-0.952833\pi$
$211$	−3.33774	+	7.30863i	−0.229779	+	0.503147i	0.759262	+	0.650785i	$0.225560\pi$
$212$		0			0
$213$	1.77593	+	3.88875i	0.121685	+	0.266453i
$214$		0			0
$215$	−1.78547	−	12.4182i	−0.121768	−	0.846914i
$216$		0			0
$217$	−12.2666	+	14.1564i	−0.832709	+	0.960997i
$218$		0			0
$219$	−6.73249	−	4.32671i	−0.454940	−	0.292372i
$220$		0			0
$221$	8.30551	+	2.43872i	0.558689	+	0.164046i
$222$		0			0
$223$	13.3211	+	15.3734i	0.892050	+	1.02948i	0.999378	+	0.0352571i	$0.0112250\pi$
$223$	13.3211	+	15.3734i	0.892050	+	1.02948i	−0.107328	+	0.994224i	$0.534230\pi$
$224$		0			0
$225$	−2.04761	+	0.601234i	−0.136508	+	0.0400823i
$226$		0			0
$227$	−2.27718	+	15.8381i	−0.151142	+	1.05121i	0.763169	+	0.646199i	$0.223643\pi$
$227$	−2.27718	+	15.8381i	−0.151142	+	1.05121i	−0.914310	+	0.405014i	$0.867267\pi$
$228$		0			0
$229$	−28.2168			−1.86462			−0.932309	−	0.361663i	$-0.882209\pi$
$229$	−28.2168			−1.86462			−0.932309	+	0.361663i	$0.882209\pi$
$230$		0			0
$231$	−5.16228			−0.339653
$232$		0			0
$233$	−2.16086	+	15.0291i	−0.141562	+	0.984589i	0.787935	+	0.615759i	$0.211151\pi$
$233$	−2.16086	+	15.0291i	−0.141562	+	0.984589i	−0.929497	+	0.368830i	$0.879759\pi$
$234$		0			0
$235$	−7.14901	+	2.09914i	−0.466350	+	0.136933i
$236$		0			0
$237$	−7.31852	−	8.44602i	−0.475389	−	0.548628i
$238$		0			0
$239$	−8.28480	−	2.43264i	−0.535899	−	0.157354i	0.00257431	−	0.999997i	$-0.499181\pi$
$239$	−8.28480	−	2.43264i	−0.535899	−	0.157354i	−0.538473	+	0.842643i	$0.680999\pi$
$240$		0			0
$241$	−2.89590	−	1.86108i	−0.186541	−	0.119883i	0.444037	−	0.896008i	$-0.353546\pi$
$241$	−2.89590	−	1.86108i	−0.186541	−	0.119883i	−0.630578	+	0.776126i	$0.717182\pi$
$242$		0			0
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$		0			0
$245$	1.44066	+	10.0200i	0.0920407	+	0.640157i
$246$		0			0
$247$	−5.80607	−	12.7135i	−0.369431	−	0.808942i
$248$		0			0
$249$	−6.04453	+	13.2357i	−0.383057	+	0.838777i
$250$		0			0
$251$	−1.10456	+	0.709856i	−0.0697190	+	0.0448057i	−0.575036	−	0.818128i	$-0.695012\pi$
$251$	−1.10456	+	0.709856i	−0.0697190	+	0.0448057i	0.505317	+	0.862934i	$0.331376\pi$
$252$		0			0
$253$	13.8088	−	0.512356i	0.868154	−	0.0322115i
$254$		0			0
$255$	3.85234	−	2.47575i	0.241243	−	0.155037i
$256$		0			0
$257$	−8.02133	+	17.5643i	−0.500357	+	1.09563i	0.475996	+	0.879447i	$0.342088\pi$
$257$	−8.02133	+	17.5643i	−0.500357	+	1.09563i	−0.976353	+	0.216182i	$0.930640\pi$
$258$		0			0
$259$	−4.47289	−	9.79426i	−0.277932	−	0.608586i
$260$		0			0
$261$	0.466156	+	3.24219i	0.0288544	+	0.200686i
$262$		0			0
$263$	−10.8933	+	12.5716i	−0.671712	+	0.775197i	−0.984643	−	0.174579i	$-0.944144\pi$
$263$	−10.8933	+	12.5716i	−0.671712	+	0.775197i	0.312931	+	0.949776i	$0.398689\pi$
$264$		0			0
$265$	−16.0079	−	10.2876i	−0.983356	−	0.631965i
$266$		0			0
$267$	−1.65516	−	0.485997i	−0.101294	−	0.0297426i
$268$		0			0
$269$	−5.49487	−	6.34142i	−0.335028	−	0.386643i	0.563091	−	0.826395i	$-0.309612\pi$
$269$	−5.49487	−	6.34142i	−0.335028	−	0.386643i	−0.898119	+	0.439752i	$0.855067\pi$
$270$		0			0
$271$	−16.3131	+	4.78995i	−0.990948	+	0.290968i	−0.736736	−	0.676180i	$-0.763634\pi$
$271$	−16.3131	+	4.78995i	−0.990948	+	0.290968i	−0.254211	+	0.967149i	$0.581816\pi$
$272$		0			0
$273$	−1.28734	+	8.95368i	−0.0779136	+	0.541901i
$274$		0			0
$275$	−6.14891			−0.370793
$276$		0			0
$277$	−10.5367			−0.633092			−0.316546	−	0.948577i	$-0.602523\pi$
$277$	−10.5367			−0.633092			−0.316546	+	0.948577i	$0.602523\pi$
$278$		0			0
$279$	1.48790	−	10.3486i	0.0890785	−	0.619554i
$280$		0			0
$281$	−7.67703	+	2.25418i	−0.457973	+	0.134473i	−0.502578	−	0.864532i	$-0.667615\pi$
$281$	−7.67703	+	2.25418i	−0.457973	+	0.134473i	0.0446053	+	0.999005i	$0.485797\pi$
$282$		0			0
$283$	4.15733	+	4.79781i	0.247128	+	0.285200i	0.865738	−	0.500497i	$-0.166850\pi$
$283$	4.15733	+	4.79781i	0.247128	+	0.285200i	−0.618610	+	0.785698i	$0.712304\pi$
$284$		0			0
$285$	−7.09439	−	2.08310i	−0.420235	−	0.123392i
$286$		0			0
$287$	2.84560	+	1.82875i	0.167970	+	0.107948i
$288$		0			0
$289$	9.20773	−	10.6263i	0.541631	−	0.625076i
$290$		0			0
$291$	2.20015	+	15.3024i	0.128975	+	0.897041i
$292$		0			0
$293$	8.44716	+	18.4967i	0.493488	+	1.08059i	0.978531	+	0.206098i	$0.0660766\pi$
$293$	8.44716	+	18.4967i	0.493488	+	1.08059i	−0.485043	+	0.874490i	$0.661196\pi$
$294$		0			0
$295$	7.41068	−	16.2271i	0.431466	−	0.944779i
$296$		0			0
$297$	2.42392	−	1.55776i	0.140650	−	0.0903904i
$298$		0			0
$299$	2.55493	−	24.0784i	0.147755	−	1.39249i
$300$		0			0
$301$	−7.07962	+	4.54979i	−0.408062	+	0.262246i
$302$		0			0
$303$	−2.26372	+	4.95686i	−0.130047	+	0.284764i
$304$		0			0
$305$	11.8027	+	25.8443i	0.675820	+	1.47984i
$306$		0			0
$307$	−0.455378	−	3.16722i	−0.0259898	−	0.180763i	0.972692	−	0.232102i	$-0.0745602\pi$
$307$	−0.455378	−	3.16722i	−0.0259898	−	0.180763i	−0.998681	+	0.0513389i	$0.983651\pi$
$308$		0			0
$309$	4.92211	−	5.68042i	0.280009	−	0.323148i
$310$		0			0
$311$	13.1925	+	8.47832i	0.748079	+	0.480761i	0.858301	−	0.513146i	$-0.171520\pi$
$311$	13.1925	+	8.47832i	0.748079	+	0.480761i	−0.110222	+	0.993907i	$0.535156\pi$
$312$		0			0
