LMFDB - Embedded newform 380.2.i.b.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(121,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("380.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.1
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	380.201
Dual form			380.2.i.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.28442 + 2.22469i) q^{3} +(0.500000 - 0.866025i) q^{5} +3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(0.500000 + 0.866025i) q^{13} +(1.28442 + 2.22469i) q^{15} +(-2.86834 + 4.96812i) q^{17} +(-4.35327 + 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(2.79949 + 4.84887i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.53871 q^{27} +(-3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(-5.86834 + 10.1643i) q^{33} +(1.78442 - 3.09071i) q^{35} +3.56885 q^{37} -2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(5.65277 - 9.79088i) q^{43} -3.59899 q^{45} +(3.38341 + 5.86024i) q^{47} +5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(1.70051 + 2.94536i) q^{53} +(2.28442 - 3.95674i) q^{55} +(5.09899 - 9.96901i) q^{57} +(3.38341 - 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(-6.42212 - 11.1234i) q^{63} +1.00000 q^{65} +(3.16784 + 5.48686i) q^{67} -14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(6.36834 - 11.0303i) q^{73} +2.56885 q^{75} +16.3055 q^{77} +(-2.43115 + 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} -9.40101 q^{83} +(2.86834 + 4.96812i) q^{85} +17.3830 q^{87} +(-6.13770 - 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(-5.90705 + 10.2313i) q^{93} +(-1.98493 + 3.88073i) q^{95} +(-1.31456 + 2.27689i) q^{97} +(-8.22162 - 14.2403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9 + 10 * q^11 + 3 * q^13 - q^15 + 3 * q^17 - 16 * q^21 + 14 * q^23 - 3 * q^25 - 20 * q^27 - 6 * q^29 + 22 * q^31 - 15 * q^33 + 2 * q^35 + 4 * q^37 + 2 * q^39 - 6 * q^41 + 5 * q^43 - 16 * q^45 + 6 * q^47 - 6 * q^49 - 24 * q^51 + 13 * q^53 + 5 * q^55 + 25 * q^57 + 6 * q^59 - 7 * q^61 + 5 * q^63 + 6 * q^65 - 4 * q^67 + 30 * q^69 + 9 * q^71 + 18 * q^73 - 2 * q^75 + 40 * q^77 - 32 * q^79 - 23 * q^81 - 62 * q^83 - 3 * q^85 - 12 * q^87 - 2 * q^89 + 2 * q^91 + 14 * q^93 - 6 * q^95 - 11 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−1.28442	+	2.22469i	−0.741563	+	1.28442i	0.210220	+	0.977654i	$0.432582\pi$
$3$	−1.28442	+	2.22469i	−0.741563	+	1.28442i	−0.951783	+	0.306771i	$0.900751\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	3.56885			1.34890			0.674449	−	0.738321i	$-0.264381\pi$
$7$	3.56885			1.34890			0.674449	+	0.738321i	$0.264381\pi$
$8$		0			0
$9$	−1.79949	−	3.11682i	−0.599831	−	1.03894i
$10$		0			0
$11$	4.56885			1.37756			0.688780	−	0.724970i	$-0.258147\pi$
$11$	4.56885			1.37756			0.688780	+	0.724970i	$0.258147\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	0.926995	−	0.375073i	$-0.122382\pi$
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i	−0.788320	+	0.615265i	$0.789049\pi$
$14$		0			0
$15$	1.28442	+	2.22469i	0.331637	+	0.574412i
$16$		0			0
$17$	−2.86834	+	4.96812i	−0.695676	+	1.20495i	0.274277	+	0.961651i	$0.411562\pi$
$17$	−2.86834	+	4.96812i	−0.695676	+	1.20495i	−0.969952	+	0.243295i	$0.921772\pi$
$18$		0			0
$19$	−4.35327	+	0.221364i	−0.998710	+	0.0507843i
$19$	−4.35327	+	0.221364i	−0.998710	+	0.0507843i
$20$		0			0
$21$	−4.58392	+	7.93958i	−1.00029	+	1.73256i
$22$		0			0
$23$	2.79949	+	4.84887i	0.583735	+	1.01106i	0.995032	+	0.0995571i	$0.0317426\pi$
$23$	2.79949	+	4.84887i	0.583735	+	1.01106i	−0.411297	+	0.911501i	$0.634924\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.53871			0.296125
$28$		0			0
$29$	−3.38341	−	5.86024i	−0.628284	−	1.08822i	−0.987896	−	0.155118i	$-0.950424\pi$
$29$	−3.38341	−	5.86024i	−0.628284	−	1.08822i	0.359612	−	0.933102i	$-0.382909\pi$
$30$		0			0
$31$	4.59899			0.826003			0.413001	−	0.910730i	$-0.364480\pi$
$31$	4.59899			0.826003			0.413001	+	0.910730i	$0.364480\pi$
$32$		0			0
$33$	−5.86834	+	10.1643i	−1.02155	+	1.76937i
$34$		0			0
$35$	1.78442	−	3.09071i	0.301623	−	0.522426i
$36$		0			0
$37$	3.56885			0.586715			0.293358	−	0.956003i	$-0.405227\pi$
$37$	3.56885			0.586715			0.293358	+	0.956003i	$0.405227\pi$
$38$		0			0
$39$	−2.56885			−0.411345
$40$		0			0
$41$	−5.35327	+	9.27214i	−0.836041	+	1.44807i	0.0571390	+	0.998366i	$0.481802\pi$
$41$	−5.35327	+	9.27214i	−0.836041	+	1.44807i	−0.893180	+	0.449699i	$0.851531\pi$
$42$		0			0
$43$	5.65277	−	9.79088i	0.862039	−	1.49310i	−0.00791826	−	0.999969i	$-0.502520\pi$
$43$	5.65277	−	9.79088i	0.862039	−	1.49310i	0.869957	−	0.493127i	$-0.164146\pi$
$44$		0			0
$45$	−3.59899			−0.536506
$46$		0			0
$47$	3.38341	+	5.86024i	0.493522	+	0.854804i	0.999972	−	0.00746461i	$-0.00237608\pi$
$47$	3.38341	+	5.86024i	0.493522	+	0.854804i	−0.506451	+	0.862269i	$0.669043\pi$
$48$		0			0
$49$	5.73669			0.819527
$50$		0			0
$51$	−7.36834	−	12.7623i	−1.03177	−	1.78709i
$52$		0			0
$53$	1.70051	+	2.94536i	0.233582	+	0.404577i	0.958860	−	0.283880i	$-0.0916218\pi$
$53$	1.70051	+	2.94536i	0.233582	+	0.404577i	−0.725277	+	0.688457i	$0.758288\pi$
$54$		0			0
$55$	2.28442	−	3.95674i	0.308032	−	0.533527i
$56$		0			0
$57$	5.09899	−	9.96901i	0.675378	−	1.32043i
$58$		0			0
$59$	3.38341	−	5.86024i	0.440483	−	0.762939i	−0.557242	−	0.830350i	$-0.688141\pi$
$59$	3.38341	−	5.86024i	0.440483	−	0.762939i	0.997725	+	0.0674112i	$0.0214739\pi$
$60$		0			0
$61$	−4.06885	−	7.04745i	−0.520963	−	0.902334i	−0.999703	−	0.0243773i	$-0.992240\pi$
$61$	−4.06885	−	7.04745i	−0.520963	−	0.902334i	0.478740	−	0.877957i	$-0.341094\pi$
$62$		0			0
$63$	−6.42212	−	11.1234i	−0.809112	−	1.40142i
$64$		0			0
$65$	1.00000			0.124035
$66$		0			0
$67$	3.16784	+	5.48686i	0.387013	+	0.670326i	0.992046	−	0.125874i	$-0.0401735\pi$
$67$	3.16784	+	5.48686i	0.387013	+	0.670326i	−0.605033	+	0.796200i	$0.706840\pi$
$68$		0			0
$69$	−14.3830			−1.73150
$70$		0			0
$71$	0.515069	−	0.892126i	0.0611275	−	0.105876i	−0.833842	−	0.552003i	$-0.813864\pi$
$71$	0.515069	−	0.892126i	0.0611275	−	0.105876i	0.894970	+	0.446127i	$0.147197\pi$
$72$		0			0
$73$	6.36834	−	11.0303i	0.745358	−	1.29100i	−0.204669	−	0.978831i	$-0.565612\pi$
$73$	6.36834	−	11.0303i	0.745358	−	1.29100i	0.950027	−	0.312167i	$-0.101055\pi$
$74$		0			0
$75$	2.56885			0.296625
$76$		0			0
$77$	16.3055			1.85819
$78$		0			0
$79$	−2.43115	+	4.21088i	−0.273526	+	0.473761i	−0.969762	−	0.244052i	$-0.921523\pi$
