LMFDB - Embedded newform 380.2.u.b.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(61,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("380.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.u (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 30 x^{15} + 192 x^{14} - 207 x^{13} + 1178 x^{12} - 705 x^{11} + \cdots + 5329 $ x^18 - 3x^17 + 21x^16 - 30x^15 + 192x^14 - 207x^13 + 1178x^12 - 705x^11 + 4413x^10 - 2224x^9 + 11430x^8 - 4101x^7 + 19237x^6 - 7125x^5 + 21573x^4 - 5266x^3 + 13851x^2 - 3285*x + 5329
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.3
Root			$-0.754364 + 1.30660i$ of defining polynomial
Character	$\chi$	$=$	380.61
Dual form			380.2.u.b.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.261988 + 1.48581i) q^{3} +(0.766044 - 0.642788i) q^{5} +(1.67550 - 2.90204i) q^{7} +(0.680094 - 0.247534i) q^{9} +O(q^{10})$	\(q+(0.261988 + 1.48581i) q^{3} +(0.766044 - 0.642788i) q^{5} +(1.67550 - 2.90204i) q^{7} +(0.680094 - 0.247534i) q^{9} +(1.23765 + 2.14367i) q^{11} +(0.324617 - 1.84100i) q^{13} +(1.15575 + 0.969791i) q^{15} +(0.341929 + 0.124452i) q^{17} +(-3.65925 - 2.36853i) q^{19} +(4.75084 + 1.72916i) q^{21} +(5.71972 + 4.79941i) q^{23} +(0.173648 - 0.984808i) q^{25} +(2.80906 + 4.86543i) q^{27} +(-3.04312 + 1.10761i) q^{29} +(-3.78440 + 6.55477i) q^{31} +(-2.86083 + 2.40052i) q^{33} +(-0.581894 - 3.30008i) q^{35} +3.34885 q^{37} +2.82041 q^{39} +(-1.49157 - 8.45909i) q^{41} +(-8.07036 + 6.77184i) q^{43} +(0.361870 - 0.626778i) q^{45} +(11.0714 - 4.02966i) q^{47} +(-2.11458 - 3.66255i) q^{49} +(-0.0953303 + 0.540645i) q^{51} +(-2.01573 - 1.69140i) q^{53} +(2.32601 + 0.846600i) q^{55} +(2.56050 - 6.05746i) q^{57} +(-11.3091 - 4.11618i) q^{59} +(-8.67810 - 7.28179i) q^{61} +(0.421140 - 2.38841i) q^{63} +(-0.934699 - 1.61895i) q^{65} +(-2.31034 + 0.840895i) q^{67} +(-5.63250 + 9.75578i) q^{69} +(-0.0802996 + 0.0673793i) q^{71} +(-1.34598 - 7.63341i) q^{73} +1.50873 q^{75} +8.29469 q^{77} +(0.948370 + 5.37847i) q^{79} +(-4.82989 + 4.05276i) q^{81} +(0.462244 - 0.800630i) q^{83} +(0.341929 - 0.124452i) q^{85} +(-2.44295 - 4.23132i) q^{87} +(-1.38660 + 7.86382i) q^{89} +(-4.79876 - 4.02664i) q^{91} +(-10.7306 - 3.90562i) q^{93} +(-4.32560 + 0.537720i) q^{95} +(-6.64008 - 2.41679i) q^{97} +(1.37235 + 1.15154i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 15 * q^9	$ 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$	$1$

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
$3$	0.261988	+	1.48581i	0.151259	+	0.857831i	0.962127	+	0.272602i	$0.0878842\pi$
$3$	0.261988	+	1.48581i	0.151259	+	0.857831i	−0.810868	+	0.585229i	$0.801005\pi$
$4$		0			0
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$		0			0
$7$	1.67550	−	2.90204i	0.633278	−	1.09687i	−0.353599	−	0.935397i	$-0.615042\pi$
$7$	1.67550	−	2.90204i	0.633278	−	1.09687i	0.986877	−	0.161473i	$-0.0516244\pi$
