LMFDB - Embedded newform 380.2.r.a.49.2

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			49.2
Root			$-2.10552 + 1.21562i$ of defining polynomial
Character	$\chi$	$=$	380.49
Dual form			380.2.r.a.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.10552 - 1.21562i) q^{3} +(-0.896156 - 2.04863i) q^{5} -0.663818i q^{7} +(1.45548 + 2.52097i) q^{9} -1.80905 q^{11} +(-1.99526 + 1.15197i) q^{13} +(-0.603493 + 5.40283i) q^{15} +(3.77643 + 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(-0.806953 + 1.39768i) q^{21} +(-1.81374 + 1.04716i) q^{23} +(-3.39381 + 3.67179i) q^{25} +0.216466i q^{27} +(0.974621 + 1.68809i) q^{29} -9.52527 q^{31} +(3.80900 + 2.19913i) q^{33} +(-1.35992 + 0.594885i) q^{35} -2.97461i q^{37} +5.60143 q^{39} +(-0.247657 + 0.428954i) q^{41} +(-6.81715 - 3.93588i) q^{43} +(3.86021 - 5.24093i) q^{45} +(5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-5.30091 - 9.18145i) q^{51} +(-1.99575 + 1.15225i) q^{53} +(1.62119 + 3.70609i) q^{55} +(10.2333 + 2.75471i) q^{57} +(3.88559 - 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(1.67347 - 0.966176i) q^{63} +(4.14802 + 3.05522i) q^{65} +(-3.96984 + 2.29199i) q^{67} +5.09182 q^{69} +(-2.95914 + 5.12538i) q^{71} +(4.86313 + 2.80773i) q^{73} +(11.6093 - 3.60545i) q^{75} +1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} +(4.62959 - 8.01868i) q^{81} -6.20090i q^{83} +(1.08242 - 9.69045i) q^{85} -4.73909i q^{87} +(-6.65028 - 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(20.0557 + 11.5791i) q^{93} +(6.07552 + 7.62155i) q^{95} +(-8.80695 - 5.08470i) q^{97} +(-2.63305 - 4.56057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{5} + 10 q^{9} - 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}+ \cdots - 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

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
$3$	−2.10552	−	1.21562i	−1.21562	−	0.701841i	−0.251645	−	0.967820i	$-0.580972\pi$
$3$	−2.10552	−	1.21562i	−1.21562	−	0.701841i	−0.963979	+	0.265979i	$0.914305\pi$
$4$		0			0
$5$	−0.896156	−	2.04863i	−0.400773	−	0.916177i
$5$	−0.896156	−	2.04863i	−0.400773	−	0.916177i
$6$		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	$-0.770181\pi$
$13$	−1.99526	+	1.15197i	−0.553386	+	0.319498i	0.197100	+	0.980383i	$0.436847\pi$
$14$		0			0
$15$	−0.603493	+	5.40283i	−0.155821	+	1.39501i
$16$		0			0
$17$	3.77643	+	2.18033i	0.915920	+	0.528807i	0.882331	−	0.470629i	$-0.155973\pi$
$17$	3.77643	+	2.18033i	0.915920	+	0.528807i	0.0335887	+	0.999436i	$0.489306\pi$
$18$		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	$-0.736734\pi$
$23$	−1.81374	+	1.04716i	−0.378191	+	0.218349i	0.298840	+	0.954303i	$0.403400\pi$
$24$		0			0
$25$	−3.39381	+	3.67179i	−0.678762	+	0.734359i
$26$		0			0
$27$			0.216466i			0.0416588i
$28$		0			0
$29$	0.974621	+	1.68809i	0.180983	+	0.313471i	0.942215	−	0.335008i	$-0.108739\pi$
$29$	0.974621	+	1.68809i	0.180983	+	0.313471i	−0.761233	+	0.648479i	$0.775406\pi$
$30$		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
$35$	−1.35992	+	0.594885i	−0.229869	+	0.100554i
$36$		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	−0.884716	−	0.466130i	$-0.845648\pi$
$41$	−0.247657	+	0.428954i	−0.0386775	+	0.0669914i	0.846039	+	0.533122i	$0.178981\pi$
$42$		0			0
$43$	−6.81715	−	3.93588i	−1.03960	−	0.600216i	−0.119884	−	0.992788i	$-0.538252\pi$
$43$	−6.81715	−	3.93588i	−1.03960	−	0.600216i	−0.919721	+	0.392572i	$0.871585\pi$
$44$		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	$-0.507462\pi$
$47$	5.69449	−	3.28772i	0.830627	−	0.479563i	0.854067	+	0.520163i	$0.174129\pi$
$48$		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	$-0.717259\pi$
$53$	−1.99575	+	1.15225i	−0.274137	+	0.158273i	0.356629	+	0.934246i	$0.383926\pi$
$54$		0			0
$55$	1.62119	+	3.70609i	0.218602	+	0.499729i
$56$		0			0
$57$	10.2333	+	2.75471i	1.35543	+	0.364871i
$58$		0			0
$59$	3.88559	−	6.73003i	0.505860	−	0.876176i	−0.494117	−	0.869396i	$-0.664508\pi$
$59$	3.88559	−	6.73003i	0.505860	−	0.876176i	0.999977	−	0.00678007i	$-0.00215818\pi$