$79$	−2.43115	+	4.21088i	−0.273526	+	0.473761i	0.696236	+	0.717813i	$0.254857\pi$
$80$		0			0
$81$	3.42212	−	5.92729i	0.380236	−	0.658588i
$82$		0			0
$83$	−9.40101			−1.03190			−0.515948	−	0.856620i	$-0.672560\pi$
$83$	−9.40101			−1.03190			−0.515948	+	0.856620i	$0.672560\pi$
$84$		0			0
$85$	2.86834	+	4.96812i	0.311116	+	0.538868i
$86$		0			0
$87$	17.3830			1.86365
$88$		0			0
$89$	−6.13770	−	10.6308i	−0.650595	−	1.12686i	−0.982979	−	0.183719i	$-0.941186\pi$
$89$	−6.13770	−	10.6308i	−0.650595	−	1.12686i	0.332384	−	0.943144i	$-0.392147\pi$
$90$		0			0
$91$	1.78442	+	3.09071i	0.187059	+	0.323995i
$92$		0			0
$93$	−5.90705	+	10.2313i	−0.612533	+	1.06094i
$94$		0			0
$95$	−1.98493	+	3.88073i	−0.203650	+	0.398154i
$96$		0			0
$97$	−1.31456	+	2.27689i	−0.133474	+	0.231183i	−0.925013	−	0.379935i	$-0.875947\pi$
$97$	−1.31456	+	2.27689i	−0.133474	+	0.231183i	0.791540	+	0.611118i	$0.209280\pi$
$98$		0			0
$99$	−8.22162	−	14.2403i	−0.826304	−	1.43120i
$100$		0			0
$101$	−4.43719	−	7.68544i	−0.441517	−	0.764730i	0.556285	−	0.830992i	$-0.312226\pi$
$101$	−4.43719	−	7.68544i	−0.441517	−	0.764730i	−0.997802	+	0.0662612i	$0.978893\pi$
$102$		0			0
$103$	−4.40101			−0.433645			−0.216822	−	0.976211i	$-0.569569\pi$
$103$	−4.40101			−0.433645			−0.216822	+	0.976211i	$0.569569\pi$
$104$		0			0
$105$	4.58392	+	7.93958i	0.447345	+	0.774824i
$106$		0			0
$107$	−13.9347			−1.34711			−0.673557	−	0.739135i	$-0.735235\pi$
$107$	−13.9347			−1.34711			−0.673557	+	0.739135i	$0.735235\pi$
$108$		0			0
$109$	−1.91608	+	3.31875i	−0.183527	+	0.317879i	−0.943079	−	0.332568i	$-0.892085\pi$
$109$	−1.91608	+	3.31875i	−0.183527	+	0.317879i	0.759552	+	0.650447i	$0.225418\pi$
$110$		0			0
$111$	−4.58392	+	7.93958i	−0.435086	+	0.753592i
$112$		0			0
$113$	−1.70655			−0.160539			−0.0802693	−	0.996773i	$-0.525578\pi$
$113$	−1.70655			−0.160539			−0.0802693	+	0.996773i	$0.525578\pi$
$114$		0			0
$115$	5.59899			0.522108
$116$		0			0
$117$	1.79949	−	3.11682i	0.166363	−	0.288150i
$118$		0			0
$119$	−10.2367	+	17.7305i	−0.938396	+	1.62535i
$120$		0			0
$121$	9.87439			0.897672
$122$		0			0
$123$	−13.7518	−	23.8187i	−1.23995	−	2.14766i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−7.53871	−	13.0574i	−0.668952	−	1.15866i	−0.978197	−	0.207677i	$-0.933410\pi$
$127$	−7.53871	−	13.0574i	−0.668952	−	1.15866i	0.309245	−	0.950982i	$-0.399924\pi$
$128$		0			0
$129$	14.5211	+	25.1513i	1.27851	+	2.21445i
$130$		0			0
$131$	6.78442	−	11.7510i	0.592758	−	1.02669i	−0.401101	−	0.916034i	$-0.631372\pi$
$131$	6.78442	−	11.7510i	0.592758	−	1.02669i	0.993859	−	0.110653i	$-0.0352943\pi$
$132$		0			0
$133$	−15.5362	+	0.790014i	−1.34716	+	0.0685029i
$134$		0			0
$135$	0.769355	−	1.33256i	0.0662156	−	0.114689i
$136$		0			0
$137$	−3.51507	−	6.08828i	−0.300313	−	0.520157i	0.675894	−	0.736999i	$-0.263758\pi$
$137$	−3.51507	−	6.08828i	−0.300313	−	0.520157i	−0.976207	+	0.216842i	$0.930424\pi$
$138$		0			0
$139$	6.09899	+	10.5638i	0.517309	+	0.896006i	0.999798	+	0.0201039i	$0.00639970\pi$
$139$	6.09899	+	10.5638i	0.517309	+	0.896006i	−0.482488	+	0.875902i	$0.660267\pi$
$140$		0			0
$141$	−17.3830			−1.46391
$142$		0			0
$143$	2.28442	+	3.95674i	0.191033	+	0.330879i
$144$		0			0
$145$	−6.76683			−0.561954
$146$		0			0
$147$	−7.36834	+	12.7623i	−0.607731	+	1.05262i
$148$		0			0
$149$	−4.76936	+	8.26077i	−0.390721	+	0.676748i	−0.992545	−	0.121880i	$-0.961108\pi$
$149$	−4.76936	+	8.26077i	−0.390721	+	0.676748i	0.601824	+	0.798629i	$0.294441\pi$
$150$		0			0
$151$	20.4131			1.66119			0.830597	−	0.556874i	$-0.187999\pi$
$151$	20.4131			1.66119			0.830597	+	0.556874i	$0.187999\pi$
$152$		0			0
$153$	20.6463			1.66915
$154$		0			0
$155$	2.29949	−	3.98284i	0.184700	−	0.319909i
$156$		0			0
$157$	7.15277	−	12.3890i	0.570853	−	0.988747i	−0.425626	−	0.904899i	$-0.639946\pi$
$157$	7.15277	−	12.3890i	0.570853	−	0.988747i	0.996479	−	0.0838472i	$-0.0267207\pi$
$158$		0			0
$159$	−8.73669			−0.692864
$160$		0			0
$161$	9.99097	+	17.3049i	0.787399	+	1.36382i
$162$		0			0
$163$	2.53871			0.198847			0.0994236	−	0.995045i	$-0.468300\pi$
$163$	2.53871			0.198847			0.0994236	+	0.995045i	$0.468300\pi$
$164$		0			0
$165$	5.86834	+	10.1643i	0.456850	+	0.791287i
$166$		0			0
$167$	6.78442	+	11.7510i	0.524995	+	0.909317i	0.999576	+	0.0291058i	$0.00926598\pi$
$167$	6.78442	+	11.7510i	0.524995	+	0.909317i	−0.474582	+	0.880211i	$0.657401\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$		0			0
$171$	8.52364	+	13.1700i	0.651819	+	1.00714i
$172$		0			0
$173$	−1.18544	+	2.05324i	−0.0901271	+	0.156105i	−0.907564	−	0.419913i	$-0.862061\pi$
$173$	−1.18544	+	2.05324i	−0.0901271	+	0.156105i	0.817437	+	0.576017i	$0.195394\pi$
$174$		0			0
$175$	−1.78442	−	3.09071i	−0.134890	−	0.233636i
$176$		0			0
$177$	8.69148	+	15.0541i	0.653292	+	1.13153i
$178$		0			0
$179$	17.8744			1.33599			0.667997	−	0.744164i	$-0.267152\pi$
$179$	17.8744			1.33599			0.667997	+	0.744164i	$0.267152\pi$
$180$		0			0
$181$	−13.2065	−	22.8744i	−0.981635	−	1.70024i	−0.656028	−	0.754737i	$-0.727765\pi$
$181$	−13.2065	−	22.8744i	−0.981635	−	1.70024i	−0.325607	−	0.945505i	$-0.605569\pi$
$182$		0			0
$183$	20.9045			1.54531
$184$		0			0
$185$	1.78442	−	3.09071i	0.131194	−	0.227234i
$186$		0			0
$187$	−13.1050	+	22.6986i	−0.958335	+	1.65988i
$188$		0			0
$189$	5.49143			0.399443
$190$		0			0
$191$	0.526625			0.0381052			0.0190526	−	0.999818i	$-0.493935\pi$
$191$	0.526625			0.0381052			0.0190526	+	0.999818i	$0.493935\pi$
$192$		0			0
$193$	2.67037	−	4.62521i	0.192217	−	0.332930i	−0.753767	−	0.657141i	$-0.771766\pi$
$193$	2.67037	−	4.62521i	0.192217	−	0.332930i	0.945985	+	0.324211i	$0.105099\pi$
$194$		0			0
$195$	−1.28442	+	2.22469i	−0.0919796	+	0.159313i
$196$		0			0
$197$	−4.43115			−0.315706			−0.157853	−	0.987463i	$-0.550457\pi$
$197$	−4.43115			−0.315706			−0.157853	+	0.987463i	$0.550457\pi$
$198$		0			0
$199$	−6.08392	−	10.5377i	−0.431278	−	0.746995i	0.565706	−	0.824607i	$-0.308604\pi$
$199$	−6.08392	−	10.5377i	−0.431278	−	0.746995i	−0.996984	+	0.0776123i	$0.975270\pi$
$200$		0			0
$201$	−16.2754			−1.14798
$202$		0			0
$203$	−12.0749	−	20.9143i	−0.847491	−	1.46790i
$204$		0			0
$205$	5.35327	+	9.27214i	0.373889	+	0.647595i
$206$		0			0
$207$	10.0753	−	17.4510i	0.700285	−	1.21293i
$208$		0			0
$209$	−19.8895	+	1.01138i	−1.37578	+	0.0699584i
$210$		0			0
$211$	10.3357	−	17.9019i	0.711537	−	1.23242i	−0.252743	−	0.967534i	$-0.581333\pi$
