LMFDB - Embedded newform 380.2.bh.a.117.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(13,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("380.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.bh (of order $36$, degree $12$, 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:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			117.1
Character	$\chi$	$=$	380.117
Dual form			380.2.bh.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.74765 - 1.28125i) q^{3} +(-1.16017 + 1.91154i) q^{5} +(-0.370262 + 1.38184i) q^{7} +(3.97961 + 4.74272i) q^{9} +O(q^{10})$	\(q+(-2.74765 - 1.28125i) q^{3} +(-1.16017 + 1.91154i) q^{5} +(-0.370262 + 1.38184i) q^{7} +(3.97961 + 4.74272i) q^{9} +(2.73107 - 4.73035i) q^{11} +(-0.160884 - 0.345016i) q^{13} +(5.63692 - 3.76578i) q^{15} +(-0.0144528 - 0.165196i) q^{17} +(1.45553 - 4.10870i) q^{19} +(2.78783 - 3.32240i) q^{21} +(0.363161 + 0.254288i) q^{23} +(-2.30799 - 4.43544i) q^{25} +(-2.50399 - 9.34503i) q^{27} +(1.09856 - 0.921802i) q^{29} +(6.67979 - 3.85658i) q^{31} +(-13.5648 + 9.49816i) q^{33} +(-2.21187 - 2.31094i) q^{35} +(6.77341 - 6.77341i) q^{37} +1.15412i q^{39} +(2.40119 + 6.59722i) q^{41} +(6.61211 + 9.44307i) q^{43} +(-13.6830 + 2.10482i) q^{45} +(-3.11441 - 0.272476i) q^{47} +(4.28980 + 2.47672i) q^{49} +(-0.171947 + 0.472419i) q^{51} +(6.56681 - 9.37838i) q^{53} +(5.87375 + 10.7086i) q^{55} +(-9.26357 + 9.42437i) q^{57} +(-8.39207 - 7.04179i) q^{59} +(2.07149 + 11.7480i) q^{61} +(-8.02716 + 3.74313i) q^{63} +(0.846167 + 0.0927428i) q^{65} +(0.773226 - 8.83802i) q^{67} +(-0.672034 - 1.16400i) q^{69} +(-0.325803 - 0.0574478i) q^{71} +(-0.964863 + 2.06915i) q^{73} +(0.658643 + 15.1442i) q^{75} +(5.52535 + 5.52535i) q^{77} +(-2.57267 + 0.936374i) q^{79} +(-1.86796 + 10.5937i) q^{81} +(-11.1195 - 2.97945i) q^{83} +(0.332548 + 0.164029i) q^{85} +(-4.19952 + 1.12526i) q^{87} +(-5.02263 - 1.82809i) q^{89} +(0.536325 - 0.0945686i) q^{91} +(-23.2950 + 2.03804i) q^{93} +(6.16528 + 7.54912i) q^{95} +(0.497197 - 0.0434991i) q^{97} +(33.3033 - 5.87227i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{7}+O(q^{10}) $ 120 * q + 6 * q^7	$ 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) $ 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−2.74765	−	1.28125i	−1.58636	−	0.739730i	−0.588713	−	0.808342i	$-0.700365\pi$
$3$	−2.74765	−	1.28125i	−1.58636	−	0.739730i	−0.997643	+	0.0686122i	$0.978143\pi$
$4$		0			0
$5$	−1.16017	+	1.91154i	−0.518846	+	0.854868i
$5$	−1.16017	+	1.91154i	−0.518846	+	0.854868i
$6$		0			0
$7$	−0.370262	+	1.38184i	−0.139946	+	0.522285i	0.859983	+	0.510323i	$0.170474\pi$
$7$	−0.370262	+	1.38184i	−0.139946	+	0.522285i	−0.999928	+	0.0119616i	$0.996192\pi$
$8$		0			0
$9$	3.97961	+	4.74272i	1.32654	+	1.58091i
$10$		0			0
$11$	2.73107	−	4.73035i	0.823448	−	1.42625i	−0.0796521	−	0.996823i	$-0.525381\pi$
$11$	2.73107	−	4.73035i	0.823448	−	1.42625i	0.903100	−	0.429431i	$-0.141286\pi$
$12$		0			0
$13$	−0.160884	−	0.345016i	−0.0446211	−	0.0956903i	0.882733	−	0.469874i	$-0.155701\pi$
$13$	−0.160884	−	0.345016i	−0.0446211	−	0.0956903i	−0.927355	+	0.374184i	$0.877923\pi$
$14$		0			0
$15$	5.63692	−	3.76578i	1.45545	−	0.972320i
$16$		0			0
$17$	−0.0144528	−	0.165196i	−0.00350532	−	0.0400660i	0.994241	−	0.107171i	$-0.0341793\pi$
$17$	−0.0144528	−	0.165196i	−0.00350532	−	0.0400660i	−0.997746	+	0.0671051i	$0.978624\pi$
$18$		0			0
$19$	1.45553	−	4.10870i	0.333922	−	0.942601i
$19$	1.45553	−	4.10870i	0.333922	−	0.942601i
$20$		0			0
$21$	2.78783	−	3.32240i	0.608354	−	0.725008i
$22$		0			0
$23$	0.363161	+	0.254288i	0.0757244	+	0.0530228i	0.610826	−	0.791765i	$-0.290838\pi$
$23$	0.363161	+	0.254288i	0.0757244	+	0.0530228i	−0.535101	+	0.844788i	$0.679727\pi$
$24$		0			0
$25$	−2.30799	−	4.43544i	−0.461599	−	0.887089i
$26$		0			0
$27$	−2.50399	−	9.34503i	−0.481894	−	1.79845i
$28$		0			0
$29$	1.09856	−	0.921802i	0.203998	−	0.171174i	−0.535065	−	0.844811i	$-0.679713\pi$
$29$	1.09856	−	0.921802i	0.203998	−	0.171174i	0.739063	+	0.673636i	$0.235269\pi$
$30$		0			0
$31$	6.67979	−	3.85658i	1.19973	−	0.692662i	0.239231	−	0.970963i	$-0.423105\pi$
$31$	6.67979	−	3.85658i	1.19973	−	0.692662i	0.960494	+	0.278301i	$0.0897712\pi$
$32$		0			0
$33$	−13.5648	+	9.49816i	−2.36132	+	1.65342i
$34$		0			0
$35$	−2.21187	−	2.31094i	−0.373874	−	0.390620i
$36$		0			0
$37$	6.77341	−	6.77341i	1.11354	−	1.11354i	0.120874	−	0.992668i	$-0.461430\pi$
$37$	6.77341	−	6.77341i	1.11354	−	1.11354i	0.992668	−	0.120874i	$-0.0385699\pi$
$38$		0			0
$39$			1.15412i			0.184807i
$40$		0			0
$41$	2.40119	+	6.59722i	0.375003	+	1.03031i	0.973400	+	0.229112i	$0.0735824\pi$
$41$	2.40119	+	6.59722i	0.375003	+	1.03031i	−0.598397	+	0.801200i	$0.704195\pi$
$42$		0			0
$43$	6.61211	+	9.44307i	1.00834	+	1.44005i	0.894772	+	0.446524i	$0.147338\pi$
$43$	6.61211	+	9.44307i	1.00834	+	1.44005i	0.113565	+	0.993531i	$0.463773\pi$
$44$		0			0
$45$	−13.6830	+	2.10482i	−2.03973	+	0.313769i
$46$		0			0
$47$	−3.11441	−	0.272476i	−0.454284	−	0.0397447i	−0.142282	−	0.989826i	$-0.545444\pi$
$47$	−3.11441	−	0.272476i	−0.454284	−	0.0397447i	−0.312002	+	0.950081i	$0.601000\pi$
$48$		0			0
$49$	4.28980	+	2.47672i	0.612829	+	0.353817i
$50$		0			0
$51$	−0.171947	+	0.472419i	−0.0240773	+	0.0661519i
$52$		0			0
$53$	6.56681	−	9.37838i	0.902021	−	1.28822i	−0.0550851	−	0.998482i	$-0.517543\pi$
$53$	6.56681	−	9.37838i	0.902021	−	1.28822i	0.957106	−	0.289738i	$-0.0935681\pi$
$54$		0			0
$55$	5.87375	+	10.7086i	0.792016	+	1.44394i
$56$		0			0
$57$	−9.26357	+	9.42437i	−1.22699	+	1.24829i
$58$		0			0
$59$	−8.39207	−	7.04179i	−1.09255	−	0.916762i	−0.0956529	−	0.995415i	$-0.530494\pi$
$59$	−8.39207	−	7.04179i	−1.09255	−	0.916762i	−0.996902	+	0.0786523i	$0.974938\pi$
$60$		0			0
$61$	2.07149	+	11.7480i	0.265227	+	1.50418i	0.768387	+	0.639986i	$0.221060\pi$
$61$	2.07149	+	11.7480i	0.265227	+	1.50418i	−0.503159	+	0.864194i	$0.667829\pi$
$62$		0			0
$63$	−8.02716	+	3.74313i	−1.01133	+	0.471589i
$64$		0			0
$65$	0.846167	+	0.0927428i	0.104954	+	0.0115033i
$66$		0			0
$67$	0.773226	−	8.83802i	0.0944646	−	1.07974i	−0.789993	−	0.613116i	$-0.789916\pi$
$67$	0.773226	−	8.83802i	0.0944646	−	1.07974i	0.884458	−	0.466620i	$-0.154528\pi$
$68$		0			0
$69$	−0.672034	−	1.16400i	−0.0809033	−	0.140129i
$70$		0			0
$71$	−0.325803	−	0.0574478i	−0.0386657	−	0.00681780i	0.154282	−	0.988027i	$-0.450694\pi$
$71$	−0.325803	−	0.0574478i	−0.0386657	−	0.00681780i	−0.192948	+	0.981209i	$0.561805\pi$
$72$		0			0
$73$	−0.964863	+	2.06915i	−0.112929	+	0.242176i	−0.954647	−	0.297741i	$-0.903767\pi$
$73$	−0.964863	+	2.06915i	−0.112929	+	0.242176i	0.841718	+	0.539917i	$0.181545\pi$
$74$		0			0
$75$	0.658643	+	15.1442i	0.0760535	+	1.74870i
$76$		0			0
$77$	5.52535	+	5.52535i	0.629672	+	0.629672i
$78$		0			0
$79$	−2.57267	+	0.936374i	−0.289447	+	0.105350i	−0.482663	−	0.875806i	$-0.660330\pi$
$79$	−2.57267	+	0.936374i	−0.289447	+	0.105350i	0.193216	+	0.981156i	$0.438108\pi$