$60$		0			0
$61$	−5.36021	−	9.28415i	−0.686304	−	1.18871i	−0.973025	−	0.230700i	$-0.925899\pi$
$61$	−5.36021	−	9.28415i	−0.686304	−	1.18871i	0.286721	−	0.958014i	$-0.407435\pi$
$62$		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	$-0.757005\pi$
$67$	−3.96984	+	2.29199i	−0.484993	+	0.280011i	0.237502	+	0.971387i	$0.423671\pi$
$68$		0			0
$69$	5.09182			0.612984
$70$		0			0
$71$	−2.95914	+	5.12538i	−0.351185	+	0.608270i	−0.986457	−	0.164018i	$-0.947554\pi$
$71$	−2.95914	+	5.12538i	−0.351185	+	0.608270i	0.635272	+	0.772288i	$0.280888\pi$
$72$		0			0
$73$	4.86313	+	2.80773i	0.569187	+	0.328620i	0.756824	−	0.653618i	$-0.226750\pi$
$73$	4.86313	+	2.80773i	0.569187	+	0.328620i	−0.187638	+	0.982238i	$0.560083\pi$
$74$		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	−0.983926	−	0.178575i	$-0.942851\pi$
$79$	−2.99810	+	5.19286i	−0.337312	+	0.584242i	0.646614	+	0.762817i	$0.276185\pi$
$80$		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
$85$	1.08242	−	9.69045i	0.117404	−	1.05108i
$86$		0			0
$87$		−	4.73909i		−	0.508084i
$88$		0			0
$89$	−6.65028	−	11.5186i	−0.704928	−	1.22097i	−0.966717	−	0.255847i	$-0.917646\pi$
$89$	−6.65028	−	11.5186i	−0.704928	−	1.22097i	0.261789	−	0.965125i	$-0.415688\pi$
$90$		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
$95$	6.07552	+	7.62155i	0.623335	+	0.781955i
$96$		0			0
$97$	−8.80695	−	5.08470i	−0.894211	−	0.516273i	−0.0188932	−	0.999822i	$-0.506014\pi$
$97$	−8.80695	−	5.08470i	−0.894211	−	0.516273i	−0.875317	+	0.483549i	$0.839348\pi$
$98$		0			0
$99$	−2.63305	−	4.56057i	−0.264631	−	0.458354i
$100$		0			0
$101$	−7.48770	−	12.9691i	−0.745054	−	1.29047i	−0.950170	−	0.311733i	$-0.899091\pi$
$101$	−7.48770	−	12.9691i	−0.745054	−	1.29047i	0.205116	−	0.978738i	$-0.434243\pi$
$102$		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
$105$	3.58650	+	0.400610i	0.350007	+	0.0390955i
$106$		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	−0.0322945	+	0.999478i	$0.510281\pi$
$109$	−9.20544	+	15.9443i	−0.881721	+	1.52719i	−0.849426	+	0.527707i	$0.823052\pi$
$110$		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	$-0.619819\pi$
$127$	2.86242	−	1.65262i	0.253998	−	0.146646i	0.621594	+	0.783340i	$0.286486\pi$
$128$		0			0
$129$	9.56910	+	16.5742i	0.842512	+	1.45927i
$130$		0			0
$131$	−0.646627	+	1.11999i	−0.0564961	+	0.0978541i	−0.892890	−	0.450274i	$-0.851326\pi$
$131$	−0.646627	+	1.11999i	−0.0564961	+	0.0978541i	0.836394	+	0.548128i	$0.184660\pi$
$132$		0			0
$133$	0.745658	+	2.79579i	0.0646567	+	0.242426i
$134$		0			0
$135$	0.443459	−	0.193987i	0.0381669	−	0.0166957i
$136$		0			0
$137$	−12.6426	+	7.29920i	−1.08013	+	0.623613i	−0.930931	−	0.365195i	$-0.881002\pi$
$137$	−12.6426	+	7.29920i	−1.08013	+	0.623613i	−0.149197	+	0.988807i	$0.547669\pi$
$138$		0			0
$139$	−1.87915	−	3.25478i	−0.159387	−	0.276067i	0.775261	−	0.631641i	$-0.217618\pi$
$139$	−1.87915	−	3.25478i	−0.159387	−	0.276067i	−0.934648	+	0.355575i	$0.884285\pi$
$140$		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	−0.664988	−	0.746854i	$-0.731563\pi$
$149$	3.83653	−	6.64507i	0.314301	−	0.544385i	0.979289	+	0.202469i	$0.0648966\pi$
$150$		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
$155$	8.53613	+	19.5138i	0.685638	+	1.56739i
$156$		0			0
$157$	−2.29893	−	1.32729i	−0.183474	−	0.105929i	0.405450	−	0.914117i	$-0.367115\pi$
$157$	−2.29893	−	1.32729i	−0.183474	−	0.105929i	−0.588924	+	0.808188i	$0.700448\pi$
$158$		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
$165$	1.09175	−	9.77401i	0.0849927	−	0.760906i
$166$		0			0
$167$	−0.0776925	+	0.0448558i	−0.00601203	+	0.00347105i	−0.503003	−	0.864285i	$-0.667772\pi$
$167$	−0.0776925	+	0.0448558i	−0.00601203	+	0.00347105i	0.496991	+	0.867756i	$0.334438\pi$
$168$		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	$-0.538918\pi$
$173$	−13.7120	−	7.91662i	−1.04250	−	0.601889i	−0.920541	+	0.390646i	$0.872252\pi$
$174$		0			0
$175$	2.43740	+	2.25287i	0.184250	+	0.170301i
