LMFDB - Embedded newform 920.2.bv.a.297.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(17,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))

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

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

chi := DirichletCharacter("920.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			297.8
Character	$\chi$	$=$	920.297
Dual form			920.2.bv.a.793.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.65448 - 1.23853i) q^{3} +(-1.12032 + 1.93517i) q^{5} +(0.362720 + 5.07149i) q^{7} +(0.358151 + 1.21975i) q^{9} +O(q^{10})$	\(q+(-1.65448 - 1.23853i) q^{3} +(-1.12032 + 1.93517i) q^{5} +(0.362720 + 5.07149i) q^{7} +(0.358151 + 1.21975i) q^{9} +(0.485630 + 0.755654i) q^{11} +(-1.98556 - 0.142010i) q^{13} +(4.25030 - 1.81416i) q^{15} +(-1.13006 - 3.02981i) q^{17} +(-1.99670 - 4.37217i) q^{19} +(5.68107 - 8.83991i) q^{21} +(2.50482 + 4.08973i) q^{23} +(-2.48978 - 4.33601i) q^{25} +(-1.24857 + 3.34755i) q^{27} +(-7.72847 - 3.52948i) q^{29} +(0.654548 - 4.55248i) q^{31} +(0.132435 - 1.85168i) q^{33} +(-10.2206 - 4.97975i) q^{35} +(5.30897 - 9.72266i) q^{37} +(3.10918 + 2.69412i) q^{39} +(4.36035 + 1.28031i) q^{41} +(-4.03615 + 5.39166i) q^{43} +(-2.76167 - 0.673423i) q^{45} +(2.11736 + 2.11736i) q^{47} +(-18.6597 + 2.68286i) q^{49} +(-1.88284 + 6.41237i) q^{51} +(2.98779 - 0.213691i) q^{53} +(-2.00638 + 0.0932047i) q^{55} +(-2.11155 + 9.70662i) q^{57} +(-3.79343 + 3.28702i) q^{59} +(-10.7259 - 1.54216i) q^{61} +(-6.05605 + 2.25879i) q^{63} +(2.49927 - 3.68330i) q^{65} +(2.95598 - 0.643035i) q^{67} +(0.921063 - 9.86865i) q^{69} +(-8.42202 - 5.41251i) q^{71} +(-11.5138 - 4.29441i) q^{73} +(-1.25098 + 10.2575i) q^{75} +(-3.65615 + 2.73696i) q^{77} +(0.786408 + 0.907563i) q^{79} +(9.42008 - 6.05392i) q^{81} +(-5.21441 - 2.84728i) q^{83} +(7.12923 + 1.20748i) q^{85} +(8.41524 + 15.4114i) q^{87} +(1.19371 + 8.30244i) q^{89} -10.1213i q^{91} +(-6.72131 + 6.72131i) q^{93} +(10.6978 + 1.03425i) q^{95} +(1.21975 - 0.666035i) q^{97} +(-0.747781 + 0.862985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q+O(q^{10}) $ 720 * q	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{13}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.65448	−	1.23853i	−0.955213	−	0.715064i	0.00333490	−	0.999994i	$-0.498938\pi$
$3$	−1.65448	−	1.23853i	−0.955213	−	0.715064i	−0.958548	+	0.284931i	$0.908029\pi$
$4$		0			0
$5$	−1.12032	+	1.93517i	−0.501021	+	0.865435i
$5$	−1.12032	+	1.93517i	−0.501021	+	0.865435i
$6$		0			0
$7$	0.362720	+	5.07149i	0.137095	+	1.91684i	0.344841	+	0.938661i	$0.387933\pi$
$7$	0.362720	+	5.07149i	0.137095	+	1.91684i	−0.207746	+	0.978183i	$0.566613\pi$
$8$		0			0
$9$	0.358151	+	1.21975i	0.119384	+	0.406583i
$10$		0			0
$11$	0.485630	+	0.755654i	0.146423	+	0.227838i	0.906716	−	0.421742i	$-0.138581\pi$
$11$	0.485630	+	0.755654i	0.146423	+	0.227838i	−0.760293	+	0.649580i	$0.774945\pi$
$12$		0			0
$13$	−1.98556	−	0.142010i	−0.550695	−	0.0393865i	−0.206780	−	0.978387i	$-0.566299\pi$
$13$	−1.98556	−	0.142010i	−0.550695	−	0.0393865i	−0.343915	+	0.939001i	$0.611753\pi$
$14$		0			0
$15$	4.25030	−	1.81416i	1.09742	−	0.468413i
$16$		0			0
$17$	−1.13006	−	3.02981i	−0.274080	−	0.734837i	−0.998944	−	0.0459451i	$-0.985370\pi$
$17$	−1.13006	−	3.02981i	−0.274080	−	0.734837i	0.724864	−	0.688892i	$-0.241903\pi$
$18$		0			0
$19$	−1.99670	−	4.37217i	−0.458075	−	1.00304i	−0.987922	−	0.154951i	$-0.950478\pi$
$19$	−1.99670	−	4.37217i	−0.458075	−	1.00304i	0.529847	−	0.848093i	$-0.322249\pi$
$20$		0			0
$21$	5.68107	−	8.83991i	1.23971	−	1.92903i
$22$		0			0
$23$	2.50482	+	4.08973i	0.522292	+	0.852767i
$23$	2.50482	+	4.08973i	0.522292	+	0.852767i
$24$		0			0
$25$	−2.48978	−	4.33601i	−0.497956	−	0.867202i
$26$		0			0
$27$	−1.24857	+	3.34755i	−0.240288	+	0.644236i
$28$		0			0
$29$	−7.72847	−	3.52948i	−1.43514	−	0.655407i	−0.462267	−	0.886741i	$-0.652964\pi$
$29$	−7.72847	−	3.52948i	−1.43514	−	0.655407i	−0.972874	+	0.231334i	$0.925691\pi$
$30$		0			0
$31$	0.654548	−	4.55248i	0.117560	−	0.817650i	−0.842668	−	0.538434i	$-0.819016\pi$
$31$	0.654548	−	4.55248i	0.117560	−	0.817650i	0.960228	−	0.279216i	$-0.0900747\pi$
$32$		0			0
$33$	0.132435	−	1.85168i	0.0230539	−	0.322336i
$34$		0			0
$35$	−10.2206	−	4.97975i	−1.72759	−	0.841732i
$36$		0			0
$37$	5.30897	−	9.72266i	0.872790	−	1.59840i	0.0736231	−	0.997286i	$-0.476544\pi$
$37$	5.30897	−	9.72266i	0.872790	−	1.59840i	0.799167	−	0.601109i	$-0.205274\pi$
$38$		0			0
$39$	3.10918	+	2.69412i	0.497867	+	0.431404i
$40$		0			0
$41$	4.36035	+	1.28031i	0.680972	+	0.199951i	0.603883	−	0.797073i	$-0.293619\pi$
$41$	4.36035	+	1.28031i	0.680972	+	0.199951i	0.0770888	+	0.997024i	$0.475437\pi$
$42$		0			0
$43$	−4.03615	+	5.39166i	−0.615507	+	0.822221i	−0.994670	−	0.103109i	$-0.967121\pi$
$43$	−4.03615	+	5.39166i	−0.615507	+	0.822221i	0.379163	+	0.925330i	$0.376212\pi$
$44$		0			0
$45$	−2.76167	−	0.673423i	−0.411685	−	0.100388i
$46$		0			0
$47$	2.11736	+	2.11736i	0.308849	+	0.308849i	0.844463	−	0.535614i	$-0.179920\pi$
$47$	2.11736	+	2.11736i	0.308849	+	0.308849i	−0.535614	+	0.844463i	$0.679920\pi$
$48$		0			0
$49$	−18.6597	+	2.68286i	−2.66567	+	0.383266i
$50$		0			0
$51$	−1.88284	+	6.41237i	−0.263650	+	0.897911i
$52$		0			0
$53$	2.98779	−	0.213691i	0.410404	−	0.0293527i	0.135389	−	0.990793i	$-0.456772\pi$
$53$	2.98779	−	0.213691i	0.410404	−	0.0293527i	0.275015	+	0.961440i	$0.411317\pi$
$54$		0			0
$55$	−2.00638	+	0.0932047i	−0.270540	+	0.0125677i
$56$		0			0
$57$	−2.11155	+	9.70662i	−0.279681	+	1.28567i
$58$		0			0
$59$	−3.79343	+	3.28702i	−0.493862	+	0.427934i	−0.865850	−	0.500304i	$-0.833222\pi$
$59$	−3.79343	+	3.28702i	−0.493862	+	0.427934i	0.371988	+	0.928238i	$0.378676\pi$
$60$		0			0
$61$	−10.7259	−	1.54216i	−1.37332	−	0.197453i	−0.584156	−	0.811641i	$-0.698575\pi$
$61$	−10.7259	−	1.54216i	−1.37332	−	0.197453i	−0.789160	+	0.614188i	$0.789484\pi$
$62$		0			0
$63$	−6.05605	+	2.25879i	−0.762990	+	0.284581i
$64$		0			0
$65$	2.49927	−	3.68330i	0.309996	−	0.456857i
$66$		0			0
$67$	2.95598	−	0.643035i	0.361131	−	0.0785592i	−0.0283391	−	0.999598i	$-0.509022\pi$
$67$	2.95598	−	0.643035i	0.361131	−	0.0785592i	0.389470	+	0.921039i	$0.372658\pi$
$68$		0			0
$69$	0.921063	−	9.86865i	0.110883	−	1.18805i
$70$		0			0
$71$	−8.42202	−	5.41251i	−0.999510	−	0.642346i	−0.0648525	−	0.997895i	$-0.520658\pi$
$71$	−8.42202	−	5.41251i	−0.999510	−	0.642346i	−0.934658	+	0.355549i	$0.884294\pi$
$72$		0			0
$73$	−11.5138	−	4.29441i	−1.34758	−	0.502623i	−0.430959	−	0.902371i	$-0.641825\pi$
$73$	−11.5138	−	4.29441i	−1.34758	−	0.502623i	−0.916625	+	0.399749i	$0.869097\pi$
$74$		0			0
$75$	−1.25098	+	10.2575i	−0.144450	+	1.18443i
$76$		0			0
$77$	−3.65615	+	2.73696i	−0.416657	+	0.311905i
$78$		0			0
$79$	0.786408	+	0.907563i	0.0884778	+	0.102109i	0.798262	−	0.602310i	$-0.205753\pi$