$313$	−17.1165	−	5.02586i	−0.967483	−	0.284079i	−0.240435	−	0.970665i	$-0.577290\pi$
$313$	−17.1165	−	5.02586i	−0.967483	−	0.284079i	−0.727048	+	0.686587i	$0.759108\pi$
$314$		0			0
$315$	3.13377	+	3.61656i	0.176568	+	0.203770i
$316$		0			0
$317$	24.1926	−	7.10358i	1.35879	−	0.398977i	0.480454	−	0.877020i	$-0.340472\pi$
$317$	24.1926	−	7.10358i	1.35879	−	0.398977i	0.878336	+	0.478043i	$0.158654\pi$
$318$		0			0
$319$	−1.34315	+	9.34179i	−0.0752018	+	0.523040i
$320$		0			0
$321$	−13.5593			−0.756809
$322$		0			0
$323$	4.74607			0.264079
$324$		0			0
$325$	−1.53339	+	10.6649i	−0.0850570	+	0.591584i
$326$		0			0
$327$	14.7527	−	4.33179i	0.815827	−	0.239548i
$328$		0			0
$329$	3.27291	+	3.77714i	0.180441	+	0.208241i
$330$		0			0
$331$	−28.8537	−	8.47221i	−1.58594	−	0.465675i	−0.634352	−	0.773044i	$-0.718733\pi$
$331$	−28.8537	−	8.47221i	−1.58594	−	0.465675i	−0.951590	+	0.307370i	$0.900551\pi$
$332$		0			0
$333$	5.05572	+	3.24912i	0.277052	+	0.178051i
$334$		0			0
$335$	−5.17341	+	5.97043i	−0.282654	+	0.326200i
$336$		0			0
$337$	−1.08860	−	7.57137i	−0.0592998	−	0.412439i	−0.997751	−	0.0670275i	$-0.978648\pi$
$337$	−1.08860	−	7.57137i	−0.0592998	−	0.412439i	0.938451	−	0.345411i	$-0.112261\pi$
$338$		0			0
$339$	0.711586	+	1.55816i	0.0386481	+	0.0846274i
$340$		0			0
$341$	12.5141	−	27.4020i	0.677675	−	1.48390i
$342$		0			0
$343$	16.2630	−	10.4516i	0.878117	−	0.564332i
$344$		0			0
$345$	−8.74162	−	9.36309i	−0.470633	−	0.504092i
$346$		0			0
$347$	−5.90760	+	3.79658i	−0.317137	+	0.203811i	−0.689518	−	0.724268i	$-0.742178\pi$
$347$	−5.90760	+	3.79658i	−0.317137	+	0.203811i	0.372382	+	0.928080i	$0.378541\pi$
$348$		0			0
$349$	10.0124	−	21.9240i	0.535949	−	1.17356i	−0.427091	−	0.904208i	$-0.640462\pi$
$349$	10.0124	−	21.9240i	0.535949	−	1.17356i	0.963041	−	0.269357i	$-0.0868110\pi$
$350$		0			0
$351$	−2.09738	−	4.59262i	−0.111950	−	0.245136i
$352$		0			0
$353$	2.92593	+	20.3503i	0.155732	+	1.08314i	0.906389	+	0.422445i	$0.138828\pi$
$353$	2.92593	+	20.3503i	0.155732	+	1.08314i	−0.750657	+	0.660692i	$0.770263\pi$
$354$		0			0
$355$	7.47760	−	8.62961i	0.396870	−	0.458012i
$356$		0			0
$357$	−2.58408	−	1.66069i	−0.136764	−	0.0878929i
$358$		0			0
$359$	−12.4477	−	3.65498i	−0.656966	−	0.192903i	−0.0637751	−	0.997964i	$-0.520314\pi$
$359$	−12.4477	−	3.65498i	−0.656966	−	0.192903i	−0.593191	+	0.805062i	$0.702132\pi$
$360$		0			0
$361$	7.42403	+	8.56778i	0.390738	+	0.450936i
$362$		0			0
$363$	−2.58869	+	0.760108i	−0.135871	+	0.0398953i
$364$		0			0
$365$	−3.04206	+	21.1580i	−0.159229	+	1.10746i
$366$		0			0
$367$	−12.0724			−0.630176			−0.315088	−	0.949062i	$-0.602034\pi$
$367$	−12.0724			−0.630176			−0.315088	+	0.949062i	$0.602034\pi$
$368$		0			0
$369$	−1.88798			−0.0982842
$370$		0			0
$371$	−1.81651	+	12.6341i	−0.0943086	+	0.655931i
$372$		0			0
$373$	−36.3345	+	10.6688i	−1.88133	+	0.552407i	−0.885123	+	0.465358i	$0.845926\pi$
$373$	−36.3345	+	10.6688i	−1.88133	+	0.552407i	−0.996204	+	0.0870494i	$0.972256\pi$
$374$		0			0
$375$	−5.01285	−	5.78514i	−0.258862	−	0.298743i
$376$		0			0
$377$	15.8679	+	4.65922i	0.817236	+	0.239962i
$378$		0			0
$379$	9.27505	+	5.96071i	0.476427	+	0.306181i	0.756727	−	0.653731i	$-0.226797\pi$
$379$	9.27505	+	5.96071i	0.476427	+	0.306181i	−0.280299	+	0.959913i	$0.590434\pi$
$380$		0			0
$381$	0.160681	−	0.185436i	0.00823193	−	0.00950016i
$382$		0			0
$383$	0.752198	+	5.23165i	0.0384355	+	0.267325i	0.999973	−	0.00734881i	$-0.00233922\pi$
$383$	0.752198	+	5.23165i	0.0384355	+	0.267325i	−0.961537	+	0.274674i	$0.911430\pi$
$384$		0			0
$385$	5.72785	+	12.5423i	0.291918	+	0.639212i
$386$		0			0
$387$	1.95126	−	4.27267i	0.0991882	−	0.217192i
$388$		0			0
$389$	4.48055	−	2.87947i	0.227173	−	0.145995i	−0.422104	−	0.906548i	$-0.638708\pi$
$389$	4.48055	−	2.87947i	0.227173	−	0.145995i	0.649276	+	0.760552i	$0.275072\pi$
$390$		0			0
$391$	7.07711	+	4.18578i	0.357905	+	0.211684i
$392$		0			0
$393$	17.3295	−	11.1370i	0.874158	−	0.561787i
$394$		0			0
$395$	−12.4001	+	27.1524i	−0.623916	+	1.36619i
$396$		0			0
$397$	12.4589	+	27.2811i	0.625292	+	1.36920i	0.911607	+	0.411063i	$0.134842\pi$
$397$	12.4589	+	27.2811i	0.625292	+	1.36920i	−0.286315	+	0.958135i	$0.592430\pi$
$398$		0			0
$399$	0.705837	+	4.90921i	0.0353361	+	0.245768i
$400$		0			0
$401$	−16.0401	+	18.5113i	−0.801007	+	0.924411i	−0.998436	−	0.0559060i	$-0.982195\pi$
$401$	−16.0401	+	18.5113i	−0.801007	+	0.924411i	0.197429	+	0.980317i	$0.436741\pi$
$402$		0			0
$403$	−44.4065	−	28.5383i	−2.21205	−	1.42160i
$404$		0			0
$405$	−2.56277	−	0.752498i	−0.127345	−	0.0373919i
$406$		0			0
$407$	11.3396	+	13.0866i	0.562083	+	0.648678i
$408$		0			0
$409$	34.5261	−	10.1378i	1.70721	−	0.501281i	0.724947	−	0.688805i	$-0.241864\pi$
$409$	34.5261	−	10.1378i	1.70721	−	0.501281i	0.982260	+	0.187524i	$0.0600461\pi$
$410$		0			0
$411$	−0.203664	+	1.41652i	−0.0100460	+	0.0698716i
$412$		0			0
$413$	−11.9662			−0.588819
$414$		0			0
$415$	38.8641			1.90777
$416$		0			0
$417$	1.89272	−	13.1642i	0.0926870	−	0.644652i
$418$		0			0
$419$	24.1740	−	7.09811i	1.18097	−	0.346765i	0.368425	−	0.929657i	$-0.379897\pi$