$80$		0			0
$81$	−1.86796	+	10.5937i	−0.207551	+	1.17708i
$82$		0			0
$83$	−11.1195	−	2.97945i	−1.22052	−	0.327037i	−0.409638	−	0.912248i	$-0.634345\pi$
$83$	−11.1195	−	2.97945i	−1.22052	−	0.327037i	−0.810881	+	0.585211i	$0.801012\pi$
$84$		0			0
$85$	0.332548	+	0.164029i	0.0360698	+	0.0177915i
$86$		0			0
$87$	−4.19952	+	1.12526i	−0.450236	+	0.120640i
$88$		0			0
$89$	−5.02263	−	1.82809i	−0.532397	−	0.193777i	0.0618111	−	0.998088i	$-0.480312\pi$
$89$	−5.02263	−	1.82809i	−0.532397	−	0.193777i	−0.594208	+	0.804311i	$0.702535\pi$
$90$		0			0
$91$	0.536325	−	0.0945686i	0.0562222	−	0.00991348i
$92$		0			0
$93$	−23.2950	+	2.03804i	−2.41557	+	0.211335i
$94$		0			0
$95$	6.16528	+	7.54912i	0.632545	+	0.774524i
$96$		0			0
$97$	0.497197	−	0.0434991i	0.0504827	−	0.00441667i	−0.0618864	−	0.998083i	$-0.519712\pi$
$97$	0.497197	−	0.0434991i	0.0504827	−	0.00441667i	0.112369	+	0.993667i	$0.464156\pi$
$98$		0			0
$99$	33.3033	−	5.87227i	3.34711	−	0.590185i
$100$		0			0
$101$	1.05706	+	0.384738i	0.105181	+	0.0382828i	0.394075	−	0.919078i	$-0.371065\pi$
$101$	1.05706	+	0.384738i	0.105181	+	0.0382828i	−0.288893	+	0.957361i	$0.593287\pi$
$102$		0			0
$103$	14.9080	−	3.99460i	1.46893	−	0.393599i	0.566367	−	0.824153i	$-0.308348\pi$
$103$	14.9080	−	3.99460i	1.46893	−	0.393599i	0.902565	+	0.430554i	$0.141682\pi$
$104$		0			0
$105$	3.11655	+	9.18362i	0.304144	+	0.896229i
$106$		0			0
$107$	−7.95396	−	2.13126i	−0.768938	−	0.206036i	−0.147036	−	0.989131i	$-0.546973\pi$
$107$	−7.95396	−	2.13126i	−0.768938	−	0.206036i	−0.621902	+	0.783095i	$0.713640\pi$
$108$		0			0
$109$	1.54408	−	8.75691i	0.147896	−	0.838760i	−0.817100	−	0.576496i	$-0.804420\pi$
$109$	1.54408	−	8.75691i	0.147896	−	0.838760i	0.964996	−	0.262264i	$-0.0844692\pi$
$110$		0			0
$111$	−27.2894	+	9.93253i	−2.59020	+	0.942754i
$112$		0			0
$113$	−6.62544	−	6.62544i	−0.623269	−	0.623269i	0.323097	−	0.946366i	$-0.395276\pi$
$113$	−6.62544	−	6.62544i	−0.623269	−	0.623269i	−0.946366	+	0.323097i	$0.895276\pi$
$114$		0			0
$115$	−0.907414	+	0.399180i	−0.0846168	+	0.0372237i
$116$		0			0
$117$	0.996061	−	2.13606i	0.0920858	−	0.197479i
$118$		0			0
$119$	0.233625	+	0.0411945i	0.0214164	+	0.00377629i
$120$		0			0
$121$	−9.41746	−	16.3115i	−0.856132	−	1.48286i
$122$		0			0
$123$	1.85505	−	21.2034i	0.167265	−	1.91184i
$124$		0			0
$125$	11.1562	+	0.734059i	0.997842	+	0.0656562i
$126$		0			0
$127$	4.55705	−	2.12499i	0.404373	−	0.188562i	−0.209781	−	0.977748i	$-0.567275\pi$
$127$	4.55705	−	2.12499i	0.404373	−	0.188562i	0.614154	+	0.789186i	$0.289497\pi$
$128$		0			0
$129$	−6.06882	−	34.4180i	−0.534330	−	3.03034i
$130$		0			0
$131$	−8.78769	−	7.37375i	−0.767784	−	0.644247i	0.172356	−	0.985035i	$-0.444862\pi$
$131$	−8.78769	−	7.37375i	−0.767784	−	0.644247i	−0.940140	+	0.340787i	$0.889306\pi$
$132$		0			0
$133$	5.13862	+	3.53260i	0.445575	+	0.306316i
$134$		0			0
$135$	20.7685	+	6.05537i	1.78747	+	0.521163i
$136$		0			0
$137$	0.732633	−	1.04631i	0.0625931	−	0.0893922i	−0.786635	−	0.617418i	$-0.788179\pi$
$137$	0.732633	−	1.04631i	0.0625931	−	0.0893922i	0.849228	+	0.528026i	$0.177068\pi$
$138$		0			0
$139$	−1.80645	+	4.96319i	−0.153222	+	0.420973i	−0.992426	−	0.122843i	$-0.960799\pi$
$139$	−1.80645	+	4.96319i	−0.153222	+	0.420973i	0.839205	+	0.543816i	$0.183021\pi$
$140$		0			0
$141$	8.20821	+	4.73901i	0.691256	+	0.399097i
$142$		0			0
$143$	−2.07143	−	0.181227i	−0.173222	−	0.0151549i
$144$		0			0
$145$	0.487542	+	3.16940i	0.0404882	+	0.263204i
$146$		0			0
$147$	−8.61358	−	12.3015i	−0.710436	−	1.01461i
$148$		0			0
$149$	4.81272	+	13.2229i	0.394274	+	1.08326i	0.965030	+	0.262139i	$0.0844278\pi$
$149$	4.81272	+	13.2229i	0.394274	+	1.08326i	−0.570756	+	0.821119i	$0.693350\pi$
$150$		0			0
$151$			20.4283i			1.66243i	0.555948	+	0.831217i	$0.312356\pi$
$151$			20.4283i			1.66243i	−0.555948	+	0.831217i	$0.687644\pi$
$152$		0			0
$153$	0.725963	−	0.725963i	0.0586906	−	0.0586906i
$154$		0			0
$155$	−0.377702	+	17.2430i	−0.0303378	+	1.38499i
$156$		0			0
$157$	13.4852	−	9.44244i	1.07624	−	0.753589i	0.105665	−	0.994402i	$-0.466303\pi$
$157$	13.4852	−	9.44244i	1.07624	−	0.753589i	0.970572	+	0.240813i	$0.0774140\pi$
$158$		0			0
$159$	−30.0593	+	17.3548i	−2.38386	+	1.37632i
$160$		0			0
$161$	−0.485850	+	0.407676i	−0.0382903	+	0.0321294i
$162$		0			0
$163$	2.35672	+	8.79540i	0.184593	+	0.688909i	0.994717	+	0.102652i	$0.0327327\pi$
$163$	2.35672	+	8.79540i	0.184593	+	0.688909i	−0.810125	+	0.586258i	$0.800601\pi$
$164$		0			0
$165$	−2.41864	−	36.9492i	−0.188291	−	2.87649i
$166$		0			0
$167$	5.11551	+	3.58192i	0.395850	+	0.277177i	0.754507	−	0.656293i	$-0.227876\pi$
$167$	5.11551	+	3.58192i	0.395850	+	0.277177i	−0.358657	+	0.933469i	$0.616765\pi$
$168$		0			0
$169$	8.26309	−	9.84756i	0.635622	−	0.757505i
$170$		0			0
$171$	25.2789	−	9.44785i	1.93312	−	0.722495i
$172$		0			0
$173$	1.37458	+	15.7116i	0.104508	+	1.19453i	0.849549	+	0.527510i	$0.176874\pi$
$173$	1.37458	+	15.7116i	0.104508	+	1.19453i	−0.745041	+	0.667019i	$0.767570\pi$
$174$		0			0
$175$	6.98362	−	1.54699i	0.527912	−	0.116942i
$176$		0			0
$177$	14.0362	+	30.1007i	1.05502	+	2.26251i
$178$		0			0
$179$	−10.6511	+	18.4482i	−0.796099	+	1.37888i	0.126041	+	0.992025i	$0.459773\pi$
$179$	−10.6511	+	18.4482i	−0.796099	+	1.37888i	−0.922139	+	0.386858i	$0.873560\pi$
$180$		0			0
$181$	−5.65911	−	6.74426i	−0.420638	−	0.501297i	0.513559	−	0.858054i	$-0.328327\pi$
$181$	−5.65911	−	6.74426i	−0.420638	−	0.501297i	−0.934197	+	0.356757i	$0.883882\pi$
$182$		0			0
$183$	9.36041	−	34.9335i	0.691942	−	2.58236i
$184$		0			0
$185$	5.08933	+	20.8060i	0.374175	+	1.52969i
$186$		0			0
$187$	−0.820907	−	0.382795i	−0.0600307	−	0.0279928i
$188$		0			0
$189$	13.8404			1.00674
$190$		0			0
$191$	11.8629			0.858369			0.429185	−	0.903217i	$-0.358801\pi$
$191$	11.8629			0.858369			0.429185	+	0.903217i	$0.358801\pi$
$192$		0			0
$193$	−2.98330	−	1.39114i	−0.214743	−	0.100136i	0.312271	−	0.949993i	$-0.398910\pi$
$193$	−2.98330	−	1.39114i	−0.214743	−	0.100136i	−0.527013	+	0.849857i	$0.676688\pi$
$194$		0			0
$195$	−2.20614	−	1.33898i	−0.157985	−	0.0958861i
$196$		0			0
$197$	5.05223	−	18.8552i	0.359956	−	1.34338i	−0.514175	−	0.857685i	$-0.671902\pi$
$197$	5.05223	−	18.8552i	0.359956	−	1.34338i	0.874131	−	0.485690i	$-0.161432\pi$
$198$		0			0
$199$	−7.32786	−	8.73301i	−0.519458	−	0.619066i	0.440994	−	0.897510i	$-0.354626\pi$
$199$	−7.32786	−	8.73301i	−0.519458	−	0.619066i	−0.960453	+	0.278443i	$0.910182\pi$
$200$		0			0
$201$	−13.4483	+	23.2931i	−0.948568	+	1.64297i
$202$		0			0
$203$	0.867024	+	1.85934i	0.0608531	+	0.130500i
$204$		0			0
$205$	−15.3967	−	3.06394i	−1.07535	−	0.213995i
$206$		0			0
$207$	0.239224	+	2.73434i	0.0166272	+	0.190050i
$208$		0			0
$209$	−15.4604	−	18.1063i	−1.06942	−	1.25244i
$210$		0			0
$211$	7.39450	−	8.81242i	0.509058	−	0.606672i	−0.448899	−	0.893582i	$-0.648184\pi$