$79$	0.786408	+	0.907563i	0.0884778	+	0.102109i	−0.709784	+	0.704419i	$0.751208\pi$
$80$		0			0
$81$	9.42008	−	6.05392i	1.04668	−	0.672658i
$82$		0			0
$83$	−5.21441	−	2.84728i	−0.572355	−	0.312530i	0.166880	−	0.985977i	$-0.446631\pi$
$83$	−5.21441	−	2.84728i	−0.572355	−	0.312530i	−0.739235	+	0.673448i	$0.764813\pi$
$84$		0			0
$85$	7.12923	+	1.20748i	0.773274	+	0.130970i
$86$		0			0
$87$	8.41524	+	15.4114i	0.902208	+	1.65227i
$88$		0			0
$89$	1.19371	+	8.30244i	0.126533	+	0.880057i	0.949901	+	0.312549i	$0.101183\pi$
$89$	1.19371	+	8.30244i	0.126533	+	0.880057i	−0.823368	+	0.567507i	$0.807908\pi$
$90$		0			0
$91$		−	10.1213i		−	1.06100i
$92$		0			0
$93$	−6.72131	+	6.72131i	−0.696967	+	0.696967i
$94$		0			0
$95$	10.6978	+	1.03425i	1.09757	+	0.106112i
$96$		0			0
$97$	1.21975	−	0.666035i	0.123847	−	0.0676256i	−0.416131	−	0.909305i	$-0.636614\pi$
$97$	1.21975	−	0.666035i	0.123847	−	0.0676256i	0.539978	+	0.841679i	$0.318432\pi$
$98$		0			0
$99$	−0.747781	+	0.862985i	−0.0751548	+	0.0867333i
$100$		0			0
$101$	2.30960	−	0.678160i	0.229814	−	0.0674794i	−0.164798	−	0.986327i	$-0.552697\pi$
$101$	2.30960	−	0.678160i	0.229814	−	0.0674794i	0.394612	+	0.918848i	$0.370879\pi$
$102$		0			0
$103$	0.901299	+	0.196066i	0.0888076	+	0.0193189i	0.256750	−	0.966478i	$-0.417348\pi$
$103$	0.901299	+	0.196066i	0.0888076	+	0.0193189i	−0.167942	+	0.985797i	$0.553712\pi$
$104$		0			0
$105$	10.7422	+	20.8973i	1.04833	+	2.03937i
$106$		0			0
$107$	−7.64065	−	10.2067i	−0.738649	−	0.986720i	−0.999771	−	0.0214142i	$-0.993183\pi$
$107$	−7.64065	−	10.2067i	−0.738649	−	0.986720i	0.261121	−	0.965306i	$-0.415908\pi$
$108$		0			0
$109$	6.62751	−	14.5122i	0.634800	−	1.39002i	−0.269450	−	0.963014i	$-0.586842\pi$
$109$	6.62751	−	14.5122i	0.634800	−	1.39002i	0.904250	−	0.427004i	$-0.140431\pi$
$110$		0			0
$111$	−20.8254	+	9.51062i	−1.97665	+	0.902708i
$112$		0			0
$113$	1.82986	+	8.41171i	0.172138	+	0.791307i	0.979531	+	0.201293i	$0.0645143\pi$
$113$	1.82986	+	8.41171i	0.172138	+	0.791307i	−0.807393	+	0.590014i	$0.799122\pi$
$114$		0			0
$115$	−10.7205	+	0.265473i	−0.999694	+	0.0247555i
$116$		0			0
$117$	−0.537913	−	2.47275i	−0.0497301	−	0.228606i
$118$		0			0
$119$	14.9558	−	6.83007i	1.37099	−	0.626112i
$120$		0			0
$121$	4.23439	−	9.27202i	0.384944	−	0.842911i
$122$		0			0
$123$	−5.62840	−	7.51866i	−0.507495	−	0.677935i
$124$		0			0
$125$	11.1803	+	0.0395479i	0.999994	+	0.00353727i
$126$		0			0
$127$	10.0547	+	2.18728i	0.892214	+	0.194089i	0.635227	−	0.772326i	$-0.280907\pi$
$127$	10.0547	+	2.18728i	0.892214	+	0.194089i	0.256987	+	0.966415i	$0.417270\pi$
$128$		0			0
$129$	13.3554	−	3.92151i	1.17588	−	0.345270i
$130$		0			0
$131$	−9.63211	+	11.1161i	−0.841562	+	0.971214i	−0.999869	−	0.0161760i	$-0.994851\pi$
$131$	−9.63211	+	11.1161i	−0.841562	+	0.971214i	0.158308	+	0.987390i	$0.449396\pi$
$132$		0			0
$133$	21.4492	−	11.7121i	1.85988	−	1.01557i
$134$		0			0
$135$	−5.07929	−	6.16652i	−0.437156	−	0.530729i
$136$		0			0
$137$	−4.17852	+	4.17852i	−0.356995	+	0.356995i	−0.862704	−	0.505709i	$-0.831231\pi$
$137$	−4.17852	+	4.17852i	−0.356995	+	0.356995i	0.505709	+	0.862704i	$0.331231\pi$
$138$		0			0
$139$		−	17.9836i		−	1.52535i	−0.646784	−	0.762673i	$-0.723886\pi$
$139$		−	17.9836i		−	1.52535i	0.646784	−	0.762673i	$-0.276114\pi$
$140$		0			0
$141$	−0.880720	−	6.12554i	−0.0741700	−	0.515864i
$142$		0			0
$143$	−0.856936	−	1.56936i	−0.0716606	−	0.131237i
$144$		0			0
$145$	15.4885	−	11.0018i	1.28625	−	0.913649i
$146$		0			0
$147$	34.1949	+	18.6718i	2.82035	+	1.54003i
$148$		0			0
$149$	0.864960	−	0.555876i	0.0708603	−	0.0455392i	−0.504731	−	0.863277i	$-0.668408\pi$
$149$	0.864960	−	0.555876i	0.0708603	−	0.0455392i	0.575591	+	0.817738i	$0.304772\pi$
$150$		0			0
$151$	3.82886	+	4.41874i	0.311588	+	0.359592i	0.889845	−	0.456263i	$-0.150812\pi$
$151$	3.82886	+	4.41874i	0.311588	+	0.359592i	−0.578257	+	0.815855i	$0.696267\pi$
$152$		0			0
$153$	3.29088	−	2.46352i	0.266052	−	0.199164i
$154$		0			0
$155$	8.07654	+	6.36688i	0.648723	+	0.511400i
$156$		0			0
$157$	6.75084	+	2.51793i	0.538776	+	0.200953i	0.604096	−	0.796911i	$-0.293534\pi$
$157$	6.75084	+	2.51793i	0.538776	+	0.200953i	−0.0653206	+	0.997864i	$0.520807\pi$
$158$		0			0
$159$	−5.20789	−	3.34691i	−0.413012	−	0.265427i
$160$		0			0
$161$	−19.8325	+	14.1866i	−1.56302	+	1.11806i
$162$		0			0
$163$	−1.71007	+	0.372002i	−0.133943	+	0.0291374i	−0.279037	−	0.960280i	$-0.590015\pi$
$163$	−1.71007	+	0.372002i	−0.133943	+	0.0291374i	0.145094	+	0.989418i	$0.453652\pi$
$164$		0			0
$165$	3.43495	+	2.33075i	0.267410	+	0.181449i
$166$		0			0
$167$	−14.6527	+	5.46519i	−1.13386	+	0.422909i	−0.845162	−	0.534510i	$-0.820496\pi$
$167$	−14.6527	+	5.46519i	−1.13386	+	0.422909i	−0.288701	+	0.957419i	$0.593224\pi$
$168$		0			0
$169$	−8.94540	−	1.28615i	−0.688108	−	0.0989350i
$170$		0			0
$171$	4.61783	−	4.00137i	0.353134	−	0.305993i
$172$		0			0
$173$	−2.13687	+	9.82302i	−0.162463	+	0.746830i	0.821751	+	0.569847i	$0.192998\pi$
$173$	−2.13687	+	9.82302i	−0.162463	+	0.746830i	−0.984214	+	0.176983i	$0.943366\pi$
$174$		0			0
$175$	21.0870	−	14.1997i	1.59402	−	1.07339i
$176$		0			0
$177$	10.3472	−	0.740047i	0.777744	−	0.0556253i
$178$		0			0
$179$	3.58961	−	12.2251i	0.268300	−	0.913747i	−0.709588	−	0.704617i	$-0.751119\pi$
$179$	3.58961	−	12.2251i	0.268300	−	0.913747i	0.977888	−	0.209129i	$-0.0670630\pi$
$180$		0			0
$181$	−8.56885	+	1.23201i	−0.636918	+	0.0915749i	−0.453207	−	0.891405i	$-0.649720\pi$
$181$	−8.56885	+	1.23201i	−0.636918	+	0.0915749i	−0.183711	+	0.982980i	$0.558811\pi$
$182$		0			0
$183$	15.8358	+	15.8358i	1.17062	+	1.17062i
$184$		0			0
$185$	12.8673	+	21.1662i	0.946022	+	1.55617i
$186$		0			0
$187$	1.74070	−	2.32530i	0.127293	−	0.170043i
$188$		0			0
$189$	−17.4300	−	5.11790i	−1.26784	−	0.372272i
$190$		0			0
$191$	−4.24164	−	3.67540i	−0.306914	−	0.265943i	0.487761	−	0.872977i	$-0.337814\pi$
$191$	−4.24164	−	3.67540i	−0.306914	−	0.265943i	−0.794676	+	0.607034i	$0.792359\pi$
$192$		0			0
$193$	−5.81837	+	10.6555i	−0.418815	+	0.767003i	−0.998868	−	0.0475764i	$-0.984850\pi$
$193$	−5.81837	+	10.6555i	−0.418815	+	0.767003i	0.580052	+	0.814579i	$0.303032\pi$
$194$		0			0
$195$	−8.69685	+	2.99853i	−0.622794	+	0.214729i
$196$		0			0
$197$	−0.873493	+	12.2130i	−0.0622338	+	0.870142i	0.866449	+	0.499266i	$0.166397\pi$
$197$	−0.873493	+	12.2130i	−0.0622338	+	0.870142i	−0.928682	+	0.370876i	$0.879058\pi$
$198$		0			0
$199$	2.03922	−	14.1831i	0.144556	−	1.00541i	−0.780385	−	0.625300i	$-0.784977\pi$
$199$	2.03922	−	14.1831i	0.144556	−	1.00541i	0.924941	−	0.380111i	$-0.124114\pi$
$200$		0			0
$201$	−5.68702	−	2.59718i	−0.401132	−	0.183191i
$202$		0			0
$203$	15.0964	−	40.4751i	1.05956	−	2.84080i
$204$		0			0
$205$	−7.36260	+	7.00367i	−0.514226	+	0.489157i
$206$		0			0