$419$	24.1740	−	7.09811i	1.18097	−	0.346765i	0.812550	+	0.582892i	$0.198079\pi$
$420$		0			0
$421$	−5.59413	−	6.45597i	−0.272641	−	0.314645i	0.602873	−	0.797837i	$-0.294023\pi$
$421$	−5.59413	−	6.45597i	−0.272641	−	0.314645i	−0.875514	+	0.483193i	$0.839477\pi$
$422$		0			0
$423$	−2.67656	−	0.785910i	−0.130139	−	0.0382122i
$424$		0			0
$425$	−3.07796	−	1.97808i	−0.149303	−	0.0959511i
$426$		0			0
$427$	12.4804	−	14.4032i	0.603969	−	0.697018i
$428$		0			0
$429$	−2.07032	−	14.3994i	−0.0999559	−	0.695209i
$430$		0			0
$431$	4.21184	+	9.22265i	0.202877	+	0.444239i	0.983535	−	0.180720i	$-0.0578428\pi$
$431$	4.21184	+	9.22265i	0.202877	+	0.444239i	−0.780657	+	0.624959i	$0.785116\pi$
$432$		0			0
$433$	−0.436675	+	0.956184i	−0.0209852	+	0.0459513i	−0.919834	−	0.392307i	$-0.871677\pi$
$433$	−0.436675	+	0.956184i	−0.0209852	+	0.0459513i	0.898849	+	0.438258i	$0.144404\pi$
$434$		0			0
$435$	7.35998	−	4.72997i	0.352884	−	0.226785i
$436$		0			0
$437$	−2.37532	−	13.0618i	−0.113627	−	0.624832i
$438$		0			0
$439$	−13.8006	+	8.86911i	−0.658667	+	0.423299i	−0.826824	−	0.562461i	$-0.809855\pi$
$439$	−13.8006	+	8.86911i	−0.658667	+	0.423299i	0.168157	+	0.985760i	$0.446218\pi$
$440$		0			0
$441$	−1.57444	+	3.44755i	−0.0749734	+	0.164169i
$442$		0			0
$443$	−3.79243	−	8.30426i	−0.180184	−	0.394547i	0.797891	−	0.602802i	$-0.205949\pi$
$443$	−3.79243	−	8.30426i	−0.180184	−	0.394547i	−0.978075	+	0.208255i	$0.933222\pi$
$444$		0			0
$445$	0.655715	+	4.56060i	0.0310839	+	0.216193i
$446$		0			0
$447$	−15.5817	+	17.9823i	−0.736991	+	0.850533i
$448$		0			0
$449$	−30.9888	−	19.9153i	−1.46245	−	0.939862i	−0.998542	−	0.0539807i	$-0.982809\pi$
$449$	−30.9888	−	19.9153i	−1.46245	−	0.939862i	−0.463912	−	0.885881i	$-0.653555\pi$
$450$		0			0
$451$	−5.21952	−	1.53259i	−0.245778	−	0.0721668i
$452$		0			0
$453$	−2.12653	−	2.45415i	−0.0999131	−	0.115306i
$454$		0			0
$455$	23.1822	−	6.80691i	1.08680	−	0.319113i
$456$		0			0
$457$	4.56275	−	31.7346i	0.213436	−	1.48448i	−0.548128	−	0.836394i	$-0.684659\pi$
$457$	4.56275	−	31.7346i	0.213436	−	1.48448i	0.761565	−	0.648089i	$-0.224432\pi$
$458$		0			0
$459$	1.71447			0.0800245
$460$		0			0
$461$	19.8536			0.924676			0.462338	−	0.886704i	$-0.347011\pi$
$461$	19.8536			0.924676			0.462338	+	0.886704i	$0.347011\pi$
$462$		0			0
$463$	−3.38232	+	23.5246i	−0.157190	+	1.09328i	0.746591	+	0.665283i	$0.231689\pi$
$463$	−3.38232	+	23.5246i	−0.157190	+	1.09328i	−0.903781	+	0.427996i	$0.859220\pi$
$464$		0			0
$465$	−26.7938	+	7.86738i	−1.24253	+	0.364841i
$466$		0			0
$467$	20.1526	+	23.2574i	0.932552	+	1.07622i	0.996930	+	0.0782963i	$0.0249480\pi$
$467$	20.1526	+	23.2574i	0.932552	+	1.07622i	−0.0643786	+	0.997926i	$0.520507\pi$
$468$		0			0
$469$	5.08453	+	1.49295i	0.234782	+	0.0689381i
$470$		0			0
$471$	−12.6925	−	8.15700i	−0.584842	−	0.375855i
$472$		0			0
$473$	8.86287	−	10.2283i	0.407515	−	0.470297i
$474$		0			0
$475$	0.840740	+	5.84747i	0.0385758	+	0.268300i
$476$		0			0
$477$	−2.95952	−	6.48044i	−0.135507	−	0.296719i
$478$		0			0
$479$	5.13972	−	11.2544i	0.234840	−	0.514228i	−0.755118	−	0.655589i	$-0.772421\pi$
$479$	5.13972	−	11.2544i	0.234840	−	0.514228i	0.989958	+	0.141361i	$0.0451478\pi$
$480$		0			0
$481$	25.5258	−	16.4044i	1.16387	−	0.747977i
$482$		0			0
$483$	−3.27715	+	7.94287i	−0.149116	+	0.361413i
$484$		0			0
$485$	34.7374	−	22.3244i	1.57734	−	1.01370i
$486$		0			0
$487$	−18.2090	+	39.8721i	−0.825128	+	1.80678i	−0.306172	+	0.951976i	$0.599048\pi$
$487$	−18.2090	+	39.8721i	−0.825128	+	1.80678i	−0.518955	+	0.854801i	$0.673679\pi$
$488$		0			0
$489$	−0.884306	−	1.93636i	−0.0399897	−	0.0875652i
$490$		0			0
$491$	−5.04975	−	35.1218i	−0.227892	−	1.58502i	−0.706965	−	0.707248i	$-0.749936\pi$
$491$	−5.04975	−	35.1218i	−0.227892	−	1.58502i	0.479074	−	0.877775i	$-0.340973\pi$
$492$		0			0
$493$	−3.67756	+	4.24413i	−0.165629	+	0.191146i
$494$		0			0
$495$	−6.47422	−	4.16073i	−0.290994	−	0.187011i
$496$		0			0
$497$	−7.34913	−	2.15790i	−0.329654	−	0.0967950i
$498$		0			0
$499$	−16.2296	−	18.7299i	−0.726536	−	0.838467i	0.265541	−	0.964100i	$-0.414449\pi$
$499$	−16.2296	−	18.7299i	−0.726536	−	0.838467i	−0.992077	+	0.125633i	$0.959904\pi$
$500$		0			0
$501$	18.1566	−	5.33127i	0.811178	−	0.238183i
$502$		0			0
$503$	−0.765858	+	5.32666i	−0.0341479	+	0.237504i	−0.999746	−	0.0225350i	$-0.992826\pi$
$503$	−0.765858	+	5.32666i	−0.0341479	+	0.237504i	0.965598	+	0.260039i	$0.0837354\pi$
$504$		0			0
$505$	14.5549			0.647685
$506$		0			0
$507$	−12.4912			−0.554754
$508$		0			0
$509$	5.71529	−	39.7507i	0.253326	−	1.76192i	−0.324619	−	0.945845i	$-0.605236\pi$
$509$	5.71529	−	39.7507i	0.253326	−	1.76192i	0.577945	−	0.816076i	$-0.303855\pi$
$510$		0			0
$511$	13.7575	−	4.03957i	0.608597	−	0.178700i
$512$		0			0
$513$	−1.81282	−	2.09210i	−0.0800378	−	0.0923686i
$514$		0			0
$515$	−19.2625	−	5.65598i	−0.848808	−	0.249232i
$516$		0			0
$517$	−6.76168	−	4.34547i	−0.297378	−	0.191113i
$518$		0			0
$519$	13.5282	−	15.6123i	0.593821	−	0.685306i
$520$		0			0
$521$	−1.24238	−	8.64091i	−0.0544295	−	0.378565i	−0.998769	−	0.0495941i	$-0.984207\pi$
$521$	−1.24238	−	8.64091i	−0.0544295	−	0.378565i	0.944340	−	0.328971i	$-0.106702\pi$