$176$		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	0.987243	−	0.159219i	$-0.0508975\pi$
$181$	4.78591	+	8.28945i	0.355734	+	0.616150i	−0.631509	+	0.775368i	$0.717564\pi$
$182$		0			0
$183$			26.0640i			1.92670i
$184$		0			0
$185$	−6.09389	+	2.66571i	−0.448032	+	0.195987i
$186$		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	$-0.640240\pi$
$193$	−19.7692	−	11.4137i	−1.42302	−	0.821579i	−0.996556	+	0.0829272i	$0.973573\pi$
$194$		0			0
$195$	−5.01975	−	11.4753i	−0.359472	−	0.821761i
$196$		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	0.892414	−	0.451218i	$-0.149010\pi$
$199$	0.782081	+	1.35460i	0.0554403	+	0.0960254i	−0.836973	+	0.547244i	$0.815677\pi$
$200$		0			0
$201$	11.1448			0.786092
$202$		0			0
$203$	1.12059	−	0.646971i	0.0786498	−	0.0454085i
$204$		0			0
$205$	1.10071	+	0.122949i	0.0768769	+	0.00858710i
$206$		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	0.244203	+	0.969724i	$0.421474\pi$
$211$	−10.4253	+	18.0571i	−0.717704	+	1.24310i	−0.961907	+	0.273376i	$0.911860\pi$
$212$		0			0
$213$	12.4611	−	7.19439i	0.853818	−	0.492952i
$214$		0			0
$215$	−1.95396	+	17.4930i	−0.133259	+	1.19301i
$216$		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	$-0.606056\pi$
$223$	−19.5472	−	11.2856i	−1.30898	−	0.755740i	−0.981926	+	0.189266i	$0.939389\pi$
$224$		0			0
$225$	−14.1961	−	3.21146i	−0.946407	−	0.214097i
$226$		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	$-0.187921\pi$
$233$	11.6621	+	6.73314i	0.764013	+	0.441103i	−0.0667219	+	0.997772i	$0.521254\pi$
$234$		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	0.939742	−	0.341886i	$-0.111066\pi$
$241$	2.69793	+	4.67295i	0.173789	+	0.301011i	−0.765953	+	0.642897i	$0.777732\pi$
$242$		0			0
$243$	−18.9330	+	10.9310i	−1.21455	+	0.701223i
$244$		0			0
$245$	−5.87820	−	13.4377i	−0.375544	−	0.858503i
$246$		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	0.916882	−	0.399158i	$-0.130697\pi$
$251$	1.78646	+	3.09424i	0.112760	+	0.195306i	−0.804122	+	0.594464i	$0.797364\pi$
$252$		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	$-0.470489\pi$
$257$	16.0500	−	9.26649i	1.00117	−	0.578028i	0.908595	+	0.417678i	$0.137156\pi$
$258$		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	$-0.225844\pi$
$263$	9.30609	+	5.37288i	0.573838	+	0.331306i	−0.184843	+	0.982768i	$0.559178\pi$
$264$		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	−0.989393	−	0.145267i	$-0.953596\pi$
$269$	−6.05027	+	10.4794i	−0.368892	+	0.638939i	0.620501	+	0.784206i	$0.286929\pi$
$270$		0			0
$271$	9.34472	−	16.1855i	0.567651	−	0.983201i	−0.429146	−	0.903235i	$-0.641185\pi$
$271$	9.34472	−	16.1855i	0.567651	−	0.983201i	0.996798	−	0.0799661i	$-0.0254812\pi$
$272$		0			0
$273$		−	3.71833i		−	0.225044i
$274$		0			0
$275$	6.13958	−	6.64247i	0.370231	−	0.400556i
$276$		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	0.999599	+	0.0283294i	$0.00901874\pi$
$281$	8.78943	+	15.2237i	0.524333	+	0.908172i	−0.475265	+	0.879843i	$0.657648\pi$
$282$		0			0
$283$	27.2029	+	15.7056i	1.61705	+	0.933603i	0.987679	+	0.156495i	$0.0500196\pi$
$283$	27.2029	+	15.7056i	1.61705	+	0.933603i	0.629368	+	0.777107i	$0.283314\pi$
$284$		0			0
$285$	−3.52721	−	23.4329i	−0.208934	−	1.38804i
$286$		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
$295$	−17.2695	−	1.92899i	−1.00547	−	0.112310i
$296$		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	$-0.0537400\pi$
$307$	23.3588	+	13.4862i	1.33316	+	0.769698i	0.347374	+	0.937727i	$0.387073\pi$
$308$		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	$-0.931417\pi$
$313$	−22.6484	+	13.0761i	−1.28017	+	0.739104i	−0.303287	+	0.952899i	$0.598084\pi$
$314$		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	$-0.405892\pi$
$317$	22.5314	−	13.0085i	1.26549	−	0.730632i	0.974131	+	0.225982i	$0.0725591\pi$
$318$		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
$325$	2.54176	−	11.2357i	0.140992	−	0.623247i
$326$		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	$-0.367724\pi$
