LMFDB - Embedded newform 380.2.r.a.349.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(49,380)]

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, 3, 4]))

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

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

chi := DirichletCharacter("380.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.9
Root			$2.10552 + 1.21562i$ of defining polynomial
Character	$\chi$	$=$	380.349
Dual form			380.2.r.a.49.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.10552 - 1.21562i) q^{3} +(2.22225 + 0.248224i) q^{5} -0.663818i q^{7} +(1.45548 - 2.52097i) q^{9} +O(q^{10})$	\(q+(2.10552 - 1.21562i) q^{3} +(2.22225 + 0.248224i) q^{5} -0.663818i q^{7} +(1.45548 - 2.52097i) q^{9} -1.80905 q^{11} +(1.99526 + 1.15197i) q^{13} +(4.98074 - 2.17878i) q^{15} +(-3.77643 + 2.18033i) q^{17} +(-4.21168 - 1.12329i) q^{19} +(-0.806953 - 1.39768i) q^{21} +(1.81374 + 1.04716i) q^{23} +(4.87677 + 1.10323i) q^{25} +0.216466i q^{27} +(0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(-3.80900 + 2.19913i) q^{33} +(0.164775 - 1.47517i) q^{35} -2.97461i q^{37} +5.60143 q^{39} +(-0.247657 - 0.428954i) q^{41} +(6.81715 - 3.93588i) q^{43} +(3.86021 - 5.24093i) q^{45} +(-5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-5.30091 + 9.18145i) q^{51} +(1.99575 + 1.15225i) q^{53} +(-4.02016 - 0.449050i) q^{55} +(-10.2333 + 2.75471i) q^{57} +(3.88559 + 6.73003i) q^{59} +(-5.36021 + 9.28415i) q^{61} +(-1.67347 - 0.966176i) q^{63} +(4.14802 + 3.05522i) q^{65} +(3.96984 + 2.29199i) q^{67} +5.09182 q^{69} +(-2.95914 - 5.12538i) q^{71} +(-4.86313 + 2.80773i) q^{73} +(11.6093 - 3.60545i) q^{75} +1.20088i q^{77} +(-2.99810 - 5.19286i) q^{79} +(4.62959 + 8.01868i) q^{81} -6.20090i q^{83} +(-8.93338 + 3.90782i) q^{85} -4.73909i q^{87} +(-6.65028 + 11.5186i) q^{89} +(0.764696 - 1.32449i) q^{91} +(-20.0557 + 11.5791i) q^{93} +(-9.08057 - 3.54166i) q^{95} +(8.80695 - 5.08470i) q^{97} +(-2.63305 + 4.56057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q + q^5 + 10 * q^9	$ 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65} + 48 q^{69} - 2 q^{71} + 46 q^{75} - 16 q^{79} + 26 q^{81} - 39 q^{85} - 40 q^{89} - 4 q^{91} - 43 q^{95} - 20 q^{99}+O(q^{100}) $ 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	2.10552	−	1.21562i	1.21562	−	0.701841i	0.251645	−	0.967820i	$-0.419028\pi$
$3$	2.10552	−	1.21562i	1.21562	−	0.701841i	0.963979	+	0.265979i	$0.0856951\pi$
$4$		0			0
$5$	2.22225	+	0.248224i	0.993819	+	0.111009i
$5$	2.22225	+	0.248224i	0.993819	+	0.111009i
$6$		0			0
$7$		−	0.663818i		−	0.250900i	−0.992100	−	0.125450i	$-0.959963\pi$
$7$		−	0.663818i		−	0.250900i	0.992100	−	0.125450i	$-0.0400374\pi$
$8$		0			0
$9$	1.45548	−	2.52097i	0.485161	−	0.840323i
$10$		0			0
$11$	−1.80905			−0.545450			−0.272725	−	0.962092i	$-0.587925\pi$
$11$	−1.80905			−0.545450			−0.272725	+	0.962092i	$0.587925\pi$
$12$		0			0
$13$	1.99526	+	1.15197i	0.553386	+	0.319498i	0.750487	−	0.660886i	$-0.229819\pi$
$13$	1.99526	+	1.15197i	0.553386	+	0.319498i	−0.197100	+	0.980383i	$0.563153\pi$
$14$		0			0
$15$	4.98074	−	2.17878i	1.28602	−	0.562558i
$16$		0			0
$17$	−3.77643	+	2.18033i	−0.915920	+	0.528807i	−0.882331	−	0.470629i	$-0.844027\pi$
$17$	−3.77643	+	2.18033i	−0.915920	+	0.528807i	−0.0335887	+	0.999436i	$0.510694\pi$
$18$		0			0
$19$	−4.21168	−	1.12329i	−0.966225	−	0.257699i
$19$	−4.21168	−	1.12329i	−0.966225	−	0.257699i
$20$		0			0
$21$	−0.806953	−	1.39768i	−0.176092	−	0.305000i
$22$		0			0
$23$	1.81374	+	1.04716i	0.378191	+	0.218349i	0.677031	−	0.735955i	$-0.263266\pi$
$23$	1.81374	+	1.04716i	0.378191	+	0.218349i	−0.298840	+	0.954303i	$0.596600\pi$
$24$		0			0
$25$	4.87677	+	1.10323i	0.975354	+	0.220646i
$26$		0			0
$27$			0.216466i			0.0416588i
$28$		0			0
$29$	0.974621	−	1.68809i	0.180983	−	0.313471i	−0.761233	−	0.648479i	$-0.775406\pi$
$29$	0.974621	−	1.68809i	0.180983	−	0.313471i	0.942215	+	0.335008i	$0.108739\pi$
$30$		0			0
$31$	−9.52527			−1.71079			−0.855394	−	0.517977i	$-0.826685\pi$
$31$	−9.52527			−1.71079			−0.855394	+	0.517977i	$0.826685\pi$
$32$		0			0
$33$	−3.80900	+	2.19913i	−0.663062	+	0.382819i
$34$		0			0
$35$	0.164775	−	1.47517i	0.0278521	−	0.249349i
$36$		0			0
$37$		−	2.97461i		−	0.489023i	−0.969646	−	0.244511i	$-0.921372\pi$
$37$		−	2.97461i		−	0.489023i	0.969646	−	0.244511i	$-0.0786276\pi$
$38$		0			0
$39$	5.60143			0.896946
$40$		0			0
$41$	−0.247657	−	0.428954i	−0.0386775	−	0.0669914i	0.846039	−	0.533122i	$-0.178981\pi$
$41$	−0.247657	−	0.428954i	−0.0386775	−	0.0669914i	−0.884716	+	0.466130i	$0.845648\pi$
$42$		0			0
$43$	6.81715	−	3.93588i	1.03960	−	0.600216i	0.119884	−	0.992788i	$-0.461748\pi$
$43$	6.81715	−	3.93588i	1.03960	−	0.600216i	0.919721	+	0.392572i	$0.128415\pi$
$44$		0			0
$45$	3.86021	−	5.24093i	0.575446	−	0.781272i
$46$		0			0
$47$	−5.69449	−	3.28772i	−0.830627	−	0.479563i	0.0234403	−	0.999725i	$-0.492538\pi$
$47$	−5.69449	−	3.28772i	−0.830627	−	0.479563i	−0.854067	+	0.520163i	$0.825871\pi$
$48$		0			0
$49$	6.55935			0.937049
$50$		0			0
$51$	−5.30091	+	9.18145i	−0.742276	+	1.28566i
$52$		0			0
$53$	1.99575	+	1.15225i	0.274137	+	0.158273i	0.630766	−	0.775973i	$-0.282741\pi$
$53$	1.99575	+	1.15225i	0.274137	+	0.158273i	−0.356629	+	0.934246i	$0.616074\pi$
$54$		0			0
$55$	−4.02016	−	0.449050i	−0.542079	−	0.0605498i
$56$		0			0
$57$	−10.2333	+	2.75471i	−1.35543	+	0.364871i
$58$		0			0
$59$	3.88559	+	6.73003i	0.505860	+	0.876176i	0.999977	+	0.00678007i	$0.00215818\pi$
$59$	3.88559	+	6.73003i	0.505860	+	0.876176i	−0.494117	+	0.869396i	$0.664508\pi$
$60$		0			0
$61$	−5.36021	+	9.28415i	−0.686304	+	1.18871i	0.286721	+	0.958014i	$0.407435\pi$
$61$	−5.36021	+	9.28415i	−0.686304	+	1.18871i	−0.973025	+	0.230700i	$0.925899\pi$
$62$		0			0
$63$	−1.67347	−	0.966176i	−0.210837	−	0.121727i
$64$		0			0
$65$	4.14802	+	3.05522i	0.514499	+	0.378954i
$66$		0			0
$67$	3.96984	+	2.29199i	0.484993	+	0.280011i	0.722495	−	0.691376i	$-0.242995\pi$
$67$	3.96984	+	2.29199i	0.484993	+	0.280011i	−0.237502	+	0.971387i	$0.576329\pi$
$68$		0			0
$69$	5.09182			0.612984
$70$		0			0
$71$	−2.95914	−	5.12538i	−0.351185	−	0.608270i	0.635272	−	0.772288i	$-0.280888\pi$
$71$	−2.95914	−	5.12538i	−0.351185	−	0.608270i	−0.986457	+	0.164018i	$0.947554\pi$
$72$		0			0
$73$	−4.86313	+	2.80773i	−0.569187	+	0.328620i	−0.756824	−	0.653618i	$-0.773250\pi$
$73$	−4.86313	+	2.80773i	−0.569187	+	0.328620i	0.187638	+	0.982238i	$0.439917\pi$
$74$		0			0
$75$	11.6093	−	3.60545i	1.34052	−	0.416321i
$76$		0			0
$77$			1.20088i			0.136853i
$78$		0			0