$211$	7.39450	−	8.81242i	0.509058	−	0.606672i	0.957957	+	0.286910i	$0.0926282\pi$
$212$		0			0
$213$	0.821587	+	0.575281i	0.0562942	+	0.0394176i
$214$		0			0
$215$	−25.7220	+	1.68373i	−1.75423	+	0.114829i
$216$		0			0
$217$	2.85589	+	10.6583i	0.193870	+	0.723534i
$218$		0			0
$219$	5.30221	−	4.44908i	0.358290	−	0.300641i
$220$		0			0
$221$	−0.0546702	+	0.0315639i	−0.00367752	+	0.00212322i
$222$		0			0
$223$	−12.8084	+	8.96853i	−0.857713	+	0.600577i	−0.917545	−	0.397632i	$-0.869832\pi$
$223$	−12.8084	+	8.96853i	−0.857713	+	0.600577i	0.0598325	+	0.998208i	$0.480943\pi$
$224$		0			0
$225$	11.8511	−	28.5975i	0.790076	−	1.90650i
$226$		0			0
$227$	6.34919	−	6.34919i	0.421410	−	0.421410i	−0.464279	−	0.885689i	$-0.653686\pi$
$227$	6.34919	−	6.34919i	0.421410	−	0.421410i	0.885689	+	0.464279i	$0.153686\pi$
$228$		0			0
$229$			1.24193i			0.0820690i	0.999158	+	0.0410345i	$0.0130654\pi$
$229$			1.24193i			0.0820690i	−0.999158	+	0.0410345i	$0.986935\pi$
$230$		0			0
$231$	−8.10238	−	22.2611i	−0.533097	−	1.46467i
$232$		0			0
$233$	10.3258	+	14.7467i	0.676465	+	0.966091i	0.999804	+	0.0198083i	$0.00630560\pi$
$233$	10.3258	+	14.7467i	0.676465	+	0.966091i	−0.323339	+	0.946283i	$0.604806\pi$
$234$		0			0
$235$	4.13411	−	5.63722i	0.269680	−	0.367731i
$236$		0			0
$237$	8.26851	+	0.723401i	0.537098	+	0.0469899i
$238$		0			0
$239$	−11.0995	−	6.40830i	−0.717967	−	0.414518i	0.0960369	−	0.995378i	$-0.469383\pi$
$239$	−11.0995	−	6.40830i	−0.717967	−	0.414518i	−0.814004	+	0.580859i	$0.802717\pi$
$240$		0			0
$241$	−4.12415	+	11.3310i	−0.265660	+	0.729894i	0.733101	+	0.680120i	$0.238072\pi$
$241$	−4.12415	+	11.3310i	−0.265660	+	0.729894i	−0.998760	+	0.0497742i	$0.984150\pi$
$242$		0			0
$243$	2.05823	−	2.93945i	0.132035	−	0.188566i
$244$		0			0
$245$	−9.71127	+	5.32672i	−0.620430	+	0.340311i
$246$		0			0
$247$	−1.65174	+	0.158840i	−0.105098	+	0.0101068i
$248$		0			0
$249$	26.7350	+	22.4333i	1.69426	+	1.42165i
$250$		0			0
$251$	−2.27798	−	12.9190i	−0.143785	−	0.815443i	−0.968335	−	0.249654i	$-0.919683\pi$
$251$	−2.27798	−	12.9190i	−0.143785	−	0.815443i	0.824550	−	0.565789i	$-0.191428\pi$
$252$		0			0
$253$	2.19469	−	1.02340i	0.137979	−	0.0643407i
$254$		0			0
$255$	−0.703562	−	0.876772i	−0.0440587	−	0.0549056i
$256$		0			0
$257$	2.27311	−	25.9817i	0.141792	−	1.62070i	−0.508535	−	0.861041i	$-0.669813\pi$
$257$	2.27311	−	25.9817i	0.141792	−	1.62070i	0.650328	−	0.759654i	$-0.274632\pi$
$258$		0			0
$259$	6.85181	+	11.8677i	0.425751	+	0.737422i
$260$		0			0
$261$	8.74369	+	1.54175i	0.541221	+	0.0954319i
$262$		0			0
$263$	6.36796	−	13.6561i	0.392665	−	0.842073i	−0.606240	−	0.795282i	$-0.707323\pi$
$263$	6.36796	−	13.6561i	0.392665	−	0.842073i	0.998905	−	0.0467907i	$-0.0148994\pi$
$264$		0			0
$265$	10.3085	+	23.4333i	0.633248	+	1.43950i
$266$		0			0
$267$	11.4582	+	11.4582i	0.701229	+	0.701229i
$268$		0			0
$269$	−15.9217	+	5.79504i	−0.970765	+	0.353330i	−0.778243	−	0.627963i	$-0.783889\pi$
$269$	−15.9217	+	5.79504i	−0.970765	+	0.353330i	−0.192522	+	0.981293i	$0.561667\pi$
$270$		0			0
$271$	5.49996	−	31.1918i	0.334099	−	1.89477i	−0.101857	−	0.994799i	$-0.532479\pi$
$271$	5.49996	−	31.1918i	0.334099	−	1.89477i	0.435956	−	0.899968i	$-0.356410\pi$
$272$		0			0
$273$	−1.59480	−	0.427325i	−0.0965217	−	0.0258629i
$274$		0			0
$275$	−27.2845	−	1.19589i	−1.64532	−	0.0721148i
$276$		0			0
$277$	6.55193	−	1.75558i	0.393667	−	0.105483i	−0.0565546	−	0.998400i	$-0.518012\pi$
$277$	6.55193	−	1.75558i	0.393667	−	0.105483i	0.450222	+	0.892917i	$0.351345\pi$
$278$		0			0
$279$	44.8736	+	16.3327i	2.68651	+	0.977811i
$280$		0			0
$281$	23.1123	−	4.07533i	1.37877	−	0.243114i	0.565376	−	0.824833i	$-0.308731\pi$
$281$	23.1123	−	4.07533i	1.37877	−	0.243114i	0.813389	+	0.581720i	$0.197620\pi$
$282$		0			0
$283$	−13.9218	+	1.21800i	−0.827564	+	0.0724025i	−0.493064	−	0.869993i	$-0.664123\pi$
$283$	−13.9218	+	1.21800i	−0.827564	+	0.0724025i	−0.334500	+	0.942396i	$0.608568\pi$
$284$		0			0
$285$	−7.26773	−	28.6416i	−0.430503	−	1.69658i
$286$		0			0
$287$	−10.0053	+	0.875354i	−0.590597	+	0.0516705i
$288$		0			0
$289$	16.7147	−	2.94724i	0.983215	−	0.173367i
$290$		0			0
$291$	−1.42186	−	0.517514i	−0.0833507	−	0.0303372i
$292$		0			0
$293$	−0.339935	+	0.0910852i	−0.0198592	+	0.00532126i	−0.268735	−	0.963214i	$-0.586606\pi$
$293$	−0.339935	+	0.0910852i	−0.0198592	+	0.00532126i	0.248876	+	0.968535i	$0.419939\pi$
$294$		0			0
$295$	23.1969	−	7.87211i	1.35058	−	0.458332i
$296$		0			0
$297$	−51.0438	−	13.6771i	−2.96186	−	0.793629i
$298$		0			0
$299$	0.0293069	−	0.166208i	0.00169486	−	0.00961203i
$300$		0			0
$301$	−15.4970	+	5.64044i	−0.893231	+	0.325110i
$302$		0			0
$303$	−2.41148	−	2.41148i	−0.138536	−	0.138536i
$304$		0			0
$305$	−24.8601	−	9.67000i	−1.42349	−	0.553702i
$306$		0			0
$307$	−1.53013	+	3.28138i	−0.0873292	+	0.187278i	−0.945122	−	0.326717i	$-0.894057\pi$
$307$	−1.53013	+	3.28138i	−0.0873292	+	0.187278i	0.857793	+	0.513996i	$0.171835\pi$
$308$		0			0
$309$	−46.0801	−	8.12517i	−2.62141	−	0.462225i
$310$		0			0
$311$	12.3076	+	21.3174i	0.697901	+	1.20880i	0.969193	+	0.246303i	$0.0792160\pi$
$311$	12.3076	+	21.3174i	0.697901	+	1.20880i	−0.271291	+	0.962497i	$0.587451\pi$
$312$		0			0
$313$	−1.42067	+	16.2383i	−0.0803008	+	0.917842i	0.844042	+	0.536278i	$0.180170\pi$
$313$	−1.42067	+	16.2383i	−0.0803008	+	0.917842i	−0.924342	+	0.381564i	$0.875386\pi$
$314$		0			0
$315$	2.15775	−	19.6869i	0.121576	−	1.10923i
$316$		0			0
$317$	−16.7901	+	7.82936i	−0.943027	+	0.439741i	−0.832433	−	0.554125i	$-0.813053\pi$
$317$	−16.7901	+	7.82936i	−0.943027	+	0.439741i	−0.110593	+	0.993866i	$0.535275\pi$
$318$		0			0
$319$	−1.36020	−	7.71407i	−0.0761565	−	0.431905i
$320$		0			0
$321$	19.1240	+	16.0470i	1.06740	+	0.895654i
$322$		0			0
$323$	−0.699779	−	0.181067i	−0.0389367	−	0.0100748i
$324$		0			0
$325$	−1.15898	+	1.50989i	−0.0642888	+	0.0837534i
$326$		0			0
$327$	−15.4624	+	22.0826i	−0.855072	+	1.22117i
$328$		0			0
$329$	1.52967	−	4.20272i	0.0843332	−	0.231704i
$330$		0			0
$331$	−11.8874	−	6.86318i	−0.653389	−	0.377235i	0.136364	−	0.990659i	$-0.456458\pi$
$331$	−11.8874	−	6.86318i	−0.653389	−	0.377235i	−0.789754	+	0.613424i	$0.789792\pi$
$332$		0			0
$333$	59.0800	+	5.16883i	3.23756	+	0.283250i
$334$		0			0
$335$	15.9972	+	11.7317i	0.874019	+	0.640971i
$336$		0			0
$337$	12.9431	+	18.4847i	0.705056	+	1.00692i	0.998698	+	0.0510088i	$0.0162437\pi$
$337$	12.9431	+	18.4847i	0.705056	+	1.00692i	−0.293642	+	0.955915i	$0.594867\pi$
$338$		0			0
$339$	9.71555	+	26.6932i	0.527676	+	1.44978i
$340$		0			0
$341$		−	42.1303i		−	2.28148i
$342$		0			0
$343$	−12.0918	+	12.0918i	−0.652895	+	0.652895i
$344$		0			0
$345$	3.00470	+	0.0658171i	0.161768	+	0.00354347i
$346$		0			0
$347$	−29.5562	+	20.6955i	−1.58666	+	1.11099i	−0.650455	+	0.759545i	$0.725422\pi$
$347$	−29.5562	+	20.6955i	−1.58666	+	1.11099i	−0.936207	+	0.351448i	$0.885689\pi$
$348$		0			0