$211$	10.3357	−	17.9019i	0.711537	−	1.23242i	0.964280	−	0.264885i	$-0.0853341\pi$
$212$		0			0
$213$	1.32314	+	2.29174i	0.0906598	+	0.157027i
$214$		0			0
$215$	−5.65277	−	9.79088i	−0.385516	−	0.667733i
$216$		0			0
$217$	16.4131			1.11419
$218$		0			0
$219$	16.3593	+	28.3352i	1.10546	+	1.91471i
$220$		0			0
$221$	−5.73669			−0.385891
$222$		0			0
$223$	−2.25429	+	3.90454i	−0.150958	+	0.261467i	−0.931580	−	0.363536i	$-0.881569\pi$
$223$	−2.25429	+	3.90454i	−0.150958	+	0.261467i	0.780622	+	0.625004i	$0.214903\pi$
$224$		0			0
$225$	−1.79949	+	3.11682i	−0.119966	+	0.207788i
$226$		0			0
$227$	−16.6714			−1.10652			−0.553258	−	0.833010i	$-0.686616\pi$
$227$	−16.6714			−1.10652			−0.553258	+	0.833010i	$0.686616\pi$
$228$		0			0
$229$	5.31060			0.350934			0.175467	−	0.984485i	$-0.443856\pi$
$229$	5.31060			0.350934			0.175467	+	0.984485i	$0.443856\pi$
$230$		0			0
$231$	−20.9432	+	36.2747i	−1.37796	+	2.38670i
$232$		0			0
$233$	1.38594	−	2.40052i	0.0907961	−	0.157263i	−0.817050	−	0.576566i	$-0.804392\pi$
$233$	1.38594	−	2.40052i	0.0907961	−	0.157263i	0.907846	+	0.419303i	$0.137726\pi$
$234$		0			0
$235$	6.76683			0.441419
$236$		0			0
$237$	−6.24526	−	10.8171i	−0.405673	−	0.702647i
$238$		0			0
$239$	−8.59899			−0.556222			−0.278111	−	0.960549i	$-0.589708\pi$
$239$	−8.59899			−0.556222			−0.278111	+	0.960549i	$0.589708\pi$
$240$		0			0
$241$	−2.83216	−	4.90545i	−0.182436	−	0.315988i	0.760274	−	0.649603i	$-0.225065\pi$
$241$	−2.83216	−	4.90545i	−0.182436	−	0.315988i	−0.942709	+	0.333615i	$0.891731\pi$
$242$		0			0
$243$	11.0990	+	19.2240i	0.712000	+	1.23322i
$244$		0			0
$245$	2.86834	−	4.96812i	0.183252	−	0.317401i
$246$		0			0
$247$	−2.36834	−	3.65936i	−0.150694	−	0.232840i
$248$		0			0
$249$	12.0749	−	20.9143i	0.765215	−	1.32539i
$250$		0			0
$251$	11.5598	+	20.0222i	0.729650	+	1.26379i	0.957031	+	0.289984i	$0.0936501\pi$
$251$	11.5598	+	20.0222i	0.729650	+	1.26379i	−0.227382	+	0.973806i	$0.573017\pi$
$252$		0			0
$253$	12.7905	+	22.1537i	0.804130	+	1.39279i
$254$		0			0
$255$	−14.7367			−0.922847
$256$		0			0
$257$	5.28442	+	9.15289i	0.329633	+	0.570942i	0.982439	−	0.186584i	$-0.0597415\pi$
$257$	5.28442	+	9.15289i	0.329633	+	0.570942i	−0.652806	+	0.757525i	$0.726408\pi$
$258$		0			0
$259$	12.7367			0.791419
$260$		0			0
$261$	−12.1769	+	21.0909i	−0.753729	+	1.30550i
$262$		0			0
$263$	−4.43115	+	7.67498i	−0.273236	+	0.473259i	−0.969689	−	0.244344i	$-0.921427\pi$
$263$	−4.43115	+	7.67498i	−0.273236	+	0.473259i	0.696452	+	0.717603i	$0.254761\pi$
$264$		0			0
$265$	3.40101			0.208922
$266$		0			0
$267$	31.5337			1.92983
$268$		0			0
$269$	−2.66784	+	4.62083i	−0.162661	+	0.281737i	−0.935822	−	0.352472i	$-0.885341\pi$
$269$	−2.66784	+	4.62083i	−0.162661	+	0.281737i	0.773161	+	0.634210i	$0.218674\pi$
$270$		0			0
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	−0.925789	−	0.378040i	$-0.876598\pi$
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	0.790287	+	0.612737i	$0.209931\pi$
$272$		0			0
$273$	−9.16784			−0.554863
$274$		0			0
$275$	−2.28442	−	3.95674i	−0.137756	−	0.238600i
$276$		0			0
$277$	−23.0774			−1.38659			−0.693294	−	0.720655i	$-0.743841\pi$
$277$	−23.0774			−1.38659			−0.693294	+	0.720655i	$0.743841\pi$
$278$		0			0
$279$	−8.27585	−	14.3342i	−0.495462	−	0.858166i
$280$		0			0
$281$	−2.01507	−	3.49020i	−0.120209	−	0.208208i	0.799641	−	0.600478i	$-0.205023\pi$
$281$	−2.01507	−	3.49020i	−0.120209	−	0.208208i	−0.919850	+	0.392270i	$0.871690\pi$
$282$		0			0
$283$	−15.9196	+	27.5735i	−0.946322	+	1.63908i	−0.193239	+	0.981152i	$0.561899\pi$
$283$	−15.9196	+	27.5735i	−0.946322	+	1.63908i	−0.753083	+	0.657925i	$0.771434\pi$
$284$		0			0
$285$	−6.08392	−	9.40036i	−0.360380	−	0.556829i
$286$		0			0
$287$	−19.1050	+	33.0909i	−1.12773	+	1.95329i
$288$		0			0
$289$	−7.95479	−	13.7781i	−0.467929	−	0.810477i
$290$		0			0
$291$	−3.37692	−	5.84899i	−0.197958	−	0.342874i
$292$		0			0
$293$	−18.6764			−1.09109			−0.545544	−	0.838082i	$-0.683677\pi$
$293$	−18.6764			−1.09109			−0.545544	+	0.838082i	$0.683677\pi$
$294$		0			0
$295$	−3.38341	−	5.86024i	−0.196990	−	0.341197i
$296$		0			0
$297$	7.03014			0.407930
$298$		0			0
$299$	−2.79949	+	4.84887i	−0.161899	+	0.280417i
$300$		0			0
$301$	20.1739	−	34.9422i	1.16280	−	2.01403i
$302$		0			0
$303$	22.7970			1.30965
$304$		0			0
$305$	−8.13770			−0.465963
$306$		0			0
$307$	15.8955	−	27.5318i	0.907204	−	1.57132i	0.0892730	−	0.996007i	$-0.471546\pi$
$307$	15.8955	−	27.5318i	0.907204	−	1.57132i	0.817931	−	0.575316i	$-0.195121\pi$
$308$		0			0
$309$	5.65277	−	9.79088i	0.321575	−	0.556984i
$310$		0			0
$311$	2.37087			0.134440			0.0672199	−	0.997738i	$-0.478587\pi$
$311$	2.37087			0.134440			0.0672199	+	0.997738i	$0.478587\pi$
$312$		0			0
$313$	6.10503	+	10.5742i	0.345077	+	0.597691i	0.985368	−	0.170442i	$-0.0545195\pi$
$313$	6.10503	+	10.5742i	0.345077	+	0.597691i	−0.640291	+	0.768132i	$0.721186\pi$
$314$		0			0
$315$	−12.8442			−0.723691
$316$		0			0
$317$	−14.2216	−	24.6326i	−0.798766	−	1.38350i	−0.920420	−	0.390930i	$-0.872153\pi$
$317$	−14.2216	−	24.6326i	−0.798766	−	1.38350i	0.121655	−	0.992572i	$-0.461180\pi$
$318$		0			0
$319$	−15.4583	−	26.7746i	−0.865499	−	1.49909i
$320$		0			0
$321$	17.8980	−	31.0003i	0.998971	−	1.73027i
$322$		0			0
$323$	11.3869	−	22.2625i	0.633586	−	1.23872i
$324$		0			0
$325$	0.500000	−	0.866025i	0.0277350	−	0.0480384i
$326$		0			0
$327$	−4.92212	−	8.52537i	−0.272194	−	0.471454i
$328$		0			0
$329$	12.0749	+	20.9143i	0.665710	+	1.15304i
$330$		0			0
$331$	−32.5930			−1.79147			−0.895737	−	0.444584i	$-0.853352\pi$
$331$	−32.5930			−1.79147			−0.895737	+	0.444584i	$0.853352\pi$
$332$		0			0
$333$	−6.42212	−	11.1234i	−0.351930	−	0.609561i
$334$		0			0
$335$	6.33568			0.346155
$336$		0			0
$337$	−5.83216	+	10.1016i	−0.317698	+	0.550269i	−0.980007	−	0.198961i	$-0.936243\pi$
$337$	−5.83216	+	10.1016i	−0.317698	+	0.550269i	0.662309	+	0.749231i	$0.269577\pi$
$338$		0			0
$339$	2.19193	−	3.79654i	0.119049	−	0.206200i
$340$		0			0
$341$	21.0121			1.13787
$342$		0			0
$343$	−4.50857			−0.243440
$344$		0			0
$345$	−7.19148	+	12.4560i	−0.387176	+	0.670609i
$346$		0			0
$347$	−15.1613	+	26.2602i	−0.813903	+	1.40972i	0.0962092	+	0.995361i	$0.469328\pi$
$347$	−15.1613	+	26.2602i	−0.813903	+	1.40972i	−0.910113	+	0.414361i	$0.864005\pi$
$348$		0			0
$349$	3.44324			0.184312			0.0921561	−	0.995745i	$-0.470624\pi$
$349$	3.44324			0.184312			0.0921561	+	0.995745i	$0.470624\pi$