$79$	−2.99810	−	5.19286i	−0.337312	−	0.584242i	0.646614	−	0.762817i	$-0.276185\pi$
$79$	−2.99810	−	5.19286i	−0.337312	−	0.584242i	−0.983926	+	0.178575i	$0.942851\pi$
$80$		0			0
$81$	4.62959	+	8.01868i	0.514399	+	0.890965i
$82$		0			0
$83$		−	6.20090i		−	0.680638i	−0.940310	−	0.340319i	$-0.889465\pi$
$83$		−	6.20090i		−	0.680638i	0.940310	−	0.340319i	$-0.110535\pi$
$84$		0			0
$85$	−8.93338	+	3.90782i	−0.968961	+	0.423863i
$86$		0			0
$87$		−	4.73909i		−	0.508084i
$88$		0			0
$89$	−6.65028	+	11.5186i	−0.704928	+	1.22097i	0.261789	+	0.965125i	$0.415688\pi$
$89$	−6.65028	+	11.5186i	−0.704928	+	1.22097i	−0.966717	+	0.255847i	$0.917646\pi$
$90$		0			0
$91$	0.764696	−	1.32449i	0.0801619	−	0.138844i
$92$		0			0
$93$	−20.0557	+	11.5791i	−2.07968	+	1.20070i
$94$		0			0
$95$	−9.08057	−	3.54166i	−0.931646	−	0.363366i
$96$		0			0
$97$	8.80695	−	5.08470i	0.894211	−	0.516273i	0.0188932	−	0.999822i	$-0.493986\pi$
$97$	8.80695	−	5.08470i	0.894211	−	0.516273i	0.875317	+	0.483549i	$0.160652\pi$
$98$		0			0
$99$	−2.63305	+	4.56057i	−0.264631	+	0.458354i
$100$		0			0
$101$	−7.48770	+	12.9691i	−0.745054	+	1.29047i	0.205116	+	0.978738i	$0.434243\pi$
$101$	−7.48770	+	12.9691i	−0.745054	+	1.29047i	−0.950170	+	0.311733i	$0.899091\pi$
$102$		0			0
$103$		−	18.1501i		−	1.78839i	−0.447681	−	0.894193i	$-0.647750\pi$
$103$		−	18.1501i		−	1.78839i	0.447681	−	0.894193i	$-0.352250\pi$
$104$		0			0
$105$	−1.44631	−	3.30631i	−0.141146	−	0.322662i
$106$		0			0
$107$			13.9698i			1.35051i	0.737584	+	0.675256i	$0.235967\pi$
$107$			13.9698i			1.35051i	−0.737584	+	0.675256i	$0.764033\pi$
$108$		0			0
$109$	−9.20544	−	15.9443i	−0.881721	−	1.52719i	−0.849426	−	0.527707i	$-0.823052\pi$
$109$	−9.20544	−	15.9443i	−0.881721	−	1.52719i	−0.0322945	−	0.999478i	$-0.510281\pi$
$110$		0			0
$111$	−3.61601	−	6.26311i	−0.343216	−	0.594468i
$112$		0			0
$113$			10.8946i			1.02487i	0.858725	+	0.512437i	$0.171257\pi$
$113$			10.8946i			1.02487i	−0.858725	+	0.512437i	$0.828743\pi$
$114$		0			0
$115$	3.77065	+	2.77727i	0.351615	+	0.258982i
$116$		0			0
$117$	5.80814	−	3.35333i	0.536963	−	0.310016i
$118$		0			0
$119$	1.44734	+	2.50687i	0.132677	+	0.229804i
$120$		0			0
$121$	−7.72733			−0.702484
$122$		0			0
$123$	−1.04289	−	0.602115i	−0.0940346	−	0.0542909i
$124$		0			0
$125$	10.5635	+	3.66218i	0.944832	+	0.327555i
$126$		0			0
$127$	−2.86242	−	1.65262i	−0.253998	−	0.146646i	0.367595	−	0.929986i	$-0.380181\pi$
$127$	−2.86242	−	1.65262i	−0.253998	−	0.146646i	−0.621594	+	0.783340i	$0.713514\pi$
$128$		0			0
$129$	9.56910	−	16.5742i	0.842512	−	1.45927i
$130$		0			0
$131$	−0.646627	−	1.11999i	−0.0564961	−	0.0978541i	0.836394	−	0.548128i	$-0.184660\pi$
$131$	−0.646627	−	1.11999i	−0.0564961	−	0.0978541i	−0.892890	+	0.450274i	$0.851326\pi$
$132$		0			0
$133$	−0.745658	+	2.79579i	−0.0646567	+	0.242426i
$134$		0			0
$135$	−0.0537319	+	0.481040i	−0.00462450	+	0.0414014i
$136$		0			0
$137$	12.6426	+	7.29920i	1.08013	+	0.623613i	0.930931	−	0.365195i	$-0.118998\pi$
$137$	12.6426	+	7.29920i	1.08013	+	0.623613i	0.149197	+	0.988807i	$0.452331\pi$
$138$		0			0
$139$	−1.87915	+	3.25478i	−0.159387	+	0.276067i	−0.934648	−	0.355575i	$-0.884285\pi$
$139$	−1.87915	+	3.25478i	−0.159387	+	0.276067i	0.775261	+	0.631641i	$0.217618\pi$
$140$		0			0
$141$	−15.9865			−1.34631
$142$		0			0
$143$	−3.60954	−	2.08397i	−0.301844	−	0.174270i
$144$		0			0
$145$	2.58487	−	3.50944i	0.214662	−	0.291443i
$146$		0			0
$147$	13.8108	−	7.97370i	1.13910	−	0.657659i
$148$		0			0
$149$	3.83653	+	6.64507i	0.314301	+	0.544385i	0.979289	−	0.202469i	$-0.0648966\pi$
$149$	3.83653	+	6.64507i	0.314301	+	0.544385i	−0.664988	+	0.746854i	$0.731563\pi$
$150$		0			0
$151$	1.62643			0.132357			0.0661785	−	0.997808i	$-0.478919\pi$
$151$	1.62643			0.132357			0.0661785	+	0.997808i	$0.478919\pi$
$152$		0			0
$153$			12.6937i			1.02622i
$154$		0			0
$155$	−21.1675	−	2.36440i	−1.70021	−	0.189913i
$156$		0			0
$157$	2.29893	−	1.32729i	0.183474	−	0.105929i	−0.405450	−	0.914117i	$-0.632885\pi$
$157$	2.29893	−	1.32729i	0.183474	−	0.105929i	0.588924	+	0.808188i	$0.299552\pi$
$158$		0			0
$159$	5.60279			0.444331
$160$		0			0
$161$	0.695126	−	1.20399i	0.0547836	−	0.0948880i
$162$		0			0
$163$		−	19.8052i		−	1.55127i	−0.631184	−	0.775633i	$-0.717431\pi$
$163$		−	19.8052i		−	1.55127i	0.631184	−	0.775633i	$-0.282569\pi$
$164$		0			0
$165$	−9.01042	+	3.94152i	−0.701460	+	0.306847i
$166$		0			0
$167$	0.0776925	+	0.0448558i	0.00601203	+	0.00347105i	0.503003	−	0.864285i	$-0.332228\pi$
$167$	0.0776925	+	0.0448558i	0.00601203	+	0.00347105i	−0.496991	+	0.867756i	$0.665562\pi$
$168$		0			0
$169$	−3.84595	−	6.66139i	−0.295842	−	0.512414i
$170$		0			0
$171$	−8.96179	+	8.98259i	−0.685325	+	0.686916i
$172$		0			0
$173$	13.7120	−	7.91662i	1.04250	−	0.601889i	0.121962	−	0.992535i	$-0.461082\pi$
$173$	13.7120	−	7.91662i	1.04250	−	0.601889i	0.920541	+	0.390646i	$0.127748\pi$
$174$		0			0
$175$	0.732343	−	3.23729i	0.0553599	−	0.244716i
$176$		0			0
$177$	16.3624	+	9.44682i	1.22987	+	0.710067i
$178$		0			0
$179$	13.5051			1.00942			0.504709	−	0.863290i	$-0.331600\pi$
$179$	13.5051			1.00942			0.504709	+	0.863290i	$0.331600\pi$
$180$		0			0
$181$	4.78591	−	8.28945i	0.355734	−	0.616150i	−0.631509	−	0.775368i	$-0.717564\pi$
$181$	4.78591	−	8.28945i	0.355734	−	0.616150i	0.987243	+	0.159219i	$0.0508975\pi$
$182$		0			0
$183$			26.0640i			1.92670i
$184$		0			0
$185$	0.738368	−	6.61032i	0.0542859	−	0.486000i
$186$		0			0
$187$	6.83177	−	3.94432i	0.499588	−	0.288438i
$188$		0			0
$189$	0.143694			0.0104522
$190$		0			0
$191$	26.9010			1.94649			0.973243	−	0.229778i	$-0.0738000\pi$
$191$	26.9010			1.94649			0.973243	+	0.229778i	$0.0738000\pi$
$192$		0			0
$193$	19.7692	−	11.4137i	1.42302	−	0.821579i	0.426461	−	0.904506i	$-0.359760\pi$
$193$	19.7692	−	11.4137i	1.42302	−	0.821579i	0.996556	+	0.0829272i	$0.0264269\pi$
$194$		0			0
$195$	12.4478	+	1.39041i	0.891402	+	0.0995690i
$196$		0			0
$197$		−	10.4172i		−	0.742192i	−0.928594	−	0.371096i	$-0.878982\pi$
$197$		−	10.4172i		−	0.742192i	0.928594	−	0.371096i	$-0.121018\pi$
$198$		0			0
$199$	0.782081	−	1.35460i	0.0554403	−	0.0960254i	−0.836973	−	0.547244i	$-0.815677\pi$
$199$	0.782081	−	1.35460i	0.0554403	−	0.0960254i	0.892414	+	0.451218i	$0.149010\pi$
$200$		0			0
$201$	11.1448			0.786092
$202$		0			0
$203$	−1.12059	−	0.646971i	−0.0786498	−	0.0454085i
$204$		0			0
$205$	−0.443879	−	1.01472i	−0.0310018	−	0.0708709i
$206$		0			0
$207$	5.27973	−	3.04825i	0.366967	−	0.211868i
$208$		0			0
$209$	7.61915	+	2.03208i	0.527028	+	0.140562i