$349$	4.78794	−	2.76432i	0.256292	−	0.147970i	−0.366350	−	0.930477i	$-0.619393\pi$
$349$	4.78794	−	2.76432i	0.256292	−	0.147970i	0.622642	+	0.782507i	$0.286059\pi$
$350$		0			0
$351$	−2.82134	+	2.36738i	−0.150592	+	0.126362i
$352$		0			0
$353$	−1.95531	−	7.29731i	−0.104071	−	0.388397i	0.894168	−	0.447733i	$-0.147768\pi$
$353$	−1.95531	−	7.29731i	−0.104071	−	0.388397i	−0.998238	+	0.0593360i	$0.981102\pi$
$354$		0			0
$355$	0.487802	−	0.556137i	0.0258898	−	0.0295167i
$356$		0			0
$357$	−0.589141	−	0.412521i	−0.0311806	−	0.0218329i
$358$		0			0
$359$	−2.56312	+	3.05461i	−0.135276	+	0.161216i	−0.829430	−	0.558611i	$-0.811335\pi$
$359$	−2.56312	+	3.05461i	−0.135276	+	0.161216i	0.694153	+	0.719827i	$0.255779\pi$
$360$		0			0
$361$	−14.7628	−	11.9607i	−0.776992	−	0.629511i
$362$		0			0
$363$	4.97674	+	56.8844i	0.261211	+	2.98566i
$364$		0			0
$365$	−2.83587	−	4.24496i	−0.148436	−	0.222191i
$366$		0			0
$367$	14.6703	+	31.4606i	0.765784	+	1.64223i	0.766512	+	0.642230i	$0.221991\pi$
$367$	14.6703	+	31.4606i	0.765784	+	1.64223i	−0.000727542		1.00000i	$0.500232\pi$
$368$		0			0
$369$	−21.7329	+	37.6426i	−1.13137	+	1.95959i
$370$		0			0
$371$	10.5279	+	12.5467i	0.546583	+	0.651393i
$372$		0			0
$373$	0.766310	−	2.85991i	0.0396781	−	0.148081i	−0.943245	−	0.332098i	$-0.892244\pi$
$373$	0.766310	−	2.85991i	0.0396781	−	0.148081i	0.982923	+	0.184017i	$0.0589103\pi$
$374$		0			0
$375$	−29.7129	−	16.3108i	−1.53437	−	0.842288i
$376$		0			0
$377$	−0.494777	−	0.230718i	−0.0254823	−	0.0118826i
$378$		0			0
$379$	−31.3437			−1.61002			−0.805010	−	0.593262i	$-0.797840\pi$
$379$	−31.3437			−1.61002			−0.805010	+	0.593262i	$0.797840\pi$
$380$		0			0
$381$	−15.2438			−0.780965
$382$		0			0
$383$	8.61928	+	4.01924i	0.440425	+	0.205373i	0.630166	−	0.776461i	$-0.282987\pi$
$383$	8.61928	+	4.01924i	0.440425	+	0.205373i	−0.189741	+	0.981834i	$0.560765\pi$
$384$		0			0
$385$	−16.9723	+	4.15158i	−0.864990	+	0.211584i
$386$		0			0
$387$	−18.4722	+	68.9391i	−0.938994	+	3.50437i
$388$		0			0
$389$	6.11064	+	7.28238i	0.309822	+	0.369231i	0.898377	−	0.439226i	$-0.144747\pi$
$389$	6.11064	+	7.28238i	0.309822	+	0.369231i	−0.588555	+	0.808457i	$0.700303\pi$
$390$		0			0
$391$	0.0367588	−	0.0636681i	0.00185897	−	0.00321983i
$392$		0			0
$393$	14.6979	+	31.5197i	0.741410	+	1.58996i
$394$		0			0
$395$	1.19482	−	6.00412i	0.0601180	−	0.302100i
$396$		0			0
$397$	−0.411018	−	4.69796i	−0.0206284	−	0.235784i	−0.999509	−	0.0313487i	$-0.990020\pi$
$397$	−0.411018	−	4.69796i	−0.0206284	−	0.235784i	0.978880	−	0.204435i	$-0.0655358\pi$
$398$		0			0
$399$	−9.59298	−	16.2902i	−0.480250	−	0.815531i
$400$		0			0
$401$	3.05550	−	3.64140i	0.152584	−	0.181843i	−0.684338	−	0.729165i	$-0.739908\pi$
$401$	3.05550	−	3.64140i	0.152584	−	0.181843i	0.836922	+	0.547323i	$0.184353\pi$
$402$		0			0
$403$	−2.40525	−	1.68418i	−0.119814	−	0.0838948i
$404$		0			0
$405$	−18.0832	−	15.8613i	−0.898563	−	0.788153i
$406$		0			0
$407$	−13.5419	−	50.5392i	−0.671250	−	2.50514i
$408$		0			0
$409$	−16.9851	+	14.2522i	−0.839858	+	0.704724i	−0.957532	−	0.288328i	$-0.906901\pi$
$409$	−16.9851	+	14.2522i	−0.839858	+	0.704724i	0.117674	+	0.993052i	$0.462456\pi$
$410$		0			0
$411$	−3.35360	+	1.93620i	−0.165421	+	0.0955059i
$412$		0			0
$413$	12.8379	−	8.98916i	0.631710	−	0.442328i
$414$		0			0
$415$	18.5958	−	17.7986i	0.912834	−	0.873701i
$416$		0			0
$417$	11.3226	−	11.3226i	0.554470	−	0.554470i
$418$		0			0
$419$			27.3929i			1.33823i	0.743159	+	0.669115i	$0.233327\pi$
$419$			27.3929i			1.33823i	−0.743159	+	0.669115i	$0.766673\pi$
$420$		0			0
$421$	−4.48082	−	12.3109i	−0.218382	−	0.599999i	0.781327	−	0.624121i	$-0.214543\pi$
$421$	−4.48082	−	12.3109i	−0.218382	−	0.599999i	−0.999709	+	0.0241228i	$0.992321\pi$
$422$		0			0
$423$	−11.1019	−	15.8551i	−0.539792	−	0.770903i
$424$		0			0
$425$	−0.699362	+	0.445376i	−0.0339240	+	0.0216039i
$426$		0			0
$427$	−17.0008	−	1.48738i	−0.822728	−	0.0719793i
$428$		0			0
$429$	5.45937	+	3.15197i	0.263581	+	0.152179i
$430$		0			0
$431$	−10.1249	+	27.8180i	−0.487701	+	1.33995i	0.415056	+	0.909796i	$0.363762\pi$
$431$	−10.1249	+	27.8180i	−0.487701	+	1.33995i	−0.902757	+	0.430151i	$0.858460\pi$
$432$		0			0
$433$	0.999898	−	1.42800i	0.0480520	−	0.0686254i	−0.794407	−	0.607386i	$-0.792218\pi$
$433$	0.999898	−	1.42800i	0.0480520	−	0.0686254i	0.842459	+	0.538760i	$0.181107\pi$
$434$		0			0
$435$	2.72119	−	9.33305i	0.130471	−	0.447486i
$436$		0			0
$437$	1.57339	−	1.12200i	0.0752654	−	0.0536724i
$438$		0			0
$439$	−6.39461	−	5.36572i	−0.305198	−	0.256092i	0.477306	−	0.878737i	$-0.341613\pi$
$439$	−6.39461	−	5.36572i	−0.305198	−	0.256092i	−0.782504	+	0.622646i	$0.786058\pi$
$440$		0			0
$441$	5.32538	+	30.2017i	0.253589	+	1.43818i
$442$		0			0
$443$	−21.4646	+	10.0091i	−1.01981	+	0.475547i	−0.859292	−	0.511485i	$-0.829095\pi$
$443$	−21.4646	+	10.0091i	−1.01981	+	0.475547i	−0.160522	+	0.987032i	$0.551318\pi$
$444$		0			0
$445$	9.32159	−	7.48007i	0.441886	−	0.354589i
$446$		0			0
$447$	3.71810	−	42.4981i	0.175860	−	2.01009i
$448$		0			0
$449$	2.36294	+	4.09274i	0.111514	+	0.193148i	0.916381	−	0.400307i	$-0.131097\pi$
$449$	2.36294	+	4.09274i	0.111514	+	0.193148i	−0.804867	+	0.593455i	$0.797763\pi$
$450$		0			0
$451$	37.7649	+	6.65898i	1.77828	+	0.313559i
$452$		0			0
$453$	26.1738	−	56.1299i	1.22975	−	2.63721i
$454$		0			0
$455$	−0.441459	+	1.13492i	−0.0206959	+	0.0532061i
$456$		0			0
$457$	−13.9975	−	13.9975i	−0.654773	−	0.654773i	0.299365	−	0.954139i	$-0.403225\pi$
$457$	−13.9975	−	13.9975i	−0.654773	−	0.654773i	−0.954139	+	0.299365i	$0.903225\pi$
$458$		0			0
$459$	−1.50757	+	0.548712i	−0.0703676	+	0.0256117i
$460$		0			0
$461$	−0.975172	+	5.53048i	−0.0454183	+	0.257580i	−0.999059	−	0.0433669i	$-0.986192\pi$
$461$	−0.975172	+	5.53048i	−0.0454183	+	0.257580i	0.953641	+	0.300947i	$0.0973027\pi$
$462$		0			0
$463$	12.6185	+	3.38111i	0.586430	+	0.157133i	0.539821	−	0.841780i	$-0.318492\pi$
$463$	12.6185	+	3.38111i	0.586430	+	0.157133i	0.0466088	+	0.998913i	$0.485159\pi$
$464$		0			0
$465$	23.1304	−	46.8938i	1.07265	−	2.17465i
$466$		0			0
$467$	30.4453	−	8.15779i	1.40884	−	0.377498i	0.527329	−	0.849661i	$-0.323194\pi$
$467$	30.4453	−	8.15779i	1.40884	−	0.377498i	0.881511	+	0.472164i	$0.156527\pi$
$468$		0			0
$469$	11.9264	+	4.34085i	0.550710	+	0.200442i
$470$		0			0
$471$	−49.1507	+	8.66660i	−2.26475	+	0.399336i
$472$		0			0
$473$	62.7271	−	5.48791i	2.88420	−	0.252334i
$474$		0			0
$475$	−21.5833	+	3.02691i	−0.990309	+	0.138884i
$476$		0			0
$477$	70.6124	−	6.17778i	3.23312	−	0.282861i
$478$		0			0
$479$	28.5377	−	5.03196i	1.30392	−	0.229916i	0.521813	−	0.853060i	$-0.325256\pi$
$479$	28.5377	−	5.03196i	1.30392	−	0.229916i	0.782107	+	0.623144i	$0.214145\pi$
$480$		0			0
$481$	−3.42667	−	1.24721i	−0.156243	−	0.0568677i
$482$		0			0
$483$	1.85728	−	0.497657i	0.0845092	−	0.0226442i
$484$		0			0
$485$	−0.493685	+	1.00088i	−0.0224171	+	0.0454476i
$486$		0			0