$522$		0			0
$523$	4.66823	+	10.2220i	0.204127	+	0.446977i	0.983814	−	0.179193i	$-0.0573488\pi$
$523$	4.66823	+	10.2220i	0.204127	+	0.446977i	−0.779686	+	0.626170i	$0.784622\pi$
$524$		0			0
$525$	1.58832	−	3.47794i	0.0693200	−	0.151790i
$526$		0			0
$527$	15.0793	−	9.69087i	0.656864	−	0.422141i
$528$		0			0
$529$	7.97789	−	21.5720i	0.346865	−	0.937915i
$530$		0			0
$531$	5.61868	−	3.61091i	0.243830	−	0.156700i
$532$		0			0
$533$	−3.95981	+	8.67077i	−0.171518	+	0.375573i
$534$		0			0
$535$	15.0449	+	32.9437i	0.650448	+	1.42428i
$536$		0			0
$537$	−0.0256712	−	0.178547i	−0.00110780	−	0.00770488i
$538$		0			0
$539$	−7.15130	+	8.25304i	−0.308028	+	0.355484i
$540$		0			0
$541$	−16.1988	−	10.4103i	−0.696439	−	0.447574i	0.143931	−	0.989588i	$-0.454026\pi$
$541$	−16.1988	−	10.4103i	−0.696439	−	0.447574i	−0.840370	+	0.542014i	$0.817662\pi$
$542$		0			0
$543$	15.6485	+	4.59480i	0.671540	+	0.197182i
$544$		0			0
$545$	−26.8935	−	31.0367i	−1.15199	−	1.32947i
$546$		0			0
$547$	21.8802	−	6.42460i	0.935529	−	0.274696i	0.221780	−	0.975097i	$-0.428813\pi$
$547$	21.8802	−	6.42460i	0.935529	−	0.274696i	0.713750	+	0.700401i	$0.246995\pi$
$548$		0			0
$549$	−1.51384	+	10.5290i	−0.0646092	+	0.449367i
$550$		0			0
$551$	9.06748			0.386287
$552$		0			0
$553$	20.0227			0.851454
$554$		0			0
$555$	2.28442	−	15.8885i	0.0969680	−	0.674427i
$556$		0			0
$557$	26.6141	−	7.81462i	1.12768	−	0.331116i	0.335883	−	0.941904i	$-0.390965\pi$
$557$	26.6141	−	7.81462i	1.12768	−	0.331116i	0.791794	+	0.610788i	$0.209147\pi$
$558$		0			0
$559$	−15.5302	−	17.9228i	−0.656858	−	0.758055i
$560$		0			0
$561$	4.73983	+	1.39174i	0.200116	+	0.0587593i
$562$		0			0
$563$	5.44343	+	3.49828i	0.229413	+	0.147435i	0.650298	−	0.759679i	$-0.274644\pi$
$563$	5.44343	+	3.49828i	0.229413	+	0.147435i	−0.420885	+	0.907114i	$0.638280\pi$
$564$		0			0
$565$	2.99614	−	3.45773i	0.126049	−	0.145468i
$566$		0			0
$567$	0.254976	+	1.77340i	0.0107080	+	0.0744757i
$568$		0			0
$569$	13.6804	+	29.9560i	0.573514	+	1.25582i	0.944905	+	0.327344i	$0.106154\pi$
$569$	13.6804	+	29.9560i	0.573514	+	1.25582i	−0.371391	+	0.928476i	$0.621119\pi$
$570$		0			0
$571$	−6.18278	+	13.5384i	−0.258741	+	0.566565i	−0.993767	−	0.111474i	$-0.964443\pi$
$571$	−6.18278	+	13.5384i	−0.258741	+	0.566565i	0.735026	+	0.678039i	$0.237170\pi$
$572$		0			0
$573$	2.59676	−	1.66884i	0.108481	−	0.0697166i
$574$		0			0
$575$	−3.90349	+	9.46095i	−0.162787	+	0.394549i
$576$		0			0
$577$	14.8013	−	9.51221i	0.616186	−	0.395999i	−0.194986	−	0.980806i	$-0.562466\pi$
$577$	14.8013	−	9.51221i	0.616186	−	0.395999i	0.811172	+	0.584807i	$0.198830\pi$
$578$		0			0
$579$	4.96474	−	10.8713i	0.206327	−	0.451794i
$580$		0			0
$581$	−10.8296	−	23.7135i	−0.449287	−	0.983802i
$582$		0			0
$583$	−2.92133	−	20.3183i	−0.120989	−	0.841498i
$584$		0			0
$585$	−8.83105	+	10.1916i	−0.365119	+	0.421370i
$586$		0			0
$587$	33.8366	+	21.7454i	1.39658	+	0.897530i	0.999792	−	0.0203787i	$-0.00648720\pi$
$587$	33.8366	+	21.7454i	1.39658	+	0.897530i	0.396792	+	0.917909i	$0.370124\pi$
$588$		0			0
$589$	−27.7697	−	8.15393i	−1.14423	−	0.335977i
$590$		0			0
$591$	13.7850	+	15.9087i	0.567039	+	0.654398i
$592$		0			0
$593$	−29.5990	+	8.69104i	−1.21548	+	0.356898i	−0.825754	−	0.564031i	$-0.809250\pi$
$593$	−29.5990	+	8.69104i	−1.21548	+	0.356898i	−0.389730	+	0.920929i	$0.627432\pi$
$594$		0			0
$595$	−1.16761	+	8.12090i	−0.0478673	+	0.332924i
$596$		0			0
$597$	−5.02531			−0.205672
$598$		0			0
$599$	11.3435			0.463482			0.231741	−	0.972778i	$-0.425558\pi$
$599$	11.3435			0.463482			0.231741	+	0.972778i	$0.425558\pi$
$600$		0			0
$601$	4.51214	−	31.3827i	0.184054	−	1.28013i	−0.663000	−	0.748619i	$-0.730717\pi$
$601$	4.51214	−	31.3827i	0.184054	−	1.28013i	0.847055	−	0.531506i	$-0.178374\pi$
$602$		0			0
$603$	−2.83793	+	0.833291i	−0.115569	+	0.0339342i
$604$		0			0
$605$	4.71906	+	5.44609i	0.191857	+	0.221415i
$606$		0			0
$607$	−33.4174	−	9.81223i	−1.35637	−	0.398266i	−0.478888	−	0.877876i	$-0.658960\pi$
$607$	−33.4174	−	9.81223i	−1.35637	−	0.398266i	−0.877482	+	0.479610i	$0.840778\pi$
$608$		0			0
$609$	−4.93694	−	3.17278i	−0.200055	−	0.128567i
$610$		0			0
$611$	−9.22316	+	10.6441i	−0.373129	+	0.430614i
$612$		0			0
$613$	3.59015	+	24.9700i	0.145005	+	1.00853i	0.924244	+	0.381803i	$0.124697\pi$
$613$	3.59015	+	24.9700i	0.145005	+	1.00853i	−0.779239	+	0.626727i	$0.784394\pi$
$614$		0			0
$615$	2.09482	+	4.58702i	0.0844714	+	0.184967i
$616$		0			0
$617$	4.47003	−	9.78799i	0.179956	−	0.394050i	−0.798060	−	0.602578i	$-0.794140\pi$
$617$	4.47003	−	9.78799i	0.179956	−	0.394050i	0.978016	+	0.208529i	$0.0668674\pi$
$618$		0			0
$619$	11.1675	−	7.17692i	0.448860	−	0.288465i	−0.296616	−	0.954997i	$-0.595858\pi$
$619$	11.1675	−	7.17692i	0.448860	−	0.288465i	0.745477	+	0.666532i	$0.232222\pi$
$620$		0			0
$621$	−0.858058	−	4.71845i	−0.0344327	−	0.189345i
$622$		0			0
$623$	2.60000	−	1.67092i	0.104167	−	0.0669439i
$624$		0			0
$625$	−12.9261	+	28.3042i	−0.517044	+	1.13217i
$626$		0			0
$627$	−3.31344	−	7.25542i	−0.132326	−	0.289754i
$628$		0			0
$629$	1.46634	+	10.1987i	0.0584670	+	0.406647i