$210$		0			0
$211$	−10.4253	−	18.0571i	−0.717704	−	1.24310i	−0.961907	−	0.273376i	$-0.911860\pi$
$211$	−10.4253	−	18.0571i	−0.717704	−	1.24310i	0.244203	−	0.969724i	$-0.421474\pi$
$212$		0			0
$213$	−12.4611	−	7.19439i	−0.853818	−	0.492952i
$214$		0			0
$215$	16.1264	−	7.05433i	1.09981	−	0.481101i
$216$		0			0
$217$			6.32305i			0.429236i
$218$		0			0
$219$	−6.82629	+	11.8235i	−0.461278	+	0.798957i
$220$		0			0
$221$	−10.0466			−0.675810
$222$		0			0
$223$	19.5472	−	11.2856i	1.30898	−	0.755740i	0.327054	−	0.945006i	$-0.393944\pi$
$223$	19.5472	−	11.2856i	1.30898	−	0.755740i	0.981926	+	0.189266i	$0.0606108\pi$
$224$		0			0
$225$	9.87926	−	10.6885i	0.658617	−	0.712564i
$226$		0			0
$227$			11.4187i			0.757883i	0.925421	+	0.378941i	$0.123712\pi$
$227$			11.4187i			0.757883i	−0.925421	+	0.378941i	$0.876288\pi$
$228$		0			0
$229$	15.8237			1.04566			0.522829	−	0.852438i	$-0.324877\pi$
$229$	15.8237			1.04566			0.522829	+	0.852438i	$0.324877\pi$
$230$		0			0
$231$	1.45982	+	2.52849i	0.0960492	+	0.166362i
$232$		0			0
$233$	−11.6621	+	6.73314i	−0.764013	+	0.441103i	−0.830735	−	0.556669i	$-0.812079\pi$
$233$	−11.6621	+	6.73314i	−0.764013	+	0.441103i	0.0667219	+	0.997772i	$0.478746\pi$
$234$		0			0
$235$	−11.8385	−	8.71963i	−0.772257	−	0.568806i
$236$		0			0
$237$	−12.6251	−	7.28912i	−0.820090	−	0.473479i
$238$		0			0
$239$	−19.7437			−1.27711			−0.638557	−	0.769574i	$-0.720468\pi$
$239$	−19.7437			−1.27711			−0.638557	+	0.769574i	$0.720468\pi$
$240$		0			0
$241$	2.69793	−	4.67295i	0.173789	−	0.301011i	−0.765953	−	0.642897i	$-0.777732\pi$
$241$	2.69793	−	4.67295i	0.173789	−	0.301011i	0.939742	+	0.341886i	$0.111066\pi$
$242$		0			0
$243$	18.9330	+	10.9310i	1.21455	+	0.701223i
$244$		0			0
$245$	14.5765	+	1.62818i	0.931258	+	0.104021i
$246$		0			0
$247$	−7.10942	−	7.09296i	−0.452361	−	0.451314i
$248$		0			0
$249$	−7.53797	−	13.0561i	−0.477699	−	0.827399i
$250$		0			0
$251$	1.78646	−	3.09424i	0.112760	−	0.195306i	−0.804122	−	0.594464i	$-0.797364\pi$
$251$	1.78646	−	3.09424i	0.112760	−	0.195306i	0.916882	+	0.399158i	$0.130697\pi$
$252$		0			0
$253$	−3.28115	−	1.89437i	−0.206284	−	0.119098i
$254$		0			0
$255$	−14.0590	+	19.0876i	−0.880408	+	1.19531i
$256$		0			0
$257$	−16.0500	−	9.26649i	−1.00117	−	0.578028i	−0.0925780	−	0.995705i	$-0.529511\pi$
$257$	−16.0500	−	9.26649i	−1.00117	−	0.578028i	−0.908595	+	0.417678i	$0.862844\pi$
$258$		0			0
$259$	−1.97460			−0.122696
$260$		0			0
$261$	−2.83709	−	4.91398i	−0.175611	−	0.304168i
$262$		0			0
$263$	−9.30609	+	5.37288i	−0.573838	+	0.331306i	−0.758681	−	0.651462i	$-0.774156\pi$
$263$	−9.30609	+	5.37288i	−0.573838	+	0.331306i	0.184843	+	0.982768i	$0.440822\pi$
$264$		0			0
$265$	4.14904	+	3.05597i	0.254873	+	0.187727i
$266$		0			0
$267$			32.3370i			1.97899i
$268$		0			0
$269$	−6.05027	−	10.4794i	−0.368892	−	0.638939i	0.620501	−	0.784206i	$-0.286929\pi$
$269$	−6.05027	−	10.4794i	−0.368892	−	0.638939i	−0.989393	+	0.145267i	$0.953596\pi$
$270$		0			0
$271$	9.34472	+	16.1855i	0.567651	+	0.983201i	0.996798	+	0.0799661i	$0.0254812\pi$
$271$	9.34472	+	16.1855i	0.567651	+	0.983201i	−0.429146	+	0.903235i	$0.641185\pi$
$272$		0			0
$273$		−	3.71833i		−	0.225044i
$274$		0			0
$275$	−8.82234	−	1.99580i	−0.532007	−	0.120351i
$276$		0			0
$277$		−	5.94922i		−	0.357454i	−0.983899	−	0.178727i	$-0.942802\pi$
$277$		−	5.94922i		−	0.357454i	0.983899	−	0.178727i	$-0.0571979\pi$
$278$		0			0
$279$	−13.8639	+	24.0129i	−0.830008	+	1.43762i
$280$		0			0
$281$	8.78943	−	15.2237i	0.524333	−	0.908172i	−0.475265	−	0.879843i	$-0.657648\pi$
$281$	8.78943	−	15.2237i	0.524333	−	0.908172i	0.999599	−	0.0283294i	$-0.00901874\pi$
$282$		0			0
$283$	−27.2029	+	15.7056i	−1.61705	+	0.933603i	−0.629368	+	0.777107i	$0.716686\pi$
$283$	−27.2029	+	15.7056i	−1.61705	+	0.933603i	−0.987679	+	0.156495i	$0.949980\pi$
$284$		0			0
$285$	−23.4247	+	3.58152i	−1.38756	+	0.212151i
$286$		0			0
$287$	−0.284748	+	0.164399i	−0.0168081	+	0.00970418i
$288$		0			0
$289$	1.00764	−	1.74528i	0.0592727	−	0.102663i
$290$		0			0
$291$	12.3622	−	21.4119i	0.724682	−	1.25519i
$292$		0			0
$293$		−	28.1435i		−	1.64416i	−0.569372	−	0.822080i	$-0.692814\pi$
$293$		−	28.1435i		−	1.64416i	0.569372	−	0.822080i	$-0.307186\pi$
$294$		0			0
$295$	6.96418	+	15.9203i	0.405470	+	0.926915i
$296$		0			0
$297$		−	0.391598i		−	0.0227228i
$298$		0			0
$299$	2.41259	+	4.17873i	0.139524	+	0.241662i
$300$		0			0
$301$	−2.61271	−	4.52535i	−0.150594	−	0.260837i
$302$		0			0
$303$			36.4089i			2.09164i
$304$		0			0
$305$	−14.2163	+	19.3012i	−0.814020	+	1.10518i
$306$		0			0
$307$	−23.3588	+	13.4862i	−1.33316	+	0.769698i	−0.985782	−	0.168028i	$-0.946260\pi$
$307$	−23.3588	+	13.4862i	−1.33316	+	0.769698i	−0.347374	+	0.937727i	$0.612927\pi$
$308$		0			0
$309$	−22.0637	−	38.2155i	−1.25516	−	2.17401i
$310$		0			0
$311$	−4.99721			−0.283366			−0.141683	−	0.989912i	$-0.545251\pi$
$311$	−4.99721			−0.283366			−0.141683	+	0.989912i	$0.545251\pi$
$312$		0			0
$313$	22.6484	+	13.0761i	1.28017	+	0.739104i	0.976878	−	0.213795i	$-0.0685825\pi$
$313$	22.6484	+	13.0761i	1.28017	+	0.739104i	0.303287	+	0.952899i	$0.401916\pi$
$314$		0			0
$315$	−3.47903	−	2.56248i	−0.196021	−	0.144379i
$316$		0			0
$317$	−22.5314	−	13.0085i	−1.26549	−	0.730632i	−0.291359	−	0.956614i	$-0.594108\pi$
$317$	−22.5314	−	13.0085i	−1.26549	−	0.730632i	−0.974131	+	0.225982i	$0.927441\pi$
$318$		0			0
$319$	−1.76314	+	3.05385i	−0.0987169	+	0.170983i
$320$		0			0
$321$	16.9820	+	29.4137i	0.947844	+	1.64171i
$322$		0			0
$323$	18.3543	−	4.94081i	1.02126	−	0.274914i
$324$		0			0
$325$	8.45955	+	7.81910i	0.469252	+	0.433726i
$326$		0			0
$327$	−38.7645	−	22.3807i	−2.14368	−	1.23766i
$328$		0			0
$329$	−2.18245	+	3.78011i	−0.120322	+	0.208404i
$330$		0			0
$331$	7.97402			0.438292			0.219146	−	0.975692i	$-0.429673\pi$
$331$	7.97402			0.438292			0.219146	+	0.975692i	$0.429673\pi$
$332$		0			0
$333$	−7.49890	−	4.32949i	−0.410937	−	0.237255i
$334$		0			0
$335$	8.25304	+	6.07877i	0.450912	+	0.332119i
$336$		0			0
$337$	3.42862	−	1.97951i	0.186769	−	0.107831i	−0.403700	−	0.914891i	$-0.632276\pi$
$337$	3.42862	−	1.97951i	0.186769	−	0.107831i	0.590469	+	0.807060i	$0.298943\pi$
$338$		0			0
$339$	13.2437	+	22.9387i	0.719299	+	1.24586i
$340$		0			0
$341$	17.2317			0.933150
$342$		0			0
$343$		−	9.00094i		−	0.486005i
$344$		0			0
$345$	11.3153	+	1.26391i	0.609195	+	0.0680467i
$346$		0			0
$347$	−4.16047	+	2.40205i	−0.223345	+	0.128949i	−0.607498	−	0.794321i	$-0.707827\pi$
$347$	−4.16047	+	2.40205i	−0.223345	+	0.128949i	0.384153	+	0.923269i	$0.374494\pi$