$8$		0			0
$9$	0.680094	−	0.247534i	0.226698	−	0.0825113i
$10$		0			0
$11$	1.23765	+	2.14367i	0.373164	+	0.646340i	0.990050	−	0.140713i	$-0.0449394\pi$
$11$	1.23765	+	2.14367i	0.373164	+	0.646340i	−0.616886	+	0.787052i	$0.711606\pi$
$12$		0			0
$13$	0.324617	−	1.84100i	0.0900327	−	0.510601i	−0.906124	−	0.423012i	$-0.860973\pi$
$13$	0.324617	−	1.84100i	0.0900327	−	0.510601i	0.996157	−	0.0875887i	$-0.0279161\pi$
$14$		0			0
$15$	1.15575	+	0.969791i	0.298414	+	0.250399i
$16$		0			0
$17$	0.341929	+	0.124452i	0.0829299	+	0.0301840i	0.383152	−	0.923685i	$-0.374839\pi$
$17$	0.341929	+	0.124452i	0.0829299	+	0.0301840i	−0.300222	+	0.953869i	$0.597061\pi$
$18$		0			0
$19$	−3.65925	−	2.36853i	−0.839488	−	0.543378i
$19$	−3.65925	−	2.36853i	−0.839488	−	0.543378i
$20$		0			0
$21$	4.75084	+	1.72916i	1.03672	+	0.377334i
$22$		0			0
$23$	5.71972	+	4.79941i	1.19264	+	1.00075i	0.999810	+	0.0195150i	$0.00621220\pi$
$23$	5.71972	+	4.79941i	1.19264	+	1.00075i	0.192834	+	0.981231i	$0.438232\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$		0			0
$27$	2.80906	+	4.86543i	0.540603	+	0.936352i
$28$		0			0
$29$	−3.04312	+	1.10761i	−0.565094	+	0.205677i	−0.608740	−	0.793370i	$-0.708325\pi$
$29$	−3.04312	+	1.10761i	−0.565094	+	0.205677i	0.0436461	+	0.999047i	$0.486103\pi$
$30$		0			0
$31$	−3.78440	+	6.55477i	−0.679698	+	1.17727i	0.295373	+	0.955382i	$0.404556\pi$
$31$	−3.78440	+	6.55477i	−0.679698	+	1.17727i	−0.975072	+	0.221890i	$0.928777\pi$
$32$		0			0
$33$	−2.86083	+	2.40052i	−0.498006	+	0.417876i
$34$		0			0
$35$	−0.581894	−	3.30008i	−0.0983580	−	0.557816i
$36$		0			0
$37$	3.34885			0.550548			0.275274	−	0.961366i	$-0.411231\pi$
$37$	3.34885			0.550548			0.275274	+	0.961366i	$0.411231\pi$
$38$		0			0
$39$	2.82041			0.451627
$40$		0			0
$41$	−1.49157	−	8.45909i	−0.232943	−	1.32109i	−0.846902	−	0.531750i	$-0.821535\pi$
$41$	−1.49157	−	8.45909i	−0.232943	−	1.32109i	0.613958	−	0.789339i	$-0.289576\pi$
$42$		0			0
$43$	−8.07036	+	6.77184i	−1.23072	+	1.03270i	−0.232527	+	0.972590i	$0.574699\pi$
$43$	−8.07036	+	6.77184i	−1.23072	+	1.03270i	−0.998192	+	0.0601056i	$0.980856\pi$
$44$		0			0
$45$	0.361870	−	0.626778i	0.0539445	−	0.0934346i
$46$		0			0
$47$	11.0714	−	4.02966i	1.61493	−	0.587786i	0.632522	−	0.774542i	$-0.282020\pi$
$47$	11.0714	−	4.02966i	1.61493	−	0.587786i	0.982406	+	0.186756i	$0.0597975\pi$
$48$		0			0
$49$	−2.11458	−	3.66255i	−0.302082	−	0.523222i
$50$		0			0
$51$	−0.0953303	+	0.540645i	−0.0133489	+	0.0757054i
$52$		0			0
$53$	−2.01573	−	1.69140i	−0.276882	−	0.232331i	0.493763	−	0.869597i	$-0.335621\pi$
$53$	−2.01573	−	1.69140i	−0.276882	−	0.232331i	−0.770645	+	0.637265i	$0.780066\pi$
$54$		0			0
$55$	2.32601	+	0.846600i	0.313640	+	0.114156i
$56$		0			0
$57$	2.56050	−	6.05746i	0.339146	−	0.802330i
$58$		0			0
$59$	−11.3091	−	4.11618i	−1.47232	−	0.535881i	−0.523591	−	0.851970i	$-0.675408\pi$