$630$		0			0
$631$	3.75435	−	4.33275i	0.149458	−	0.172484i	−0.676083	−	0.736825i	$-0.736324\pi$
$631$	3.75435	−	4.33275i	0.149458	−	0.172484i	0.825542	+	0.564341i	$0.190870\pi$
$632$		0			0
$633$	6.75923	+	4.34389i	0.268655	+	0.172654i
$634$		0			0
$635$	−0.628819	−	0.184638i	−0.0249539	−	0.00732713i
$636$		0			0
$637$	12.5311	+	14.4616i	0.496499	+	0.572991i
$638$		0			0
$639$	4.10191	−	1.20443i	0.162269	−	0.0476465i
$640$		0			0
$641$	−2.71555	+	18.8871i	−0.107258	+	0.745994i	0.863224	+	0.504821i	$0.168441\pi$
$641$	−2.71555	+	18.8871i	−0.107258	+	0.745994i	−0.970482	+	0.241173i	$0.922468\pi$
$642$		0			0
$643$	14.6908			0.579350			0.289675	−	0.957125i	$-0.406453\pi$
$643$	14.6908			0.579350			0.289675	+	0.957125i	$0.406453\pi$
$644$		0			0
$645$	−12.5459			−0.493994
$646$		0			0
$647$	6.05082	−	42.0844i	0.237882	−	1.65451i	−0.424564	−	0.905398i	$-0.639573\pi$
$647$	6.05082	−	42.0844i	0.237882	−	1.65451i	0.662447	−	0.749109i	$-0.269518\pi$
$648$		0			0
$649$	18.4646	−	5.42171i	0.724801	−	0.212821i
$650$		0			0
$651$	12.2666	+	14.1564i	0.480765	+	0.554832i
$652$		0			0
$653$	−37.6522	−	11.0557i	−1.47345	−	0.432643i	−0.556229	−	0.831029i	$-0.687752\pi$
$653$	−37.6522	−	11.0557i	−1.47345	−	0.432643i	−0.917218	+	0.398386i	$0.869570\pi$
$654$		0			0
$655$	−46.2865	−	29.7465i	−1.80856	−	1.16229i
$656$		0			0
$657$	−5.24080	+	6.04821i	−0.204463	+	0.235963i
$658$		0			0
$659$	3.39110	+	23.5856i	0.132098	+	0.918765i	0.942813	+	0.333323i	$0.108170\pi$
$659$	3.39110	+	23.5856i	0.132098	+	0.918765i	−0.810714	+	0.585442i	$0.800921\pi$
$660$		0			0
$661$	16.9017	+	37.0096i	0.657401	+	1.43951i	0.884924	+	0.465735i	$0.154210\pi$
$661$	16.9017	+	37.0096i	0.657401	+	1.43951i	−0.227523	+	0.973773i	$0.573063\pi$
$662$		0			0
$663$	3.59589	−	7.87391i	0.139653	−	0.305797i
$664$		0			0
$665$	11.1442	−	7.16196i	0.432154	−	0.277729i
$666$		0			0
$667$	13.5210	+	7.99703i	0.523534	+	0.309646i
$668$		0			0
$669$	17.1127	−	10.9977i	0.661617	−	0.425195i
$670$		0			0
$671$	−12.7322	+	27.8797i	−0.491522	+	1.07628i
$672$		0			0
$673$	−8.81984	−	19.3128i	−0.339980	−	0.744452i	0.659997	−	0.751268i	$-0.270558\pi$
$673$	−8.81984	−	19.3128i	−0.339980	−	0.744452i	−0.999977	+	0.00681639i	$0.997830\pi$
$674$		0			0
$675$	0.303708	+	2.11234i	0.0116897	+	0.0813039i
$676$		0			0
$677$	−13.3048	+	15.3545i	−0.511344	+	0.590122i	−0.951442	−	0.307827i	$-0.900398\pi$
$677$	−13.3048	+	15.3545i	−0.511344	+	0.590122i	0.440098	+	0.897950i	$0.354944\pi$
$678$		0			0
$679$	−23.3012	−	14.9748i	−0.894218	−	0.574679i
$680$		0			0
$681$	15.3528	+	4.50800i	0.588322	+	0.172747i
$682$		0			0
$683$	13.9709	+	16.1233i	0.534581	+	0.616939i	0.957221	−	0.289358i	$-0.0934419\pi$
$683$	13.9709	+	16.1233i	0.534581	+	0.616939i	−0.422640	+	0.906298i	$0.638896\pi$
$684$		0			0
$685$	3.66754	−	1.07689i	0.140129	−	0.0411457i
$686$		0			0
$687$	−4.01567	+	27.9296i	−0.153207	+	1.06558i
$688$		0			0
$689$	−35.9695			−1.37033
$690$		0			0
$691$	33.0700			1.25804			0.629021	−	0.777389i	$-0.283456\pi$
$691$	33.0700			1.25804			0.629021	+	0.777389i	$0.283456\pi$
$692$		0			0
$693$	−0.734669	+	5.10973i	−0.0279078	+	0.194103i
$694$		0			0
$695$	−34.0837	+	10.0079i	−1.29287	+	0.379620i
$696$		0			0
$697$	−2.11970	−	2.44627i	−0.0802895	−	0.0926590i
$698$		0			0
$699$	14.5686	+	4.27773i	0.551035	+	0.161798i
$700$		0			0
$701$	−20.0574	−	12.8901i	−0.757556	−	0.486852i	0.103960	−	0.994581i	$-0.466849\pi$
$701$	−20.0574	−	12.8901i	−0.757556	−	0.486852i	−0.861517	+	0.507729i	$0.830485\pi$
$702$		0			0
$703$	10.8946	−	12.5730i	0.410897	−	0.474200i
$704$		0			0
$705$	1.06036	+	7.37498i	0.0399356	+	0.277758i
$706$		0			0
$707$	−4.05576	−	8.88088i	−0.152533	−	0.334000i
$708$		0			0
$709$	14.7873	−	32.3798i	0.555350	−	1.21605i	−0.398888	−	0.917000i	$-0.630604\pi$
$709$	14.7873	−	32.3798i	0.555350	−	1.21605i	0.954238	−	0.299048i	$-0.0966690\pi$
$710$		0			0
$711$	−9.40159	+	6.04203i	−0.352587	+	0.226594i
$712$		0			0
$713$	−34.2175	−	36.6501i	−1.28145	−	1.37256i
$714$		0			0
$715$	−32.6875	+	21.0070i	−1.22244	+	0.785618i
$716$		0			0
$717$	−3.58693	+	7.85427i	−0.133956	+	0.293323i
$718$		0			0
$719$	2.91898	+	6.39167i	0.108860	+	0.238369i	0.956220	−	0.292649i	$-0.0945368\pi$
$719$	2.91898	+	6.39167i	0.108860	+	0.238369i	−0.847360	+	0.531018i	$0.821810\pi$
$720$		0			0
$721$	1.91647	+	13.3294i	0.0713731	+	0.496411i
$722$		0			0
$723$	−2.25427	+	2.60156i	−0.0838371	+	0.0967531i
$724$		0			0
$725$	−5.88051	−	3.77917i	−0.218396	−	0.140355i
$726$		0			0
$727$	−46.0952	−	13.5348i	−1.70957	−	0.501976i	−0.726810	−	0.686838i	$-0.758998\pi$
$727$	−46.0952	−	13.5348i	−1.70957	−	0.501976i	−0.982764	+	0.184862i	$0.940816\pi$
$728$		0			0
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$		0			0
$731$	7.72689	−	2.26882i	0.285789	−	0.0839153i
$732$		0			0
$733$	−4.64401	+	32.2998i	−0.171530	+	1.19302i	0.704122	+	0.710079i	$0.251341\pi$
$733$	−4.64401	+	32.2998i	−0.171530	+	1.19302i	−0.875653	+	0.482941i	$0.839568\pi$
$734$		0			0
$735$	10.1231			0.373395
$736$		0			0
$737$	−8.52219			−0.313919
$738$		0			0
$739$	−5.49379	+	38.2102i	−0.202092	+	1.40558i	0.595969	+	0.803008i	$0.296768\pi$