$348$		0			0
$349$	−9.02058			−0.482861			−0.241430	−	0.970418i	$-0.577617\pi$
$349$	−9.02058			−0.482861			−0.241430	+	0.970418i	$0.577617\pi$
$350$		0			0
$351$	−0.249361	+	0.431906i	−0.0133099	+	0.0230534i
$352$		0			0
$353$		−	18.0910i		−	0.962889i	−0.876477	−	0.481444i	$-0.840112\pi$
$353$		−	18.0910i		−	0.962889i	0.876477	−	0.481444i	$-0.159888\pi$
$354$		0			0
$355$	−5.30370	−	12.1244i	−0.281491	−	0.643495i
$356$		0			0
$357$	6.09481	+	3.51884i	0.322572	+	0.186237i
$358$		0			0
$359$	17.4849	+	30.2848i	0.922820	+	1.59837i	0.795030	+	0.606571i	$0.207455\pi$
$359$	17.4849	+	30.2848i	0.922820	+	1.59837i	0.127791	+	0.991801i	$0.459211\pi$
$360$		0			0
$361$	16.4765	+	9.46183i	0.867182	+	0.497991i
$362$		0			0
$363$	−16.2701	+	9.39352i	−0.853957	+	0.493032i
$364$		0			0
$365$	−11.5040	+	5.03233i	−0.602149	+	0.263404i
$366$		0			0
$367$	−8.55319	−	4.93819i	−0.446473	−	0.257771i	0.259866	−	0.965645i	$-0.416321\pi$
$367$	−8.55319	−	4.93819i	−0.446473	−	0.257771i	−0.706339	+	0.707873i	$0.749655\pi$
$368$		0			0
$369$	−1.44184			−0.0750593
$370$		0			0
$371$	0.764883	−	1.32482i	0.0397107	−	0.0687810i
$372$		0			0
$373$		−	18.9698i		−	0.982220i	−0.871098	−	0.491110i	$-0.836591\pi$
$373$		−	18.9698i		−	0.982220i	0.871098	−	0.491110i	$-0.163409\pi$
$374$		0			0
$375$	26.6936	−	5.13050i	1.37845	−	0.264938i
$376$		0			0
$377$	3.88925	−	2.24546i	0.200306	−	0.115647i
$378$		0			0
$379$	−8.93773			−0.459101			−0.229550	−	0.973297i	$-0.573726\pi$
$379$	−8.93773			−0.459101			−0.229550	+	0.973297i	$0.573726\pi$
$380$		0			0
$381$	−8.03584			−0.411689
$382$		0			0
$383$	13.9643	−	8.06230i	0.713543	−	0.411964i	−0.0988287	−	0.995104i	$-0.531510\pi$
$383$	13.9643	−	8.06230i	0.713543	−	0.411964i	0.812371	+	0.583140i	$0.198176\pi$
$384$		0			0
$385$	−0.298087	+	2.66866i	−0.0151919	+	0.136007i
$386$		0			0
$387$		−	22.9144i		−	1.16481i
$388$		0			0
$389$	−10.0603	+	17.4249i	−0.510075	+	0.883476i	0.489857	+	0.871803i	$0.337049\pi$
$389$	−10.0603	+	17.4249i	−0.510075	+	0.883476i	−0.999932	+	0.0116730i	$0.996284\pi$
$390$		0			0
$391$	−9.13262			−0.461857
$392$		0			0
$393$	−2.72298	−	1.57211i	−0.137356	−	0.0793025i
$394$		0			0
$395$	−5.37353	−	12.2840i	−0.270372	−	0.618076i
$396$		0			0
$397$	−13.8674	+	8.00633i	−0.695983	+	0.401826i	−0.805850	−	0.592120i	$-0.798291\pi$
$397$	−13.8674	+	8.00633i	−0.695983	+	0.401826i	0.109866	+	0.993946i	$0.464958\pi$
$398$		0			0
$399$	1.82863	+	6.79304i	0.0915460	+	0.340077i
$400$		0			0
$401$	6.83602	+	11.8403i	0.341375	+	0.591278i	0.984688	−	0.174324i	$-0.0557741\pi$
$401$	6.83602	+	11.8403i	0.341375	+	0.591278i	−0.643313	+	0.765603i	$0.722441\pi$
$402$		0			0
$403$	−19.0054	−	10.9728i	−0.946727	−	0.546593i
$404$		0			0
$405$	8.29767	+	18.9687i	0.412314	+	0.942561i
$406$		0			0
$407$			5.38123i			0.266738i
$408$		0			0
$409$	3.03518	−	5.25709i	0.150080	−	0.259946i	−0.781177	−	0.624310i	$-0.785380\pi$
$409$	3.03518	−	5.25709i	0.150080	−	0.259946i	0.931257	+	0.364364i	$0.118713\pi$
$410$		0			0
$411$	35.4923			1.75071
$412$		0			0
$413$	4.46752	−	2.57932i	0.219832	−	0.126920i
$414$		0			0
$415$	1.53921	−	13.7799i	0.0755569	−	0.676431i
$416$		0			0
$417$			9.13735i			0.447458i
$418$		0			0
$419$	6.33985			0.309722			0.154861	−	0.987936i	$-0.450507\pi$
$419$	6.33985			0.309722			0.154861	+	0.987936i	$0.450507\pi$
$420$		0			0
$421$	3.52768	+	6.11011i	0.171928	+	0.297789i	0.939094	−	0.343660i	$-0.111667\pi$
$421$	3.52768	+	6.11011i	0.171928	+	0.297789i	−0.767166	+	0.641449i	$0.778334\pi$
$422$		0			0
$423$	−16.5765	+	9.57043i	−0.805975	+	0.465330i
$424$		0			0
$425$	−20.8222	+	6.46668i	−1.01002	+	0.313680i
$426$		0			0
$427$	6.16299	+	3.55820i	0.298248	+	0.172194i
$428$		0			0
$429$	−10.1333			−0.489239
$430$		0			0
$431$	13.0390	−	22.5843i	0.628069	−	1.08785i	−0.359870	−	0.933002i	$-0.617179\pi$
$431$	13.0390	−	22.5843i	0.628069	−	1.08785i	0.987939	−	0.154845i	$-0.0494877\pi$
$432$		0			0
$433$	29.6662	+	17.1278i	1.42567	+	0.823109i	0.996775	−	0.0802463i	$-0.0255707\pi$
$433$	29.6662	+	17.1278i	1.42567	+	0.823109i	0.428892	+	0.903356i	$0.358904\pi$
$434$		0			0
$435$	1.17635	−	10.5314i	0.0564018	−	0.504943i
$436$		0			0
$437$	−6.46262	−	6.44766i	−0.309149	−	0.308433i
$438$		0			0
$439$	3.13427	+	5.42872i	0.149591	+	0.259099i	0.931076	−	0.364825i	$-0.118871\pi$
$439$	3.13427	+	5.42872i	0.149591	+	0.259099i	−0.781485	+	0.623923i	$0.785538\pi$
$440$		0			0
$441$	9.54701	−	16.5359i	0.454620	−	0.787424i
$442$		0			0
$443$	−28.3099	−	16.3447i	−1.34504	−	0.776561i	−0.357500	−	0.933913i	$-0.616371\pi$
$443$	−28.3099	−	16.3447i	−1.34504	−	0.776561i	−0.987543	+	0.157352i	$0.949704\pi$
$444$		0			0
$445$	−17.6378	+	23.9465i	−0.836110	+	1.13517i
$446$		0			0
$447$	16.1558	+	9.32756i	0.764143	+	0.441178i
$448$		0			0
$449$	23.0822			1.08932			0.544659	−	0.838658i	$-0.316659\pi$
$449$	23.0822			1.08932			0.544659	+	0.838658i	$0.316659\pi$
$450$		0			0
$451$	0.448025	+	0.776001i	0.0210967	+	0.0365405i
$452$		0			0
$453$	3.42448	−	1.97713i	0.160896	−	0.0928935i
$454$		0			0
$455$	2.02811	−	2.75353i	0.0950794	−	0.129088i
$456$		0			0
$457$			19.9166i			0.931661i	0.884874	+	0.465830i	$0.154244\pi$
$457$			19.9166i			0.931661i	−0.884874	+	0.465830i	$0.845756\pi$
$458$		0			0
$459$	−0.471966	−	0.817468i	−0.0220295	−	0.0381562i
$460$		0			0
$461$	−21.2586	−	36.8209i	−0.990111	−	1.71492i	−0.616548	−	0.787317i	$-0.711470\pi$
$461$	−21.2586	−	36.8209i	−0.990111	−	1.71492i	−0.373562	−	0.927605i	$-0.621864\pi$
$462$		0			0
$463$			27.2843i			1.26801i	0.773329	+	0.634005i	$0.218590\pi$
$463$			27.2843i			1.26801i	−0.773329	+	0.634005i	$0.781410\pi$
$464$		0			0
$465$	−47.4429	+	20.7534i	−2.20011	+	0.962418i
$466$		0			0
$467$			39.5912i			1.83206i	0.401107	+	0.916031i	$0.368625\pi$
$467$			39.5912i			1.83206i	−0.401107	+	0.916031i	$0.631375\pi$
$468$		0			0
$469$	1.52146	−	2.63525i	0.0702547	−	0.121685i
$470$		0			0
$471$	3.22696	−	5.58927i	0.148691	−	0.257540i
$472$		0			0
$473$	−12.3326	+	7.12022i	−0.567053	+	0.327388i
$474$		0			0
$475$	−19.3001	−	10.1244i	−0.885551	−	0.464541i
$476$		0			0
$477$	5.80956	−	3.35415i	0.266001	−	0.153576i
$478$		0			0
$479$	−13.7954	+	23.8943i	−0.630326	+	1.09176i	0.357159	+	0.934044i	$0.383745\pi$
$479$	−13.7954	+	23.8943i	−0.630326	+	1.09176i	−0.987485	+	0.157713i	$0.949588\pi$
$480$		0			0
$481$	3.42665	−	5.93513i	0.156242	−	0.270618i
$482$		0			0
$483$		−	3.38005i		−	0.153797i
$484$		0			0
$485$	20.8334	−	9.11336i	0.945995	−	0.413817i
$486$		0			0
$487$		−	29.9289i		−	1.35621i	−0.734966	−	0.678104i	$-0.762802\pi$