$207$	−4.09134	+	4.52000i	−0.284368	+	0.314162i
$208$		0			0
$209$	2.33419	−	3.63207i	0.161459	−	0.251235i
$210$		0			0
$211$	11.2619	+	24.6601i	0.775299	+	1.69767i	0.714621	+	0.699511i	$0.246599\pi$
$211$	11.2619	+	24.6601i	0.775299	+	1.69767i	0.0606779	+	0.998157i	$0.480674\pi$
$212$		0			0
$213$	7.23052	+	19.3858i	0.495427	+	1.32829i
$214$		0			0
$215$	−5.91203	−	13.8510i	−0.403197	−	0.944631i
$216$		0			0
$217$	23.3253	+	1.66826i	1.58342	+	0.113249i
$218$		0			0
$219$	13.7305	+	21.3651i	0.927823	+	1.44372i
$220$		0			0
$221$	1.81354	+	6.17635i	0.121992	+	0.415466i
$222$		0			0
$223$	1.39105	+	19.4495i	0.0931518	+	1.30243i	0.802107	+	0.597180i	$0.203712\pi$
$223$	1.39105	+	19.4495i	0.0931518	+	1.30243i	−0.708956	+	0.705253i	$0.750833\pi$
$224$		0			0
$225$	4.39713	−	4.58986i	0.293142	−	0.305991i
$226$		0			0
$227$	−18.9296	−	14.1705i	−1.25640	−	0.940530i	−0.256737	−	0.966481i	$-0.582648\pi$
$227$	−18.9296	−	14.1705i	−1.25640	−	0.940530i	−0.999663	+	0.0259516i	$0.991738\pi$
$228$		0			0
$229$	−10.9041			−0.720565			−0.360282	−	0.932843i	$-0.617320\pi$
$229$	−10.9041			−0.720565			−0.360282	+	0.932843i	$0.617320\pi$
$230$		0			0
$231$	9.43881			0.621028
$232$		0			0
$233$	−11.6710	−	8.73678i	−0.764591	−	0.572366i	0.144234	−	0.989544i	$-0.453928\pi$
$233$	−11.6710	−	8.73678i	−0.764591	−	0.572366i	−0.908825	+	0.417178i	$0.863019\pi$
$234$		0			0
$235$	−6.46958	+	1.72535i	−0.422029	+	0.112549i
$236$		0			0
$237$	−0.177053	−	2.47553i	−0.0115008	−	0.160803i
$238$		0			0
$239$	8.28105	+	28.2026i	0.535656	+	1.82428i	0.565535	+	0.824724i	$0.308670\pi$
$239$	8.28105	+	28.2026i	0.535656	+	1.82428i	−0.0298788	+	0.999554i	$0.509512\pi$
$240$		0			0
$241$	−11.6288	−	18.0947i	−0.749075	−	1.16558i	−0.981218	−	0.192902i	$-0.938210\pi$
$241$	−11.6288	−	18.0947i	−0.749075	−	1.16558i	0.232143	−	0.972682i	$-0.425426\pi$
$242$		0			0
$243$	−12.3921	−	0.886301i	−0.794954	−	0.0568563i
$244$		0			0
$245$	15.7130	−	39.1154i	1.00387	−	2.49899i
$246$		0			0
$247$	3.34368	+	8.96475i	0.212753	+	0.570413i
$248$		0			0
$249$	5.10069	+	11.1689i	0.323243	+	0.707803i
$250$		0			0
$251$	−0.392947	+	0.611438i	−0.0248026	+	0.0385936i	−0.853433	−	0.521202i	$-0.825484\pi$
$251$	−0.392947	+	0.611438i	−0.0248026	+	0.0385936i	0.828631	+	0.559795i	$0.189120\pi$
$252$		0			0
$253$	−1.87400	+	3.87887i	−0.117818	+	0.243863i
$254$		0			0
$255$	−10.2997	−	10.8275i	−0.644989	−	0.678044i
$256$		0			0
$257$	−2.53147	+	6.78712i	−0.157908	+	0.423369i	−0.991678	−	0.128744i	$-0.958906\pi$
$257$	−2.53147	+	6.78712i	−0.157908	+	0.423369i	0.833769	+	0.552113i	$0.186178\pi$
$258$		0			0
$259$	51.2341	+	23.3978i	3.18353	+	1.45387i
$260$		0			0
$261$	1.53712	−	10.6909i	0.0951452	−	0.661750i
$262$		0			0
$263$	−1.06861	+	14.9411i	−0.0658933	+	0.921309i	0.851761	+	0.523930i	$0.175535\pi$
$263$	−1.06861	+	14.9411i	−0.0658933	+	0.921309i	−0.917655	+	0.397379i	$0.869920\pi$
$264$		0			0
$265$	−2.93374	+	6.02128i	−0.180218	+	0.369885i
$266$		0			0
$267$	8.30782	−	15.2146i	0.508430	−	0.931121i
$268$		0			0
$269$	21.5965	+	18.7135i	1.31676	+	1.14098i	0.979913	+	0.199425i	$0.0639073\pi$
$269$	21.5965	+	18.7135i	1.31676	+	1.14098i	0.336851	+	0.941558i	$0.390638\pi$
$270$		0			0
$271$	−13.4794	−	3.95792i	−0.818817	−	0.240426i	−0.154610	−	0.987976i	$-0.549412\pi$
$271$	−13.4794	−	3.95792i	−0.818817	−	0.240426i	−0.664206	+	0.747549i	$0.731230\pi$
$272$		0			0
$273$	−12.5354	+	16.7454i	−0.758680	+	1.01348i
$274$		0			0
$275$	2.06741	−	3.98711i	0.124670	−	0.240432i
$276$		0			0
$277$	−5.48934	−	5.48934i	−0.329823	−	0.329823i	0.522696	−	0.852519i	$-0.324926\pi$
$277$	−5.48934	−	5.48934i	−0.329823	−	0.329823i	−0.852519	+	0.522696i	$0.824926\pi$
$278$		0			0
$279$	5.78732	−	0.832091i	0.346478	−	0.0498160i
$280$		0			0
$281$	−1.69705	+	5.77962i	−0.101237	+	0.344783i	−0.994498	−	0.104756i	$-0.966594\pi$
$281$	−1.69705	+	5.77962i	−0.101237	+	0.344783i	0.893260	+	0.449540i	$0.148412\pi$
$282$		0			0
$283$	−1.66226	+	0.118887i	−0.0988112	+	0.00706711i	−0.120657	−	0.992694i	$-0.538500\pi$
$283$	−1.66226	+	0.118887i	−0.0988112	+	0.00706711i	0.0218460	+	0.999761i	$0.493046\pi$
$284$		0			0
$285$	−16.4184	−	14.9607i	−0.972541	−	0.886195i
$286$		0			0
$287$	−4.91152	+	22.5779i	−0.289918	+	1.33273i
$288$		0			0
$289$	4.94502	−	4.28489i	0.290884	−	0.252052i
$290$		0			0
$291$	−2.84295	−	0.408755i	−0.166657	−	0.0239617i
$292$		0			0
$293$	−23.2531	+	8.67297i	−1.35846	+	0.506680i	−0.919947	−	0.392043i	$-0.871768\pi$
$293$	−23.2531	+	8.67297i	−1.35846	+	0.506680i	−0.438516	+	0.898724i	$0.644496\pi$
$294$		0			0
$295$	−2.11112	−	11.0234i	−0.122914	−	0.641810i
$296$		0			0
$297$	−3.13593	+	0.682181i	−0.181965	+	0.0395841i
$298$		0			0
$299$	−4.39269	−	8.47610i	−0.254036	−	0.490186i
$300$		0			0
$301$	−28.8078	−	18.5136i	−1.66045	−	1.06711i
$302$		0			0
$303$	−4.66110	−	1.73850i	−0.267773	−	0.0998743i
$304$		0			0
$305$	15.0008	−	19.0288i	0.858943	−	1.08959i
$306$		0			0
$307$	−11.6297	+	8.70588i	−0.663742	+	0.496871i	−0.877227	−	0.480075i	$-0.840609\pi$
$307$	−11.6297	+	8.70588i	−0.663742	+	0.496871i	0.213486	+	0.976946i	$0.431518\pi$
$308$		0			0
$309$	−1.24835	−	1.44067i	−0.0710160	−	0.0819568i
$310$		0			0
$311$	1.58660	−	1.01965i	0.0899678	−	0.0578188i	−0.494883	−	0.868959i	$-0.664789\pi$
$311$	1.58660	−	1.01965i	0.0899678	−	0.0578188i	0.584851	+	0.811141i	$0.301153\pi$
$312$		0			0
$313$	−13.4045	−	7.31943i	−0.757669	−	0.413719i	0.0534720	−	0.998569i	$-0.482971\pi$
$313$	−13.4045	−	7.31943i	−0.757669	−	0.413719i	−0.811141	+	0.584851i	$0.801153\pi$
$314$		0			0
$315$	2.41354	−	14.2501i	0.135988	−	0.802899i
$316$		0			0
$317$	−14.6587	−	26.8453i	−0.823313	−	1.50778i	−0.861063	−	0.508497i	$-0.830201\pi$
$317$	−14.6587	−	26.8453i	−0.823313	−	1.50778i	0.0377508	−	0.999287i	$-0.487981\pi$
$318$		0			0
$319$	−1.08611	−	7.55407i	−0.0608106	−	0.422947i
$320$		0			0
$321$			26.3499i			1.47071i
$322$		0			0
$323$	−10.9904	+	10.9904i	−0.611525	+	0.611525i
$324$		0			0
$325$	4.32785	+	8.96298i	0.240066	+	0.497177i
$326$		0			0
$327$	−28.9388	+	15.8018i	−1.60032	+	0.873841i
$328$		0			0
$329$	−9.97018	+	11.5062i	−0.549674	+	0.634358i
$330$		0			0
$331$	29.0054	−	8.51674i	1.59428	−	0.468122i	0.640332	−	0.768099i	$-0.278797\pi$
$331$	29.0054	−	8.51674i	1.59428	−	0.468122i	0.953947	+	0.299976i	$0.0969787\pi$
$332$		0			0
$333$	13.7606	+	2.99344i	0.754078	+	0.164040i
$334$		0			0
$335$	−2.06725	+	6.44074i	−0.112946	+	0.351895i
$336$		0			0
$337$	11.8738	+	15.8615i	0.646807	+	0.864033i	0.997368	−	0.0725072i	$-0.0231000\pi$
$337$	11.8738	+	15.8615i	0.646807	+	0.864033i	−0.350561	+	0.936540i	$0.614009\pi$
$338$		0			0
$339$	7.39067	−	16.1833i	0.401406	−	0.878957i
$340$		0			0
$341$	3.75797	−	1.71621i	0.203506	−	0.0929379i
$342$		0			0
$343$	−12.8089	−	58.8817i	−0.691618	−	3.17932i
$344$		0			0