$487$	26.8569	+	7.19630i	1.21700	+	0.326095i	0.809507	−	0.587111i	$-0.199735\pi$
$487$	26.8569	+	7.19630i	1.21700	+	0.326095i	0.407498	+	0.913206i	$0.366401\pi$
$488$		0			0
$489$	4.79367	−	27.1862i	0.216777	−	1.22940i
$490$		0			0
$491$	19.2426	−	7.00372i	0.868404	−	0.316073i	0.130883	−	0.991398i	$-0.458219\pi$
$491$	19.2426	−	7.00372i	0.868404	−	0.316073i	0.737521	+	0.675324i	$0.235996\pi$
$492$		0			0
$493$	−0.168155	−	0.168155i	−0.00757334	−	0.00757334i
$494$		0			0
$495$	−27.4125	+	70.4735i	−1.23210	+	3.16755i
$496$		0			0
$497$	0.200016	−	0.428935i	0.00897194	−	0.0192404i
$498$		0			0
$499$	−11.8732	−	2.09357i	−0.531519	−	0.0937211i	−0.0985537	−	0.995132i	$-0.531422\pi$
$499$	−11.8732	−	2.09357i	−0.531519	−	0.0937211i	−0.432965	+	0.901411i	$0.642533\pi$
$500$		0			0
$501$	−9.46629	−	16.3961i	−0.422923	−	0.732523i
$502$		0			0
$503$	2.40329	−	27.4697i	0.107157	−	1.22481i	−0.732145	−	0.681149i	$-0.761480\pi$
$503$	2.40329	−	27.4697i	0.107157	−	1.22481i	0.839302	−	0.543666i	$-0.182964\pi$
$504$		0			0
$505$	−1.96181	+	1.57425i	−0.0872996	+	0.0700532i
$506$		0			0
$507$	−35.3213	+	16.4706i	−1.56867	+	0.731484i
$508$		0			0
$509$	2.22736	+	12.6320i	0.0987260	+	0.559903i	0.993542	+	0.113467i	$0.0361957\pi$
$509$	2.22736	+	12.6320i	0.0987260	+	0.559903i	−0.894816	+	0.446436i	$0.852693\pi$
$510$		0			0
$511$	−2.50198	−	2.09941i	−0.110681	−	0.0928725i
$512$		0			0
$513$	−42.0406	−	3.31385i	−1.85614	−	0.146310i
$514$		0			0
$515$	−9.66007	+	33.1318i	−0.425674	+	1.45996i
$516$		0			0
$517$	−9.79458	+	13.9881i	−0.430765	+	0.615196i
$518$		0			0
$519$	16.3536	−	44.9311i	0.717842	−	1.97226i
$520$		0			0
$521$	−14.6741	−	8.47209i	−0.642884	−	0.371169i	0.142841	−	0.989746i	$-0.454376\pi$
$521$	−14.6741	−	8.47209i	−0.642884	−	0.371169i	−0.785725	+	0.618577i	$0.787710\pi$
$522$		0			0
$523$	24.1464	+	2.11254i	1.05585	+	0.0923748i	0.601836	−	0.798620i	$-0.294436\pi$
$523$	24.1464	+	2.11254i	1.05585	+	0.0923748i	0.454013	+	0.890995i	$0.349992\pi$
$524$		0			0
$525$	−21.1706	−	4.69717i	−0.923962	−	0.205001i
$526$		0			0
$527$	−0.733634	−	1.04774i	−0.0319576	−	0.0456402i
$528$		0			0
$529$	−7.79924	−	21.4282i	−0.339097	−	0.931662i
$530$		0			0
$531$		−	67.8248i		−	2.94335i
$532$		0			0
$533$	1.88984	−	1.88984i	0.0818579	−	0.0818579i
$534$		0			0
$535$	13.3020	−	12.7317i	0.575094	−	0.550439i
$536$		0			0
$537$	52.9022	−	37.0425i	2.28290	−	1.59850i
$538$		0			0
$539$	23.4315	−	13.5282i	1.00926	−	0.582699i
$540$		0			0
$541$	−27.0758	+	22.7193i	−1.16408	+	0.976779i	−0.999953	−	0.00966081i	$-0.996925\pi$
$541$	−27.0758	+	22.7193i	−1.16408	+	0.976779i	−0.164126	+	0.986439i	$0.552480\pi$
$542$		0			0
$543$	6.90816	+	25.7816i	0.296457	+	1.10639i
$544$		0			0
$545$	14.9478	+	13.1111i	0.640294	+	0.561619i
$546$		0			0
$547$	18.0598	+	12.6456i	0.772183	+	0.540689i	0.891961	−	0.452112i	$-0.149329\pi$
$547$	18.0598	+	12.6456i	0.772183	+	0.540689i	−0.119778	+	0.992801i	$0.538218\pi$
$548$		0			0
$549$	−47.4738	+	56.5771i	−2.02613	+	2.41465i
$550$		0			0
$551$	−2.18841	−	5.85537i	−0.0932296	−	0.249447i
$552$		0			0
$553$	−0.341355	−	3.90170i	−0.0145159	−	0.165917i
$554$		0			0
$555$	12.6740	−	63.6883i	0.537981	−	2.70342i
$556$		0			0
$557$	10.4168	+	22.3390i	0.441376	+	0.946534i	0.993612	+	0.112846i	$0.0359968\pi$
$557$	10.4168	+	22.3390i	0.441376	+	0.946534i	−0.552237	+	0.833687i	$0.686225\pi$
$558$		0			0
$559$	2.19423	−	3.80052i	0.0928062	−	0.160745i
$560$		0			0
$561$	1.76511	+	2.10358i	0.0745230	+	0.0888130i
$562$		0			0
$563$	0.147798	−	0.551590i	0.00622894	−	0.0232467i	−0.962741	−	0.270424i	$-0.912836\pi$
$563$	0.147798	−	0.551590i	0.00622894	−	0.0232467i	0.968970	+	0.247177i	$0.0795029\pi$
$564$		0			0
$565$	20.3515	−	4.97815i	0.856193	−	0.209432i
$566$		0			0
$567$	−13.9472	−	6.50368i	−0.585727	−	0.273129i
$568$		0			0
$569$	−34.0442			−1.42721			−0.713603	−	0.700551i	$-0.752938\pi$
$569$	−34.0442			−1.42721			−0.713603	+	0.700551i	$0.752938\pi$
$570$		0			0
$571$	26.6659			1.11593			0.557967	−	0.829863i	$-0.311582\pi$
$571$	26.6659			1.11593			0.557967	+	0.829863i	$0.311582\pi$
$572$		0			0
$573$	−32.5951	−	15.1993i	−1.36168	−	0.634962i
$574$		0			0
$575$	0.289708	−	2.19768i	0.0120817	−	0.0916495i
$576$		0			0
$577$	1.99204	−	7.43441i	0.0829298	−	0.309498i	−0.911984	−	0.410225i	$-0.865450\pi$
$577$	1.99204	−	7.43441i	0.0829298	−	0.309498i	0.994914	+	0.100727i	$0.0321168\pi$
$578$		0			0
$579$	6.41467	+	7.64471i	0.266585	+	0.317703i
$580$		0			0
$581$	8.23422	−	14.2621i	0.341613	−	0.591691i
$582$		0			0
$583$	−26.4286	−	56.6763i	−1.09456	−	2.34729i
$584$		0			0
$585$	2.92756	+	4.38221i	0.121040	+	0.181182i
$586$		0			0
$587$	−0.646976	−	7.39497i	−0.0267036	−	0.305223i	−0.997787	−	0.0664847i	$-0.978822\pi$
$587$	−0.646976	−	7.39497i	−0.0267036	−	0.305223i	0.971084	−	0.238739i	$-0.0767339\pi$
$588$		0			0
$589$	−6.12286	−	33.0586i	−0.252288	−	1.36216i
$590$		0			0
$591$	−38.0399	+	45.3342i	−1.56475	+	1.86480i
$592$		0			0
$593$	−9.53664	−	6.67763i	−0.391623	−	0.274217i	0.361137	−	0.932513i	$-0.382389\pi$
$593$	−9.53664	−	6.67763i	−0.391623	−	0.274217i	−0.752760	+	0.658296i	$0.771278\pi$
$594$		0			0
$595$	−0.349791	+	0.398792i	−0.0143400	+	0.0163489i
$596$		0			0
$597$	8.94523	+	33.3841i	0.366104	+	1.36632i
$598$		0			0
$599$	−1.68646	+	1.41511i	−0.0689069	+	0.0578197i	−0.676591	−	0.736359i	$-0.736543\pi$
$599$	−1.68646	+	1.41511i	−0.0689069	+	0.0578197i	0.607684	+	0.794179i	$0.292099\pi$
$600$		0			0
$601$	−12.0611	+	6.96346i	−0.491981	+	0.284045i	−0.725396	−	0.688332i	$-0.758343\pi$
$601$	−12.0611	+	6.96346i	−0.491981	+	0.284045i	0.233415	+	0.972377i	$0.425010\pi$
$602$		0			0
$603$	44.9934	−	31.5047i	1.83227	−	1.28297i
$604$		0			0
$605$	42.1060	+	0.922319i	1.71185	+	0.0374976i
$606$		0			0
$607$	−27.3635	+	27.3635i	−1.11065	+	1.11065i	−0.117588	+	0.993062i	$0.537516\pi$
$607$	−27.3635	+	27.3635i	−1.11065	+	1.11065i	−0.993062	+	0.117588i	$0.962484\pi$
$608$		0			0
$609$		−	6.21968i		−	0.252034i
$610$		0			0
$611$	0.407050	+	1.11836i	0.0164675	+	0.0452440i
$612$		0			0
$613$	−16.0911	−	22.9805i	−0.649913	−	0.928172i	0.350050	−	0.936731i	$-0.386165\pi$
$613$	−16.0911	−	22.9805i	−0.649913	−	0.928172i	−0.999963	+	0.00855863i	$0.997276\pi$
$614$		0			0
$615$	38.3790	+	28.1456i	1.54759	+	1.13494i
$616$		0			0
$617$	1.72373	+	0.150807i	0.0693949	+	0.00607127i	0.121800	−	0.992555i	$-0.461133\pi$
$617$	1.72373	+	0.150807i	0.0693949	+	0.00607127i	−0.0524054	+	0.998626i	$0.516689\pi$
$618$		0			0
$619$	16.7870	+	9.69196i	0.674725	+	0.389553i	0.797865	−	0.602837i	$-0.205963\pi$
$619$	16.7870	+	9.69196i	0.674725	+	0.389553i	−0.123140	+	0.992389i	$0.539296\pi$
$620$		0			0
$621$	1.46698	−	4.03049i	0.0588678	−	0.161738i
$622$		0			0
$623$	4.38580	−	6.26357i	0.175713	−	0.250945i
$624$		0			0
$625$	−14.3463	+	20.4740i	−0.573853	+	0.818958i
$626$		0			0
$627$	19.2811	+	69.5585i	0.770013	+	2.77790i
$628$		0			0