$487$		−	29.9289i		−	1.35621i	0.734966	−	0.678104i	$-0.237198\pi$
$488$		0			0
$489$	−24.0757	−	41.7004i	−1.08874	−	1.88576i
$490$		0			0
$491$	−7.23550	−	12.5323i	−0.326534	−	0.565573i	0.655288	−	0.755379i	$-0.272547\pi$
$491$	−7.23550	−	12.5323i	−0.326534	−	0.565573i	−0.981822	+	0.189806i	$0.939214\pi$
$492$		0			0
$493$			8.49996i			0.382819i
$494$		0			0
$495$	−6.98332	+	9.48113i	−0.313877	+	0.426145i
$496$		0			0
$497$	−3.40232	+	1.96433i	−0.152615	+	0.0881122i
$498$		0			0
$499$	−9.06799	−	15.7062i	−0.405939	−	0.703107i	0.588491	−	0.808504i	$-0.299722\pi$
$499$	−9.06799	−	15.7062i	−0.405939	−	0.703107i	−0.994430	+	0.105396i	$0.966389\pi$
$500$		0			0
$501$	0.218111			0.00974449
$502$		0			0
$503$	14.7022	+	8.48833i	0.655539	+	0.378476i	0.790575	−	0.612365i	$-0.209782\pi$
$503$	14.7022	+	8.48833i	0.655539	+	0.378476i	−0.135036	+	0.990841i	$0.543115\pi$
$504$		0			0
$505$	−19.8587	+	26.9619i	−0.883703	+	1.19979i
$506$		0			0
$507$	−16.1955	−	9.35046i	−0.719266	−	0.415269i
$508$		0			0
$509$	−16.6888	+	28.9058i	−0.739717	+	1.28123i	0.212906	+	0.977073i	$0.431707\pi$
$509$	−16.6888	+	28.9058i	−0.739717	+	1.28123i	−0.952623	+	0.304155i	$0.901626\pi$
$510$		0			0
$511$	1.86382	+	3.22824i	0.0824507	+	0.142809i
$512$		0			0
$513$	0.243153	−	0.911684i	0.0107355	−	0.0402518i
$514$		0			0
$515$	4.50529	−	40.3341i	0.198527	−	1.77733i
$516$		0			0
$517$	10.3016	+	5.94765i	0.453065	+	0.261577i
$518$		0			0
$519$	19.2473	−	33.3372i	0.844861	−	1.46334i
$520$		0			0
$521$	1.09359			0.0479110			0.0239555	−	0.999713i	$-0.492374\pi$
$521$	1.09359			0.0479110			0.0239555	+	0.999713i	$0.492374\pi$
$522$		0			0
$523$	−3.51597	−	2.02994i	−0.153742	−	0.0887633i	0.421155	−	0.906989i	$-0.361625\pi$
$523$	−3.51597	−	2.02994i	−0.153742	−	0.0887633i	−0.574898	+	0.818225i	$0.694958\pi$
$524$		0			0
$525$	−2.39336	−	7.70644i	−0.104455	−	0.336337i
$526$		0			0
$527$	35.9715	−	20.7682i	1.56695	−	0.904676i
$528$		0			0
$529$	−9.30690	−	16.1200i	−0.404648	−	0.700871i
$530$		0			0
$531$	22.6216			0.981694
$532$		0			0
$533$		−	1.14117i		−	0.0494295i
$534$		0			0
$535$	−3.46763	+	31.0443i	−0.149919	+	1.34216i
$536$		0			0
$537$	28.4352	−	16.4171i	1.22707	−	0.708450i
$538$		0			0
$539$	−11.8662			−0.511114
$540$		0			0
$541$	−6.65097	+	11.5198i	−0.285947	+	0.495275i	−0.972838	−	0.231485i	$-0.925642\pi$
$541$	−6.65097	+	11.5198i	−0.285947	+	0.495275i	0.686891	+	0.726760i	$0.258975\pi$
$542$		0			0
$543$		−	23.2715i		−	0.998675i
$544$		0			0
$545$	−16.4990	−	37.7172i	−0.706740	−	1.61563i
$546$		0			0
$547$	29.6808	+	17.1362i	1.26906	+	0.732692i	0.974810	−	0.223036i	$-0.0715969\pi$
$547$	29.6808	+	17.1362i	1.26906	+	0.732692i	0.294250	+	0.955729i	$0.404930\pi$
$548$		0			0
$549$	15.6034	+	27.0258i	0.665936	+	1.15343i
$550$		0			0
$551$	−6.00100	+	6.01493i	−0.255651	+	0.256244i
$552$		0			0
$553$	−3.44712	+	1.99019i	−0.146586	+	0.0846316i
$554$		0			0
$555$	−6.48101	−	14.8158i	−0.275104	−	0.628894i
$556$		0			0
$557$	35.2047	+	20.3255i	1.49167	+	0.861217i	0.999955	−	0.00953795i	$-0.00303607\pi$
$557$	35.2047	+	20.3255i	1.49167	+	0.861217i	0.491717	+	0.870755i	$0.336369\pi$
$558$		0			0
$559$	18.1360			0.767071
$560$		0			0
$561$	9.58963	−	16.6097i	0.404874	−	0.701263i
$562$		0			0
$563$			20.7137i			0.872980i	0.899709	+	0.436490i	$0.143779\pi$
$563$			20.7137i			0.872980i	−0.899709	+	0.436490i	$0.856221\pi$
$564$		0			0
$565$	−2.70429	+	24.2104i	−0.113770	+	1.01854i
$566$		0			0
$567$	5.32295	−	3.07321i	0.223543	−	0.129063i
$568$		0			0
$569$	−34.0551			−1.42766			−0.713831	−	0.700318i	$-0.753042\pi$
$569$	−34.0551			−1.42766			−0.713831	+	0.700318i	$0.753042\pi$
$570$		0			0
$571$	18.5413			0.775929			0.387965	−	0.921674i	$-0.373178\pi$
$571$	18.5413			0.775929			0.387965	+	0.921674i	$0.373178\pi$
$572$		0			0
$573$	56.6406	−	32.7015i	2.36620	−	1.36612i
$574$		0			0
$575$	7.68993	+	7.10774i	0.320692	+	0.296413i
$576$		0			0
$577$		−	2.96818i		−	0.123567i	−0.998090	−	0.0617834i	$-0.980321\pi$
$577$		−	2.96818i		−	0.123567i	0.998090	−	0.0617834i	$-0.0196788\pi$
$578$		0			0
$579$	27.7496	−	48.0638i	1.15324	−	1.99746i
$580$		0			0
$581$	−4.11627			−0.170772
$582$		0			0
$583$	−3.61042	−	2.08448i	−0.149528	−	0.0863302i
$584$		0			0
$585$	13.7395	−	6.01021i	0.568058	−	0.248492i
$586$		0			0
$587$	32.9328	−	19.0138i	1.35928	−	0.784781i	0.369754	−	0.929130i	$-0.379442\pi$
$587$	32.9328	−	19.0138i	1.35928	−	0.784781i	0.989527	+	0.144348i	$0.0461085\pi$
$588$		0			0
$589$	40.1174	+	10.6996i	1.65301	+	0.440869i
$590$		0			0
$591$	−12.6634	−	21.9336i	−0.520901	−	0.902227i
$592$		0			0
$593$	38.0060	+	21.9428i	1.56072	+	0.901081i	0.997184	+	0.0749876i	$0.0238917\pi$
$593$	38.0060	+	21.9428i	1.56072	+	0.901081i	0.563533	+	0.826093i	$0.309442\pi$
$594$		0			0
$595$	2.59408	+	5.93014i	0.106347	+	0.243112i
$596$		0			0
$597$		−	3.80287i		−	0.155641i
$598$		0			0
$599$	−17.4883	+	30.2906i	−0.714552	+	1.23764i	0.248581	+	0.968611i	$0.420036\pi$
$599$	−17.4883	+	30.2906i	−0.714552	+	1.23764i	−0.963132	+	0.269029i	$0.913297\pi$
$600$		0			0
$601$	31.9988			1.30526			0.652630	−	0.757677i	$-0.273666\pi$
$601$	31.9988			1.30526			0.652630	+	0.757677i	$0.273666\pi$
$602$		0			0
$603$	11.5561	−	6.67190i	0.470599	−	0.271701i
$604$		0			0
$605$	−17.1720	−	1.91810i	−0.698143	−	0.0779820i
$606$		0			0
$607$		−	2.10357i		−	0.0853814i	−0.999088	−	0.0426907i	$-0.986407\pi$
$607$		−	2.10357i		−	0.0853814i	0.999088	−	0.0426907i	$-0.0135930\pi$
$608$		0			0
$609$	−3.14589			−0.127478
$610$		0			0
$611$	−7.57467	−	13.1197i	−0.306438	−	0.530767i
$612$		0			0
$613$	−30.1598	+	17.4127i	−1.21814	+	0.703294i	−0.964520	−	0.264010i	$-0.914955\pi$
$613$	−30.1598	+	17.4127i	−1.21814	+	0.703294i	−0.253621	+	0.967304i	$0.581622\pi$
$614$		0			0
$615$	−2.16811	−	1.59692i	−0.0874267	−	0.0643941i
$616$		0			0
$617$	−15.8782	−	9.16726i	−0.639231	−	0.369060i	0.145087	−	0.989419i	$-0.453654\pi$
$617$	−15.8782	−	9.16726i	−0.639231	−	0.369060i	−0.784318	+	0.620359i	$0.786987\pi$
$618$		0			0
$619$	−32.4325			−1.30357			−0.651786	−	0.758403i	$-0.725980\pi$
$619$	−32.4325			−1.30357			−0.651786	+	0.758403i	$0.725980\pi$
$620$		0			0
$621$	−0.226675	+	0.392612i	−0.00909615	+	0.0157550i
$622$		0			0
$623$	7.64628	+	4.41458i	0.306342	+	0.176866i
$624$		0			0
$625$	22.5658	+	10.7604i	0.902631	+	0.430415i
$626$		0			0
$627$	18.5125	−	4.98342i	0.739319	−	0.199019i
$628$		0			0
$629$	6.48562	+	11.2334i	0.258598	+	0.447906i
$630$		0			0
$631$	−7.25551	+	12.5669i	−0.288837	+	0.500281i	−0.973532	−	0.228549i	$-0.926602\pi$