$345$	18.0657	+	12.8384i	0.972622	+	0.691198i
$346$		0			0
$347$	6.59614	+	30.3220i	0.354100	+	1.62777i	0.717797	+	0.696252i	$0.245150\pi$
$347$	6.59614	+	30.3220i	0.354100	+	1.62777i	−0.363698	+	0.931517i	$0.618486\pi$
$348$		0			0
$349$	4.51867	−	2.06361i	0.241879	−	0.110462i	−0.290788	−	0.956788i	$-0.593917\pi$
$349$	4.51867	−	2.06361i	0.241879	−	0.110462i	0.532667	+	0.846325i	$0.321190\pi$
$350$		0			0
$351$	2.95450	−	6.46945i	0.157699	−	0.345314i
$352$		0			0
$353$	11.7562	+	15.7044i	0.625717	+	0.835860i	0.995647	−	0.0931995i	$-0.0297094\pi$
$353$	11.7562	+	15.7044i	0.625717	+	0.835860i	−0.369931	+	0.929059i	$0.620619\pi$
$354$		0			0
$355$	19.9095	−	10.2343i	1.05668	−	0.543183i
$356$		0			0
$357$	−33.2032	−	7.22292i	−1.75730	−	0.382277i
$358$		0			0
$359$	2.43545	−	0.715112i	0.128538	−	0.0377422i	−0.216831	−	0.976209i	$-0.569572\pi$
$359$	2.43545	−	0.715112i	0.128538	−	0.0377422i	0.345369	+	0.938467i	$0.387754\pi$
$360$		0			0
$361$	−2.68667	+	3.10058i	−0.141404	+	0.163188i
$362$		0			0
$363$	−18.4893	+	10.0959i	−0.970439	+	0.529900i
$364$		0			0
$365$	21.2095	−	17.4700i	1.11016	−	0.914422i
$366$		0			0
$367$	−0.590168	+	0.590168i	−0.0308065	+	0.0308065i	−0.722342	−	0.691536i	$-0.756934\pi$
$367$	−0.590168	+	0.590168i	−0.0308065	+	0.0308065i	0.691536	+	0.722342i	$0.256934\pi$
$368$		0			0
$369$			5.77708i			0.300743i
$370$		0			0
$371$	2.16746	+	15.0750i	0.112529	+	0.782657i
$372$		0			0
$373$	1.62545	+	2.97678i	0.0841624	+	0.154132i	0.916370	−	0.400332i	$-0.131105\pi$
$373$	1.62545	+	2.97678i	0.0841624	+	0.154132i	−0.832208	+	0.554464i	$0.812923\pi$
$374$		0			0
$375$	−18.4485	−	13.9125i	−0.952678	−	0.718438i
$376$		0			0
$377$	14.8441	+	8.10550i	0.764511	+	0.417455i
$378$		0			0
$379$	−20.0856	+	12.9082i	−1.03173	+	0.663050i	−0.942927	−	0.332999i	$-0.891939\pi$
$379$	−20.0856	+	12.9082i	−1.03173	+	0.663050i	−0.0887991	+	0.996050i	$0.528303\pi$
$380$		0			0
$381$	−13.9263	−	16.0719i	−0.713468	−	0.823386i
$382$		0			0
$383$	−4.67157	+	3.49709i	−0.238706	+	0.178693i	−0.711933	−	0.702247i	$-0.752180\pi$
$383$	−4.67157	+	3.49709i	−0.238706	+	0.178693i	0.473227	+	0.880941i	$0.343089\pi$
$384$		0			0
$385$	−1.20044	−	10.1415i	−0.0611802	−	0.516860i
$386$		0			0
$387$	−8.02203	−	2.99206i	−0.407783	−	0.152095i
$388$		0			0
$389$	27.7489	+	17.8332i	1.40693	+	0.904177i	0.999957	−	0.00926428i	$-0.00294896\pi$
$389$	27.7489	+	17.8332i	1.40693	+	0.904177i	0.406970	+	0.913441i	$0.366585\pi$
$390$		0			0
$391$	9.56050	−	12.2108i	0.483495	−	0.617526i
$392$		0			0
$393$	29.7036	−	6.46163i	1.49835	−	0.325946i
$394$		0			0
$395$	−2.63732	+	0.505076i	−0.132698	+	0.0254132i
$396$		0			0
$397$	−20.1715	+	7.52359i	−1.01238	+	0.377598i	−0.800265	−	0.599647i	$-0.795308\pi$
$397$	−20.1715	+	7.52359i	−1.01238	+	0.377598i	−0.212115	+	0.977245i	$0.568035\pi$
$398$		0			0
$399$	−49.9930	−	7.18790i	−2.50278	−	0.359845i
$400$		0			0
$401$	−13.0781	+	11.3322i	−0.653087	+	0.565903i	−0.917120	−	0.398610i	$-0.869493\pi$
$401$	−13.0781	+	11.3322i	−0.653087	+	0.565903i	0.264033	+	0.964514i	$0.414947\pi$
$402$		0			0
$403$	−1.94614	+	8.94627i	−0.0969442	+	0.445645i
$404$		0			0
$405$	1.16190	+	25.0118i	0.0577353	+	1.24285i
$406$		0			0
$407$	9.92516	−	0.709862i	0.491972	−	0.0351865i
$408$		0			0
$409$	0.0117176	−	0.0399066i	0.000579400	−	0.00197326i	−0.959203	−	0.282719i	$-0.908764\pi$
$409$	0.0117176	−	0.0399066i	0.000579400	−	0.00197326i	0.959782	+	0.280746i	$0.0905818\pi$
$410$		0			0
$411$	12.0885	−	1.73806i	0.596280	−	0.0857322i
$412$		0			0
$413$	−18.0461	−	18.0461i	−0.887989	−	0.887989i
$414$		0			0
$415$	11.3518	−	6.90092i	0.557236	−	0.338753i
$416$		0			0
$417$	−22.2731	+	29.7534i	−1.09072	+	1.45703i
$418$		0			0
$419$	−8.72539	−	2.56201i	−0.426263	−	0.125162i	0.0615624	−	0.998103i	$-0.480392\pi$
$419$	−8.72539	−	2.56201i	−0.426263	−	0.125162i	−0.487826	+	0.872941i	$0.662210\pi$
$420$		0			0
$421$	14.3173	+	12.4060i	0.697784	+	0.604633i	0.929794	−	0.368080i	$-0.119985\pi$
$421$	14.3173	+	12.4060i	0.697784	+	0.604633i	−0.232010	+	0.972713i	$0.574530\pi$
$422$		0			0
$423$	−1.82432	+	3.34099i	−0.0887014	+	0.162445i
$424$		0			0
$425$	−10.3237	+	12.4435i	−0.500772	+	0.603600i
$426$		0			0
$427$	3.93052	−	54.9559i	0.190211	−	2.65950i
$428$		0			0
$429$	−0.525914	+	3.65781i	−0.0253913	+	0.176601i
$430$		0			0
$431$	20.8997	+	9.54455i	1.00670	+	0.459745i	0.849368	−	0.527801i	$-0.176983\pi$
$431$	20.8997	+	9.54455i	1.00670	+	0.459745i	0.157333	+	0.987546i	$0.449710\pi$
$432$		0			0
$433$	10.1339	−	27.1701i	0.487005	−	1.30571i	−0.428550	−	0.903518i	$-0.640975\pi$
$433$	10.1339	−	27.1701i	0.487005	−	1.30571i	0.915555	−	0.402193i	$-0.131752\pi$
$434$		0			0
$435$	−39.2514	−	0.980665i	−1.88196	−	0.0470193i
$436$		0			0
$437$	12.8796	−	19.1175i	0.616114	−	0.914512i
$438$		0			0
$439$	6.69521	−	10.4180i	0.319545	−	0.497222i	−0.643907	−	0.765104i	$-0.722688\pi$
$439$	6.69521	−	10.4180i	0.319545	−	0.497222i	0.963452	+	0.267882i	$0.0863239\pi$
$440$		0			0
$441$	−9.95542	−	21.7993i	−0.474068	−	1.03806i
$442$		0			0
$443$	−11.5139	−	30.8699i	−0.547040	−	1.46667i	−0.856695	−	0.515823i	$-0.827486\pi$
$443$	−11.5139	−	30.8699i	−0.547040	−	1.46667i	0.309655	−	0.950849i	$-0.399787\pi$
$444$		0			0
$445$	−17.4040	−	6.99132i	−0.825028	−	0.331421i
$446$		0			0
$447$	−2.11952	−	0.151591i	−0.100250	−	0.00717003i
$448$		0			0
$449$	−12.9904	−	20.2134i	−0.613055	−	0.953932i	−0.999500	−	0.0316193i	$-0.989934\pi$
$449$	−12.9904	−	20.2134i	−0.613055	−	0.953932i	0.386445	−	0.922312i	$-0.373703\pi$
$450$		0			0
$451$	1.15004	+	3.91667i	0.0541532	+	0.184429i
$452$		0			0
$453$	−0.862036	−	12.0528i	−0.0405020	−	0.566292i
$454$		0			0
$455$	19.5864	+	11.3390i	0.918223	+	0.531581i
$456$		0			0
$457$	14.8358	+	11.1060i	0.693991	+	0.519515i	0.887051	−	0.461672i	$-0.152750\pi$
$457$	14.8358	+	11.1060i	0.693991	+	0.519515i	−0.193060	+	0.981187i	$0.561841\pi$
$458$		0			0
$459$	11.5534			0.539267
$460$		0			0
$461$	4.00114			0.186352			0.0931758	−	0.995650i	$-0.470298\pi$
$461$	4.00114			0.186352			0.0931758	+	0.995650i	$0.470298\pi$
$462$		0			0
$463$	−21.2826	−	15.9320i	−0.989088	−	0.740422i	−0.0232933	−	0.999729i	$-0.507415\pi$
$463$	−21.2826	−	15.9320i	−0.989088	−	0.740422i	−0.965795	+	0.259306i	$0.916506\pi$
$464$		0			0
$465$	−5.47689	−	20.5369i	−0.253985	−	0.952375i
$466$		0			0
$467$	0.832606	+	11.6414i	0.0385284	+	0.538698i	0.979661	+	0.200660i	$0.0643086\pi$
$467$	0.832606	+	11.6414i	0.0385284	+	0.538698i	−0.941133	+	0.338038i	$0.890237\pi$
$468$		0			0
$469$	4.33334	+	14.7580i	0.200095	+	0.681461i
$470$		0			0
$471$	−8.05059	−	12.5270i	−0.370951	−	0.577212i
$472$		0			0
$473$	−6.03430	−	0.431582i	−0.277458	−	0.0198442i
$474$		0			0
$475$	−13.9864	+	19.5435i	−0.641740	+	0.896715i
$476$		0			0
$477$	1.33073	+	3.56782i	0.0609299	+	0.163359i