$739$	−5.49379	+	38.2102i	−0.202092	+	1.40558i	−0.798061	+	0.602576i	$0.794141\pi$
$740$		0			0
$741$	−13.4104	+	3.93765i	−0.492644	+	0.144653i
$742$		0			0
$743$	−7.46481	−	8.61486i	−0.273857	−	0.316048i	0.602115	−	0.798409i	$-0.294325\pi$
$743$	−7.46481	−	8.61486i	−0.273857	−	0.316048i	−0.875973	+	0.482361i	$0.839779\pi$
$744$		0			0
$745$	60.9785	+	17.9049i	2.23408	+	0.655985i
$746$		0			0
$747$	12.2407	+	7.86664i	0.447865	+	0.287825i
$748$		0			0
$749$	15.9088	−	18.3597i	0.581295	−	0.670850i
$750$		0			0
$751$	−2.94343	−	20.4720i	−0.107407	−	0.747033i	−0.970345	−	0.241723i	$-0.922287\pi$
$751$	−2.94343	−	20.4720i	−0.107407	−	0.747033i	0.862938	−	0.505310i	$-0.168622\pi$
$752$		0			0
$753$	0.545435	+	1.19434i	0.0198768	+	0.0435241i
$754$		0			0
$755$	−3.60307	+	7.88963i	−0.131129	+	0.287133i
$756$		0			0
$757$	−16.9384	+	10.8856i	−0.615635	+	0.395645i	−0.810967	−	0.585093i	$-0.801058\pi$
$757$	−16.9384	+	10.8856i	−0.615635	+	0.395645i	0.195331	+	0.980737i	$0.437422\pi$
$758$		0			0
$759$	1.45806	−	13.7412i	0.0529243	−	0.498774i
$760$		0			0
$761$	8.05262	−	5.17510i	0.291907	−	0.187597i	−0.386488	−	0.922294i	$-0.626312\pi$
$761$	8.05262	−	5.17510i	0.291907	−	0.187597i	0.678395	+	0.734697i	$0.262676\pi$
$762$		0			0
$763$	−11.4436	+	25.0579i	−0.414285	+	0.907158i
$764$		0			0
$765$	−1.90230	−	4.16546i	−0.0687779	−	0.150603i
$766$		0			0
$767$	−4.79902	−	33.3779i	−0.173283	−	1.20521i
$768$		0			0
$769$	9.94431	−	11.4763i	0.358601	−	0.413848i	−0.547569	−	0.836760i	$-0.684447\pi$
$769$	9.94431	−	11.4763i	0.358601	−	0.413848i	0.906170	+	0.422913i	$0.138992\pi$
$770$		0			0
$771$	16.2439	+	10.4393i	0.585011	+	0.375964i
$772$		0			0
$773$	35.3350	+	10.3753i	1.27091	+	0.373174i	0.846546	−	0.532316i	$-0.178678\pi$
$773$	35.3350	+	10.3753i	1.27091	+	0.373174i	0.424368	+	0.905490i	$0.360496\pi$
$774$		0			0
$775$	14.6110	+	16.8620i	0.524843	+	0.605701i
$776$		0			0
$777$	−10.3311	+	3.03349i	−0.370627	+	0.108826i
$778$		0			0
$779$	−0.743793	+	5.17319i	−0.0266491	+	0.185349i
$780$		0			0
$781$	12.3179			0.440769
$782$		0			0
$783$	3.27553			0.117058
$784$		0			0
$785$	−5.73509	+	39.8884i	−0.204694	+	1.42368i
$786$		0			0
$787$	2.45563	−	0.721039i	0.0875339	−	0.0257023i	−0.237672	−	0.971345i	$-0.576384\pi$
$787$	2.45563	−	0.721039i	0.0875339	−	0.0257023i	0.325206	+	0.945643i	$0.394566\pi$
$788$		0			0
$789$	10.8933	+	12.5716i	0.387813	+	0.447560i
$790$		0			0
$791$	−2.94467	−	0.864633i	−0.104700	−	0.0307428i
$792$		0			0
$793$	45.1806	+	29.0358i	1.60441	+	1.03109i
$794$		0			0
$795$	−12.4611	+	14.3809i	−0.441949	+	0.510037i
$796$		0			0
$797$	−5.61948	−	39.0844i	−0.199052	−	1.38444i	−0.807042	−	0.590494i	$-0.798933\pi$
$797$	−5.61948	−	39.0844i	−0.199052	−	1.38444i	0.607990	−	0.793945i	$-0.291976\pi$
$798$		0			0
$799$	−1.98677	−	4.35042i	−0.0702868	−	0.153907i
$800$		0			0
$801$	−0.716604	+	1.56914i	−0.0253200	+	0.0554430i
$802$		0			0
$803$	−19.3985	+	12.4666i	−0.684558	+	0.439939i
$804$		0			0
$805$	22.9342	−	0.850937i	0.808323	−	0.0299916i
$806$		0			0
$807$	−7.05888	+	4.53646i	−0.248484	+	0.159691i
$808$		0			0
$809$	−5.94791	+	13.0241i	−0.209117	+	0.457903i	−0.984906	−	0.173089i	$-0.944625\pi$
$809$	−5.94791	+	13.0241i	−0.209117	+	0.457903i	0.775789	+	0.630993i	$0.217352\pi$
$810$		0			0
$811$	20.0117	+	43.8194i	0.702704	+	1.53871i	0.836661	+	0.547720i	$0.184504\pi$
$811$	20.0117	+	43.8194i	0.702704	+	1.53871i	−0.133957	+	0.990987i	$0.542768\pi$
$812$		0			0
$813$	2.41960	+	16.8287i	0.0848591	+	0.590208i
$814$		0			0
$815$	−3.72338	+	4.29701i	−0.130424	+	0.150518i
$816$		0			0
$817$	−10.9387	−	7.02987i	−0.382696	−	0.245944i
$818$		0			0
$819$	8.67933	+	2.54848i	0.303281	+	0.0890512i
$820$		0			0
$821$	4.57223	+	5.27664i	0.159572	+	0.184156i	0.829905	−	0.557904i	$-0.188394\pi$
$821$	4.57223	+	5.27664i	0.159572	+	0.184156i	−0.670333	+	0.742060i	$0.733849\pi$
$822$		0			0
$823$	−30.9459	+	9.08654i	−1.07871	+	0.316737i	−0.772361	−	0.635184i	$-0.780924\pi$
$823$	−30.9459	+	9.08654i	−1.07871	+	0.316737i	−0.306345	+	0.951920i	$0.599106\pi$
$824$		0			0
$825$	−0.875081	+	6.08632i	−0.0304664	+	0.211899i
$826$		0			0
$827$	23.4405			0.815106			0.407553	−	0.913182i	$-0.366382\pi$
$827$	23.4405			0.815106			0.407553	+	0.913182i	$0.366382\pi$
$828$		0			0
$829$	−10.9397			−0.379952			−0.189976	−	0.981789i	$-0.560841\pi$
$829$	−10.9397			−0.379952			−0.189976	+	0.981789i	$0.560841\pi$
$830$		0			0
$831$	−1.49953	+	10.4295i	−0.0520183	+	0.361795i
$832$		0			0
$833$	−6.23470	+	1.83067i	−0.216020	+	0.0634291i
$834$		0			0
$835$	−33.0987	−	38.1979i	−1.14543	−	1.32189i
$836$		0			0
$837$	−10.0315	−	2.94552i	−0.346740	−	0.101812i
$838$		0			0
$839$	−44.0776	−	28.3270i	−1.52173	−	0.977956i	−0.991501	−	0.130100i	$-0.958470\pi$
$839$	−44.0776	−	28.3270i	−1.52173	−	0.977956i	−0.530228	−	0.847855i	$-0.677894\pi$
$840$		0			0
$841$	11.9649	−	13.8082i	0.412583	−	0.476146i
$842$		0			0
$843$	1.13868	+	7.91969i	0.0392182	+	0.272769i
$844$		0			0
$845$	13.8597	+	30.3486i	0.476789	+	1.04402i
$846$		0			0
$847$	2.00803	−	4.39697i	0.0689967	−	0.151082i
$848$		0			0