$350$		0			0
$351$	0.769355	+	1.33256i	0.0410652	+	0.0711269i
$352$		0			0
$353$	−6.53871			−0.348020			−0.174010	−	0.984744i	$-0.555673\pi$
$353$	−6.53871			−0.348020			−0.174010	+	0.984744i	$0.555673\pi$
$354$		0			0
$355$	−0.515069	−	0.892126i	−0.0273370	−	0.0473491i
$356$		0			0
$357$	−26.2965	−	45.5469i	−1.39176	−	2.41060i
$358$		0			0
$359$	11.2392	−	19.4669i	0.593183	−	1.02742i	−0.400617	−	0.916245i	$-0.631204\pi$
$359$	11.2392	−	19.4669i	0.593183	−	1.02742i	0.993801	−	0.111178i	$-0.0354623\pi$
$360$		0			0
$361$	18.9020	−	1.92731i	0.994842	−	0.101438i
$362$		0			0
$363$	−12.6829	+	21.9674i	−0.665680	+	1.15299i
$364$		0			0
$365$	−6.36834	−	11.0303i	−0.333334	−	0.577352i
$366$		0			0
$367$	−4.29696	−	7.44256i	−0.224300	−	0.388499i	0.731809	−	0.681509i	$-0.238676\pi$
$367$	−4.29696	−	7.44256i	−0.224300	−	0.388499i	−0.956109	+	0.293011i	$0.905343\pi$
$368$		0			0
$369$	38.5327			2.00593
$370$		0			0
$371$	6.06885	+	10.5116i	0.315079	+	0.545733i
$372$		0			0
$373$	37.2453			1.92849			0.964243	−	0.265019i	$-0.0853782\pi$
$373$	37.2453			1.92849			0.964243	+	0.265019i	$0.0853782\pi$
$374$		0			0
$375$	1.28442	−	2.22469i	0.0663274	−	0.114882i
$376$		0			0
$377$	3.38341	−	5.86024i	0.174255	−	0.301818i
$378$		0			0
$379$	12.1678			0.625020			0.312510	−	0.949914i	$-0.398830\pi$
$379$	12.1678			0.625020			0.312510	+	0.949914i	$0.398830\pi$
$380$		0			0
$381$	38.7316			1.98428
$382$		0			0
$383$	12.5272	−	21.6977i	0.640108	−	1.10870i	−0.345301	−	0.938492i	$-0.612223\pi$
$383$	12.5272	−	21.6977i	0.640108	−	1.10870i	0.985408	−	0.170207i	$-0.0544436\pi$
$384$		0			0
$385$	8.15277	−	14.1210i	0.415504	−	0.719673i
$386$		0			0
$387$	−40.6885			−2.06831
$388$		0			0
$389$	−11.0211	−	19.0891i	−0.558793	−	0.967857i	−0.997598	−	0.0692748i	$-0.977931\pi$
$389$	−11.0211	−	19.0891i	−0.558793	−	0.967857i	0.438805	−	0.898582i	$-0.355402\pi$
$390$		0			0
$391$	−32.1196			−1.62436
$392$		0			0
$393$	17.4282	+	30.1865i	0.879135	+	1.52271i
$394$		0			0
$395$	2.43115	+	4.21088i	0.122324	+	0.211872i
$396$		0			0
$397$	−18.0900	+	31.3327i	−0.907909	+	1.57254i	−0.0909453	+	0.995856i	$0.528989\pi$
$397$	−18.0900	+	31.3327i	−0.907909	+	1.57254i	−0.816964	+	0.576689i	$0.804344\pi$
$398$		0			0
$399$	18.1975	−	35.5779i	0.911016	−	1.78112i
$400$		0			0
$401$	−13.9583	+	24.1765i	−0.697045	+	1.20732i	0.272442	+	0.962172i	$0.412169\pi$
$401$	−13.9583	+	24.1765i	−0.697045	+	1.20732i	−0.969487	+	0.245144i	$0.921165\pi$
$402$		0			0
$403$	2.29949	+	3.98284i	0.114546	+	0.198399i
$404$		0			0
$405$	−3.42212	−	5.92729i	−0.170047	−	0.294530i
$406$		0			0
$407$	16.3055			0.808235
$408$		0			0
$409$	−4.06281	−	7.03699i	−0.200893	−	0.347957i	0.747924	−	0.663785i	$-0.231051\pi$
$409$	−4.06281	−	7.03699i	−0.200893	−	0.347957i	−0.948816	+	0.315828i	$0.897718\pi$
$410$		0			0
$411$	18.0594			0.890803
$412$		0			0
$413$	12.0749	−	20.9143i	0.594167	−	1.02913i
$414$		0			0
$415$	−4.70051	+	8.14151i	−0.230739	+	0.399651i
$416$		0			0
$417$	−31.3348			−1.53447
$418$		0			0
$419$	−2.87439			−0.140423			−0.0702115	−	0.997532i	$-0.522367\pi$
$419$	−2.87439			−0.140423			−0.0702115	+	0.997532i	$0.522367\pi$
$420$		0			0
$421$	3.48240	−	6.03170i	0.169722	−	0.293967i	−0.768600	−	0.639729i	$-0.779046\pi$
$421$	3.48240	−	6.03170i	0.169722	−	0.293967i	0.938322	+	0.345763i	$0.112380\pi$
$422$		0			0
$423$	12.1769	−	21.0909i	0.592059	−	1.02548i
$424$		0			0
$425$	5.73669			0.278270
$426$		0			0
$427$	−14.5211	−	25.1513i	−0.702726	−	1.21716i
$428$		0			0
$429$	−11.7367			−0.566653
$430$		0			0
$431$	5.08996	+	8.81607i	0.245175	+	0.424655i	0.962181	−	0.272412i	$-0.0878213\pi$
$431$	5.08996	+	8.81607i	0.245175	+	0.424655i	−0.717006	+	0.697067i	$0.754488\pi$
$432$		0			0
$433$	9.88341	+	17.1186i	0.474967	+	0.822666i	0.999589	−	0.0286689i	$-0.00912683\pi$
$433$	9.88341	+	17.1186i	0.474967	+	0.822666i	−0.524622	+	0.851335i	$0.675793\pi$
$434$		0			0
$435$	8.69148	−	15.0541i	0.416725	−	0.721788i
$436$		0			0
$437$	−13.2603	−	20.4887i	−0.634328	−	0.980109i
$438$		0			0
$439$	−19.3266	+	33.4747i	−0.922411	+	1.59766i	−0.126737	+	0.991936i	$0.540450\pi$
$439$	−19.3266	+	33.4747i	−0.922411	+	1.59766i	−0.795673	+	0.605726i	$0.792883\pi$
$440$		0			0
$441$	−10.3231	−	17.8802i	−0.491578	−	0.851438i
$442$		0			0
$443$	−5.35327	−	9.27214i	−0.254342	−	0.440533i	0.710375	−	0.703824i	$-0.248525\pi$
$443$	−5.35327	−	9.27214i	−0.254342	−	0.440533i	−0.964717	+	0.263291i	$0.915192\pi$
$444$		0			0
$445$	−12.2754			−0.581910
$446$		0			0
$447$	−12.2518	−	21.2207i	−0.579488	−	1.00370i
$448$		0			0
$449$	23.0724			1.08885			0.544426	−	0.838809i	$-0.316747\pi$
$449$	23.0724			1.08885			0.544426	+	0.838809i	$0.316747\pi$
$450$		0			0
$451$	−24.4583	+	42.3630i	−1.15170	+	1.99480i
$452$		0			0
$453$	−26.2191	+	45.4128i	−1.23188	+	2.13368i
$454$		0			0
$455$	3.56885			0.167310
$456$		0			0
$457$	−6.87439			−0.321570			−0.160785	−	0.986989i	$-0.551403\pi$
$457$	−6.87439			−0.321570			−0.160785	+	0.986989i	$0.551403\pi$
$458$		0			0
$459$	−4.41355	+	7.64450i	−0.206007	+	0.356815i
$460$		0			0
$461$	1.41355	−	2.44834i	0.0658357	−	0.114031i	−0.831229	−	0.555931i	$-0.812362\pi$
$461$	1.41355	−	2.44834i	0.0658357	−	0.114031i	0.897064	+	0.441900i	$0.145695\pi$
$462$		0			0
$463$	−23.9347			−1.11234			−0.556169	−	0.831069i	$-0.687729\pi$
$463$	−23.9347			−1.11234			−0.556169	+	0.831069i	$0.687729\pi$
$464$		0			0
$465$	5.90705	+	10.2313i	0.273933	+	0.474466i
$466$		0			0
$467$	33.5508			1.55255			0.776273	−	0.630397i	$-0.217108\pi$
$467$	33.5508			1.55255			0.776273	+	0.630397i	$0.217108\pi$
$468$		0			0
$469$	11.3055	+	19.5818i	0.522041	+	0.904202i
$470$		0			0
$471$	18.3744	+	31.8254i	0.846647	+	1.46644i
$472$		0			0
$473$	25.8266	−	44.7331i	1.18751	−	2.05683i
$474$		0			0
$475$	2.36834	+	3.65936i	0.108667	+	0.167903i
$476$		0			0
$477$	6.12010	−	10.6003i	0.280220	−	0.485356i
$478$		0			0
$479$	18.4583	+	31.9707i	0.843382	+	1.46078i	0.887019	+	0.461732i	$0.152772\pi$
$479$	18.4583	+	31.9707i	0.843382	+	1.46078i	−0.0436379	+	0.999047i	$0.513895\pi$
$480$		0			0
$481$	1.78442	+	3.09071i	0.0813628	+	0.140924i
$482$		0			0
$483$	−51.3306			−2.33562
$484$		0			0
$485$	1.31456	+	2.27689i	0.0596913	+	0.103388i
$486$		0			0
$487$	−12.8744			−0.583394			−0.291697	−	0.956511i	$-0.594220\pi$
$487$	−12.8744			−0.583394			−0.291697	+	0.956511i	$0.594220\pi$
$488$		0			0
$489$	−3.26078	+	5.64784i	−0.147458	+	0.255404i