$478$		0			0
$479$	−14.2807	−	31.2703i	−0.652500	−	1.42878i	−0.889349	−	0.457229i	$-0.848842\pi$
$479$	−14.2807	−	31.2703i	−0.652500	−	1.42878i	0.236849	−	0.971546i	$-0.423885\pi$
$480$		0			0
$481$	−11.9220	+	18.5510i	−0.543596	+	0.845852i
$482$		0			0
$483$	50.3829	+	1.09160i	2.29250	+	0.0496697i
$484$		0			0
$485$	−0.0776160	+	3.10660i	−0.00352436	+	0.141063i
$486$		0			0
$487$	4.36599	−	11.7057i	0.197842	−	0.530434i	−0.799708	−	0.600389i	$-0.795013\pi$
$487$	4.36599	−	11.7057i	0.197842	−	0.530434i	0.997550	+	0.0699543i	$0.0222853\pi$
$488$		0			0
$489$	3.29000	+	1.50249i	0.148779	+	0.0679451i
$490$		0			0
$491$	−4.24048	+	29.4932i	−0.191370	+	1.33101i	0.637015	+	0.770851i	$0.280169\pi$
$491$	−4.24048	+	29.4932i	−0.191370	+	1.33101i	−0.828386	+	0.560158i	$0.810740\pi$
$492$		0			0
$493$	−1.96000	+	27.4043i	−0.0882738	+	1.23423i
$494$		0			0
$495$	−0.832273	−	2.41390i	−0.0374079	−	0.108497i
$496$		0			0
$497$	24.3946	−	44.6755i	1.09425	−	2.00397i
$498$		0			0
$499$	8.85331	+	7.67143i	0.396328	+	0.343421i	0.830112	−	0.557596i	$-0.188276\pi$
$499$	8.85331	+	7.67143i	0.396328	+	0.343421i	−0.433784	+	0.901017i	$0.642822\pi$
$500$		0			0
$501$	31.0114	+	9.10578i	1.38549	+	0.406816i
$502$		0			0
$503$	8.18558	−	10.9347i	0.364977	−	0.487552i	−0.580033	−	0.814593i	$-0.696961\pi$
$503$	8.18558	−	10.9347i	0.364977	−	0.487552i	0.945010	+	0.327041i	$0.106051\pi$
$504$		0			0
$505$	−1.27513	+	5.22923i	−0.0567424	+	0.232698i
$506$		0			0
$507$	13.2070	+	13.2070i	0.586545	+	0.586545i
$508$		0			0
$509$	−12.2271	+	1.75799i	−0.541955	+	0.0779214i	−0.407856	−	0.913046i	$-0.633723\pi$
$509$	−12.2271	+	1.75799i	−0.541955	+	0.0779214i	−0.134100	+	0.990968i	$0.542814\pi$
$510$		0			0
$511$	17.6028	−	59.9496i	0.778702	−	2.65202i
$512$		0			0
$513$	17.1291	−	1.22510i	0.756267	−	0.0540893i
$514$		0			0
$515$	−1.38916	+	1.52451i	−0.0612137	+	0.0671781i
$516$		0			0
$517$	−0.571741	+	2.62825i	−0.0251451	+	0.115590i
$518$		0			0
$519$	15.7015	−	13.6054i	0.689218	−	0.597211i
$520$		0			0
$521$	16.3399	+	2.34932i	0.715862	+	0.102925i	0.490615	−	0.871376i	$-0.336772\pi$
$521$	16.3399	+	2.34932i	0.715862	+	0.102925i	0.225247	+	0.974302i	$0.427681\pi$
$522$		0			0
$523$	−33.1553	+	12.3663i	−1.44978	+	0.540740i	−0.946306	−	0.323272i	$-0.895217\pi$
$523$	−33.1553	+	12.3663i	−1.44978	+	0.540740i	−0.503473	+	0.864011i	$0.667945\pi$
$524$		0			0
$525$	−52.4746	−	2.62371i	−2.29018	−	0.114508i
$526$		0			0
$527$	−14.5328	+	3.16143i	−0.633061	+	0.137714i
$528$		0			0
$529$	−10.4517	+	20.4881i	−0.454423	+	0.890786i
$530$		0			0
$531$	−5.36797	−	3.44978i	−0.232950	−	0.149708i
$532$		0			0
$533$	−8.47591	−	3.16135i	−0.367132	−	0.136933i
$534$		0			0
$535$	28.3117	−	3.35122i	1.22402	−	0.144886i
$536$		0			0
$537$	−21.0800	+	15.7803i	−0.909671	+	0.680971i
$538$		0			0
$539$	−11.0890	−	12.7974i	−0.477638	−	0.551224i
$540$		0			0
$541$	−22.6678	+	14.5677i	−0.974564	+	0.626314i	−0.927992	−	0.372601i	$-0.878466\pi$
$541$	−22.6678	+	14.5677i	−0.974564	+	0.626314i	−0.0465724	+	0.998915i	$0.514830\pi$
$542$		0			0
$543$	15.7029	+	8.57441i	0.673874	+	0.367963i
$544$		0			0
$545$	20.6587	+	29.0836i	0.884923	+	1.24581i
$546$		0			0
$547$	−5.70851	−	10.4544i	−0.244078	−	0.446996i	0.726706	−	0.686948i	$-0.241050\pi$
$547$	−5.70851	−	10.4544i	−0.244078	−	0.446996i	−0.970785	+	0.239952i	$0.922868\pi$
$548$		0			0
$549$	−1.96046	−	13.6353i	−0.0836704	−	0.581940i
$550$		0			0
$551$			40.8375i			1.73974i
$552$		0			0
$553$	−4.31745	+	4.31745i	−0.183597	+	0.183597i
$554$		0			0
$555$	4.92630	−	50.9555i	0.209110	−	2.16294i
$556$		0			0
$557$	14.2694	−	7.79169i	0.604615	−	0.330145i	−0.147616	−	0.989045i	$-0.547160\pi$
$557$	14.2694	−	7.79169i	0.604615	−	0.330145i	0.752230	+	0.658900i	$0.228978\pi$
$558$		0			0
$559$	8.77968	−	10.1323i	0.371341	−	0.428550i
$560$		0			0
$561$	−5.75990	+	1.69126i	−0.243183	+	0.0714050i
$562$		0			0
$563$	11.0925	+	2.41304i	0.467495	+	0.101697i	0.440141	−	0.897928i	$-0.354928\pi$
$563$	11.0925	+	2.41304i	0.467495	+	0.101697i	0.0273538	+	0.999626i	$0.491292\pi$
$564$		0			0
$565$	−18.3281	−	5.88269i	−0.771070	−	0.247487i
$566$		0			0
$567$	34.1193	+	45.5780i	1.43287	+	1.91410i
$568$		0			0
$569$	−1.42491	+	3.12012i	−0.0597353	+	0.130802i	−0.937145	−	0.348939i	$-0.886542\pi$
$569$	−1.42491	+	3.12012i	−0.0597353	+	0.130802i	0.877410	+	0.479741i	$0.159269\pi$
$570$		0			0
$571$	−40.0605	+	18.2950i	−1.67648	+	0.765622i	−0.676915	+	0.736061i	$0.736684\pi$
$571$	−40.0605	+	18.2950i	−1.67648	+	0.765622i	−0.999563	+	0.0295611i	$0.990589\pi$
$572$		0			0
$573$	2.46562	+	11.3343i	0.103003	+	0.473496i
$574$		0			0
$575$	11.4966	−	21.0435i	0.479443	−	0.877573i
$576$		0			0
$577$	−1.62874	−	7.48718i	−0.0678051	−	0.311695i	0.930736	−	0.365692i	$-0.119168\pi$
$577$	−1.62874	−	7.48718i	−0.0678051	−	0.311695i	−0.998541	+	0.0539967i	$0.982804\pi$
$578$		0			0
$579$	22.8235	−	10.4232i	0.948514	−	0.433172i
$580$		0			0
$581$	12.5486	−	27.4776i	0.520603	−	1.13996i
$582$		0			0
$583$	1.61243	+	2.15396i	0.0667802	+	0.0892079i
$584$		0			0
$585$	5.38782	+	1.72930i	0.222759	+	0.0714980i
$586$		0			0
$587$	−24.5822	−	5.34753i	−1.01462	−	0.220716i	−0.325635	−	0.945496i	$-0.605578\pi$
$587$	−24.5822	−	5.34753i	−1.01462	−	0.220716i	−0.688981	+	0.724780i	$0.741942\pi$
$588$		0			0
$589$	−21.2111	+	6.22816i	−0.873990	+	0.256627i
$590$		0			0
$591$	16.5713	−	19.1243i	0.681653	−	0.786670i
$592$		0			0
$593$	−14.5505	+	7.94520i	−0.597519	+	0.326270i	−0.749389	−	0.662130i	$-0.769653\pi$
$593$	−14.5505	+	7.94520i	−0.597519	+	0.326270i	0.151869	+	0.988401i	$0.451471\pi$
$594$		0			0
$595$	−3.53783	+	36.5938i	−0.145037	+	1.50020i
$596$		0			0
$597$	−20.9399	+	20.9399i	−0.857015	+	0.857015i
$598$		0			0
$599$			3.74112i			0.152858i	0.997075	+	0.0764290i	$0.0243518\pi$
$599$			3.74112i			0.152858i	−0.997075	+	0.0764290i	$0.975648\pi$
$600$		0			0
$601$	−4.32244	−	30.0632i	−0.176316	−	1.22630i	−0.865198	−	0.501431i	$-0.832807\pi$
$601$	−4.32244	−	30.0632i	−0.176316	−	1.22630i	0.688882	−	0.724874i	$-0.258102\pi$
$602$		0			0
$603$	1.84303	+	3.37526i	0.0750540	+	0.137451i
$604$		0			0
$605$	13.1991	+	18.5819i	0.536619	+	0.755460i
$606$		0			0
$607$	−2.70023	−	1.47444i	−0.109599	−	0.0598455i	0.423514	−	0.905889i	$-0.360796\pi$
$607$	−2.70023	−	1.47444i	−0.109599	−	0.0598455i	−0.533113	+	0.846044i	$0.678978\pi$
$608$		0			0
$609$	−75.1062	+	48.2678i	−3.04346	+	1.95591i
$610$		0			0
$611$	−3.90346	−	4.50484i	−0.157917	−	0.182246i
$612$		0			0
$613$	29.3224	−	21.9505i	1.18432	−	0.886571i	0.188884	−	0.981999i	$-0.439513\pi$
$613$	29.3224	−	21.9505i	1.18432	−	0.886571i	0.995436	+	0.0954285i	$0.0304221\pi$
$614$		0			0
$615$	20.8555	−	2.46864i	0.840974	−	0.0995452i
$616$		0			0
$617$	14.5564	+	5.42926i	0.586019	+	0.218574i	0.624946	−	0.780668i	$-0.285121\pi$