$59$	−11.3091	−	4.11618i	−1.47232	−	0.535881i	−0.948730	+	0.316089i	$0.897630\pi$
$60$		0			0
$61$	−8.67810	−	7.28179i	−1.11112	−	0.932338i	−0.112995	−	0.993596i	$-0.536044\pi$
$61$	−8.67810	−	7.28179i	−1.11112	−	0.932338i	−0.998122	+	0.0612578i	$0.980489\pi$
$62$		0			0
$63$	0.421140	−	2.38841i	0.0530587	−	0.300911i
$64$		0			0
$65$	−0.934699	−	1.61895i	−0.115935	−	0.200806i
$66$		0			0
$67$	−2.31034	+	0.840895i	−0.282253	+	0.102732i	−0.479267	−	0.877669i	$-0.659098\pi$
$67$	−2.31034	+	0.840895i	−0.282253	+	0.102732i	0.197015	+	0.980401i	$0.436875\pi$
$68$		0			0
$69$	−5.63250	+	9.75578i	−0.678074	+	1.17446i
$70$		0			0
$71$	−0.0802996	+	0.0673793i	−0.00952980	+	0.00799646i	−0.647540	−	0.762031i	$-0.724202\pi$
$71$	−0.0802996	+	0.0673793i	−0.00952980	+	0.00799646i	0.638010	+	0.770028i	$0.279758\pi$
$72$		0			0
$73$	−1.34598	−	7.63341i	−0.157535	−	0.893423i	−0.956432	−	0.291956i	$-0.905694\pi$
$73$	−1.34598	−	7.63341i	−0.157535	−	0.893423i	0.798897	−	0.601468i	$-0.205417\pi$
$74$		0			0
$75$	1.50873			0.174213
$76$		0			0
$77$	8.29469			0.945267
$78$		0			0
$79$	0.948370	+	5.37847i	0.106700	+	0.605125i	0.990528	+	0.137313i	$0.0438466\pi$
$79$	0.948370	+	5.37847i	0.106700	+	0.605125i	−0.883828	+	0.467812i	$0.845042\pi$
$80$		0			0
$81$	−4.82989	+	4.05276i	−0.536655	+	0.450307i
$82$		0			0
$83$	0.462244	−	0.800630i	0.0507378	−	0.0878805i	−0.839541	−	0.543296i	$-0.817176\pi$
$83$	0.462244	−	0.800630i	0.0507378	−	0.0878805i	0.890279	+	0.455416i	$0.150509\pi$
$84$		0			0
$85$	0.341929	−	0.124452i	0.0370874	−	0.0134987i
$86$		0			0
$87$	−2.44295	−	4.23132i	−0.261912	−	0.453645i
$88$		0			0
$89$	−1.38660	+	7.86382i	−0.146980	+	0.833563i	0.818777	+	0.574112i	$0.194653\pi$
$89$	−1.38660	+	7.86382i	−0.146980	+	0.833563i	−0.965756	+	0.259451i	$0.916458\pi$
$90$		0			0
$91$	−4.79876	−	4.02664i	−0.503047	−	0.422106i
$92$		0			0
$93$	−10.7306	−	3.90562i	−1.11271	−	0.404993i
$94$		0			0
$95$	−4.32560	+	0.537720i	−0.443798	+	0.0551689i
$96$		0			0
$97$	−6.64008	−	2.41679i	−0.674198	−	0.245388i	−0.0178439	−	0.999841i	$-0.505680\pi$
$97$	−6.64008	−	2.41679i	−0.674198	−	0.245388i	−0.656354	+	0.754453i	$0.727902\pi$
$98$		0			0
$99$	1.37235	+	1.15154i	0.137926	+	0.115734i
$100$		0			0
$101$	−0.0936052	+	0.530861i	−0.00931406	+	0.0528227i	−0.989111	−	0.147174i	$-0.952982\pi$
$101$	−0.0936052	+	0.530861i	−0.00931406	+	0.0528227i	0.979796	+	0.199997i	$0.0640933\pi$
$102$		0			0
$103$	3.81344	+	6.60507i	0.375749	+	0.650817i	0.990439	−	0.137952i	$-0.0440521\pi$
$103$	3.81344	+	6.60507i	0.375749	+	0.650817i	−0.614690	+	0.788769i	$0.710719\pi$
$104$		0			0
$105$	4.75084	−	1.72916i	0.463634	−	0.168749i
$106$		0			0
$107$	4.25568	−	7.37105i	0.411412	−	0.712586i	−0.583633	−	0.812018i	$-0.698369\pi$
$107$	4.25568	−	7.37105i	0.411412	−	0.712586i	0.995044	+	0.0994318i	$0.0317025\pi$
$108$		0			0
$109$	−10.0485	+	8.43168i	−0.962471	+	0.807609i	−0.981353	−	0.192213i	$-0.938434\pi$