$337$	−3.42862	−	1.97951i	−0.186769	−	0.107831i	−0.590469	+	0.807060i	$0.701057\pi$
$338$		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
$345$	−4.56307	−	10.4313i	−0.245667	−	0.561602i
$346$		0			0
$347$	4.16047	+	2.40205i	0.223345	+	0.128949i	0.607498	−	0.794321i	$-0.292173\pi$
$347$	4.16047	+	2.40205i	0.223345	+	0.128949i	−0.384153	+	0.923269i	$0.625506\pi$
$348$		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
$355$	13.1519	+	1.46905i	0.698029	+	0.0779693i
$356$		0			0
$357$	−6.09481	+	3.51884i	−0.322572	+	0.186237i
$358$		0			0
$359$	17.4849	−	30.2848i	0.922820	−	1.59837i	0.127791	−	0.991801i	$-0.459211\pi$
$359$	17.4849	−	30.2848i	0.922820	−	1.59837i	0.795030	−	0.606571i	$-0.207455\pi$
$360$		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
$365$	1.39389	−	12.4789i	0.0729595	−	0.653178i
$366$		0			0
$367$	8.55319	−	4.93819i	0.446473	−	0.257771i	−0.259866	−	0.965645i	$-0.583679\pi$
$367$	8.55319	−	4.93819i	0.446473	−	0.257771i	0.706339	+	0.707873i	$0.250345\pi$
$368$		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
$375$	−17.7899	−	20.5521i	−0.918669	−	1.06131i
$376$		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	$-0.468490\pi$
$383$	−13.9643	−	8.06230i	−0.713543	−	0.411964i	−0.812371	+	0.583140i	$0.801824\pi$
$384$		0			0
$385$	2.46017	−	1.07618i	0.125382	−	0.0548471i
$386$		0			0
$387$		−	22.9144i		−	1.16481i
$388$		0			0
$389$	−10.0603	−	17.4249i	−0.510075	−	0.883476i	−0.999932	−	0.0116730i	$-0.996284\pi$
$389$	−10.0603	−	17.4249i	−0.510075	−	0.883476i	0.489857	−	0.871803i	$-0.337049\pi$
$390$		0			0
$391$	−9.13262			−0.461857
$392$		0			0
$393$	2.72298	−	1.57211i	0.137356	−	0.0793025i
$394$		0			0
$395$	13.3250	+	1.48840i	0.670455	+	0.0748894i
$396$		0			0
$397$	13.8674	+	8.00633i	0.695983	+	0.401826i	0.805850	−	0.592120i	$-0.201709\pi$
$397$	13.8674	+	8.00633i	0.695983	+	0.401826i	−0.109866	+	0.993946i	$0.535042\pi$
$398$		0			0
$399$	1.82863	−	6.79304i	0.0915460	−	0.340077i
$400$		0			0
$401$	6.83602	−	11.8403i	0.341375	−	0.591278i	−0.643313	−	0.765603i	$-0.722441\pi$
$401$	6.83602	−	11.8403i	0.341375	−	0.591278i	0.984688	+	0.174324i	$0.0557741\pi$
$402$		0			0
$403$	19.0054	−	10.9728i	0.946727	−	0.546593i
$404$		0			0
$405$	−20.5762	−	2.29835i	−1.02244	−	0.114206i
$406$		0			0
$407$			5.38123i			0.266738i
$408$		0			0
$409$	3.03518	+	5.25709i	0.150080	+	0.259946i	0.931257	−	0.364364i	$-0.118713\pi$
$409$	3.03518	+	5.25709i	0.150080	+	0.259946i	−0.781177	+	0.624310i	$0.785380\pi$
$410$		0			0
$411$	35.4923			1.75071
$412$		0			0
$413$	−4.46752	−	2.57932i	−0.219832	−	0.126920i
$414$		0			0
$415$	−12.7034	+	5.55698i	−0.623585	+	0.272781i
$416$		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	−0.767166	−	0.641449i	$-0.778334\pi$
$421$	3.52768	−	6.11011i	0.171928	−	0.297789i	0.939094	+	0.343660i	$0.111667\pi$
$422$		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	0.987939	+	0.154845i	$0.0494877\pi$
$431$	13.0390	+	22.5843i	0.628069	+	1.08785i	−0.359870	+	0.933002i	$0.617179\pi$
$432$		0			0
$433$	−29.6662	+	17.1278i	−1.42567	+	0.823109i	−0.996775	−	0.0802463i	$-0.974429\pi$
$433$	−29.6662	+	17.1278i	−1.42567	+	0.823109i	−0.428892	+	0.903356i	$0.641096\pi$
$434$		0			0
$435$	−9.70866	+	4.24696i	−0.465495	+	0.203626i
$436$		0			0
$437$	6.46262	−	6.44766i	0.309149	−	0.308433i
$438$		0			0
$439$	3.13427	−	5.42872i	0.149591	−	0.259099i	−0.781485	−	0.623923i	$-0.785538\pi$
$439$	3.13427	−	5.42872i	0.149591	−	0.259099i	0.931076	+	0.364825i	$0.118871\pi$
$440$		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	$-0.383629\pi$
$443$	28.3099	−	16.3447i	1.34504	−	0.776561i	0.987543	+	0.157352i	$0.0502958\pi$
$444$		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	−0.373562	+	0.927605i	$0.621864\pi$
$461$	−21.2586	+	36.8209i	−0.990111	+	1.71492i	−0.616548	+	0.787317i	$0.711470\pi$
$462$		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
$465$	5.74843	−	51.4634i	0.266577	−	2.38656i
$466$		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