$490$		0			0
$491$	12.3382	−	21.3704i	0.556815	−	0.964433i	−0.440944	−	0.897534i	$-0.645356\pi$
$491$	12.3382	−	21.3704i	0.556815	−	0.964433i	0.997760	−	0.0668981i	$-0.0213103\pi$
$492$		0			0
$493$	38.8192			1.74833
$494$		0			0
$495$	−16.4432			−0.739069
$496$		0			0
$497$	1.83821	−	3.18386i	0.0824548	−	0.142816i
$498$		0			0
$499$	−15.7603	+	27.2977i	−0.705529	+	1.22201i	0.260971	+	0.965347i	$0.415957\pi$
$499$	−15.7603	+	27.2977i	−0.705529	+	1.22201i	−0.966500	+	0.256666i	$0.917376\pi$
$500$		0			0
$501$	−34.8563			−1.55727
$502$		0			0
$503$	−6.08645	−	10.5420i	−0.271381	−	0.470046i	0.697834	−	0.716259i	$-0.254147\pi$
$503$	−6.08645	−	10.5420i	−0.271381	−	0.470046i	−0.969216	+	0.246213i	$0.920814\pi$
$504$		0			0
$505$	−8.87439			−0.394905
$506$		0			0
$507$	15.4131	+	26.6963i	0.684520	+	1.18562i
$508$		0			0
$509$	4.70051	+	8.14151i	0.208346	+	0.360866i	0.951194	−	0.308594i	$-0.0998586\pi$
$509$	4.70051	+	8.14151i	0.208346	+	0.360866i	−0.742847	+	0.669461i	$0.766525\pi$
$510$		0			0
$511$	22.7277	−	39.3655i	1.00541	−	1.74143i
$512$		0			0
$513$	−6.69843	+	0.340615i	−0.295743	+	0.0150385i
$514$		0			0
$515$	−2.20051	+	3.81139i	−0.0969659	+	0.167950i
$516$		0			0
$517$	15.4583	+	26.7746i	0.679856	+	1.17754i
$518$		0			0
$519$	−3.04521	−	5.27446i	−0.133670	−	0.231523i
$520$		0			0
$521$	8.49649			0.372238			0.186119	−	0.982527i	$-0.440409\pi$
$521$	8.49649			0.372238			0.186119	+	0.982527i	$0.440409\pi$
$522$		0			0
$523$	−11.2191	−	19.4320i	−0.490577	−	0.849703i	0.509365	−	0.860551i	$-0.329880\pi$
$523$	−11.2191	−	19.4320i	−0.490577	−	0.849703i	−0.999941	+	0.0108473i	$0.996547\pi$
$524$		0			0
$525$	9.16784			0.400117
$526$		0			0
$527$	−13.1915	+	22.8483i	−0.574630	+	0.995288i
$528$		0			0
$529$	−4.17434	+	7.23016i	−0.181493	+	0.314355i
$530$		0			0
$531$	−24.3537			−1.05686
$532$		0			0
$533$	−10.7065			−0.463752
$534$		0			0
$535$	−6.96733	+	12.0678i	−0.301224	+	0.521735i
$536$		0			0
$537$	−22.9583	+	39.7650i	−0.990724	+	1.71598i
$538$		0			0
$539$	26.2101			1.12895
$540$		0			0
$541$	13.7603	+	23.8336i	0.591603	+	1.02469i	0.994017	+	0.109228i	$0.0348379\pi$
$541$	13.7603	+	23.8336i	0.591603	+	1.02469i	−0.402414	+	0.915458i	$0.631829\pi$
$542$		0			0
$543$	67.8513			2.91178
$544$		0			0
$545$	1.91608	+	3.31875i	0.0820759	+	0.142160i
$546$		0			0
$547$	0.425107	+	0.736308i	0.0181763	+	0.0314822i	0.874970	−	0.484176i	$-0.160881\pi$
$547$	0.425107	+	0.736308i	0.0181763	+	0.0314822i	−0.856794	+	0.515659i	$0.827547\pi$
$548$		0			0
$549$	−14.6437	+	25.3637i	−0.624980	+	1.08250i
$550$		0			0
$551$	16.0262	+	24.7623i	0.682738	+	1.05491i
$552$		0			0
$553$	−8.67641	+	15.0280i	−0.368958	+	0.639055i
$554$		0			0
$555$	4.58392	+	7.93958i	0.194577	+	0.337016i
$556$		0			0
$557$	19.6950	+	34.1127i	0.834504	+	1.44540i	0.894434	+	0.447200i	$0.147579\pi$
$557$	19.6950	+	34.1127i	0.834504	+	1.44540i	−0.0599303	+	0.998203i	$0.519088\pi$
$558$		0			0
$559$	11.3055			0.478173
$560$		0			0
$561$	−33.6649	−	58.3092i	−1.42133	−	2.46182i
$562$		0			0
$563$	−22.0774			−0.930452			−0.465226	−	0.885192i	$-0.654027\pi$
$563$	−22.0774			−0.930452			−0.465226	+	0.885192i	$0.654027\pi$
$564$		0			0
$565$	−0.853274	+	1.47791i	−0.0358975	+	0.0621763i
$566$		0			0
$567$	12.2130	−	21.1536i	0.512900	−	0.888368i
$568$		0			0
$569$	−7.53365			−0.315827			−0.157914	−	0.987453i	$-0.550477\pi$
$569$	−7.53365			−0.315827			−0.157914	+	0.987453i	$0.550477\pi$
$570$		0			0
$571$	−38.2824			−1.60207			−0.801035	−	0.598618i	$-0.795717\pi$
$571$	−38.2824			−1.60207			−0.801035	+	0.598618i	$0.795717\pi$
$572$		0			0
$573$	−0.676410	+	1.17158i	−0.0282574	+	0.0489433i
$574$		0			0
$575$	2.79949	−	4.84887i	0.116747	−	0.202212i
$576$		0			0
$577$	−3.21006			−0.133637			−0.0668183	−	0.997765i	$-0.521285\pi$
$577$	−3.21006			−0.133637			−0.0668183	+	0.997765i	$0.521285\pi$
$578$		0			0
$579$	6.85977	+	11.8815i	0.285082	+	0.493777i
$580$		0			0
$581$	−33.5508			−1.39192
$582$		0			0
$583$	7.76936	+	13.4569i	0.321774	+	0.557329i
$584$		0			0
$585$	−1.79949	−	3.11682i	−0.0743999	−	0.128864i
$586$		0			0
$587$	1.24824	−	2.16202i	0.0515205	−	0.0892361i	−0.839115	−	0.543954i	$-0.816927\pi$
$587$	1.24824	−	2.16202i	0.0515205	−	0.0892361i	0.890636	+	0.454718i	$0.150260\pi$
$588$		0			0
$589$	−20.0207	+	1.01805i	−0.824937	+	0.0419480i
$590$		0			0
$591$	5.69148	−	9.85793i	0.234116	−	0.405501i
$592$		0			0
$593$	−7.03014	−	12.1766i	−0.288693	−	0.500031i	0.684805	−	0.728726i	$-0.259887\pi$
$593$	−7.03014	−	12.1766i	−0.288693	−	0.500031i	−0.973498	+	0.228695i	$0.926554\pi$
$594$		0			0
$595$	10.2367	+	17.7305i	0.419663	+	0.726878i
$596$		0			0
$597$	31.2573			1.27928
$598$		0			0
$599$	11.6678	+	20.2093i	0.476735	+	0.825729i	0.999645	−	0.0266590i	$-0.00848682\pi$
$599$	11.6678	+	20.2093i	0.476735	+	0.825729i	−0.522910	+	0.852388i	$0.675153\pi$
$600$		0			0
$601$	46.6111			1.90131			0.950653	−	0.310257i	$-0.100415\pi$
$601$	46.6111			1.90131			0.950653	+	0.310257i	$0.100415\pi$
$602$		0			0
$603$	11.4010	−	19.7471i	0.464285	−	0.804165i
$604$		0			0
$605$	4.93719	−	8.55147i	0.200725	−	0.347667i
$606$		0			0
$607$	11.1929			0.454307			0.227153	−	0.973859i	$-0.427058\pi$
$607$	11.1929			0.454307			0.227153	+	0.973859i	$0.427058\pi$
$608$		0			0
$609$	62.0372			2.51387
$610$		0			0
$611$	−3.38341	+	5.86024i	−0.136878	+	0.237080i
$612$		0			0
$613$	−16.9794	+	29.4092i	−0.685792	+	1.18783i	0.287395	+	0.957812i	$0.407211\pi$
$613$	−16.9794	+	29.4092i	−0.685792	+	1.18783i	−0.973187	+	0.230015i	$0.926123\pi$
$614$		0			0
$615$	−27.5035			−1.10905
$616$		0			0
$617$	−8.27287	−	14.3290i	−0.333053	−	0.576865i	0.650056	−	0.759887i	$-0.274746\pi$
$617$	−8.27287	−	14.3290i	−0.333053	−	0.576865i	−0.983109	+	0.183022i	$0.941412\pi$
$618$		0			0
$619$	21.4312			0.861391			0.430695	−	0.902497i	$-0.358268\pi$
$619$	21.4312			0.861391			0.430695	+	0.902497i	$0.358268\pi$
$620$		0			0
$621$	4.30761	+	7.46100i	0.172859	+	0.299400i
$622$		0			0
$623$	−21.9045	−	37.9398i	−0.877586	−	1.52002i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	23.2965	−	45.5469i	0.930373	−	1.81897i
$628$		0			0
$629$	−10.2367	+	17.7305i	−0.408163	+	0.706960i
$630$		0			0
$631$	−10.5035	−	18.1926i	−0.418138	−	0.724237i	0.577614	−	0.816310i	$-0.303984\pi$
$631$	−10.5035	−	18.1926i	−0.418138	−	0.724237i	−0.995752	+	0.0920733i	$0.970651\pi$
$632$		0			0
$633$	26.5508	+	45.9873i	1.05530	+	1.82783i
$634$		0			0