$629$	−1.21684	−	1.02105i	−0.0485185	−	0.0407118i
$630$		0			0
$631$	−1.43123	−	8.11694i	−0.0569766	−	0.323130i	0.942976	−	0.332860i	$-0.108014\pi$
$631$	−1.43123	−	8.11694i	−0.0569766	−	0.323130i	−0.999953	+	0.00973032i	$0.996903\pi$
$632$		0			0
$633$	−31.6084	+	14.7392i	−1.25632	+	0.585832i
$634$		0			0
$635$	−1.22497	+	11.1764i	−0.0486113	+	0.443520i
$636$		0			0
$637$	0.164349	−	1.87852i	0.00651174	−	0.0744295i
$638$		0			0
$639$	−1.02411	−	1.77381i	−0.0405132	−	0.0701709i
$640$		0			0
$641$	3.01863	+	0.532266i	0.119229	+	0.0210232i	0.232944	−	0.972490i	$-0.425164\pi$
$641$	3.01863	+	0.532266i	0.119229	+	0.0210232i	−0.113715	+	0.993513i	$0.536275\pi$
$642$		0			0
$643$	−11.3967	+	24.4403i	−0.449442	+	0.963832i	0.542840	+	0.839836i	$0.317349\pi$
$643$	−11.3967	+	24.4403i	−0.449442	+	0.963832i	−0.992283	+	0.123996i	$0.960429\pi$
$644$		0			0
$645$	72.8324	+	28.3301i	2.86777	+	1.11549i
$646$		0			0
$647$	−9.43474	−	9.43474i	−0.370918	−	0.370918i	0.496894	−	0.867812i	$-0.334474\pi$
$647$	−9.43474	−	9.43474i	−0.370918	−	0.370918i	−0.867812	+	0.496894i	$0.834474\pi$
$648$		0			0
$649$	−56.2294	+	20.4658i	−2.20720	+	0.803354i
$650$		0			0
$651$	5.80899	−	32.9444i	0.227672	−	1.29119i
$652$		0			0
$653$	25.7176	+	6.89102i	1.00641	+	0.269666i	0.724128	−	0.689665i	$-0.242242\pi$
$653$	25.7176	+	6.89102i	1.00641	+	0.269666i	0.282281	+	0.959332i	$0.408909\pi$
$654$		0			0
$655$	24.2905	−	8.24322i	0.949108	−	0.322089i
$656$		0			0
$657$	−13.6532	+	3.65836i	−0.532662	+	0.142726i
$658$		0			0
$659$	8.38583	+	3.05219i	0.326666	+	0.118897i	0.500147	−	0.865941i	$-0.333279\pi$
$659$	8.38583	+	3.05219i	0.326666	+	0.118897i	−0.173481	+	0.984837i	$0.555502\pi$
$660$		0			0
$661$	−15.1515	+	2.67162i	−0.589325	+	0.103914i	−0.460356	−	0.887735i	$-0.652278\pi$
$661$	−15.1515	+	2.67162i	−0.589325	+	0.103914i	−0.128970	+	0.991649i	$0.541167\pi$
$662$		0			0
$663$	0.190656	−	0.0166802i	0.00740446	−	0.000647806i
$664$		0			0
$665$	−12.7144	+	5.72426i	−0.493044	+	0.221977i
$666$		0			0
$667$	0.633358	−	0.0554117i	0.0245237	−	0.00214555i
$668$		0			0
$669$	46.6839	−	8.23163i	1.80490	−	0.318253i
$670$		0			0
$671$	61.2296	+	22.2857i	2.36374	+	0.860332i
$672$		0			0
$673$	1.76147	−	0.471984i	0.0678996	−	0.0181936i	−0.224709	−	0.974426i	$-0.572143\pi$
$673$	1.76147	−	0.471984i	0.0678996	−	0.0181936i	0.292609	+	0.956232i	$0.405477\pi$
$674$		0			0
$675$	−35.6702	+	32.6746i	−1.37295	+	1.25765i
$676$		0			0
$677$	2.89080	+	0.774587i	0.111102	+	0.0297698i	0.313942	−	0.949442i	$-0.398350\pi$
$677$	2.89080	+	0.774587i	0.111102	+	0.0297698i	−0.202839	+	0.979212i	$0.565017\pi$
$678$		0			0
$679$	−0.123984	+	0.703151i	−0.00475809	+	0.0269845i
$680$		0			0
$681$	−25.5802	+	9.31045i	−0.980237	+	0.356777i
$682$		0			0
$683$	16.7520	+	16.7520i	0.640998	+	0.640998i	0.950801	−	0.309803i	$-0.100263\pi$
$683$	16.7520	+	16.7520i	0.640998	+	0.640998i	−0.309803	+	0.950801i	$0.600263\pi$
$684$		0			0
$685$	1.15008	+	2.61436i	0.0439424	+	0.0998896i
$686$		0			0
$687$	1.59122	−	3.41239i	0.0607089	−	0.130191i
$688$		0			0
$689$	−4.29219	−	0.756829i	−0.163519	−	0.0288329i
$690$		0			0
$691$	−4.79488	−	8.30497i	−0.182406	−	0.315936i	0.760294	−	0.649580i	$-0.225055\pi$
$691$	−4.79488	−	8.30497i	−0.182406	−	0.315936i	−0.942699	+	0.333644i	$0.891722\pi$
$692$		0			0
$693$	−4.21643	+	48.1940i	−0.160169	+	1.83074i
$694$		0			0
$695$	−7.39156	−	9.21128i	−0.280378	−	0.349404i
$696$		0			0
$697$	1.05513	−	0.492016i	0.0399660	−	0.0186364i
$698$		0			0
$699$	−9.47736	−	53.7488i	−0.358467	−	2.03297i
$700$		0			0
$701$	−30.5097	−	25.6007i	−1.15234	−	0.966925i	−0.152564	−	0.988294i	$-0.548753\pi$
$701$	−30.5097	−	25.6007i	−1.15234	−	0.966925i	−0.999772	+	0.0213689i	$0.993198\pi$
$702$		0			0
$703$	−17.9710	−	37.6889i	−0.677789	−	1.42146i
$704$		0			0
$705$	−18.5818	+	10.1923i	−0.699830	+	0.383863i
$706$		0			0
$707$	−0.923033	+	1.31823i	−0.0347142	+	0.0495770i
$708$		0			0
$709$	−0.312288	+	0.858004i	−0.0117282	+	0.0322230i	−0.945419	−	0.325858i	$-0.894347\pi$
$709$	−0.312288	+	0.858004i	−0.0117282	+	0.0322230i	0.933690	+	0.358081i	$0.116569\pi$
$710$		0			0
$711$	−14.6792	−	8.47502i	−0.550512	−	0.317838i
$712$		0			0
$713$	3.40653	+	0.298032i	0.127575	+	0.0111614i
$714$		0			0
$715$	2.74964	−	3.74938i	0.102831	−	0.140219i
$716$		0			0
$717$	22.2869	+	31.8290i	0.832320	+	1.18868i
$718$		0			0
$719$	0.148862	+	0.408995i	0.00555161	+	0.0152529i	0.942437	−	0.334382i	$-0.108528\pi$
$719$	0.148862	+	0.408995i	0.00555161	+	0.0152529i	−0.936886	+	0.349635i	$0.886305\pi$
$720$		0			0
$721$			22.0795i			0.822284i
$722$		0			0
$723$	25.8496	−	25.8496i	0.961356	−	0.961356i
$724$		0			0
$725$	−6.62407	−	2.74509i	−0.246012	−	0.101950i
$726$		0			0
$727$	17.2496	−	12.0783i	0.639752	−	0.447959i	−0.208161	−	0.978095i	$-0.566748\pi$
$727$	17.2496	−	12.0783i	0.639752	−	0.447959i	0.847913	+	0.530135i	$0.177859\pi$
$728$		0			0
$729$	18.5265	−	10.6963i	0.686166	−	0.396158i
$730$		0			0
$731$	1.46440	−	1.22877i	0.0541627	−	0.0454479i
$732$		0			0
$733$	3.37563	+	12.5980i	0.124682	+	0.465318i	0.999828	−	0.0185400i	$-0.00590180\pi$
$733$	3.37563	+	12.5980i	0.124682	+	0.465318i	−0.875147	+	0.483858i	$0.839235\pi$
$734$		0			0
$735$	33.5080	−	2.19339i	1.23596	−	0.0809043i
$736$		0			0
$737$	−39.6952	−	27.7949i	−1.46219	−	1.02384i
$738$		0			0
$739$	2.05518	−	2.44926i	0.0756009	−	0.0900976i	−0.726918	−	0.686724i	$-0.759048\pi$
$739$	2.05518	−	2.44926i	0.0756009	−	0.0900976i	0.802519	+	0.596626i	$0.203493\pi$
$740$		0			0
$741$	4.74192	+	1.67986i	0.174199	+	0.0617111i
$742$		0			0
$743$	−1.79419	−	20.5077i	−0.0658225	−	0.752355i	−0.955351	−	0.295474i	$-0.904522\pi$
$743$	−1.79419	−	20.5077i	−0.0658225	−	0.752355i	0.889528	−	0.456880i	$-0.151033\pi$
$744$		0			0
$745$	−30.8596	−	6.14108i	−1.13061	−	0.224992i
$746$		0			0
$747$	−30.1205	−	64.5935i	−1.10205	−	2.36335i
$748$		0			0
$749$	5.89009	−	10.2019i	0.215219	−	0.372771i
$750$		0			0
$751$	9.43710	+	11.2467i	0.344365	+	0.410398i	0.910232	−	0.414098i	$-0.135903\pi$
$751$	9.43710	+	11.2467i	0.344365	+	0.410398i	−0.565867	+	0.824496i	$0.691459\pi$
$752$		0			0
$753$	−10.2934	+	38.4157i	−0.375114	+	1.39994i
$754$		0			0
$755$	−39.0496	−	23.7004i	−1.42116	−	0.862547i
$756$		0			0
$757$	−27.4326	−	12.7920i	−0.997055	−	0.464935i	−0.145590	−	0.989345i	$-0.546508\pi$
$757$	−27.4326	−	12.7920i	−0.997055	−	0.464935i	−0.851466	+	0.524411i	$0.824286\pi$
$758$		0			0
$759$	−7.34147			−0.266479
$760$		0			0
$761$	45.9564			1.66592			0.832958	−	0.553336i	$-0.186645\pi$
$761$	45.9564			1.66592			0.832958	+	0.553336i	$0.186645\pi$
$762$		0			0
$763$	11.5289	+	5.37602i	0.417374	+	0.194625i
$764$		0			0
$765$	0.545466	+	2.22995i	0.0197214	+	0.0806241i
$766$		0			0
$767$	−1.07938	+	4.02831i	−0.0389743	+	0.145454i
$768$		0			0
$769$	−20.5141	−	24.4477i	−0.739757	−	0.881608i	0.256633	−	0.966509i	$-0.417387\pi$
$769$	−20.5141	−	24.4477i	−0.739757	−	0.881608i	−0.996389	+	0.0849013i	$0.972943\pi$