$631$	−7.25551	+	12.5669i	−0.288837	+	0.500281i	0.684695	+	0.728830i	$0.259935\pi$
$632$		0			0
$633$	−43.9012	−	25.3464i	−1.74492	−	1.00743i
$634$		0			0
$635$	−5.95078	−	4.38304i	−0.236150	−	0.173936i
$636$		0			0
$637$	13.0876	+	7.55614i	0.518550	+	0.299385i
$638$		0			0
$639$	−17.2279			−0.681525
$640$		0			0
$641$	13.8849	+	24.0494i	0.548421	+	0.949892i	0.998383	+	0.0568449i	$0.0181041\pi$
$641$	13.8849	+	24.0494i	0.548421	+	0.949892i	−0.449962	+	0.893048i	$0.648563\pi$
$642$		0			0
$643$	−9.72615	+	5.61539i	−0.383562	+	0.221450i	−0.679367	−	0.733799i	$-0.737745\pi$
$643$	−9.72615	+	5.61539i	−0.383562	+	0.221450i	0.295805	+	0.955248i	$0.404412\pi$
$644$		0			0
$645$	25.3790	−	34.4566i	0.999298	−	1.35673i
$646$		0			0
$647$		−	2.00223i		−	0.0787157i	−0.999225	−	0.0393578i	$-0.987469\pi$
$647$		−	2.00223i		−	0.0787157i	0.999225	−	0.0393578i	$-0.0125312\pi$
$648$		0			0
$649$	−7.02923	−	12.1750i	−0.275921	−	0.477910i
$650$		0			0
$651$	7.68645	+	13.3133i	0.301256	+	0.521790i
$652$		0			0
$653$		−	3.23945i		−	0.126770i	−0.997989	−	0.0633848i	$-0.979810\pi$
$653$		−	3.23945i		−	0.126770i	0.997989	−	0.0633848i	$-0.0201895\pi$
$654$		0			0
$655$	−1.15896	−	2.64941i	−0.0452842	−	0.103521i
$656$		0			0
$657$			16.3464i			0.637734i
$658$		0			0
$659$	−3.14745	+	5.45154i	−0.122607	+	0.212362i	−0.920795	−	0.390047i	$-0.872459\pi$
$659$	−3.14745	+	5.45154i	−0.122607	+	0.212362i	0.798188	+	0.602409i	$0.205792\pi$
$660$		0			0
$661$	−0.196536	+	0.340410i	−0.00764435	+	0.0132404i	−0.869822	−	0.493365i	$-0.835767\pi$
$661$	−0.196536	+	0.340410i	−0.00764435	+	0.0132404i	0.862178	+	0.506606i	$0.169100\pi$
$662$		0			0
$663$	−21.1534	+	12.2129i	−0.821530	+	0.474311i
$664$		0			0
$665$	−2.35102	+	6.02785i	−0.0911685	+	0.233750i
$666$		0			0
$667$	3.53542	−	2.04117i	0.136892	−	0.0790346i
$668$		0			0
$669$	27.4381	−	47.5242i	1.06082	−	1.83739i
$670$		0			0
$671$	9.69690	−	16.7955i	0.374345	−	0.648384i
$672$		0			0
$673$		−	43.1041i		−	1.66154i	−0.556616	−	0.830770i	$-0.687900\pi$
$673$		−	43.1041i		−	1.66154i	0.556616	−	0.830770i	$-0.312100\pi$
$674$		0			0
$675$	−0.238811	+	1.05565i	−0.00919184	+	0.0406321i
$676$		0			0
$677$			12.3727i			0.475522i	0.971324	+	0.237761i	$0.0764134\pi$
$677$			12.3727i			0.475522i	−0.971324	+	0.237761i	$0.923587\pi$
$678$		0			0
$679$	−3.37532	−	5.84622i	−0.129533	−	0.224357i
$680$		0			0
$681$	13.8808	+	24.0422i	0.531913	+	0.921300i
$682$		0			0
$683$			32.8415i			1.25664i	0.777954	+	0.628322i	$0.216258\pi$
$683$			32.8415i			1.25664i	−0.777954	+	0.628322i	$0.783742\pi$
$684$		0			0
$685$	26.2831	+	19.3588i	1.00423	+	0.739662i
$686$		0			0
$687$	33.3171	−	19.2356i	1.27113	−	0.733885i
$688$		0			0
$689$	2.65470	+	4.59807i	0.101136	+	0.175172i
$690$		0			0
$691$	−16.6704			−0.634171			−0.317085	−	0.948397i	$-0.602704\pi$
$691$	−16.6704			−0.634171			−0.317085	+	0.948397i	$0.602704\pi$
$692$		0			0
$693$	3.02739	+	1.74786i	0.115001	+	0.0663959i
$694$		0			0
$695$	−4.98384	+	6.76648i	−0.189048	+	0.256667i
$696$		0			0
$697$	1.87052	+	1.07995i	0.0708510	+	0.0409059i
$698$		0			0
$699$	−16.3699	+	28.3536i	−0.619168	+	1.07243i
$700$		0			0
$701$	−15.9399	−	27.6087i	−0.602041	−	1.04277i	−0.992512	−	0.122151i	$-0.961021\pi$
$701$	−15.9399	−	27.6087i	−0.602041	−	1.04277i	0.390470	−	0.920616i	$-0.372312\pi$
$702$		0			0
$703$	−3.34134	+	12.5281i	−0.126021	+	0.472506i
$704$		0			0
$705$	−35.5260	−	3.96823i	−1.33799	−	0.149452i
$706$		0			0
$707$	8.60911	+	4.97047i	0.323779	+	0.186934i
$708$		0			0
$709$	−2.99202	+	5.18233i	−0.112368	+	0.194626i	−0.916724	−	0.399520i	$-0.869177\pi$
$709$	−2.99202	+	5.18233i	−0.112368	+	0.194626i	0.804357	+	0.594147i	$0.202510\pi$
$710$		0			0
$711$	−17.4547			−0.654603
$712$		0			0
$713$	−17.2764	−	9.97451i	−0.647004	−	0.373548i
$714$		0			0
$715$	−7.50399	−	5.52706i	−0.280633	−	0.206700i
$716$		0			0
$717$	−41.5708	+	24.0009i	−1.55249	+	0.896331i
$718$		0			0
$719$	−0.345920	−	0.599151i	−0.0129006	−	0.0223446i	0.859503	−	0.511131i	$-0.170773\pi$
$719$	−0.345920	−	0.599151i	−0.0129006	−	0.0223446i	−0.872404	+	0.488786i	$0.837440\pi$
$720$		0			0
$721$	−12.0484			−0.448706
$722$		0			0
$723$		−	13.1187i		−	0.487889i
$724$		0			0
$725$	6.61535	−	7.15721i	0.245688	−	0.265812i
$726$		0			0
$727$	−19.1410	+	11.0511i	−0.709902	+	0.409862i	−0.811025	−	0.585012i	$-0.801090\pi$
$727$	−19.1410	+	11.0511i	−0.709902	+	0.409862i	0.101123	+	0.994874i	$0.467756\pi$
$728$		0			0
$729$	25.3743			0.939789
$730$		0			0
$731$	−17.1630	+	29.7272i	−0.634796	+	1.09950i
$732$		0			0
$733$			19.0945i			0.705271i	0.935761	+	0.352635i	$0.114714\pi$
$733$			19.0945i			0.705271i	−0.935761	+	0.352635i	$0.885286\pi$
$734$		0			0
$735$	32.6704	−	14.2914i	1.20507	−	0.527144i
$736$		0			0
$737$	−7.18165	−	4.14633i	−0.264540	−	0.152732i
$738$		0			0
$739$	6.05045	+	10.4797i	0.222569	+	0.385501i	0.955587	−	0.294708i	$-0.0952223\pi$
$739$	6.05045	+	10.4797i	0.222569	+	0.385501i	−0.733018	+	0.680209i	$0.761889\pi$
$740$		0			0
$741$	−23.5914	−	6.29200i	−0.866652	−	0.231142i
$742$		0			0
$743$	13.6722	−	7.89364i	0.501584	−	0.289590i	−0.227783	−	0.973712i	$-0.573148\pi$
$743$	13.6722	−	7.89364i	0.501584	−	0.289590i	0.729368	+	0.684122i	$0.239814\pi$
$744$		0			0
$745$	6.87626	+	15.7193i	0.251927	+	0.575911i
$746$		0			0
$747$	−15.6323	−	9.02531i	−0.571956	−	0.330219i
$748$		0			0
$749$	9.27341			0.338843
$750$		0			0
$751$	−17.5848	+	30.4578i	−0.641678	+	1.11142i	0.343380	+	0.939197i	$0.388428\pi$
$751$	−17.5848	+	30.4578i	−0.641678	+	1.11142i	−0.985058	+	0.172223i	$0.944905\pi$
$752$		0			0
$753$		−	8.68664i		−	0.316559i
$754$		0			0
$755$	3.61433	+	0.403718i	0.131539	+	0.0146928i
$756$		0			0
$757$	−12.7465	+	7.35917i	−0.463278	+	0.267473i	−0.713421	−	0.700735i	$-0.752855\pi$
$757$	−12.7465	+	7.35917i	−0.463278	+	0.267473i	0.250144	+	0.968209i	$0.419522\pi$
$758$		0			0
$759$	−9.21138			−0.334352
$760$		0			0
$761$	−39.9486			−1.44814			−0.724068	−	0.689728i	$-0.757730\pi$
$761$	−39.9486			−1.44814			−0.724068	+	0.689728i	$0.757730\pi$
$762$		0			0
$763$	−10.5841	+	6.11074i	−0.383170	+	0.221224i
$764$		0			0
$765$	−3.15088	+	28.2085i	−0.113920	+	1.01988i
$766$		0			0
$767$			17.9042i			0.646485i
$768$		0			0
$769$	24.9729	−	43.2544i	0.900547	−	1.55979i	0.0737605	−	0.997276i	$-0.476500\pi$
$769$	24.9729	−	43.2544i	0.900547	−	1.55979i	0.826786	−	0.562516i	$-0.190167\pi$
$770$		0			0
$771$	−45.0583			−1.62273
$772$		0			0
$773$	−20.1384	−	11.6269i	−0.724327	−	0.418190i	0.0920165	−	0.995757i	$-0.470669\pi$