$635$	−15.0774			−0.598329
$636$		0			0
$637$	2.86834	+	4.96812i	0.113648	+	0.196844i
$638$		0			0
$639$	−3.70746			−0.146665
$640$		0			0
$641$	15.9106	−	27.5579i	0.628430	−	1.08847i	−0.359437	−	0.933169i	$-0.617031\pi$
$641$	15.9106	−	27.5579i	0.628430	−	1.08847i	0.987867	−	0.155303i	$-0.0496353\pi$
$642$		0			0
$643$	4.44369	−	7.69670i	0.175242	−	0.303528i	−0.765003	−	0.644027i	$-0.777263\pi$
$643$	4.44369	−	7.69670i	0.175242	−	0.303528i	0.940245	+	0.340499i	$0.110596\pi$
$644$		0			0
$645$	29.0422			1.14354
$646$		0			0
$647$	1.37593			0.0540934			0.0270467	−	0.999634i	$-0.491390\pi$
$647$	1.37593			0.0540934			0.0270467	+	0.999634i	$0.491390\pi$
$648$		0			0
$649$	15.4583	−	26.7746i	0.606792	−	1.05099i
$650$		0			0
$651$	−21.0814	+	36.5140i	−0.826245	+	1.43110i
$652$		0			0
$653$	−24.7237			−0.967513			−0.483756	−	0.875203i	$-0.660728\pi$
$653$	−24.7237			−0.967513			−0.483756	+	0.875203i	$0.660728\pi$
$654$		0			0
$655$	−6.78442	−	11.7510i	−0.265089	−	0.459148i
$656$		0			0
$657$	−45.8392			−1.78836
$658$		0			0
$659$	20.9020	+	36.2033i	0.814226	+	1.41028i	0.909882	+	0.414867i	$0.136172\pi$
$659$	20.9020	+	36.2033i	0.814226	+	1.41028i	−0.0956561	+	0.995414i	$0.530495\pi$
$660$		0			0
$661$	11.5211	+	19.9552i	0.448119	+	0.776165i	0.998264	−	0.0589041i	$-0.0187606\pi$
$661$	11.5211	+	19.9552i	0.448119	+	0.776165i	−0.550144	+	0.835070i	$0.685427\pi$
$662$		0			0
$663$	7.36834	−	12.7623i	0.286163	−	0.495648i
$664$		0			0
$665$	−7.08392	+	13.8497i	−0.274703	+	0.537070i
$666$		0			0
$667$	18.9437	−	32.8114i	0.733503	−	1.27046i
$668$		0			0
$669$	−5.79092	−	10.0302i	−0.223890	−	0.387789i
$670$		0			0
$671$	−18.5900	−	32.1988i	−0.717658	−	1.24302i
$672$		0			0
$673$	29.5156			1.13774			0.568871	−	0.822427i	$-0.307380\pi$
$673$	29.5156			1.13774			0.568871	+	0.822427i	$0.307380\pi$
$674$		0			0
$675$	−0.769355	−	1.33256i	−0.0296125	−	0.0512904i
$676$		0			0
$677$	12.5035			0.480549			0.240275	−	0.970705i	$-0.422763\pi$
$677$	12.5035			0.480549			0.240275	+	0.970705i	$0.422763\pi$
$678$		0			0
$679$	−4.69148	+	8.12588i	−0.180042	+	0.311843i
$680$		0			0
$681$	21.4131	−	37.0886i	0.820552	−	1.42124i
$682$		0			0
$683$	12.9045			0.493778			0.246889	−	0.969044i	$-0.420592\pi$
$683$	12.9045			0.493778			0.246889	+	0.969044i	$0.420592\pi$
$684$		0			0
$685$	−7.03014			−0.268608
$686$		0			0
$687$	−6.82106	+	11.8144i	−0.260240	+	0.450748i
$688$		0			0
$689$	−1.70051	+	2.94536i	−0.0647841	+	0.112209i
$690$		0			0
$691$	23.3779			0.889337			0.444669	−	0.895695i	$-0.353321\pi$
$691$	23.3779			0.889337			0.444669	+	0.895695i	$0.353321\pi$
$692$		0			0
$693$	−29.3417	−	50.8213i	−1.11460	−	1.93054i
$694$		0			0
$695$	12.1980			0.462696
$696$		0			0
$697$	−30.7101	−	53.1914i	−1.16323	−	2.01477i
$698$		0			0
$699$	3.56028	+	6.16658i	0.134662	+	0.233242i
$700$		0			0
$701$	5.82314	−	10.0860i	0.219937	−	0.380942i	−0.734852	−	0.678228i	$-0.762748\pi$
$701$	5.82314	−	10.0860i	0.219937	−	0.380942i	0.954788	+	0.297286i	$0.0960816\pi$
$702$		0			0
$703$	−15.5362	+	0.790014i	−0.585958	+	0.0297959i
$704$		0			0
$705$	−8.69148	+	15.0541i	−0.327340	+	0.566970i
$706$		0			0
$707$	−15.8357	−	27.4282i	−0.595562	−	1.03154i
$708$		0			0
$709$	6.58645	+	11.4081i	0.247359	+	0.428439i	0.962792	−	0.270243i	$-0.0871039\pi$
$709$	6.58645	+	11.4081i	0.247359	+	0.428439i	−0.715433	+	0.698681i	$0.753771\pi$
$710$		0			0
$711$	17.4994			0.656277
$712$		0			0
$713$	12.8748	+	22.2999i	0.482167	+	0.835137i
$714$		0			0
$715$	4.56885			0.170865
$716$		0			0
$717$	11.0448	−	19.1301i	0.412474	−	0.714426i
$718$		0			0
$719$	2.43972	−	4.22572i	0.0909863	−	0.157593i	−0.816940	−	0.576723i	$-0.804331\pi$
$719$	2.43972	−	4.22572i	0.0909863	−	0.157593i	0.907926	+	0.419130i	$0.137665\pi$
$720$		0			0
$721$	−15.7065			−0.584942
$722$		0			0
$723$	14.5508			0.541150
$724$		0			0
$725$	−3.38341	+	5.86024i	−0.125657	+	0.217644i
$726$		0			0
$727$	−24.9884	+	43.2813i	−0.926770	+	1.60521i	−0.138081	+	0.990421i	$0.544093\pi$
$727$	−24.9884	+	43.2813i	−0.926770	+	1.60521i	−0.788689	+	0.614792i	$0.789240\pi$
$728$		0			0
$729$	−36.4905			−1.35150
$730$		0			0
$731$	32.4282	+	56.1672i	1.19940	+	2.07742i
$732$		0			0
$733$	−39.0493			−1.44232			−0.721159	−	0.692770i	$-0.756390\pi$
$733$	−39.0493			−1.44232			−0.721159	+	0.692770i	$0.756390\pi$
$734$		0			0
$735$	7.36834	+	12.7623i	0.271785	+	0.470746i
$736$		0			0
$737$	14.4734	+	25.0686i	0.533134	+	0.923415i
$738$		0			0
$739$	12.4020	−	21.4809i	0.456215	−	0.790187i	−0.542542	−	0.840028i	$-0.682538\pi$
$739$	12.4020	−	21.4809i	0.456215	−	0.790187i	0.998757	+	0.0498412i	$0.0158715\pi$
$740$		0			0
$741$	11.1829	−	0.568650i	0.410814	−	0.0208899i
$742$		0			0
$743$	9.92817	−	17.1961i	0.364229	−	0.630863i	−0.624423	−	0.781086i	$-0.714666\pi$
$743$	9.92817	−	17.1961i	0.364229	−	0.630863i	0.988652	+	0.150223i	$0.0479992\pi$
$744$		0			0
$745$	4.76936	+	8.26077i	0.174736	+	0.302651i
$746$		0			0
$747$	16.9171	+	29.3012i	0.618963	+	1.07208i
$748$		0			0
$749$	−49.7307			−1.81712
$750$		0			0
$751$	13.7191	+	23.7622i	0.500617	+	0.867094i	1.00000		0.000712212i	$0.000226704\pi$
$751$	13.7191	+	23.7622i	0.500617	+	0.867094i	−0.499383	+	0.866381i	$0.666440\pi$
$752$		0			0
$753$	−59.3909			−2.16432
$754$		0			0
$755$	10.2065	−	17.6783i	0.371454	−	0.643378i
$756$		0			0
$757$	−5.77540	+	10.0033i	−0.209910	+	0.363576i	−0.951686	−	0.307073i	$-0.900651\pi$
$757$	−5.77540	+	10.0033i	−0.209910	+	0.363576i	0.741776	+	0.670648i	$0.233984\pi$
$758$		0			0
$759$	−65.7136			−2.38525
$760$		0			0
$761$	−46.9940			−1.70353			−0.851766	−	0.523922i	$-0.824468\pi$
$761$	−46.9940			−1.70353			−0.851766	+	0.523922i	$0.824468\pi$
$762$		0			0
$763$	−6.83821	+	11.8441i	−0.247560	+	0.428786i
$764$		0			0
$765$	10.3231	−	17.8802i	0.373234	−	0.646460i
$766$		0			0
$767$	6.76683			0.244336
$768$		0			0
$769$	6.43719	+	11.1495i	0.232131	+	0.402063i	0.958435	−	0.285311i	$-0.0920968\pi$
$769$	6.43719	+	11.1495i	0.232131	+	0.402063i	−0.726304	+	0.687374i	$0.758763\pi$
$770$		0			0
$771$	−27.1498			−0.977776
$772$		0			0
$773$	14.0151	+	24.2748i	0.504087	+	0.873104i	0.999989	+	0.00472572i	$0.00150425\pi$
$773$	14.0151	+	24.2748i	0.504087	+	0.873104i	−0.495902	+	0.868379i	$0.665162\pi$
$774$		0			0
$775$	−2.29949	−	3.98284i	−0.0826003	−	0.143068i
$776$		0			0
$777$	−16.3593	+	28.3352i	−0.586887	+	1.01652i
$778$		0			0
$779$	21.2518	−	41.5492i	0.761423	−	1.48865i