$617$	14.5564	+	5.42926i	0.586019	+	0.218574i	−0.0389264	+	0.999242i	$0.512394\pi$
$618$		0			0
$619$	−14.7257	−	9.46361i	−0.591874	−	0.380375i	0.210147	−	0.977670i	$-0.432606\pi$
$619$	−14.7257	−	9.46361i	−0.591874	−	0.380375i	−0.802021	+	0.597295i	$0.796242\pi$
$620$		0			0
$621$	−16.8180	+	3.27870i	−0.674884	+	0.131570i
$622$		0			0
$623$	−41.6728	+	9.06536i	−1.66958	+	0.363196i
$624$		0			0
$625$	−12.6020	+	21.5914i	−0.504079	+	0.863658i
$626$		0			0
$627$	−8.36028	+	3.11822i	−0.333877	+	0.124530i
$628$		0			0
$629$	−35.4573	−	5.09799i	−1.41377	−	0.203270i
$630$		0			0
$631$	−20.9003	+	18.1102i	−0.832027	+	0.720955i	−0.962729	−	0.270466i	$-0.912822\pi$
$631$	−20.9003	+	18.1102i	−0.832027	+	0.720955i	0.130703	+	0.991422i	$0.458277\pi$
$632$		0			0
$633$	11.9096	−	54.7477i	0.473365	−	2.17602i
$634$		0			0
$635$	−15.4972	+	17.0072i	−0.614989	+	0.674911i
$636$		0			0
$637$	37.4310	−	2.67712i	1.48307	−	0.106071i
$638$		0			0
$639$	3.58555	−	12.2113i	0.141842	−	0.483070i
$640$		0			0
$641$	−19.1931	+	2.75955i	−0.758081	+	0.108996i	−0.510507	−	0.859873i	$-0.670542\pi$
$641$	−19.1931	+	2.75955i	−0.758081	+	0.108996i	−0.247574	+	0.968869i	$0.579633\pi$
$642$		0			0
$643$	4.01259	+	4.01259i	0.158241	+	0.158241i	0.781787	−	0.623546i	$-0.214309\pi$
$643$	4.01259	+	4.01259i	0.158241	+	0.158241i	−0.623546	+	0.781787i	$0.714309\pi$
$644$		0			0
$645$	−7.37352	+	30.2384i	−0.290332	+	1.19064i
$646$		0			0
$647$	−19.0050	+	25.3877i	−0.747163	+	0.998093i	0.252373	+	0.967630i	$0.418789\pi$
$647$	−19.0050	+	25.3877i	−0.747163	+	0.998093i	−0.999536	+	0.0304630i	$0.990302\pi$
$648$		0			0
$649$	−4.32605	−	1.27024i	−0.169812	−	0.0498614i
$650$		0			0
$651$	−36.5250	−	31.6491i	−1.43153	−	1.24043i
$652$		0			0
$653$	0.0580865	−	0.106377i	0.00227310	−	0.00416287i	−0.876540	−	0.481329i	$-0.840154\pi$
$653$	0.0580865	−	0.106377i	0.00227310	−	0.00416287i	0.878813	+	0.477166i	$0.158336\pi$
$654$		0			0
$655$	−10.7205	−	31.0933i	−0.418883	−	1.21492i
$656$		0			0
$657$	1.11444	−	15.5820i	0.0434786	−	0.607910i
$658$		0			0
$659$	2.33221	−	16.2209i	0.0908499	−	0.631875i	−0.892621	−	0.450808i	$-0.851136\pi$
$659$	2.33221	−	16.2209i	0.0908499	−	0.631875i	0.983471	−	0.181067i	$-0.0579550\pi$
$660$		0			0
$661$	0.844692	+	0.385758i	0.0328547	+	0.0150042i	0.431775	−	0.901982i	$-0.357888\pi$
$661$	0.844692	+	0.385758i	0.0328547	+	0.0150042i	−0.398920	+	0.916986i	$0.630615\pi$
$662$		0			0
$663$	4.64911	−	12.4647i	0.180557	−	0.484091i
$664$		0			0
$665$	−1.36487	+	54.6291i	−0.0529273	+	2.11843i
$666$		0			0
$667$	−4.92386	−	40.4481i	−0.190653	−	1.56615i
$668$		0			0
$669$	21.7872	−	33.9016i	0.842342	−	1.31071i
$670$		0			0
$671$	−4.04350	−	8.85402i	−0.156097	−	0.341806i
$672$		0			0
$673$	−6.92916	−	18.5778i	−0.267100	−	0.716122i	−0.999383	−	0.0351217i	$-0.988818\pi$
$673$	−6.92916	−	18.5778i	−0.267100	−	0.716122i	0.732283	−	0.681000i	$-0.238455\pi$
$674$		0			0
$675$	17.6237	−	2.92085i	0.678336	−	0.112424i
$676$		0			0
$677$	−11.5630	−	0.826999i	−0.444401	−	0.0317842i	−0.152654	−	0.988280i	$-0.548782\pi$
$677$	−11.5630	−	0.826999i	−0.444401	−	0.0317842i	−0.291747	+	0.956496i	$0.594236\pi$
$678$		0			0
$679$	3.82022	+	5.94438i	0.146607	+	0.228124i
$680$		0			0
$681$	13.7680	+	46.8896i	0.527592	+	1.79681i
$682$		0			0
$683$	2.06354	+	28.8520i	0.0789591	+	1.10399i	0.870269	+	0.492577i	$0.163945\pi$
$683$	2.06354	+	28.8520i	0.0789591	+	1.10399i	−0.791310	+	0.611415i	$0.790600\pi$
$684$		0			0
$685$	−3.40489	−	12.7674i	−0.130094	−	0.487818i
$686$		0			0
$687$	18.0406	+	13.5050i	0.688293	+	0.515250i
$688$		0			0
$689$	−5.96277			−0.227164
$690$		0			0
$691$	29.2400			1.11234			0.556172	−	0.831068i	$-0.312270\pi$
$691$	29.2400			1.11234			0.556172	+	0.831068i	$0.312270\pi$
$692$		0			0
$693$	−4.64786	−	3.47934i	−0.176558	−	0.132169i
$694$		0			0
$695$	34.8013	+	20.1473i	1.32009	+	0.764231i
$696$		0			0
$697$	−1.04835	−	14.6579i	−0.0397091	−	0.555206i
$698$		0			0
$699$	8.48863	+	28.9096i	0.321070	+	1.09346i
$700$		0			0
$701$	5.00282	+	7.78453i	0.188954	+	0.294018i	0.922786	−	0.385313i	$-0.125907\pi$
$701$	5.00282	+	7.78453i	0.188954	+	0.294018i	−0.733832	+	0.679331i	$0.762270\pi$
$702$		0			0
$703$	−53.1095	−	3.79847i	−2.00306	−	0.143262i
$704$		0			0
$705$	12.8407	+	5.15820i	0.483607	+	0.194269i
$706$		0			0
$707$	4.27702	+	11.4671i	0.160854	+	0.431266i
$708$		0			0
$709$	17.3487	+	37.9883i	0.651543	+	1.42668i	0.890197	+	0.455576i	$0.150567\pi$
$709$	17.3487	+	37.9883i	0.651543	+	1.42668i	−0.238654	+	0.971105i	$0.576706\pi$
$710$		0			0
$711$	−0.825347	+	1.28427i	−0.0309529	+	0.0481637i
$712$		0			0
$713$	20.2579	−	8.72624i	0.758666	−	0.326800i
$714$		0			0
$715$	3.99702	+	0.0998625i	0.149480	+	0.00373465i
$716$		0			0
$717$	21.2289	−	56.9170i	0.792809	−	2.12560i
$718$		0			0
$719$	2.99639	+	1.36840i	0.111746	+	0.0510329i	0.470504	−	0.882398i	$-0.344072\pi$
$719$	2.99639	+	1.36840i	0.111746	+	0.0510329i	−0.358757	+	0.933431i	$0.616799\pi$
$720$		0			0
$721$	−0.667426	+	4.64205i	−0.0248562	+	0.172879i
$722$		0			0
$723$	−3.17125	+	44.3399i	−0.117940	+	1.64902i
$724$		0			0
$725$	3.93837	+	42.2984i	0.146267	+	1.57092i
$726$		0			0
$727$	−7.08676	+	12.9784i	−0.262834	+	0.481344i	−0.975453	−	0.220207i	$-0.929327\pi$
$727$	−7.08676	+	12.9784i	−0.262834	+	0.481344i	0.712620	+	0.701551i	$0.247509\pi$
$728$		0			0
$729$	−5.98314	−	5.18442i	−0.221598	−	0.192016i
$730$		0			0
$731$	20.8968	+	6.13586i	0.772897	+	0.226943i
$732$		0			0
$733$	22.0570	−	29.4647i	0.814692	−	1.08830i	−0.179822	−	0.983699i	$-0.557552\pi$
$733$	22.0570	−	29.4647i	0.814692	−	1.08830i	0.994514	−	0.104602i	$-0.0333570\pi$
$734$		0			0
$735$	−74.4423	+	45.2546i	−2.74585	+	1.66924i
$736$		0			0
$737$	1.92142	+	1.92142i	0.0707766	+	0.0707766i
$738$		0			0
$739$	−20.7894	+	2.98906i	−0.764750	+	0.109954i	−0.513642	−	0.858005i	$-0.671704\pi$
$739$	−20.7894	+	2.98906i	−0.764750	+	0.109954i	−0.251108	+	0.967959i	$0.580795\pi$
$740$		0			0
$741$	5.57104	−	18.9732i	0.204657	−	0.696998i
$742$		0			0
$743$	−9.76512	+	0.698415i	−0.358248	+	0.0256224i	−0.249303	−	0.968425i	$-0.580202\pi$
$743$	−9.76512	+	0.698415i	−0.358248	+	0.0256224i	−0.108944	+	0.994048i	$0.534747\pi$
$744$		0			0
$745$	0.106687	+	2.29660i	0.00390870	+	0.0841411i
$746$		0			0
$747$	1.60543	−	7.38003i	0.0587395	−	0.270021i
$748$		0			0
$749$	48.9919	−	42.4517i	1.79012	−	1.55115i
$750$		0			0
$751$	−13.2264	−	1.90167i	−0.482639	−	0.0693930i	−0.103299	−	0.994650i	$-0.532940\pi$
$751$	−13.2264	−	1.90167i	−0.482639	−	0.0693930i	−0.379340	+	0.925257i	$0.623849\pi$
$752$		0			0
$753$	1.40740	−	0.524935i	0.0512887	−	0.0191297i
$754$		0			0
$755$	−12.8405	+	2.45911i	−0.467315	+	0.0894963i
$756$		0			0
$757$	6.39401	−	1.39093i	0.232394	−	0.0505543i	−0.0948599	−	0.995491i	$-0.530240\pi$