$849$	5.34063	−	3.43221i	0.183290	−	0.117793i
$850$		0			0
$851$	27.3342	−	9.13981i	0.937004	−	0.313309i
$852$		0			0
$853$	−28.9423	+	18.6001i	−0.990964	+	0.636854i	−0.932399	−	0.361430i	$-0.882289\pi$
$853$	−28.9423	+	18.6001i	−0.990964	+	0.636854i	−0.0585646	+	0.998284i	$0.518652\pi$
$854$		0			0
$855$	−3.07154	+	6.72572i	−0.105044	+	0.230015i
$856$		0			0
$857$	−13.3491	−	29.2304i	−0.455995	−	0.998491i	−0.988382	−	0.151989i	$-0.951432\pi$
$857$	−13.3491	−	29.2304i	−0.455995	−	0.998491i	0.532387	−	0.846501i	$-0.321295\pi$
$858$		0			0
$859$	1.38441	+	9.62878i	0.0472354	+	0.328530i	0.999714	+	0.0239234i	$0.00761578\pi$
$859$	1.38441	+	9.62878i	0.0472354	+	0.328530i	−0.952478	+	0.304606i	$0.901475\pi$
$860$		0			0
$861$	2.21511	−	2.55637i	0.0754908	−	0.0871210i
$862$		0			0
$863$	−40.2227	−	25.8496i	−1.36920	−	0.879930i	−0.370396	−	0.928874i	$-0.620778\pi$
$863$	−40.2227	−	25.8496i	−1.36920	−	0.879930i	−0.998802	+	0.0489437i	$0.984415\pi$
$864$		0			0
$865$	−52.9420	−	15.5452i	−1.80008	−	0.528552i
$866$		0			0
$867$	−9.20773	−	10.6263i	−0.312711	−	0.360888i
$868$		0			0
$869$	−30.8964	+	9.07200i	−1.04809	+	0.307747i
$870$		0			0
$871$	−2.12522	+	14.7813i	−0.0720105	+	0.500844i
$872$		0			0
$873$	15.4597			0.523233
$874$		0			0
$875$	13.7147			0.463640
$876$		0			0
$877$	−3.24260	+	22.5528i	−0.109495	+	0.761554i	0.858902	+	0.512140i	$0.171147\pi$
$877$	−3.24260	+	22.5528i	−0.109495	+	0.761554i	−0.968397	+	0.249414i	$0.919762\pi$
$878$		0			0
$879$	19.5106	−	5.72882i	0.658076	−	0.193228i
$880$		0			0
$881$	−9.36780	−	10.8110i	−0.315609	−	0.364233i	0.575674	−	0.817679i	$-0.304740\pi$
$881$	−9.36780	−	10.8110i	−0.315609	−	0.364233i	−0.891283	+	0.453447i	$0.850194\pi$
$882$		0			0
$883$	−23.7491	−	6.97338i	−0.799223	−	0.234673i	−0.143476	−	0.989654i	$-0.545828\pi$
$883$	−23.7491	−	6.97338i	−0.799223	−	0.234673i	−0.655747	+	0.754981i	$0.727646\pi$
$884$		0			0
$885$	−15.0073	−	9.64461i	−0.504465	−	0.324200i
$886$		0			0
$887$	−17.8646	+	20.6168i	−0.599834	+	0.692245i	−0.971748	−	0.236022i	$-0.924156\pi$
$887$	−17.8646	+	20.6168i	−0.599834	+	0.692245i	0.371914	+	0.928267i	$0.378702\pi$
$888$		0			0
$889$	0.0625626	+	0.435133i	0.00209828	+	0.0145939i
$890$		0			0
$891$	−1.19694	−	2.62094i	−0.0400992	−	0.0878049i
$892$		0			0
$893$	−3.20792	+	7.02436i	−0.107349	+	0.235061i
$894$		0			0
$895$	−0.405314	+	0.260480i	−0.0135482	+	0.00870687i
$896$		0			0
$897$	−23.4697	−	5.95564i	−0.783631	−	0.198853i
$898$		0			0
$899$	28.8093	−	18.5146i	0.960845	−	0.617497i
$900$		0			0
$901$	5.07400	−	11.1105i	0.169039	−	0.370145i
$902$		0			0
$903$	3.49595	+	7.65506i	0.116338	+	0.254744i
$904$		0			0
$905$	−6.19938	−	43.1176i	−0.206074	−	1.43328i
$906$		0			0
$907$	28.9496	−	33.4097i	0.961257	−	1.10935i	−0.0326872	−	0.999466i	$-0.510407\pi$
$907$	28.9496	−	33.4097i	0.961257	−	1.10935i	0.993944	−	0.109884i	$-0.0350480\pi$
$908$		0			0
$909$	4.58425	+	2.94612i	0.152050	+	0.0977165i
$910$		0			0
$911$	−8.50295	−	2.49669i	−0.281715	−	0.0827190i	0.137823	−	0.990457i	$-0.455990\pi$
$911$	−8.50295	−	2.49669i	−0.281715	−	0.0827190i	−0.419538	+	0.907738i	$0.637808\pi$
$912$		0			0
$913$	27.4550	+	31.6848i	0.908628	+	1.04861i
$914$		0			0
$915$	27.2609	−	8.00453i	0.901218	−	0.264621i
$916$		0			0
$917$	−5.25241	+	36.5313i	−0.173450	+	1.20637i
$918$		0			0
$919$	−8.92405			−0.294377			−0.147189	−	0.989108i	$-0.547022\pi$
$919$	−8.92405			−0.294377			−0.147189	+	0.989108i	$0.547022\pi$
$920$		0			0
$921$	−3.19979			−0.105437
$922$		0			0
$923$	3.07178	−	21.3647i	0.101109	−	0.703227i
$924$		0			0
$925$	−12.3057	+	3.61327i	−0.404607	+	0.118803i
$926$		0			0
$927$	−4.92211	−	5.68042i	−0.161663	−	0.186570i
$928$		0			0
$929$	37.3510	+	10.9673i	1.22545	+	0.359824i	0.829530	−	0.558462i	$-0.188608\pi$
$929$	37.3510	+	10.9673i	1.22545	+	0.359824i	0.395918	+	0.918286i	$0.370426\pi$
$930$		0			0
$931$	8.82625	+	5.67229i	0.289269	+	0.185902i
$932$		0			0
$933$	10.2695	−	11.8516i	0.336209	−	0.388005i
$934$		0			0
$935$	−1.87776	−	13.0601i	−0.0614093	−	0.427111i
$936$		0			0
$937$	−1.81591	−	3.97629i	−0.0593233	−	0.129900i	0.877649	−	0.479305i	$-0.159111\pi$
$937$	−1.81591	−	3.97629i	−0.0593233	−	0.129900i	−0.936972	+	0.349405i	$0.886384\pi$
$938$		0			0
$939$	−7.41064	+	16.2270i	−0.241837	+	0.529550i
$940$		0			0
$941$	−23.8943	+	15.3559i	−0.778932	+	0.500589i	−0.868679	−	0.495375i	$-0.835030\pi$
$941$	−23.8943	+	15.3559i	−0.778932	+	0.500589i	0.0897471	+	0.995965i	$0.471394\pi$
$942$		0			0
$943$	−5.67159	+	7.05802i	−0.184692	+	0.229841i
$944$		0			0
$945$	4.02573	−	2.58718i	0.130957	−	0.0841610i
$946$		0			0
$947$	−3.30011	+	7.22623i	−0.107239	+	0.234821i	−0.955642	−	0.294530i	$-0.904837\pi$
$947$	−3.30011	+	7.22623i	−0.107239	+	0.234821i	0.848403	+	0.529350i	$0.177564\pi$
$948$		0			0
$949$	16.7852	+	36.7544i	0.544870	+	1.19310i
$950$		0			0
$951$	−3.58831	−	24.9573i	−0.116359	−	0.809295i
$952$		0			0
$953$	−11.3572	+	13.1069i	−0.367896	+	0.424575i	−0.909270	−	0.416207i	$-0.863359\pi$
$953$	−11.3572	+	13.1069i	−0.367896	+	0.424575i	0.541373	+	0.840782i	$0.317905\pi$
$954$		0			0
$955$	−6.93586	−	4.45740i	−0.224439	−	0.144238i