$780$		0			0
$781$	2.35327	−	4.07599i	0.0842068	−	0.145850i
$782$		0			0
$783$	−5.20609	−	9.01722i	−0.186051	−	0.322249i
$784$		0			0
$785$	−7.15277	−	12.3890i	−0.255293	−	0.442181i
$786$		0			0
$787$	22.3478			0.796612			0.398306	−	0.917253i	$-0.369598\pi$
$787$	22.3478			0.796612			0.398306	+	0.917253i	$0.369598\pi$
$788$		0			0
$789$	−11.3830	−	19.7159i	−0.405244	−	0.701903i
$790$		0			0
$791$	−6.09042			−0.216550
$792$		0			0
$793$	4.06885	−	7.04745i	0.144489	−	0.250262i
$794$		0			0
$795$	−4.36834	+	7.56619i	−0.154929	+	0.268345i
$796$		0			0
$797$	16.3176			0.578000			0.289000	−	0.957329i	$-0.406677\pi$
$797$	16.3176			0.578000			0.289000	+	0.957329i	$0.406677\pi$
$798$		0			0
$799$	−38.8192			−1.37332
$800$		0			0
$801$	−22.0895	+	38.2601i	−0.780494	+	1.35186i
$802$		0			0
$803$	29.0960	−	50.3958i	1.02678	−	1.77843i
$804$		0			0
$805$	19.9819			0.704271
$806$		0			0
$807$	−6.85327	−	11.8702i	−0.241247	−	0.417852i
$808$		0			0
$809$	−17.1859			−0.604224			−0.302112	−	0.953272i	$-0.597692\pi$
$809$	−17.1859			−0.604224			−0.302112	+	0.953272i	$0.597692\pi$
$810$		0			0
$811$	−18.5774	−	32.1770i	−0.652342	−	1.12989i	−0.982553	−	0.185982i	$-0.940453\pi$
$811$	−18.5774	−	32.1770i	−0.652342	−	1.12989i	0.330212	−	0.943907i	$-0.392880\pi$
$812$		0			0
$813$	−5.73019	−	9.92498i	−0.200967	−	0.348084i
$814$		0			0
$815$	1.26936	−	2.19859i	0.0444636	−	0.0770132i
$816$		0			0
$817$	−22.4407	+	43.8737i	−0.785101	+	1.53495i
$818$		0			0
$819$	6.42212	−	11.1234i	0.224407	−	0.388685i
$820$		0			0
$821$	22.7638	+	39.4281i	0.794464	+	1.37605i	0.923179	+	0.384370i	$0.125581\pi$
$821$	22.7638	+	39.4281i	0.794464	+	1.37605i	−0.128716	+	0.991682i	$0.541085\pi$
$822$		0			0
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	0.971102	−	0.238664i	$-0.0767093\pi$
$823$	8.00000	+	13.8564i	0.278862	+	0.483004i	−0.692240	+	0.721668i	$0.743376\pi$
$824$		0			0
$825$	11.7367			0.408619
$826$		0			0
$827$	6.58996	+	11.4141i	0.229155	+	0.396909i	0.957558	−	0.288240i	$-0.0930703\pi$
$827$	6.58996	+	11.4141i	0.229155	+	0.396909i	−0.728403	+	0.685149i	$0.759737\pi$
$828$		0			0
$829$	−33.4503			−1.16178			−0.580888	−	0.813984i	$-0.697295\pi$
$829$	−33.4503			−1.16178			−0.580888	+	0.813984i	$0.697295\pi$
$830$		0			0
$831$	29.6412	−	51.3401i	1.02824	−	1.78097i
$832$		0			0
$833$	−16.4548	+	28.5005i	−0.570125	+	0.987485i
$834$		0			0
$835$	13.5688			0.469569
$836$		0			0
$837$	7.07651			0.244600
$838$		0			0
$839$	22.6774	−	39.2784i	0.782911	−	1.35604i	−0.147329	−	0.989088i	$-0.547068\pi$
$839$	22.6774	−	39.2784i	0.782911	−	1.35604i	0.930239	−	0.366953i	$-0.119599\pi$
$840$		0			0
$841$	−8.39497	+	14.5405i	−0.289482	+	0.501397i
$842$		0			0
$843$	10.3528			0.356570
$844$		0			0
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	35.2402			1.21087
$848$		0			0
$849$	−40.8950	−	70.8323i	−1.40351	−	2.43096i
$850$		0			0
$851$	9.99097	+	17.3049i	0.342486	+	0.593203i
$852$		0			0
$853$	5.56632	−	9.64115i	0.190587	−	0.330107i	−0.754858	−	0.655888i	$-0.772294\pi$
$853$	5.56632	−	9.64115i	0.190587	−	0.330107i	0.945445	+	0.325782i	$0.105627\pi$
$854$		0			0
$855$	15.6674	−	0.796685i	0.535813	−	0.0272461i
$856$		0			0
$857$	7.27585	−	12.6021i	0.248538	−	0.430481i	−0.714582	−	0.699552i	$-0.753383\pi$
$857$	7.27585	−	12.6021i	0.248538	−	0.430481i	0.963120	+	0.269070i	$0.0867165\pi$
$858$		0			0
$859$	5.68797	+	9.85185i	0.194071	+	0.336141i	0.946596	−	0.322423i	$-0.104497\pi$
$859$	5.68797	+	9.85185i	0.194071	+	0.336141i	−0.752525	+	0.658564i	$0.771164\pi$
$860$		0			0
$861$	−49.0780	−	85.0055i	−1.67257	−	2.89698i
$862$		0			0
$863$	0.778912			0.0265145			0.0132572	−	0.999912i	$-0.495780\pi$
$863$	0.778912			0.0265145			0.0132572	+	0.999912i	$0.495780\pi$
$864$		0			0
$865$	1.18544	+	2.05324i	0.0403060	+	0.0698121i
$866$		0			0
$867$	40.8693			1.38800
$868$		0			0
$869$	−11.1076	+	19.2389i	−0.376798	+	0.652634i
$870$		0			0
$871$	−3.16784	+	5.48686i	−0.107338	+	0.185915i
$872$		0			0
$873$	9.46220			0.320247
$874$		0			0
$875$	−3.56885			−0.120649
$876$		0			0
$877$	5.69401	−	9.86231i	0.192273	−	0.333027i	−0.753730	−	0.657184i	$-0.771747\pi$
$877$	5.69401	−	9.86231i	0.192273	−	0.333027i	0.946003	+	0.324157i	$0.105081\pi$
$878$		0			0
$879$	23.9884	−	41.5492i	0.809110	−	1.40142i
$880$		0			0
$881$	35.0171			1.17976			0.589879	−	0.807492i	$-0.299176\pi$
$881$	35.0171			1.17976			0.589879	+	0.807492i	$0.299176\pi$
$882$		0			0
$883$	−17.3171	−	29.9941i	−0.582767	−	1.00938i	−0.995150	−	0.0983709i	$-0.968637\pi$
$883$	−17.3171	−	29.9941i	−0.582767	−	1.00938i	0.412383	−	0.911010i	$-0.364696\pi$
$884$		0			0
$885$	17.3830			0.584322
$886$		0			0
$887$	−5.41608	−	9.38093i	−0.181854	−	0.314981i	0.760658	−	0.649153i	$-0.224877\pi$
$887$	−5.41608	−	9.38093i	−0.181854	−	0.314981i	−0.942512	+	0.334172i	$0.891543\pi$
$888$		0			0
$889$	−26.9045	−	46.6000i	−0.902349	−	1.56291i
$890$		0			0
$891$	15.6352	−	27.0809i	0.523798	−	0.907245i
$892$		0			0
$893$	−16.0262	−	24.7623i	−0.536295	−	0.828638i
$894$		0			0
$895$	8.93719	−	15.4797i	0.298737	−	0.517428i
$896$		0			0
$897$	−7.19148	−	12.4560i	−0.240117	−	0.415894i
$898$		0			0
$899$	−15.5603	−	26.9512i	−0.518964	−	0.898873i
$900$		0			0
$901$	−19.5105			−0.649990
$902$		0			0
$903$	51.8237	+	89.7612i	1.72458	+	2.98707i
$904$		0			0
$905$	−26.4131			−0.878001
$906$		0			0
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	−0.770996	−	0.636841i	$-0.780241\pi$
$907$	5.00000	−	8.66025i	0.166022	−	0.287559i	0.937018	+	0.349281i	$0.113574\pi$
$908$		0			0
$909$	−15.9694	+	27.6598i	−0.529672	+	0.917418i
$910$		0			0
$911$	−40.8794			−1.35440			−0.677198	−	0.735801i	$-0.736806\pi$
$911$	−40.8794			−1.35440			−0.677198	+	0.735801i	$0.736806\pi$
$912$		0			0
$913$	−42.9518			−1.42150
$914$		0			0
$915$	10.4523	−	18.1039i	0.345541	−	0.598495i
$916$		0			0
$917$	24.2126	−	41.9374i	0.799570	−	1.38490i
$918$		0			0
$919$	−10.1146			−0.333649			−0.166825	−	0.985987i	$-0.553351\pi$
$919$	−10.1146			−0.333649			−0.166825	+	0.985987i	$0.553351\pi$
$920$		0			0
$921$	40.8331	+	70.7251i	1.34550	+	2.33047i
$922$		0			0
$923$	1.03014			0.0339074
$924$		0			0
$925$	−1.78442	−	3.09071i	−0.0586715	−	0.101622i
$926$		0			0
$927$	7.91959	+	13.7171i	0.260114	+	0.450530i
$928$		0			0
$929$	−9.16134	+	15.8679i	−0.300574	+	0.520609i	−0.976266	−	0.216575i	$-0.930512\pi$
$929$	−9.16134	+	15.8679i	−0.300574	+	0.520609i	0.675692	+	0.737184i	$0.263845\pi$