$773$	−20.1384	−	11.6269i	−0.724327	−	0.418190i	−0.816343	+	0.577567i	$0.804002\pi$
$774$		0			0
$775$	−46.4525	−	10.5085i	−1.66862	−	0.377478i
$776$		0			0
$777$	−4.15757	+	2.40037i	−0.149152	+	0.0861129i
$778$		0			0
$779$	0.561213	+	2.08481i	0.0201075	+	0.0746960i
$780$		0			0
$781$	5.35324	+	9.27208i	0.191554	+	0.331781i
$782$		0			0
$783$	0.365414	+	0.210972i	0.0130588	+	0.00753952i
$784$		0			0
$785$	5.43825	−	2.37891i	0.194100	−	0.0849070i
$786$		0			0
$787$			19.5711i			0.697636i	0.937191	+	0.348818i	$0.113417\pi$
$787$			19.5711i			0.697636i	−0.937191	+	0.348818i	$0.886583\pi$
$788$		0			0
$789$	−13.0628	+	22.6254i	−0.465048	+	0.805486i
$790$		0			0
$791$	7.23201			0.257141
$792$		0			0
$793$	−21.3900	+	12.3495i	−0.759582	+	0.438545i
$794$		0			0
$795$	12.4508	+	1.39075i	0.441584	+	0.0493247i
$796$		0			0
$797$		−	47.6782i		−	1.68885i	−0.535676	−	0.844424i	$-0.679943\pi$
$797$		−	47.6782i		−	1.68885i	0.535676	−	0.844424i	$-0.320057\pi$
$798$		0			0
$799$	28.6732			1.01438
$800$		0			0
$801$	19.3587	+	33.5303i	0.684007	+	1.18474i
$802$		0			0
$803$	8.79767	−	5.07933i	0.310463	−	0.179246i
$804$		0			0
$805$	1.84360	−	2.50303i	0.0649784	−	0.0882200i
$806$		0			0
$807$	−25.4780	−	14.7097i	−0.896867	−	0.517806i
$808$		0			0
$809$	24.4485			0.859565			0.429782	−	0.902933i	$-0.358590\pi$
$809$	24.4485			0.859565			0.429782	+	0.902933i	$0.358590\pi$
$810$		0			0
$811$	5.38004	−	9.31850i	0.188919	−	0.327217i	−0.755971	−	0.654605i	$-0.772835\pi$
$811$	5.38004	−	9.31850i	0.188919	−	0.327217i	0.944890	+	0.327388i	$0.106168\pi$
$812$		0			0
$813$	39.3510	+	22.7193i	1.38010	+	0.796802i
$814$		0			0
$815$	4.91613	−	44.0121i	0.172204	−	1.54168i
$816$		0			0
$817$	−33.1327	+	8.91906i	−1.15917	+	0.312038i
$818$		0			0
$819$	−2.22600	−	3.85555i	−0.0777828	−	0.134724i
$820$		0			0
$821$	3.60434	−	6.24289i	0.125792	−	0.217879i	−0.796250	−	0.604968i	$-0.793186\pi$
$821$	3.60434	−	6.24289i	0.125792	−	0.217879i	0.922042	+	0.387089i	$0.126519\pi$
$822$		0			0
$823$	6.70433	+	3.87075i	0.233698	+	0.134926i	0.612277	−	0.790643i	$-0.290254\pi$
$823$	6.70433	+	3.87075i	0.233698	+	0.134926i	−0.378579	+	0.925569i	$0.623587\pi$
$824$		0			0
$825$	−21.0018	+	6.52244i	−0.731188	+	0.227082i
$826$		0			0
$827$	−23.0605	−	13.3140i	−0.801891	−	0.462972i	0.0422411	−	0.999107i	$-0.486550\pi$
$827$	−23.0605	−	13.3140i	−0.801891	−	0.462972i	−0.844132	+	0.536136i	$0.819884\pi$
$828$		0			0
$829$	12.1093			0.420572			0.210286	−	0.977640i	$-0.432561\pi$
$829$	12.1093			0.420572			0.210286	+	0.977640i	$0.432561\pi$
$830$		0			0
$831$	−7.23201	−	12.5262i	−0.250876	−	0.434530i
$832$		0			0
$833$	−24.7709	+	14.3015i	−0.858262	+	0.495518i
$834$		0			0
$835$	0.161518	+	0.118966i	0.00558955	+	0.00411698i
$836$		0			0
$837$		−	2.06189i		−	0.0712695i
$838$		0			0
$839$	−1.20591	−	2.08869i	−0.0416325	−	0.0721096i	0.844458	−	0.535621i	$-0.179923\pi$
$839$	−1.20591	−	2.08869i	−0.0416325	−	0.0721096i	−0.886091	+	0.463512i	$0.846589\pi$
$840$		0			0
$841$	12.6002	+	21.8242i	0.434491	+	0.752560i
$842$		0			0
$843$		−	42.7386i		−	1.47199i
$844$		0			0
$845$	−6.89315	−	15.7579i	−0.237131	−	0.542088i
$846$		0			0
$847$			5.12954i			0.176253i
$848$		0			0
$849$	−38.1843	+	66.1371i	−1.31048	+	2.26982i
$850$		0			0
$851$	3.11490	−	5.39517i	0.106777	−	0.184944i
$852$		0			0
$853$	−23.9717	+	13.8401i	−0.820775	+	0.473875i	−0.850684	−	0.525678i	$-0.823812\pi$
$853$	−23.9717	+	13.8401i	−0.820775	+	0.473875i	0.0299085	+	0.999553i	$0.490478\pi$
$854$		0			0
$855$	−22.1450	+	17.7370i	−0.757343	+	0.606593i
$856$		0			0
$857$	−14.2071	+	8.20245i	−0.485304	+	0.280190i	−0.722624	−	0.691241i	$-0.757064\pi$
$857$	−14.2071	+	8.20245i	−0.485304	+	0.280190i	0.237320	+	0.971431i	$0.423731\pi$
$858$		0			0
$859$	−17.4715	+	30.2616i	−0.596121	+	1.03251i	0.397267	+	0.917703i	$0.369959\pi$
$859$	−17.4715	+	30.2616i	−0.596121	+	1.03251i	−0.993388	+	0.114808i	$0.963375\pi$
$860$		0			0
$861$	−0.399695	+	0.692293i	−0.0136216	+	0.0235933i
$862$		0			0
$863$		−	18.6243i		−	0.633979i	−0.948429	−	0.316990i	$-0.897328\pi$
$863$		−	18.6243i		−	0.633979i	0.948429	−	0.316990i	$-0.102672\pi$
$864$		0			0
$865$	32.4365	−	14.1890i	1.10287	−	0.482442i
$866$		0			0
$867$		−	4.89962i		−	0.166400i
$868$		0			0
$869$	5.42372	+	9.39416i	0.183987	+	0.318675i
$870$		0			0
$871$	5.28058	+	9.14624i	0.178926	+	0.309908i
$872$		0			0
$873$		−	29.6028i		−	1.00190i
$874$		0			0
$875$	2.43102	−	7.01228i	0.0821835	−	0.237058i
$876$		0			0
$877$	−26.3087	+	15.1893i	−0.888381	+	0.512907i	−0.873413	−	0.486981i	$-0.838098\pi$
$877$	−26.3087	+	15.1893i	−0.888381	+	0.512907i	−0.0149683	+	0.999888i	$0.504765\pi$
$878$		0			0
$879$	−34.2119	−	59.2567i	−1.15394	−	1.99868i
$880$		0			0
$881$	−26.3772			−0.888670			−0.444335	−	0.895861i	$-0.646560\pi$
$881$	−26.3772			−0.888670			−0.444335	+	0.895861i	$0.646560\pi$
$882$		0			0
$883$	25.2183	+	14.5598i	0.848664	+	0.489977i	0.860200	−	0.509957i	$-0.170339\pi$
$883$	25.2183	+	14.5598i	0.848664	+	0.489977i	−0.0115356	+	0.999933i	$0.503672\pi$
$884$		0			0
$885$	34.0163	+	25.0547i	1.14345	+	0.842205i
$886$		0			0
$887$	−17.3379	−	10.0100i	−0.582148	−	0.336104i	0.179838	−	0.983696i	$-0.442443\pi$
$887$	−17.3379	−	10.0100i	−0.582148	−	0.336104i	−0.761987	+	0.647593i	$0.775776\pi$
$888$		0			0
$889$	−1.09704	+	1.90012i	−0.0367935	+	0.0637281i
$890$		0			0
$891$	−8.37517	−	14.5062i	−0.280579	−	0.485977i
$892$		0			0
$893$	20.2903	+	20.2433i	0.678990	+	0.677418i
$894$		0			0
$895$	30.0116	+	3.35228i	1.00318	+	0.112054i
$896$		0			0
$897$	10.1595	+	5.86560i	0.339217	+	0.195847i
$898$		0			0
$899$	−9.28352	+	16.0795i	−0.309623	+	0.536283i
$900$		0			0
$901$	−10.0491			−0.334784
$902$		0			0
$903$	−11.0022	−	6.35215i	−0.366132	−	0.211386i
$904$		0			0
$905$	12.6931	−	17.2332i	0.421934	−	0.572852i
$906$		0			0
$907$	−6.50159	+	3.75370i	−0.215882	+	0.124639i	−0.604042	−	0.796952i	$-0.706444\pi$
$907$	−6.50159	+	3.75370i	−0.215882	+	0.124639i	0.388160	+	0.921592i	$0.373111\pi$
$908$		0			0
$909$	21.7964	+	37.7525i	0.722942	+	1.25217i
$910$		0			0
$911$	38.3882			1.27186			0.635929	−	0.771748i	$-0.280617\pi$
$911$	38.3882			1.27186			0.635929	+	0.771748i	$0.280617\pi$
$912$		0			0
$913$			11.2178i			0.371254i
$914$		0			0
$915$	−6.46969	+	57.9206i	−0.213881	+	1.91480i
$916$		0			0
$917$	−0.743471	+	0.429243i	−0.0245516	+	0.0141749i
$918$		0			0
$919$	37.8811			1.24958			0.624791	−	0.780792i	$-0.285184\pi$
$919$	37.8811			1.24958			0.624791	+	0.780792i	$0.285184\pi$
$920$		0			0
$921$	−32.7883	+	56.7910i	−1.08041	+	1.87133i