$475$	10.1692	−	19.2766i	0.466593	−	0.884472i
$476$		0			0
$477$	−5.80956	−	3.35415i	−0.266001	−	0.153576i
$478$		0			0
$479$	−13.7954	−	23.8943i	−0.630326	−	1.09176i	−0.987485	−	0.157713i	$-0.949588\pi$
$479$	−13.7954	−	23.8943i	−0.630326	−	1.09176i	0.357159	−	0.934044i	$-0.383745\pi$
$480$		0			0
$481$	3.42665	+	5.93513i	0.156242	+	0.270618i
$482$		0			0
$483$		−	3.38005i		−	0.153797i
$484$		0			0
$485$	−2.52428	+	22.5989i	−0.114622	+	1.02616i
$486$		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	−0.981822	−	0.189806i	$-0.939214\pi$
$491$	−7.23550	+	12.5323i	−0.326534	+	0.565573i	0.655288	+	0.755379i	$0.272547\pi$
$492$		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	−0.994430	−	0.105396i	$-0.966389\pi$
$499$	−9.06799	+	15.7062i	−0.405939	+	0.703107i	0.588491	+	0.808504i	$0.299722\pi$
$500$		0			0
$501$	0.218111			0.00974449
$502$		0			0
$503$	−14.7022	+	8.48833i	−0.655539	+	0.378476i	−0.790575	−	0.612365i	$-0.790218\pi$
$503$	−14.7022	+	8.48833i	−0.655539	+	0.378476i	0.135036	+	0.990841i	$0.456885\pi$
$504$		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	−0.952623	−	0.304155i	$-0.901626\pi$
$509$	−16.6888	−	28.9058i	−0.739717	−	1.28123i	0.212906	−	0.977073i	$-0.431707\pi$
$510$		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
$515$	−37.1830	+	16.2654i	−1.63848	+	0.716737i
$516$		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	$-0.638375\pi$
$523$	3.51597	−	2.02994i	0.153742	−	0.0887633i	0.574898	+	0.818225i	$0.305042\pi$
$524$		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
$535$	28.6190	−	12.5191i	1.23731	−	0.541249i
$536$		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	0.686891	−	0.726760i	$-0.258975\pi$
$541$	−6.65097	−	11.5198i	−0.285947	−	0.495275i	−0.972838	+	0.231485i	$0.925642\pi$
$542$		0			0
$543$		−	23.2715i		−	0.998675i
$544$		0			0
$545$	40.9135	+	4.57001i	1.75254	+	0.195758i
$546$		0			0
$547$	−29.6808	+	17.1362i	−1.26906	+	0.732692i	−0.974810	−	0.223036i	$-0.928403\pi$
$547$	−29.6808	+	17.1362i	−1.26906	+	0.732692i	−0.294250	+	0.955729i	$0.595070\pi$
$548$		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
$555$	16.0713	+	1.79516i	0.682190	+	0.0762001i
$556$		0			0
$557$	−35.2047	+	20.3255i	−1.49167	+	0.861217i	−0.999955	−	0.00953795i	$-0.996964\pi$
$557$	−35.2047	+	20.3255i	−1.49167	+	0.861217i	−0.491717	+	0.870755i	$0.663631\pi$
$558$		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
$565$	22.3190	−	9.76323i	0.938967	−	0.410742i
$566$		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
$575$	2.31052	−	10.2135i	0.0963553	−	0.425934i
$576$		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
$585$	−1.66475	+	14.9039i	−0.0688290	+	0.616199i
$586$		0			0
$587$	−32.9328	−	19.0138i	−1.35928	−	0.784781i	−0.369754	−	0.929130i	$-0.620558\pi$
$587$	−32.9328	−	19.0138i	−1.35928	−	0.784781i	−0.989527	+	0.144348i	$0.953892\pi$
$588$		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	−0.563533	+	0.826093i	$0.690558\pi$
$593$	−38.0060	+	21.9428i	−1.56072	+	0.901081i	−0.997184	+	0.0749876i	$0.976108\pi$
$594$		0			0
$595$	−6.43270	−	0.718528i	−0.263715	−	0.0294568i
$596$		0			0
$597$		−	3.80287i		−	0.155641i
$598$		0			0
$599$	−17.4883	−	30.2906i	−0.714552	−	1.23764i	−0.963132	−	0.269029i	$-0.913297\pi$
$599$	−17.4883	−	30.2906i	−0.714552	−	1.23764i	0.248581	−	0.968611i	$-0.420036\pi$
$600$		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
$605$	6.92489	+	15.8305i	0.281537	+	0.643600i
$606$		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	$-0.0850450\pi$
$613$	30.1598	+	17.4127i	1.21814	+	0.703294i	0.253621	+	0.967304i	$0.418378\pi$
$614$		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	$-0.546346\pi$
$617$	15.8782	−	9.16726i	0.639231	−	0.369060i	0.784318	+	0.620359i	$0.213013\pi$
$618$		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
$625$	−1.96412	−	24.9227i	−0.0785649	−	0.996909i
$626$		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	0.684695	−	0.728830i	$-0.259935\pi$