$930$		0			0
$931$	−24.9734	+	1.26989i	−0.818469	+	0.0416191i
$932$		0			0
$933$	−3.04521	+	5.27446i	−0.0996956	+	0.172678i
$934$		0			0
$935$	13.1050	+	22.6986i	0.428580	+	0.742323i
$936$		0			0
$937$	7.01507	+	12.1505i	0.229172	+	0.396938i	0.957563	−	0.288224i	$-0.0930647\pi$
$937$	7.01507	+	12.1505i	0.229172	+	0.396938i	−0.728391	+	0.685162i	$0.759731\pi$
$938$		0			0
$939$	−31.3658			−1.02358
$940$		0			0
$941$	6.67641	+	11.5639i	0.217645	+	0.376972i	0.954087	−	0.299528i	$-0.0968292\pi$
$941$	6.67641	+	11.5639i	0.217645	+	0.376972i	−0.736443	+	0.676500i	$0.763496\pi$
$942$		0			0
$943$	−59.9458			−1.95211
$944$		0			0
$945$	2.74571	−	4.75572i	0.0893181	−	0.154703i
$946$		0			0
$947$	13.9247	−	24.1182i	0.452490	−	0.783736i	−0.546050	−	0.837753i	$-0.683869\pi$
$947$	13.9247	−	24.1182i	0.452490	−	0.783736i	0.998540	+	0.0540164i	$0.0172023\pi$
$948$		0			0
$949$	12.7367			0.413450
$950$		0			0
$951$	73.0664			2.36934
$952$		0			0
$953$	23.5598	−	40.8068i	0.763178	−	1.32186i	−0.178027	−	0.984026i	$-0.556972\pi$
$953$	23.5598	−	40.8068i	0.763178	−	1.32186i	0.941205	−	0.337837i	$-0.109695\pi$
$954$		0			0
$955$	0.263312	−	0.456071i	0.00852059	−	0.0147581i
$956$		0			0
$957$	79.4201			2.56729
$958$		0			0
$959$	−12.5448	−	21.7282i	−0.405091	−	0.701639i
$960$		0			0
$961$	−9.84931			−0.317720
$962$		0			0
$963$	25.0753	+	43.4318i	0.808042	+	1.39957i
$964$		0			0
$965$	−2.67037	−	4.62521i	−0.0859622	−	0.148891i
$966$		0			0
$967$	−6.19798	+	10.7352i	−0.199313	+	0.345221i	−0.948306	−	0.317357i	$-0.897205\pi$
$967$	−6.19798	+	10.7352i	−0.199313	+	0.345221i	0.748993	+	0.662578i	$0.230538\pi$
$968$		0			0
$969$	34.9015	+	53.9269i	1.12120	+	1.73238i
$970$		0			0
$971$	24.0925	−	41.7294i	0.773165	−	1.33916i	−0.162655	−	0.986683i	$-0.552006\pi$
$971$	24.0925	−	41.7294i	0.773165	−	1.33916i	0.935820	−	0.352478i	$-0.114661\pi$
$972$		0			0
$973$	21.7664	+	37.7005i	0.697798	+	1.20862i
$974$		0			0
$975$	1.28442	+	2.22469i	0.0411345	+	0.0712471i
$976$		0			0
$977$	4.86736			0.155721			0.0778603	−	0.996964i	$-0.475191\pi$
$977$	4.86736			0.155721			0.0778603	+	0.996964i	$0.475191\pi$
$978$		0			0
$979$	−28.0422	−	48.5706i	−0.896233	−	1.55232i
$980$		0			0
$981$	13.7919			0.440342
$982$		0			0
$983$	−11.7251	+	20.3085i	−0.373974	+	0.647741i	−0.990173	−	0.139849i	$-0.955338\pi$
$983$	−11.7251	+	20.3085i	−0.373974	+	0.647741i	0.616199	+	0.787590i	$0.288672\pi$
$984$		0			0
$985$	−2.21558	+	3.83749i	−0.0705941	+	0.122273i
$986$		0			0
$987$	−62.0372			−1.97466
$988$		0			0
$989$	63.2996			2.01281
$990$		0			0
$991$	−23.5688	+	40.8224i	−0.748689	+	1.29677i	0.199762	+	0.979844i	$0.435983\pi$
$991$	−23.5688	+	40.8224i	−0.748689	+	1.29677i	−0.948451	+	0.316923i	$0.897350\pi$
$992$		0			0
$993$	41.8633	−	72.5093i	1.32849	−	2.30101i
$994$		0			0
$995$	−12.1678			−0.385746
$996$		0			0
$997$	8.74526	+	15.1472i	0.276965	+	0.479718i	0.970629	−	0.240581i	$-0.0773380\pi$
$997$	8.74526	+	15.1472i	0.276965	+	0.479718i	−0.693664	+	0.720299i	$0.744005\pi$
$998$		0			0
$999$	5.49143			0.173741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.i.b.201.1	yes	6
3.2	odd	2		3420.2.t.v.3241.3		6
4.3	odd	2		1520.2.q.i.961.3		6
5.2	odd	4		1900.2.s.c.49.5		12
5.3	odd	4		1900.2.s.c.49.2		12
5.4	even	2		1900.2.i.c.201.3		6
19.7	even	3	inner	380.2.i.b.121.1	✓	6
19.8	odd	6		7220.2.a.o.1.1		3
19.11	even	3		7220.2.a.n.1.3		3
57.26	odd	6		3420.2.t.v.1261.3		6
76.7	odd	6		1520.2.q.i.881.3		6
95.7	odd	12		1900.2.s.c.349.2		12
95.64	even	6		1900.2.i.c.501.3		6
95.83	odd	12		1900.2.s.c.349.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.1	✓	6	19.7	even	3	inner
380.2.i.b.201.1	yes	6	1.1	even	1	trivial
1520.2.q.i.881.3		6	76.7	odd	6
1520.2.q.i.961.3		6	4.3	odd	2
1900.2.i.c.201.3		6	5.4	even	2
1900.2.i.c.501.3		6	95.64	even	6
1900.2.s.c.49.2		12	5.3	odd	4
1900.2.s.c.49.5		12	5.2	odd	4
1900.2.s.c.349.2		12	95.7	odd	12
1900.2.s.c.349.5		12	95.83	odd	12
3420.2.t.v.1261.3		6	57.26	odd	6
3420.2.t.v.3241.3		6	3.2	odd	2
7220.2.a.n.1.3		3	19.11	even	3
7220.2.a.o.1.1		3	19.8	odd	6

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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28442 + 2.22469i) q^{3} +(0.500000 - 0.866025i) q^{5} +3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(0.500000 + 0.866025i) q^{13} +(1.28442 + 2.22469i) q^{15} +(-2.86834 + 4.96812i) q^{17} +(-4.35327 + 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(2.79949 + 4.84887i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.53871 q^{27} +(-3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(-5.86834 + 10.1643i) q^{33} +(1.78442 - 3.09071i) q^{35} +3.56885 q^{37} -2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(5.65277 - 9.79088i) q^{43} -3.59899 q^{45} +(3.38341 + 5.86024i) q^{47} +5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(1.70051 + 2.94536i) q^{53} +(2.28442 - 3.95674i) q^{55} +(5.09899 - 9.96901i) q^{57} +(3.38341 - 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(-6.42212 - 11.1234i) q^{63} +1.00000 q^{65} +(3.16784 + 5.48686i) q^{67} -14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(6.36834 - 11.0303i) q^{73} +2.56885 q^{75} +16.3055 q^{77} +(-2.43115 + 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} -9.40101 q^{83} +(2.86834 + 4.96812i) q^{85} +17.3830 q^{87} +(-6.13770 - 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(-5.90705 + 10.2313i) q^{93} +(-1.98493 + 3.88073i) q^{95} +(-1.31456 + 2.27689i) q^{97} +(-8.22162 - 14.2403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 3 q^{5} + 4 q^{7} - 8 q^{9} + 10 q^{11} + 3 q^{13} - q^{15} + 3 q^{17} - 16 q^{21} + 14 q^{23} - 3 q^{25} - 20 q^{27} - 6 q^{29} + 22 q^{31} - 15 q^{33} + 2 q^{35} + 4 q^{37} + 2 q^{39}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + q^3 + 3 * q^5 + 4 * q^7 - 8 * q^9 + 10 * q^11 + 3 * q^13 - q^15 + 3 * q^17 - 16 * q^21 + 14 * q^23 - 3 * q^25 - 20 * q^27 - 6 * q^29 + 22 * q^31 - 15 * q^33 + 2 * q^35 + 4 * q^37 + 2 * q^39 - 6 * q^41 + 5 * q^43 - 16 * q^45 + 6 * q^47 - 6 * q^49 - 24 * q^51 + 13 * q^53 + 5 * q^55 + 25 * q^57 + 6 * q^59 - 7 * q^61 + 5 * q^63 + 6 * q^65 - 4 * q^67 + 30 * q^69 + 9 * q^71 + 18 * q^73 - 2 * q^75 + 40 * q^77 - 32 * q^79 - 23 * q^81 - 62 * q^83 - 3 * q^85 - 12 * q^87 - 2 * q^89 + 2 * q^91 + 14 * q^93 - 6 * q^95 - 11 * q^97 - 3 * q^99

Introduction

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