$757$	6.39401	−	1.39093i	0.232394	−	0.0505543i	0.327254	+	0.944936i	$0.393877\pi$
$758$		0			0
$759$	7.90458	−	4.09650i	0.286918	−	0.148694i
$760$		0			0
$761$	23.2992	+	14.9735i	0.844595	+	0.542789i	0.889885	−	0.456185i	$-0.150785\pi$
$761$	23.2992	+	14.9735i	0.844595	+	0.542789i	−0.0452893	+	0.998974i	$0.514421\pi$
$762$		0			0
$763$	76.0025	+	28.3475i	2.75148	+	1.02625i
$764$		0			0
$765$	1.08051	+	9.12835i	0.0390660	+	0.330036i
$766$		0			0
$767$	7.99886	−	5.98787i	0.288822	−	0.216210i
$768$		0			0
$769$	−5.82522	−	6.72266i	−0.210063	−	0.242425i	0.640934	−	0.767596i	$-0.278547\pi$
$769$	−5.82522	−	6.72266i	−0.210063	−	0.242425i	−0.850997	+	0.525170i	$0.824002\pi$
$770$		0			0
$771$	12.5943	−	8.09385i	0.453572	−	0.291493i
$772$		0			0
$773$	13.5353	+	7.39082i	0.486830	+	0.265829i	0.703864	−	0.710335i	$-0.251456\pi$
$773$	13.5353	+	7.39082i	0.486830	+	0.265829i	−0.217034	+	0.976164i	$0.569638\pi$
$774$		0			0
$775$	−21.3693	+	8.49656i	−0.767608	+	0.305205i
$776$		0			0
$777$	−55.7868	−	102.166i	−2.00134	−	3.66518i
$778$		0			0
$779$	−3.10857	−	21.6206i	−0.111376	−	0.774637i
$780$		0			0
$781$		−	8.99261i		−	0.321781i
$782$		0			0
$783$	21.4646	−	21.4646i	0.767084	−	0.767084i
$784$		0			0
$785$	−12.4357	+	10.2432i	−0.443850	+	0.365594i
$786$		0			0
$787$	13.8357	−	7.55484i	0.493188	−	0.269301i	−0.213350	−	0.976976i	$-0.568438\pi$
$787$	13.8357	−	7.55484i	0.493188	−	0.269301i	0.706538	+	0.707675i	$0.250256\pi$
$788$		0			0
$789$	20.2730	−	23.3962i	0.721736	−	0.832928i
$790$		0			0
$791$	−41.9962	+	12.3312i	−1.49321	+	0.438447i
$792$		0			0
$793$	21.0780	+	4.58524i	0.748501	+	0.162826i
$794$		0			0
$795$	12.3113	−	6.32857i	0.436638	−	0.224451i
$796$		0			0
$797$	15.4888	+	20.6906i	0.548640	+	0.732898i	0.986066	−	0.166357i	$-0.0532004\pi$
$797$	15.4888	+	20.6906i	0.548640	+	0.732898i	−0.437425	+	0.899255i	$0.644109\pi$
$798$		0			0
$799$	4.02246	−	8.80796i	0.142304	−	0.311603i
$800$		0			0
$801$	−9.69937	+	4.42956i	−0.342711	+	0.156511i
$802$		0			0
$803$	−2.34633	−	10.7859i	−0.0828003	−	0.380627i
$804$		0			0
$805$	−5.23489	−	54.2727i	−0.184506	−	1.91286i
$806$		0			0
$807$	−12.5538	−	57.7090i	−0.441915	−	2.03145i
$808$		0			0
$809$	−16.0035	+	7.30856i	−0.562654	+	0.256955i	−0.676375	−	0.736557i	$-0.736450\pi$
$809$	−16.0035	+	7.30856i	−0.562654	+	0.256955i	0.113721	+	0.993513i	$0.463723\pi$
$810$		0			0
$811$	6.67777	−	14.6223i	0.234488	−	0.513458i	−0.755407	−	0.655255i	$-0.772561\pi$
$811$	6.67777	−	14.6223i	0.234488	−	0.513458i	0.989896	+	0.141798i	$0.0452882\pi$
$812$		0			0
$813$	17.3994	+	23.2429i	0.610224	+	0.815164i
$814$		0			0
$815$	1.19593	−	3.72603i	0.0418915	−	0.130517i
$816$		0			0
$817$	31.6322	+	6.88117i	1.10667	+	0.240742i
$818$		0			0
$819$	12.3454	−	3.62494i	0.431383	−	0.126666i
$820$		0			0
$821$	36.7521	−	42.4141i	1.28266	−	1.48026i	0.488481	−	0.872575i	$-0.337551\pi$
$821$	36.7521	−	42.4141i	1.28266	−	1.48026i	0.794175	−	0.607689i	$-0.207903\pi$
$822$		0			0
$823$	−29.1783	+	15.9326i	−1.01709	+	0.555375i	−0.899148	−	0.437646i	$-0.855812\pi$
$823$	−29.1783	+	15.9326i	−1.01709	+	0.555375i	−0.117945	+	0.993020i	$0.537631\pi$
$824$		0			0
$825$	−8.35863	+	4.03604i	−0.291010	+	0.140517i
$826$		0			0
$827$	−28.0802	+	28.0802i	−0.976445	+	0.976445i	−0.999729	−	0.0232837i	$-0.992588\pi$
$827$	−28.0802	+	28.0802i	−0.976445	+	0.976445i	0.0232837	+	0.999729i	$0.492588\pi$
$828$		0			0
$829$			44.4304i			1.54313i	0.636150	+	0.771566i	$0.280526\pi$
$829$			44.4304i			1.54313i	−0.636150	+	0.771566i	$0.719474\pi$
$830$		0			0
$831$	2.28330	+	15.8807i	0.0792068	+	0.550895i
$832$		0			0
$833$	29.2152	+	53.5036i	1.01225	+	1.85379i
$834$		0			0
$835$	5.83963	−	34.4783i	0.202089	−	1.19317i
$836$		0			0
$837$	14.4224	+	7.87523i	0.498511	+	0.272208i
$838$		0			0
$839$	1.11811	−	0.718567i	0.0386015	−	0.0248077i	−0.521198	−	0.853436i	$-0.674515\pi$
$839$	1.11811	−	0.718567i	0.0386015	−	0.0248077i	0.559799	+	0.828628i	$0.310878\pi$
$840$		0			0
$841$	28.2811	+	32.6382i	0.975212	+	1.12545i
$842$		0			0
$843$	9.96594	−	7.46041i	0.343245	−	0.256950i
$844$		0			0
$845$	12.5106	−	15.8700i	0.430378	−	0.545944i
$846$		0			0
$847$	48.5589	+	18.1115i	1.66850	+	0.622319i
$848$		0			0
$849$	2.89742	+	1.86206i	0.0994392	+	0.0639057i
$850$		0			0
$851$	53.0611	−	2.64128i	1.81891	−	0.0905419i
$852$		0			0
$853$	15.8325	−	3.44416i	0.542096	−	0.117926i	0.0668242	−	0.997765i	$-0.478713\pi$
$853$	15.8325	−	3.44416i	0.542096	−	0.117926i	0.475272	+	0.879839i	$0.342350\pi$
$854$		0			0
$855$	2.56991	+	13.4191i	0.0878892	+	0.458924i
$856$		0			0
$857$	51.9878	−	19.3905i	1.77587	−	0.662366i	0.776387	−	0.630257i	$-0.217050\pi$
$857$	51.9878	−	19.3905i	1.77587	−	0.662366i	0.999484	−	0.0321087i	$-0.0102223\pi$
$858$		0			0
$859$	−43.0981	−	6.19657i	−1.47049	−	0.211424i	−0.639963	−	0.768405i	$-0.721051\pi$
$859$	−43.0981	−	6.19657i	−1.47049	−	0.211424i	−0.830525	+	0.556981i	$0.811960\pi$
$860$		0			0
$861$	36.0893	−	31.2715i	1.22992	−	1.06573i
$862$		0			0
$863$	−6.54759	+	30.0988i	−0.222883	+	1.02458i	0.720651	+	0.693298i	$0.243843\pi$
$863$	−6.54759	+	30.0988i	−0.222883	+	1.02458i	−0.943534	+	0.331277i	$0.892521\pi$
$864$		0			0
$865$	−16.6153	−	15.1401i	−0.564936	−	0.514779i
$866$		0			0
$867$	−13.4884	+	0.964708i	−0.458089	+	0.0327632i
$868$		0			0
$869$	−0.303901	+	1.03499i	−0.0103091	+	0.0351097i
$870$		0			0
$871$	−5.96060	+	0.857004i	−0.201967	+	0.0290385i
$872$		0			0
$873$	1.24925	+	1.24925i	0.0422808	+	0.0422808i
$874$		0			0
$875$	3.85474	+	56.7150i	0.130314	+	1.91732i
$876$		0			0
$877$	6.35442	−	8.48852i	0.214574	−	0.286637i	−0.680321	−	0.732914i	$-0.738160\pi$
$877$	6.35442	−	8.48852i	0.214574	−	0.286637i	0.894895	+	0.446277i	$0.147251\pi$
$878$		0			0
$879$	49.2135	+	14.4504i	1.65993	+	0.487399i
$880$		0			0
$881$	−16.5043	−	14.3011i	−0.556046	−	0.481816i	0.330915	−	0.943660i	$-0.392642\pi$
$881$	−16.5043	−	14.3011i	−0.556046	−	0.481816i	−0.886961	+	0.461844i	$0.847188\pi$
$882$		0			0
$883$	7.16000	−	13.1126i	0.240953	−	0.441273i	−0.729017	−	0.684495i	$-0.760023\pi$
$883$	7.16000	−	13.1126i	0.240953	−	0.441273i	0.969971	+	0.243222i	$0.0782045\pi$
$884$		0			0
$885$	−10.1600	+	20.8527i	−0.341526	+	0.700956i
$886$		0			0
$887$	2.69174	−	37.6354i	0.0903798	−	1.26367i	−0.726621	−	0.687038i	$-0.758911\pi$
$887$	2.69174	−	37.6354i	0.0903798	−	1.26367i	0.817001	−	0.576636i	$-0.195635\pi$
$888$		0			0
$889$	−7.44569	+	51.7859i	−0.249720	+	1.73684i
$890$		0			0
$891$	9.14934	+	4.17836i	0.306514	+	0.139980i
$892$		0			0
$893$	5.02972	−	13.4852i	0.168313	−	0.451265i
$894$		0			0
$895$	19.6362	+	20.6425i	0.656365	+	0.690002i
$896$		0			0
$897$	−3.23027	+	19.4640i	−0.107856	+	0.649884i
$898$		0			0
$899$	−21.1265	+	32.8735i	−0.704609	+	1.09639i
$900$		0			0
$901$	−4.02383	−	8.81095i	−0.134053	−	0.293535i
$902$		0			0
$903$	24.7322	+	66.3096i	0.823036	+	2.20664i