$631$	−7.25551	−	12.5669i	−0.288837	−	0.500281i	−0.973532	+	0.228549i	$0.926602\pi$
$632$		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	−0.449962	−	0.893048i	$-0.648563\pi$
$641$	13.8849	−	24.0494i	0.548421	−	0.949892i	0.998383	−	0.0568449i	$-0.0181041\pi$
$642$		0			0
$643$	9.72615	+	5.61539i	0.383562	+	0.221450i	0.679367	−	0.733799i	$-0.262255\pi$
$643$	9.72615	+	5.61539i	0.383562	+	0.221450i	−0.295805	+	0.955248i	$0.595588\pi$
$644$		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
$655$	2.87393	+	0.321016i	0.112294	+	0.0125431i
$656$		0			0
$657$			16.3464i			0.637734i
$658$		0			0
$659$	−3.14745	−	5.45154i	−0.122607	−	0.212362i	0.798188	−	0.602409i	$-0.205792\pi$
$659$	−3.14745	−	5.45154i	−0.122607	−	0.212362i	−0.920795	+	0.390047i	$0.872459\pi$
$660$		0			0
$661$	−0.196536	−	0.340410i	−0.00764435	−	0.0132404i	0.862178	−	0.506606i	$-0.169100\pi$
$661$	−0.196536	−	0.340410i	−0.00764435	−	0.0132404i	−0.869822	+	0.493365i	$0.835767\pi$
$662$		0			0
$663$	21.1534	+	12.2129i	0.821530	+	0.474311i
$664$		0			0
$665$	5.05933	−	4.03304i	0.196192	−	0.156395i
$666$		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
$675$	−0.794817	−	0.734643i	−0.0305925	−	0.0282764i
$676$		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	0.390470	+	0.920616i	$0.372312\pi$
$701$	−15.9399	+	27.6087i	−0.602041	+	1.04277i	−0.992512	+	0.122151i	$0.961021\pi$
$702$		0			0
$703$	3.34134	+	12.5281i	0.126021	+	0.472506i
$704$		0			0
$705$	14.3264	+	32.7505i	0.539564	+	1.23346i
$706$		0			0
$707$	−8.60911	+	4.97047i	−0.323779	+	0.186934i
$708$		0			0
$709$	−2.99202	−	5.18233i	−0.112368	−	0.194626i	0.804357	−	0.594147i	$-0.202510\pi$
$709$	−2.99202	−	5.18233i	−0.112368	−	0.194626i	−0.916724	+	0.399520i	$0.869177\pi$
$710$		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	−0.872404	−	0.488786i	$-0.837440\pi$
$719$	−0.345920	+	0.599151i	−0.0129006	+	0.0223446i	0.859503	+	0.511131i	$0.170773\pi$
$720$		0			0
$721$	−12.0484			−0.448706
$722$		0			0
$723$		−	13.1187i		−	0.487889i
$724$		0			0
$725$	−9.50600	−	2.15046i	−0.353044	−	0.0798660i
$726$		0			0
$727$	19.1410	+	11.0511i	0.709902	+	0.409862i	0.811025	−	0.585012i	$-0.198910\pi$
$727$	19.1410	+	11.0511i	0.709902	+	0.409862i	−0.101123	+	0.994874i	$0.532244\pi$
$728$		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
$735$	−3.95852	+	35.4391i	−0.146012	+	1.30719i
$736$		0			0
$737$	7.18165	−	4.14633i	0.264540	−	0.152732i
$738$		0			0
$739$	6.05045	−	10.4797i	0.222569	−	0.385501i	−0.733018	−	0.680209i	$-0.761889\pi$
$739$	6.05045	−	10.4797i	0.222569	−	0.385501i	0.955587	+	0.294708i	$0.0952223\pi$
$740$		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	$-0.426852\pi$
$743$	−13.6722	−	7.89364i	−0.501584	−	0.289590i	−0.729368	+	0.684122i	$0.760186\pi$
$744$		0			0
$745$	−17.0514	−	1.90463i	−0.624717	−	0.0697804i
$746$		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	−0.985058	−	0.172223i	$-0.944905\pi$
$751$	−17.5848	−	30.4578i	−0.641678	−	1.11142i	0.343380	−	0.939197i	$-0.388428\pi$
$752$		0			0
$753$		−	8.68664i		−	0.316559i
$754$		0			0
$755$	−1.45753	−	3.33196i	−0.0530451	−	0.121262i
$756$		0			0
$757$	12.7465	+	7.35917i	0.463278	+	0.267473i	0.713421	−	0.700735i	$-0.247145\pi$
$757$	12.7465	+	7.35917i	0.463278	+	0.267473i	−0.250144	+	0.968209i	$0.580478\pi$
$758$		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
$765$	26.0048	−	11.3755i	0.940204	−	0.411283i
$766$		0			0
$767$			17.9042i			0.646485i
$768$		0			0
$769$	24.9729	+	43.2544i	0.900547	+	1.55979i	0.826786	+	0.562516i	$0.190167\pi$
$769$	24.9729	+	43.2544i	0.900547	+	1.55979i	0.0737605	+	0.997276i	$0.476500\pi$
$770$		0			0
$771$	−45.0583			−1.62273
$772$		0			0
$773$	20.1384	−	11.6269i	0.724327	−	0.418190i	−0.0920165	−	0.995757i	$-0.529331\pi$
$773$	20.1384	−	11.6269i	0.724327	−	0.418190i	0.816343	+	0.577567i	$0.195998\pi$
$774$		0			0
$775$	32.3269	−	34.9748i	1.16122	−	1.25633i
$776$		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
$785$	−0.658928	+	5.89912i	−0.0235181	+	0.210549i