$770$		0			0
$771$	−39.5348	+	68.4762i	−1.42381	+	2.46611i
$772$		0			0
$773$	1.37825	+	2.95567i	0.0495722	+	0.106308i	0.929534	−	0.368737i	$-0.120210\pi$
$773$	1.37825	+	2.95567i	0.0495722	+	0.106308i	−0.879962	+	0.475045i	$0.842432\pi$
$774$		0			0
$775$	−32.5225	−	20.7269i	−1.16824	−	0.744531i
$776$		0			0
$777$	−3.62090	−	41.3871i	−0.129899	−	1.48475i
$778$		0			0
$779$	30.6010	−	0.263299i	1.09639	−	0.00943366i
$780$		0			0
$781$	−1.16154	+	1.38427i	−0.0415631	+	0.0495330i
$782$		0			0
$783$	−11.3651	−	7.95790i	−0.406154	−	0.284392i
$784$		0			0
$785$	2.40445	+	36.7324i	0.0858185	+	1.31104i
$786$		0			0
$787$	−8.61435	−	32.1492i	−0.307068	−	1.14599i	−0.931150	−	0.364636i	$-0.881194\pi$
$787$	−8.61435	−	32.1492i	−0.307068	−	1.14599i	0.624082	−	0.781359i	$-0.285473\pi$
$788$		0			0
$789$	−34.9938	+	29.3633i	−1.24581	+	1.04536i
$790$		0			0
$791$	11.6084	−	6.70213i	0.412748	−	0.238300i
$792$		0			0
$793$	3.71999	−	2.60476i	0.132101	−	0.0924979i
$794$		0			0
$795$	1.69968	−	77.5943i	0.0602813	−	2.75199i
$796$		0			0
$797$	−24.8027	+	24.8027i	−0.878558	+	0.878558i	−0.993385	−	0.114828i	$-0.963368\pi$
$797$	−24.8027	+	24.8027i	−0.878558	+	0.878558i	0.114828	+	0.993385i	$0.463368\pi$
$798$		0			0
$799$			0.518428i			0.0183407i
$800$		0			0
$801$	−11.3180	−	31.0960i	−0.399902	−	1.09872i
$802$		0			0
$803$	7.15271	+	10.2151i	0.252414	+	0.360484i
$804$		0			0
$805$	−0.215621	−	1.40170i	−0.00759963	−	0.0494034i
$806$		0			0
$807$	51.1722	+	4.47699i	1.80135	+	0.157597i
$808$		0			0
$809$	43.2476	+	24.9690i	1.52050	+	0.877864i	0.999708	+	0.0241837i	$0.00769865\pi$
$809$	43.2476	+	24.9690i	1.52050	+	0.877864i	0.520797	+	0.853680i	$0.325635\pi$
$810$		0			0
$811$	−4.57286	+	12.5638i	−0.160575	+	0.441176i	−0.993722	−	0.111875i	$-0.964314\pi$
$811$	−4.57286	+	12.5638i	−0.160575	+	0.441176i	0.833147	+	0.553051i	$0.186536\pi$
$812$		0			0
$813$	−55.0765	+	78.6573i	−1.93162	+	2.75863i
$814$		0			0
$815$	−19.5470	−	5.69922i	−0.684701	−	0.199635i
$816$		0			0
$817$	48.4229	−	13.4225i	1.69410	−	0.469593i
$818$		0			0
$819$	2.58288	+	2.16729i	0.0902531	+	0.0757314i
$820$		0			0
$821$	7.37576	+	41.8300i	0.257416	+	1.45988i	0.789795	+	0.613371i	$0.210187\pi$
$821$	7.37576	+	41.8300i	0.257416	+	1.45988i	−0.532379	+	0.846506i	$0.678702\pi$
$822$		0			0
$823$	−5.82682	+	2.71709i	−0.203110	+	0.0947119i	−0.521512	−	0.853244i	$-0.674632\pi$
$823$	−5.82682	+	2.71709i	−0.203110	+	0.0947119i	0.318402	+	0.947956i	$0.396854\pi$
$824$		0			0
$825$	73.4359	+	38.2441i	2.55671	+	1.33149i
$826$		0			0
$827$	3.71091	−	42.4159i	0.129041	−	1.47495i	−0.605209	−	0.796067i	$-0.706910\pi$
$827$	3.71091	−	42.4159i	0.129041	−	1.47495i	0.734250	−	0.678879i	$-0.237534\pi$
$828$		0			0
$829$	6.49254	+	11.2454i	0.225495	+	0.390569i	0.956468	−	0.291837i	$-0.0942666\pi$
$829$	6.49254	+	11.2454i	0.225495	+	0.390569i	−0.730973	+	0.682407i	$0.760933\pi$
$830$		0			0
$831$	−20.2518	−	3.57093i	−0.702526	−	0.123874i
$832$		0			0
$833$	0.347145	−	0.744455i	0.0120279	−	0.0257938i
$834$		0			0
$835$	−12.7819	+	5.62286i	−0.442335	+	0.194587i
$836$		0			0
$837$	−52.7660	−	52.7660i	−1.82386	−	1.82386i
$838$		0			0
$839$	10.1482	−	3.69363i	0.350354	−	0.127518i	−0.160848	−	0.986979i	$-0.551423\pi$
$839$	10.1482	−	3.69363i	0.350354	−	0.127518i	0.511201	+	0.859461i	$0.329201\pi$
$840$		0			0
$841$	−4.67868	+	26.5341i	−0.161334	+	0.914969i
$842$		0			0
$843$	−68.7261	−	18.4151i	−2.36705	−	0.634250i
$844$		0			0
$845$	9.23742	+	27.2201i	0.317777	+	0.936401i
$846$		0			0
$847$	26.0268	−	6.97385i	0.894290	−	0.239624i
$848$		0			0
$849$	39.8127	+	14.4907i	1.36637	+	0.497318i
$850$		0			0
$851$	4.18224	−	0.737442i	0.143365	−	0.0252792i
$852$		0			0
$853$	31.1952	−	2.72923i	1.06810	−	0.0934469i	0.460478	−	0.887671i	$-0.347678\pi$
$853$	31.1952	−	2.72923i	1.06810	−	0.0934469i	0.607625	+	0.794224i	$0.292122\pi$
$854$		0			0
$855$	−11.2679	+	59.2828i	−0.385355	+	2.02743i
$856$		0			0
$857$	−19.4140	+	1.69851i	−0.663171	+	0.0580199i	−0.413772	−	0.910381i	$-0.635789\pi$
$857$	−19.4140	+	1.69851i	−0.663171	+	0.0580199i	−0.249399	+	0.968401i	$0.580233\pi$
$858$		0			0
$859$	−5.61823	+	0.990645i	−0.191691	+	0.0338004i	−0.268670	−	0.963232i	$-0.586584\pi$
$859$	−5.61823	+	0.990645i	−0.191691	+	0.0338004i	0.0769781	+	0.997033i	$0.475473\pi$
$860$		0			0
$861$	28.6127	+	10.4142i	0.975119	+	0.354914i
$862$		0			0
$863$	−15.9626	+	4.27717i	−0.543374	+	0.145597i	−0.520057	−	0.854131i	$-0.674089\pi$
$863$	−15.9626	+	4.27717i	−0.543374	+	0.145597i	−0.0233169	+	0.999728i	$0.507423\pi$
$864$		0			0
$865$	−31.6281	−	15.6006i	−1.07539	−	0.530436i
$866$		0			0
$867$	−49.7022	−	13.3177i	−1.68797	−	0.452291i
$868$		0			0
$869$	−2.59675	+	14.7269i	−0.0880887	+	0.499576i
$870$		0			0
$871$	−3.17366	+	1.15512i	−0.107535	+	0.0391397i
$872$		0			0
$873$	2.18496	+	2.18496i	0.0739496	+	0.0739496i
$874$		0			0
$875$	−5.14507	+	15.1443i	−0.173935	+	0.511970i
$876$		0			0
$877$	−23.2792	+	49.9224i	−0.786082	+	1.68576i	−0.0599519	+	0.998201i	$0.519095\pi$
$877$	−23.2792	+	49.9224i	−0.786082	+	1.68576i	−0.726130	+	0.687557i	$0.758683\pi$
$878$		0			0
$879$	1.05072	+	0.185271i	0.0354401	+	0.00624904i
$880$		0			0
$881$	−5.41082	−	9.37181i	−0.182295	−	0.315744i	0.760367	−	0.649494i	$-0.225019\pi$
$881$	−5.41082	−	9.37181i	−0.182295	−	0.315744i	−0.942662	+	0.333750i	$0.891686\pi$
$882$		0			0
$883$	−2.30914	+	26.3935i	−0.0777086	+	0.888213i	0.852870	+	0.522123i	$0.174860\pi$
$883$	−2.30914	+	26.3935i	−0.0777086	+	0.888213i	−0.930579	+	0.366091i	$0.880696\pi$
$884$		0			0
$885$	−73.8232	−	8.09127i	−2.48154	−	0.271985i
$886$		0			0
$887$	−13.6051	+	6.34415i	−0.456814	+	0.213016i	−0.637384	−	0.770546i	$-0.719983\pi$
$887$	−13.6051	+	6.34415i	−0.456814	+	0.213016i	0.180570	+	0.983562i	$0.442206\pi$
$888$		0			0
$889$	1.24908	+	7.08390i	0.0418929	+	0.237587i
$890$		0			0
$891$	45.0106	+	37.7683i	1.50791	+	1.26529i
$892$		0			0
$893$	−5.65266	+	12.3996i	−0.189159	+	0.414937i
$894$		0			0
$895$	−22.9074	−	41.7631i	−0.765711	−	1.39599i
$896$		0			0
$897$	−0.293479	+	0.419131i	−0.00979896	+	0.0139944i
$898$		0			0
$899$	3.78315	−	10.3941i	0.126175	−	0.346663i
$900$		0			0
$901$	−1.64418	−	0.949269i	−0.0547757	−	0.0316247i
$902$		0			0
$903$	49.8071	+	4.35756i	1.65748	+	0.145010i
$904$		0			0
$905$	19.4575	−	2.99311i	0.646789	−	0.0994943i
$906$		0			0
$907$	0.341941	+	0.488342i	0.0113540	+	0.0162151i	0.824789	−	0.565441i	$-0.191294\pi$
$907$	0.341941	+	0.488342i	0.0113540	+	0.0162151i	−0.813435	+	0.581656i	$0.802405\pi$
$908$		0			0
$909$	2.38198	+	6.54444i	0.0790053	+	0.217065i
$910$		0			0
$911$		−	8.85098i		−	0.293246i	−0.989192	−	0.146623i	$-0.953160\pi$
$911$		−	8.85098i		−	0.293246i	0.989192	−	0.146623i	$-0.0468404\pi$
$912$		0			0
$913$	−44.4618	+	44.4618i	−1.47147	+	1.47147i
$914$		0			0
$915$	55.9172	+	58.4218i	1.84857	+	1.93137i
$916$		0			0