$922$		0			0
$923$		−	13.6353i		−	0.448811i
$924$		0			0
$925$	3.28167	−	14.5065i	0.107901	−	0.476970i
$926$		0			0
$927$	−45.7560	−	26.4172i	−1.50282	−	0.867655i
$928$		0			0
$929$	−5.96821	−	10.3372i	−0.195811	−	0.339154i	0.751355	−	0.659898i	$-0.229400\pi$
$929$	−5.96821	−	10.3372i	−0.195811	−	0.339154i	−0.947166	+	0.320744i	$0.896067\pi$
$930$		0			0
$931$	−27.6258	−	7.36802i	−0.905401	−	0.241477i
$932$		0			0
$933$	−10.5217	+	6.07473i	−0.344466	+	0.198878i
$934$		0			0
$935$	16.1610	−	7.06946i	0.528520	−	0.231196i
$936$		0			0
$937$	−11.7299	−	6.77228i	−0.383200	−	0.221241i	0.296010	−	0.955185i	$-0.404344\pi$
$937$	−11.7299	−	6.77228i	−0.383200	−	0.221241i	−0.679210	+	0.733944i	$0.737677\pi$
$938$		0			0
$939$	63.5824			2.07493
$940$		0			0
$941$	−7.04614	+	12.2043i	−0.229698	+	0.397848i	−0.957718	−	0.287707i	$-0.907107\pi$
$941$	−7.04614	+	12.2043i	−0.229698	+	0.397848i	0.728021	+	0.685555i	$0.240440\pi$
$942$		0			0
$943$		−	1.03735i		−	0.0337807i
$944$		0			0
$945$	0.319323	+	0.0356682i	0.0103876	+	0.00116029i
$946$		0			0
$947$	9.58806	−	5.53567i	0.311570	−	0.179885i	−0.336059	−	0.941841i	$-0.609094\pi$
$947$	9.58806	−	5.53567i	0.311570	−	0.179885i	0.647629	+	0.761956i	$0.275761\pi$
$948$		0			0
$949$	−12.9376			−0.419973
$950$		0			0
$951$	−63.2539			−2.05115
$952$		0			0
$953$	6.40004	−	3.69507i	0.207318	−	0.119695i	−0.392747	−	0.919647i	$-0.628475\pi$
$953$	6.40004	−	3.69507i	0.207318	−	0.119695i	0.600064	+	0.799952i	$0.295142\pi$
$954$		0			0
$955$	59.7806	+	6.67745i	1.93446	+	0.216077i
$956$		0			0
$957$			8.57326i			0.277134i
$958$		0			0
$959$	4.84534	−	8.39238i	0.156464	−	0.271004i
$960$		0			0
$961$	59.7307			1.92680
$962$		0			0
$963$	35.2174	+	20.3328i	1.13487	+	0.655215i
$964$		0			0
$965$	46.7652	−	20.4570i	1.50542	−	0.658534i
$966$		0			0
$967$	1.31785	−	0.760861i	0.0423792	−	0.0244676i	−0.478661	−	0.878000i	$-0.658878\pi$
$967$	1.31785	−	0.760861i	0.0423792	−	0.0244676i	0.521040	+	0.853532i	$0.325544\pi$
$968$		0			0
$969$	32.6391	−	32.7149i	1.04852	−	1.05095i
$970$		0			0
$971$	27.2897	+	47.2671i	0.875768	+	1.51687i	0.855942	+	0.517071i	$0.172978\pi$
$971$	27.2897	+	47.2671i	0.875768	+	1.51687i	0.0198254	+	0.999803i	$0.493689\pi$
$972$		0			0
$973$	2.16058	+	1.24741i	0.0692651	+	0.0399902i
$974$		0			0
$975$	27.3169	+	6.17965i	0.874840	+	0.197907i
$976$		0			0
$977$		−	13.0130i		−	0.416321i	−0.978095	−	0.208161i	$-0.933252\pi$
$977$		−	13.0130i		−	0.416321i	0.978095	−	0.208161i	$-0.0667477\pi$
$978$		0			0
$979$	12.0307	−	20.8378i	0.384503	−	0.665979i
$980$		0			0
$981$	−53.5934			−1.71111
$982$		0			0
$983$	−17.6166	+	10.1709i	−0.561882	+	0.324402i	−0.753900	−	0.656989i	$-0.771830\pi$
$983$	−17.6166	+	10.1709i	−0.561882	+	0.324402i	0.192019	+	0.981391i	$0.438497\pi$
$984$		0			0
$985$	2.58579	−	23.1495i	0.0823900	−	0.737605i
$986$		0			0
$987$			10.6121i			0.337788i
$988$		0			0
$989$	16.4860			0.524225
$990$		0			0
$991$	−16.9449	−	29.3495i	−0.538274	−	0.932318i	−0.998997	−	0.0447741i	$-0.985743\pi$
$991$	−16.9449	−	29.3495i	−0.538274	−	0.932318i	0.460723	−	0.887544i	$-0.347590\pi$
$992$		0			0
$993$	16.7895	−	9.69341i	0.532798	−	0.307611i
$994$		0			0
$995$	2.07422	−	2.81614i	0.0657573	−	0.0892775i
$996$		0			0
$997$	3.05162	+	1.76185i	0.0966458	+	0.0557985i	0.547544	−	0.836777i	$-0.315563\pi$
$997$	3.05162	+	1.76185i	0.0966458	+	0.0557985i	−0.450898	+	0.892575i	$0.648896\pi$
$998$		0			0
$999$	0.643901			0.0203721

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.r.a.349.9	yes	20
3.2	odd	2		3420.2.bj.c.2629.1		20
5.2	odd	4		1900.2.i.g.501.2		20
5.3	odd	4		1900.2.i.g.501.9		20
5.4	even	2	inner	380.2.r.a.349.2	yes	20
15.14	odd	2		3420.2.bj.c.2629.7		20
19.11	even	3	inner	380.2.r.a.49.2	✓	20
57.11	odd	6		3420.2.bj.c.1189.7		20
95.49	even	6	inner	380.2.r.a.49.9	yes	20
95.68	odd	12		1900.2.i.g.201.9		20
95.87	odd	12		1900.2.i.g.201.2		20
285.239	odd	6		3420.2.bj.c.1189.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.2	✓	20	19.11	even	3	inner
380.2.r.a.49.9	yes	20	95.49	even	6	inner
380.2.r.a.349.2	yes	20	5.4	even	2	inner
380.2.r.a.349.9	yes	20	1.1	even	1	trivial
1900.2.i.g.201.2		20	95.87	odd	12
1900.2.i.g.201.9		20	95.68	odd	12
1900.2.i.g.501.2		20	5.2	odd	4
1900.2.i.g.501.9		20	5.3	odd	4
3420.2.bj.c.1189.1		20	285.239	odd	6
3420.2.bj.c.1189.7		20	57.11	odd	6
3420.2.bj.c.2629.1		20	3.2	odd	2
3420.2.bj.c.2629.7		20	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.10552 - 1.21562i) q^{3} +(2.22225 + 0.248224i) q^{5} -0.663818i q^{7} +(1.45548 - 2.52097i) q^{9} +O(q^{10})\)	\(q+(2.10552 - 1.21562i) q^{3} +(2.22225 + 0.248224i) q^{5} -0.663818i q^{7} +(1.45548 - 2.52097i) q^{9} -1.80905 q^{11} +(1.99526 + 1.15197i) q^{13} +(4.98074 - 2.17878i) q^{15} +(-3.77643 + 2.18033i) q^{17} +(-4.21168 - 1.12329i) q^{19} +(-0.806953 - 1.39768i) q^{21} +(1.81374 + 1.04716i) q^{23} +(4.87677 + 1.10323i) q^{25} +0.216466i q^{27} +(0.974621 - 1.68809i) q^{29} -9.52527 q^{31} +(-3.80900 + 2.19913i) q^{33} +(0.164775 - 1.47517i) q^{35} -2.97461i q^{37} +5.60143 q^{39} +(-0.247657 - 0.428954i) q^{41} +(6.81715 - 3.93588i) q^{43} +(3.86021 - 5.24093i) q^{45} +(-5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-5.30091 + 9.18145i) q^{51} +(1.99575 + 1.15225i) q^{53} +(-4.02016 - 0.449050i) q^{55} +(-10.2333 + 2.75471i) q^{57} +(3.88559 + 6.73003i) q^{59} +(-5.36021 + 9.28415i) q^{61} +(-1.67347 - 0.966176i) q^{63} +(4.14802 + 3.05522i) q^{65} +(3.96984 + 2.29199i) q^{67} +5.09182 q^{69} +(-2.95914 - 5.12538i) q^{71} +(-4.86313 + 2.80773i) q^{73} +(11.6093 - 3.60545i) q^{75} +1.20088i q^{77} +(-2.99810 - 5.19286i) q^{79} +(4.62959 + 8.01868i) q^{81} -6.20090i q^{83} +(-8.93338 + 3.90782i) q^{85} -4.73909i q^{87} +(-6.65028 + 11.5186i) q^{89} +(0.764696 - 1.32449i) q^{91} +(-20.0557 + 11.5791i) q^{93} +(-9.08057 - 3.54166i) q^{95} +(8.80695 - 5.08470i) q^{97} +(-2.63305 + 4.56057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q + q^5 + 10 * q^9	\( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65} + 48 q^{69} - 2 q^{71} + 46 q^{75} - 16 q^{79} + 26 q^{81} - 39 q^{85} - 40 q^{89} - 4 q^{91} - 43 q^{95} - 20 q^{99}+O(q^{100}) \) 20 * q + q^5 + 10 * q^9 - 5 * q^15 + 14 * q^19 - 8 * q^21 + 9 * q^25 - 16 * q^29 + 8 * q^31 - 2 * q^35 - 8 * q^39 + 26 * q^41 - 32 * q^45 - 44 * q^49 + 26 * q^51 - 12 * q^55 + 4 * q^59 + 2 * q^61 - 18 * q^65 + 48 * q^69 - 2 * q^71 + 46 * q^75 - 16 * q^79 + 26 * q^81 - 39 * q^85 - 40 * q^89 - 4 * q^91 - 43 * q^95 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more