$786$		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
$795$	−5.02098	−	11.4781i	−0.178076	−	0.407086i
$796$		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	0.944890	−	0.327388i	$-0.106168\pi$
$811$	5.38004	+	9.31850i	0.188919	+	0.327217i	−0.755971	+	0.654605i	$0.772835\pi$
$812$		0			0
$813$	−39.3510	+	22.7193i	−1.38010	+	0.796802i
$814$		0			0
$815$	−40.5737	+	17.7486i	−1.42123	+	0.621706i
$816$		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	0.922042	−	0.387089i	$-0.126519\pi$
$821$	3.60434	+	6.24289i	0.125792	+	0.217879i	−0.796250	+	0.604968i	$0.793186\pi$
$822$		0			0
$823$	−6.70433	+	3.87075i	−0.233698	+	0.134926i	−0.612277	−	0.790643i	$-0.709746\pi$
$823$	−6.70433	+	3.87075i	−0.233698	+	0.134926i	0.378579	+	0.925569i	$0.376413\pi$
$824$		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	$-0.513450\pi$
$827$	23.0605	−	13.3140i	0.801891	−	0.462972i	0.844132	+	0.536136i	$0.180116\pi$
$828$		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	−0.886091	−	0.463512i	$-0.846589\pi$
$839$	−1.20591	+	2.08869i	−0.0416325	+	0.0721096i	0.844458	+	0.535621i	$0.179923\pi$
$840$		0			0
$841$	12.6002	−	21.8242i	0.434491	−	0.752560i
$842$		0			0
$843$		−	42.7386i		−	1.47199i
$844$		0			0
$845$	17.0933	+	1.90931i	0.588028	+	0.0656823i
$846$		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	$-0.176188\pi$
$853$	23.9717	+	13.8401i	0.820775	+	0.473875i	−0.0299085	+	0.999553i	$0.509522\pi$
$854$		0			0
$855$	−10.3709	+	26.4092i	−0.354677	+	0.903177i
$856$		0			0
$857$	14.2071	+	8.20245i	0.485304	+	0.280190i	0.722624	−	0.691241i	$-0.242936\pi$
$857$	14.2071	+	8.20245i	0.485304	+	0.280190i	−0.237320	+	0.971431i	$0.576269\pi$
$858$		0			0
$859$	−17.4715	−	30.2616i	−0.596121	−	1.03251i	−0.993388	−	0.114808i	$-0.963375\pi$
$859$	−17.4715	−	30.2616i	−0.596121	−	1.03251i	0.397267	−	0.917703i	$-0.369959\pi$
$860$		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
$865$	−3.93018	+	35.1854i	−0.133630	+	1.19634i
$866$		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	$-0.161902\pi$
$877$	26.3087	+	15.1893i	0.888381	+	0.512907i	0.0149683	+	0.999888i	$0.495235\pi$
$878$		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	$-0.829661\pi$
$883$	−25.2183	+	14.5598i	−0.848664	+	0.489977i	0.0115356	+	0.999933i	$0.496328\pi$
$884$		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	$-0.557557\pi$
$887$	17.3379	−	10.0100i	0.582148	−	0.336104i	0.761987	+	0.647593i	$0.224224\pi$
$888$		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
$895$	−12.1027	−	27.6670i	−0.404547	−	0.924805i
$896$		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	$-0.293556\pi$
$907$	6.50159	+	3.75370i	0.215882	+	0.124639i	−0.388160	+	0.921592i	$0.626889\pi$
$908$		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
$915$	53.3956	−	23.3574i	1.76520	−	0.772172i
$916$		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
$925$	10.9222	+	10.0953i	0.359118	+	0.331930i
$926$		0			0
$927$	45.7560	−	26.4172i	1.50282	−	0.867655i
$928$		0			0
$929$	−5.96821	+	10.3372i	−0.195811	+	0.339154i	−0.947166	−	0.320744i	$-0.896067\pi$
$929$	−5.96821	+	10.3372i	−0.195811	+	0.339154i	0.751355	+	0.659898i	$0.229400\pi$
$930$		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
$935$	−1.95815	+	17.5305i	−0.0640383	+	0.573310i
$936$		0			0
$937$	11.7299	−	6.77228i	0.383200	−	0.221241i	−0.296010	−	0.955185i	$-0.595656\pi$
$937$	11.7299	−	6.77228i	0.383200	−	0.221241i	0.679210	+	0.733944i	$0.262323\pi$
$938$		0			0
$939$	63.5824			2.07493
$940$		0			0
$941$	−7.04614	−	12.2043i	−0.229698	−	0.397848i	0.728021	−	0.685555i	$-0.240440\pi$
$941$	−7.04614	−	12.2043i	−0.229698	−	0.397848i	−0.957718	+	0.287707i	$0.907107\pi$
$942$		0			0
$943$		−	1.03735i		−	0.0337807i
$944$		0			0
$945$	−0.128772	−	0.294376i	−0.00418896	−	0.00957606i
$946$		0			0
$947$	−9.58806	−	5.53567i	−0.311570	−	0.179885i	0.336059	−	0.941841i	$-0.390906\pi$
$947$	−9.58806	−	5.53567i	−0.311570	−	0.179885i	−0.647629	+	0.761956i	$0.724239\pi$