$956$		0			0
$957$	9.05556	+	2.65895i	0.292725	+	0.0859517i
$958$		0			0
$959$	−1.67905	−	1.93772i	−0.0542193	−	0.0625724i
$960$		0			0
$961$	−75.1354	+	22.0617i	−2.42372	+	0.711669i
$962$		0			0
$963$	−1.92970	+	13.4213i	−0.0621836	+	0.432496i
$964$		0			0
$965$	−31.9214			−1.02759
$966$		0			0
$967$	49.3529			1.58708			0.793541	−	0.608517i	$-0.208235\pi$
$967$	49.3529			1.58708			0.793541	+	0.608517i	$0.208235\pi$
$968$		0			0
$969$	0.675437	−	4.69776i	0.0216982	−	0.150914i
$970$		0			0
$971$	−36.4401	+	10.6998i	−1.16942	+	0.343372i	−0.808086	−	0.589065i	$-0.799496\pi$
$971$	−36.4401	+	10.6998i	−1.16942	+	0.343372i	−0.361333	+	0.932437i	$0.617678\pi$
$972$		0			0
$973$	15.6040	+	18.0079i	0.500240	+	0.577308i
$974$		0			0
$975$	10.3382	+	3.03556i	0.331086	+	0.0972157i
$976$		0			0
$977$	34.0839	+	21.9044i	1.09044	+	0.700783i	0.956946	−	0.290267i	$-0.0937441\pi$
$977$	34.0839	+	21.9044i	1.09044	+	0.700783i	0.133493	+	0.991050i	$0.457380\pi$
$978$		0			0
$979$	−3.25490	+	3.75636i	−0.104027	+	0.120054i
$980$		0			0
$981$	−2.18817	−	15.2190i	−0.0698627	−	0.485906i
$982$		0			0
$983$	−14.1855	−	31.0619i	−0.452447	−	0.990720i	−0.989145	−	0.146945i	$-0.953056\pi$
$983$	−14.1855	−	31.0619i	−0.452447	−	0.990720i	0.536698	−	0.843774i	$-0.319671\pi$
$984$		0			0
$985$	23.3565	−	51.1437i	0.744201	−	1.62957i
$986$		0			0
$987$	4.20448	−	2.70205i	0.133830	−	0.0860073i
$988$		0			0
$989$	−10.1113	−	20.1299i	−0.321519	−	0.640095i
$990$		0			0
$991$	−12.2771	+	7.89004i	−0.389996	+	0.250635i	−0.720914	−	0.693024i	$-0.756278\pi$
$991$	−12.2771	+	7.89004i	−0.389996	+	0.250635i	0.330918	+	0.943659i	$0.392642\pi$
$992$		0			0
$993$	−12.4923	+	27.3543i	−0.396431	+	0.868062i
$994$		0			0
$995$	5.57588	+	12.2095i	0.176767	+	0.387066i
$996$		0			0
$997$	−0.180698	−	1.25678i	−0.00572275	−	0.0398026i	0.986760	−	0.162187i	$-0.0518549\pi$
$997$	−0.180698	−	1.25678i	−0.00572275	−	0.0398026i	−0.992483	+	0.122385i	$0.960946\pi$
$998$		0			0
$999$	3.93555	−	4.54187i	0.124515	−	0.143698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.d.265.1	yes	30
23.2	even	11	inner	552.2.q.d.25.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.d.25.1	✓	30	23.2	even	11	inner
552.2.q.d.265.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{3} +(-2.56277 + 0.752498i) q^{5} +(1.17327 + 1.35403i) q^{7} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{3} +(-2.56277 + 0.752498i) q^{5} +(1.17327 + 1.35403i) q^{7} +(-0.959493 - 0.281733i) q^{9} +(-2.42392 - 1.55776i) q^{11} +(-3.30631 + 3.81569i) q^{13} +(0.380118 + 2.64378i) q^{15} +(-0.712216 - 1.55954i) q^{17} +(-1.14997 + 2.51809i) q^{19} +(1.50722 - 0.968631i) q^{21} +(-3.93560 + 2.74063i) q^{23} +(1.79528 - 1.15376i) q^{25} +(-0.415415 + 0.909632i) q^{27} +(-1.36070 - 2.97953i) q^{29} +(1.48790 + 10.3486i) q^{31} +(-1.88687 + 2.17756i) q^{33} +(-4.02573 - 2.58718i) q^{35} +(-5.76631 - 1.69314i) q^{37} +(3.30631 + 3.81569i) q^{39} +(1.81150 - 0.531905i) q^{41} +(-0.668472 + 4.64933i) q^{43} +2.67097 q^{45} +2.78956 q^{47} +(0.539380 - 3.75147i) q^{49} +(-1.64502 + 0.483021i) q^{51} +(4.66539 + 5.38414i) q^{53} +(7.38418 + 2.16819i) q^{55} +(2.32880 + 1.49663i) q^{57} +(-4.37377 + 5.04760i) q^{59} +(-1.51384 - 10.5290i) q^{61} +(-0.744272 - 1.62973i) q^{63} +(5.60203 - 12.2667i) q^{65} +(2.48821 - 1.59907i) q^{67} +(2.15264 + 4.28557i) q^{69} +(-3.59643 + 2.31129i) q^{71} +(3.32454 - 7.27972i) q^{73} +(-0.886520 - 1.94121i) q^{75} +(-0.734669 - 5.10973i) q^{77} +(7.31852 - 8.44602i) q^{79} +(0.841254 + 0.540641i) q^{81} +(-13.9612 - 4.09938i) q^{83} +(2.99879 + 3.46079i) q^{85} +(-3.14285 + 0.922823i) q^{87} +(0.245498 - 1.70747i) q^{89} -9.04575 q^{91} +10.4550 q^{93} +(1.05226 - 7.31864i) q^{95} +(-14.8335 + 4.35551i) q^{97} +(1.88687 + 2.17756i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9	\( 30 q + 3 q^{3} + 2 q^{5} + 4 q^{7} - 3 q^{9} - 15 q^{11} - 5 q^{13} - 2 q^{15} + 9 q^{17} - 3 q^{19} + 7 q^{21} + 18 q^{23} - 19 q^{25} + 3 q^{27} - 21 q^{29} + 17 q^{31} - 7 q^{33} - 36 q^{35} + 9 q^{37} + 5 q^{39} + 18 q^{41} + 50 q^{43} + 2 q^{45} + 74 q^{47} - 17 q^{49} + 13 q^{51} + 43 q^{53} - 42 q^{55} - 8 q^{57} + 7 q^{59} - 10 q^{61} + 4 q^{63} - 4 q^{65} + 33 q^{67} + 15 q^{69} + 3 q^{71} + 30 q^{73} - 25 q^{75} - 82 q^{77} - 40 q^{79} - 3 q^{81} + 9 q^{83} - 54 q^{85} + 10 q^{87} + 25 q^{89} - 30 q^{91} + 38 q^{93} - 49 q^{95} - 69 q^{97} + 7 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 2 * q^5 + 4 * q^7 - 3 * q^9 - 15 * q^11 - 5 * q^13 - 2 * q^15 + 9 * q^17 - 3 * q^19 + 7 * q^21 + 18 * q^23 - 19 * q^25 + 3 * q^27 - 21 * q^29 + 17 * q^31 - 7 * q^33 - 36 * q^35 + 9 * q^37 + 5 * q^39 + 18 * q^41 + 50 * q^43 + 2 * q^45 + 74 * q^47 - 17 * q^49 + 13 * q^51 + 43 * q^53 - 42 * q^55 - 8 * q^57 + 7 * q^59 - 10 * q^61 + 4 * q^63 - 4 * q^65 + 33 * q^67 + 15 * q^69 + 3 * q^71 + 30 * q^73 - 25 * q^75 - 82 * q^77 - 40 * q^79 - 3 * q^81 + 9 * q^83 - 54 * q^85 + 10 * q^87 + 25 * q^89 - 30 * q^91 + 38 * q^93 - 49 * q^95 - 69 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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