$904$		0			0
$905$	7.21566	−	17.9624i	0.239857	−	0.597092i
$906$		0			0
$907$	10.7646	+	0.769899i	0.357432	+	0.0255641i	0.248901	−	0.968529i	$-0.419931\pi$
$907$	10.7646	+	0.769899i	0.357432	+	0.0255641i	0.108531	+	0.994093i	$0.465385\pi$
$908$		0			0
$909$	1.65437	+	2.57425i	0.0548720	+	0.0853825i
$910$		0			0
$911$	−4.16489	−	14.1843i	−0.137989	−	0.469948i	0.861282	−	0.508128i	$-0.169662\pi$
$911$	−4.16489	−	14.1843i	−0.137989	−	0.469948i	−0.999271	+	0.0381799i	$0.987844\pi$
$912$		0			0
$913$	−0.380709	−	5.32301i	−0.0125996	−	0.176166i
$914$		0			0
$915$	−48.3862	+	12.9039i	−1.59960	+	0.426590i
$916$		0			0
$917$	−59.8687	−	44.8172i	−1.97704	−	1.47999i
$918$		0			0
$919$	−42.0171			−1.38602			−0.693009	−	0.720929i	$-0.743715\pi$
$919$	−42.0171			−1.38602			−0.693009	+	0.720929i	$0.743715\pi$
$920$		0			0
$921$	30.0235			0.989309
$922$		0			0
$923$	15.9538	+	11.9429i	0.525126	+	0.393104i
$924$		0			0
$925$	−55.3757	+	1.18754i	−1.82074	+	0.0390459i
$926$		0			0
$927$	0.0836501	+	1.16958i	0.00274743	+	0.0384141i
$928$		0			0
$929$	−4.20389	−	14.3171i	−0.137925	−	0.469730i	0.861341	−	0.508027i	$-0.169625\pi$
$929$	−4.20389	−	14.3171i	−0.137925	−	0.469730i	−0.999266	+	0.0382968i	$0.987807\pi$
$930$		0			0
$931$	48.9878	+	76.2265i	1.60551	+	2.49822i
$932$		0			0
$933$	−3.88785	−	0.278065i	−0.127283	−	0.00910343i
$934$		0			0
$935$	2.54972	+	5.97363i	0.0833849	+	0.195358i
$936$		0			0
$937$	4.86912	+	13.0546i	0.159067	+	0.426476i	0.991896	−	0.127056i	$-0.0405527\pi$
$937$	4.86912	+	13.0546i	0.159067	+	0.426476i	−0.832828	+	0.553531i	$0.813280\pi$
$938$		0			0
$939$	13.1122	+	28.7117i	0.427900	+	0.936971i
$940$		0			0
$941$	−10.2390	+	15.9322i	−0.333781	+	0.519374i	−0.967060	−	0.254550i	$-0.918073\pi$
$941$	−10.2390	+	15.9322i	−0.333781	+	0.519374i	0.633278	+	0.773924i	$0.281709\pi$
$942$		0			0
$943$	5.68576	+	21.0396i	0.185154	+	0.685143i
$944$		0			0
$945$	29.4311	−	27.9963i	0.957393	−	0.910720i
$946$		0			0
$947$	2.83135	−	7.59115i	0.0920065	−	0.246679i	−0.882793	−	0.469763i	$-0.844340\pi$
$947$	2.83135	−	7.59115i	0.0920065	−	0.246679i	0.974799	+	0.223083i	$0.0716123\pi$
$948$		0			0
$949$	22.2514	+	10.1619i	0.722311	+	0.329868i
$950$		0			0
$951$	−8.99623	+	62.5702i	−0.291723	+	2.02898i
$952$		0			0
$953$	1.54463	−	21.5968i	0.0500355	−	0.699588i	−0.909089	−	0.416603i	$-0.863221\pi$
$953$	1.54463	−	21.5968i	0.0500355	−	0.699588i	0.959124	−	0.282986i	$-0.0913249\pi$
$954$		0			0
$955$	11.8645	−	4.09069i	0.383927	−	0.132372i
$956$		0			0
$957$	−7.55897	+	13.8432i	−0.244347	+	0.447488i
$958$		0			0
$959$	−22.7070	−	19.6757i	−0.733246	−	0.635361i
$960$		0			0
$961$	9.44762	+	2.77407i	0.304762	+	0.0894862i
$962$		0			0
$963$	9.71314	−	12.9752i	0.313001	−	0.418121i
$964$		0			0
$965$	−14.1019	−	23.1971i	−0.453956	−	0.746742i
$966$		0			0
$967$	−3.06364	−	3.06364i	−0.0985201	−	0.0985201i	0.656129	−	0.754649i	$-0.272193\pi$
$967$	−3.06364	−	3.06364i	−0.0985201	−	0.0985201i	−0.754649	+	0.656129i	$0.772193\pi$
$968$		0			0
$969$	31.7954	−	4.57149i	1.02142	−	0.146857i
$970$		0			0
$971$	−1.16952	+	3.98301i	−0.0375316	+	0.127821i	−0.976128	−	0.217196i	$-0.930309\pi$
$971$	−1.16952	+	3.98301i	−0.0375316	+	0.127821i	0.938596	+	0.345017i	$0.112127\pi$
$972$		0			0
$973$	91.2036	−	6.52301i	2.92385	−	0.209118i
$974$		0			0
$975$	3.94055	−	20.1892i	0.126199	−	0.646572i
$976$		0			0
$977$	7.95539	−	36.5703i	0.254516	−	1.16999i	−0.655428	−	0.755257i	$-0.727512\pi$
$977$	7.95539	−	36.5703i	0.254516	−	1.16999i	0.909944	−	0.414732i	$-0.136124\pi$
$978$		0			0
$979$	−5.69407	+	4.93394i	−0.181983	+	0.157689i
$980$		0			0
$981$	20.0749	+	2.88634i	0.640943	+	0.0921537i
$982$		0			0
$983$	30.7469	−	11.4680i	0.980673	−	0.365772i	0.192548	−	0.981287i	$-0.438325\pi$
$983$	30.7469	−	11.4680i	0.980673	−	0.365772i	0.788125	+	0.615515i	$0.211052\pi$
$984$		0			0
$985$	−22.6557	−	15.3728i	−0.721871	−	0.489819i
$986$		0			0
$987$	30.7462	−	6.68842i	0.978662	−	0.212895i
$988$		0			0
$989$	−32.1603	−	3.00159i	−1.02264	−	0.0954449i
$990$		0			0
$991$	46.3069	+	29.7596i	1.47099	+	0.945346i	0.997930	+	0.0643144i	$0.0204861\pi$
$991$	46.3069	+	29.7596i	1.47099	+	0.945346i	0.473057	+	0.881032i	$0.343150\pi$
$992$		0			0
$993$	−58.5369	−	21.8331i	−1.85761	−	0.692854i
$994$		0			0
$995$	25.1621	+	19.8358i	0.797693	+	0.628836i
$996$		0			0
$997$	−38.8668	+	29.0953i	−1.23092	+	0.921458i	−0.998688	−	0.0512020i	$-0.983695\pi$
$997$	−38.8668	+	29.0953i	−1.23092	+	0.921458i	−0.232235	+	0.972660i	$0.574604\pi$
$998$		0			0
$999$	25.9185	+	29.9115i	0.820024	+	0.946358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.297.8	yes	720
5.3	odd	4	inner	920.2.bv.a.113.29	yes	720
23.11	odd	22	inner	920.2.bv.a.57.29	✓	720
115.103	even	44	inner	920.2.bv.a.793.8	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.57.29	✓	720	23.11	odd	22	inner
920.2.bv.a.113.29	yes	720	5.3	odd	4	inner
920.2.bv.a.297.8	yes	720	1.1	even	1	trivial
920.2.bv.a.793.8	yes	720	115.103	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65448 - 1.23853i) q^{3} +(-1.12032 + 1.93517i) q^{5} +(0.362720 + 5.07149i) q^{7} +(0.358151 + 1.21975i) q^{9} +O(q^{10})\)	\(q+(-1.65448 - 1.23853i) q^{3} +(-1.12032 + 1.93517i) q^{5} +(0.362720 + 5.07149i) q^{7} +(0.358151 + 1.21975i) q^{9} +(0.485630 + 0.755654i) q^{11} +(-1.98556 - 0.142010i) q^{13} +(4.25030 - 1.81416i) q^{15} +(-1.13006 - 3.02981i) q^{17} +(-1.99670 - 4.37217i) q^{19} +(5.68107 - 8.83991i) q^{21} +(2.50482 + 4.08973i) q^{23} +(-2.48978 - 4.33601i) q^{25} +(-1.24857 + 3.34755i) q^{27} +(-7.72847 - 3.52948i) q^{29} +(0.654548 - 4.55248i) q^{31} +(0.132435 - 1.85168i) q^{33} +(-10.2206 - 4.97975i) q^{35} +(5.30897 - 9.72266i) q^{37} +(3.10918 + 2.69412i) q^{39} +(4.36035 + 1.28031i) q^{41} +(-4.03615 + 5.39166i) q^{43} +(-2.76167 - 0.673423i) q^{45} +(2.11736 + 2.11736i) q^{47} +(-18.6597 + 2.68286i) q^{49} +(-1.88284 + 6.41237i) q^{51} +(2.98779 - 0.213691i) q^{53} +(-2.00638 + 0.0932047i) q^{55} +(-2.11155 + 9.70662i) q^{57} +(-3.79343 + 3.28702i) q^{59} +(-10.7259 - 1.54216i) q^{61} +(-6.05605 + 2.25879i) q^{63} +(2.49927 - 3.68330i) q^{65} +(2.95598 - 0.643035i) q^{67} +(0.921063 - 9.86865i) q^{69} +(-8.42202 - 5.41251i) q^{71} +(-11.5138 - 4.29441i) q^{73} +(-1.25098 + 10.2575i) q^{75} +(-3.65615 + 2.73696i) q^{77} +(0.786408 + 0.907563i) q^{79} +(9.42008 - 6.05392i) q^{81} +(-5.21441 - 2.84728i) q^{83} +(7.12923 + 1.20748i) q^{85} +(8.41524 + 15.4114i) q^{87} +(1.19371 + 8.30244i) q^{89} -10.1213i q^{91} +(-6.72131 + 6.72131i) q^{93} +(10.6978 + 1.03425i) q^{95} +(1.21975 - 0.666035i) q^{97} +(-0.747781 + 0.862985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q+O(q^{10}) \) 720 * q	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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