$948$		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	$-0.371525\pi$
$953$	−6.40004	−	3.69507i	−0.207318	−	0.119695i	−0.600064	+	0.799952i	$0.704858\pi$
$954$		0			0
$955$	−24.1075	−	55.1103i	−0.780099	−	1.78333i
$956$		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
$965$	−5.66632	+	50.7283i	−0.182405	+	1.63300i
$966$		0			0
$967$	−1.31785	−	0.760861i	−0.0423792	−	0.0244676i	0.478661	−	0.878000i	$-0.341122\pi$
$967$	−1.31785	−	0.760861i	−0.0423792	−	0.0244676i	−0.521040	+	0.853532i	$0.674456\pi$
$968$		0			0
$969$	32.6391	+	32.7149i	1.04852	+	1.05095i
$970$		0			0
$971$	27.2897	−	47.2671i	0.875768	−	1.51687i	0.0198254	−	0.999803i	$-0.493689\pi$
$971$	27.2897	−	47.2671i	0.875768	−	1.51687i	0.855942	−	0.517071i	$-0.172978\pi$
$972$		0			0
$973$	−2.16058	+	1.24741i	−0.0692651	+	0.0399902i
$974$		0			0
$975$	−19.0102	+	20.5673i	−0.608813	+	0.658680i
$976$		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	$-0.228170\pi$
$983$	17.6166	+	10.1709i	0.561882	+	0.324402i	−0.192019	+	0.981391i	$0.561503\pi$
$984$		0			0
$985$	−21.3410	+	9.33541i	−0.679980	+	0.297451i
$986$		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	0.460723	+	0.887544i	$0.347590\pi$
$991$	−16.9449	+	29.3495i	−0.538274	+	0.932318i	−0.998997	+	0.0447741i	$0.985743\pi$
$992$		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	$-0.684437\pi$
$997$	−3.05162	+	1.76185i	−0.0966458	+	0.0557985i	0.450898	+	0.892575i	$0.351104\pi$
$998$		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.49.2	✓	20
3.2	odd	2		3420.2.bj.c.1189.7		20
5.2	odd	4		1900.2.i.g.201.2		20
5.3	odd	4		1900.2.i.g.201.9		20
5.4	even	2	inner	380.2.r.a.49.9	yes	20
15.14	odd	2		3420.2.bj.c.1189.1		20
19.7	even	3	inner	380.2.r.a.349.9	yes	20
57.26	odd	6		3420.2.bj.c.2629.1		20
95.7	odd	12		1900.2.i.g.501.2		20
95.64	even	6	inner	380.2.r.a.349.2	yes	20
95.83	odd	12		1900.2.i.g.501.9		20
285.254	odd	6		3420.2.bj.c.2629.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.2	✓	20	1.1	even	1	trivial
380.2.r.a.49.9	yes	20	5.4	even	2	inner
380.2.r.a.349.2	yes	20	95.64	even	6	inner
380.2.r.a.349.9	yes	20	19.7	even	3	inner
1900.2.i.g.201.2		20	5.2	odd	4
1900.2.i.g.201.9		20	5.3	odd	4
1900.2.i.g.501.2		20	95.7	odd	12
1900.2.i.g.501.9		20	95.83	odd	12
3420.2.bj.c.1189.1		20	15.14	odd	2
3420.2.bj.c.1189.7		20	3.2	odd	2
3420.2.bj.c.2629.1		20	57.26	odd	6
3420.2.bj.c.2629.7		20	285.254	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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.10552 - 1.21562i) q^{3} +(-0.896156 - 2.04863i) q^{5} -0.663818i q^{7} +(1.45548 + 2.52097i) q^{9} -1.80905 q^{11} +(-1.99526 + 1.15197i) q^{13} +(-0.603493 + 5.40283i) q^{15} +(3.77643 + 2.18033i) q^{17} +(-4.21168 + 1.12329i) q^{19} +(-0.806953 + 1.39768i) q^{21} +(-1.81374 + 1.04716i) q^{23} +(-3.39381 + 3.67179i) q^{25} +0.216466i q^{27} +(0.974621 + 1.68809i) q^{29} -9.52527 q^{31} +(3.80900 + 2.19913i) q^{33} +(-1.35992 + 0.594885i) q^{35} -2.97461i q^{37} +5.60143 q^{39} +(-0.247657 + 0.428954i) q^{41} +(-6.81715 - 3.93588i) q^{43} +(3.86021 - 5.24093i) q^{45} +(5.69449 - 3.28772i) q^{47} +6.55935 q^{49} +(-5.30091 - 9.18145i) q^{51} +(-1.99575 + 1.15225i) q^{53} +(1.62119 + 3.70609i) q^{55} +(10.2333 + 2.75471i) q^{57} +(3.88559 - 6.73003i) q^{59} +(-5.36021 - 9.28415i) q^{61} +(1.67347 - 0.966176i) q^{63} +(4.14802 + 3.05522i) q^{65} +(-3.96984 + 2.29199i) q^{67} +5.09182 q^{69} +(-2.95914 + 5.12538i) q^{71} +(4.86313 + 2.80773i) q^{73} +(11.6093 - 3.60545i) q^{75} +1.20088i q^{77} +(-2.99810 + 5.19286i) q^{79} +(4.62959 - 8.01868i) q^{81} -6.20090i q^{83} +(1.08242 - 9.69045i) q^{85} -4.73909i q^{87} +(-6.65028 - 11.5186i) q^{89} +(0.764696 + 1.32449i) q^{91} +(20.0557 + 11.5791i) q^{93} +(6.07552 + 7.62155i) q^{95} +(-8.80695 - 5.08470i) q^{97} +(-2.63305 - 4.56057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65}+ \cdots - 20 q^{99}+O(q^{100}) \) 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

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