$917$	13.4431	−	9.41293i	0.443929	−	0.310842i
$918$		0			0
$919$	−19.2508	+	11.1144i	−0.635025	+	0.366632i	−0.782695	−	0.622405i	$-0.786156\pi$
$919$	−19.2508	+	11.1144i	−0.635025	+	0.366632i	0.147671	+	0.989037i	$0.452822\pi$
$920$		0			0
$921$	8.40853	−	7.05560i	0.277071	−	0.232490i
$922$		0			0
$923$	0.0325960	+	0.121650i	0.00107291	+	0.00400415i
$924$		0			0
$925$	−45.6761	−	14.4101i	−1.50182	−	0.473801i
$926$		0			0
$927$	78.2735	+	54.8077i	2.57084	+	1.80012i
$928$		0			0
$929$	19.0299	−	22.6790i	0.624352	−	0.744074i	−0.357460	−	0.933928i	$-0.616357\pi$
$929$	19.0299	−	22.6790i	0.624352	−	0.744074i	0.981812	+	0.189855i	$0.0608017\pi$
$930$		0			0
$931$	16.4200	−	14.0206i	0.538145	−	0.459505i
$932$		0			0
$933$	−6.50408	−	74.3420i	−0.212934	−	2.43385i
$934$		0			0
$935$	1.68413	−	1.12509i	0.0550768	−	0.0367944i
$936$		0			0
$937$	7.65894	+	16.4246i	0.250207	+	0.536570i	0.990792	−	0.135392i	$-0.0432295\pi$
$937$	7.65894	+	16.4246i	0.250207	+	0.536570i	−0.740585	+	0.671962i	$0.765452\pi$
$938$		0			0
$939$	24.7088	−	42.7969i	0.806341	−	1.39662i
$940$		0			0
$941$	15.3669	+	18.3136i	0.500948	+	0.597006i	0.955967	−	0.293475i	$-0.0948119\pi$
$941$	15.3669	+	18.3136i	0.500948	+	0.597006i	−0.455019	+	0.890482i	$0.650367\pi$
$942$		0			0
$943$	−0.805576	+	3.00645i	−0.0262332	+	0.0979035i
$944$		0			0
$945$	−16.0573	+	26.4566i	−0.522344	+	0.860633i
$946$		0			0
$947$	−43.5035	−	20.2860i	−1.41367	−	0.659207i	−0.442323	−	0.896856i	$-0.645845\pi$
$947$	−43.5035	−	20.2860i	−1.41367	−	0.659207i	−0.971351	+	0.237649i	$0.923623\pi$
$948$		0			0
$949$	0.869123			0.0282129
$950$		0			0
$951$	56.1647			1.82127
$952$		0			0
$953$	−18.6957	−	8.71794i	−0.605612	−	0.282402i	0.0955259	−	0.995427i	$-0.469547\pi$
$953$	−18.6957	−	8.71794i	−0.605612	−	0.282402i	−0.701138	+	0.713025i	$0.747324\pi$
$954$		0			0
$955$	−13.7630	+	22.6764i	−0.445361	+	0.733793i
$956$		0			0
$957$	−6.14631	+	22.9383i	−0.198682	+	0.741491i
$958$		0			0
$959$	1.17456	+	1.39979i	0.0379285	+	0.0452015i
$960$		0			0
$961$	14.2464	−	24.6755i	0.459561	−	0.795983i
$962$		0			0
$963$	−21.5457	−	46.2050i	−0.694301	−	1.48893i
$964$		0			0
$965$	6.12036	−	4.08875i	0.197021	−	0.131621i
$966$		0			0
$967$	3.10021	+	35.4356i	0.0996961	+	1.13953i	0.867021	+	0.498272i	$0.166032\pi$
$967$	3.10021	+	35.4356i	0.0996961	+	1.13953i	−0.767325	+	0.641259i	$0.778412\pi$
$968$		0			0
$969$	1.69075	+	1.39410i	0.0543149	+	0.0447849i
$970$		0			0
$971$	−11.8621	+	14.1367i	−0.380674	+	0.453670i	−0.922027	−	0.387126i	$-0.873468\pi$
$971$	−11.8621	+	14.1367i	−0.380674	+	0.453670i	0.541353	+	0.840796i	$0.317912\pi$
$972$		0			0
$973$	−6.18946	−	4.33391i	−0.198425	−	0.138939i
$974$		0			0
$975$	5.11902	−	2.66369i	0.163940	−	0.0853065i
$976$		0			0
$977$	4.55193	+	16.9880i	0.145629	+	0.543495i	0.999727	+	0.0233823i	$0.00744348\pi$
$977$	4.55193	+	16.9880i	0.145629	+	0.543495i	−0.854097	+	0.520113i	$0.825890\pi$
$978$		0			0
$979$	−22.3646	+	18.7661i	−0.714776	+	0.599768i
$980$		0			0
$981$	47.6764	−	27.5260i	1.52219	−	0.878837i
$982$		0			0
$983$	−27.7628	+	19.4397i	−0.885494	+	0.620030i	−0.925324	−	0.379177i	$-0.876207\pi$
$983$	−27.7628	+	19.4397i	−0.885494	+	0.620030i	0.0398299	+	0.999206i	$0.487318\pi$
$984$		0			0
$985$	30.1810	+	31.5328i	0.961647	+	1.00472i
$986$		0			0
$987$	−9.58772	+	9.58772i	−0.305181	+	0.305181i
$988$		0			0
$989$			5.11074i			0.162512i
$990$		0			0
$991$	−1.98331	−	5.44910i	−0.0630019	−	0.173096i	0.904198	−	0.427115i	$-0.140470\pi$
$991$	−1.98331	−	5.44910i	−0.0630019	−	0.173096i	−0.967199	+	0.254018i	$0.918248\pi$
$992$		0			0
$993$	23.8689	+	34.0883i	0.757457	+	1.08176i
$994$		0			0
$995$	25.1951	−	3.87572i	0.798739	−	0.122869i
$996$		0			0
$997$	−29.9828	−	2.62315i	−0.949565	−	0.0830761i	−0.398162	−	0.917315i	$-0.630352\pi$
$997$	−29.9828	−	2.62315i	−0.949565	−	0.0830761i	−0.551403	+	0.834239i	$0.685907\pi$
$998$		0			0
$999$	−80.2583	−	46.3372i	−2.53926	−	1.46604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.bh.a.117.1	yes	120
5.3	odd	4	inner	380.2.bh.a.193.10	yes	120
19.13	odd	18	inner	380.2.bh.a.317.10	yes	120
95.13	even	36	inner	380.2.bh.a.13.1	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.bh.a.13.1	✓	120	95.13	even	36	inner
380.2.bh.a.117.1	yes	120	1.1	even	1	trivial
380.2.bh.a.193.10	yes	120	5.3	odd	4	inner
380.2.bh.a.317.10	yes	120	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.74765 - 1.28125i) q^{3} +(-1.16017 + 1.91154i) q^{5} +(-0.370262 + 1.38184i) q^{7} +(3.97961 + 4.74272i) q^{9} +O(q^{10})\)	\(q+(-2.74765 - 1.28125i) q^{3} +(-1.16017 + 1.91154i) q^{5} +(-0.370262 + 1.38184i) q^{7} +(3.97961 + 4.74272i) q^{9} +(2.73107 - 4.73035i) q^{11} +(-0.160884 - 0.345016i) q^{13} +(5.63692 - 3.76578i) q^{15} +(-0.0144528 - 0.165196i) q^{17} +(1.45553 - 4.10870i) q^{19} +(2.78783 - 3.32240i) q^{21} +(0.363161 + 0.254288i) q^{23} +(-2.30799 - 4.43544i) q^{25} +(-2.50399 - 9.34503i) q^{27} +(1.09856 - 0.921802i) q^{29} +(6.67979 - 3.85658i) q^{31} +(-13.5648 + 9.49816i) q^{33} +(-2.21187 - 2.31094i) q^{35} +(6.77341 - 6.77341i) q^{37} +1.15412i q^{39} +(2.40119 + 6.59722i) q^{41} +(6.61211 + 9.44307i) q^{43} +(-13.6830 + 2.10482i) q^{45} +(-3.11441 - 0.272476i) q^{47} +(4.28980 + 2.47672i) q^{49} +(-0.171947 + 0.472419i) q^{51} +(6.56681 - 9.37838i) q^{53} +(5.87375 + 10.7086i) q^{55} +(-9.26357 + 9.42437i) q^{57} +(-8.39207 - 7.04179i) q^{59} +(2.07149 + 11.7480i) q^{61} +(-8.02716 + 3.74313i) q^{63} +(0.846167 + 0.0927428i) q^{65} +(0.773226 - 8.83802i) q^{67} +(-0.672034 - 1.16400i) q^{69} +(-0.325803 - 0.0574478i) q^{71} +(-0.964863 + 2.06915i) q^{73} +(0.658643 + 15.1442i) q^{75} +(5.52535 + 5.52535i) q^{77} +(-2.57267 + 0.936374i) q^{79} +(-1.86796 + 10.5937i) q^{81} +(-11.1195 - 2.97945i) q^{83} +(0.332548 + 0.164029i) q^{85} +(-4.19952 + 1.12526i) q^{87} +(-5.02263 - 1.82809i) q^{89} +(0.536325 - 0.0945686i) q^{91} +(-23.2950 + 2.03804i) q^{93} +(6.16528 + 7.54912i) q^{95} +(0.497197 - 0.0434991i) q^{97} +(33.3033 - 5.87227i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{7}+O(q^{10}) \) 120 * q + 6 * q^7	\( 120 q + 6 q^{7} + 18 q^{15} - 18 q^{17} + 48 q^{21} - 36 q^{23} - 24 q^{25} - 60 q^{33} - 18 q^{35} - 12 q^{41} - 36 q^{43} + 18 q^{45} - 24 q^{47} + 96 q^{51} - 18 q^{53} + 72 q^{55} - 6 q^{57} - 24 q^{61} + 36 q^{63} + 90 q^{65} - 24 q^{67} + 18 q^{73} - 36 q^{77} - 30 q^{83} - 24 q^{85} - 72 q^{87} - 144 q^{91} - 132 q^{93} - 12 q^{95} - 60 q^{97}+O(q^{100}) \) 120 * q + 6 * q^7 + 18 * q^15 - 18 * q^17 + 48 * q^21 - 36 * q^23 - 24 * q^25 - 60 * q^33 - 18 * q^35 - 12 * q^41 - 36 * q^43 + 18 * q^45 - 24 * q^47 + 96 * q^51 - 18 * q^53 + 72 * q^55 - 6 * q^57 - 24 * q^61 + 36 * q^63 + 90 * q^65 - 24 * q^67 + 18 * q^73 - 36 * q^77 - 30 * q^83 - 24 * q^85 - 72 * q^87 - 144 * q^91 - 132 * q^93 - 12 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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