$109$	−10.0485	+	8.43168i	−0.962471	+	0.807609i	0.0188826	+	0.999822i	$0.493989\pi$
$110$		0			0
$111$	0.877359	+	4.97575i	0.0832752	+	0.472277i
$112$		0			0
$113$	−13.9017			−1.30776			−0.653880	−	0.756598i	$-0.726860\pi$
$113$	−13.9017			−1.30776			−0.653880	+	0.756598i	$0.726860\pi$
$114$		0			0
$115$	7.46656			0.696260
$116$		0			0
$117$	−0.234939	−	1.33241i	−0.0217201	−	0.123181i
$118$		0			0
$119$	0.934065	−	0.783774i	0.0856256	−	0.0718484i
$120$		0			0
$121$	2.43646	−	4.22008i	0.221497	−	0.383644i
$122$		0			0
$123$	12.1778	−	4.43236i	1.09804	−	0.399652i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	0.295034	−	1.67322i	0.0261801	−	0.148474i	−0.968916	−	0.247391i	$-0.920427\pi$
$127$	0.295034	−	1.67322i	0.0261801	−	0.148474i	0.995096	+	0.0989168i	$0.0315378\pi$
$128$		0			0
$129$	−12.1760	−	10.2169i	−1.07204	−	0.899544i
$130$		0			0
$131$	4.40967	+	1.60499i	0.385275	+	0.140228i	0.527394	−	0.849621i	$-0.323169\pi$
$131$	4.40967	+	1.60499i	0.385275	+	0.140228i	−0.142119	+	0.989850i	$0.545392\pi$
$132$		0			0
$133$	−13.0046	+	6.65083i	−1.12764	+	0.576700i
$134$		0			0
$135$	5.27930	+	1.92151i	0.454370	+	0.165377i
$136$		0			0
$137$	9.17290	+	7.69698i	0.783694	+	0.657597i	0.944176	−	0.329441i	$-0.106860\pi$
$137$	9.17290	+	7.69698i	0.783694	+	0.657597i	−0.160482	+	0.987039i	$0.551305\pi$
$138$		0			0
$139$	−2.26678	+	12.8556i	−0.192266	+	1.09039i	0.723993	+	0.689807i	$0.242305\pi$
$139$	−2.26678	+	12.8556i	−0.192266	+	1.09039i	−0.916259	+	0.400587i	$0.868806\pi$
$140$		0			0
$141$	8.88786	+	15.3942i	0.748493	+	1.29643i
$142$		0			0
$143$	4.34825	−	1.58263i	0.363619	−	0.132346i
$144$		0			0
$145$	−1.61921	+	2.80456i	−0.134468	+	0.232906i
$146$		0			0
$147$	4.88785	−	4.10140i	0.403143	−	0.338277i
$148$		0			0
$149$	−0.928070	−	5.26334i	−0.0760304	−	0.431190i	−0.998934	−	0.0461591i	$-0.985302\pi$
$149$	−0.928070	−	5.26334i	−0.0760304	−	0.431190i	0.922904	−	0.385031i	$-0.125809\pi$
$150$		0			0
$151$	−19.7726			−1.60907			−0.804534	−	0.593907i	$-0.797585\pi$
$151$	−19.7726			−1.60907			−0.804534	+	0.593907i	$0.797585\pi$
$152$		0			0
$153$	0.263350			0.0212906
$154$		0			0
$155$	1.31431	+	7.45381i	0.105568	+	0.598705i
$156$		0			0
$157$	−2.31736	+	1.94449i	−0.184945	+	0.155187i	−0.730560	−	0.682849i	$-0.760741\pi$
$157$	−2.31736	+	1.94449i	−0.184945	+	0.155187i	0.545615	+	0.838036i	$0.316296\pi$
$158$		0			0
$159$	1.98499	−	3.43811i	0.157420	−	0.272660i
$160$		0			0
$161$	23.5115	−	8.55748i	1.85296	−	0.674424i
$162$		0			0
$163$	−3.62815	−	6.28414i	−0.284178	−	0.492211i	0.688231	−	0.725491i	$-0.258387\pi$
$163$	−3.62815	−	6.28414i	−0.284178	−	0.492211i	−0.972410	+	0.233280i	$0.925054\pi$
$164$		0			0
$165$	−0.648496	+	3.67781i	−0.0504854	+	0.286317i
$166$		0			0
$167$	−2.02319	−	1.69766i	−0.156559	−	0.131369i	0.561143	−	0.827719i	$-0.310362\pi$
$167$	−2.02319	−	1.69766i	−0.156559	−	0.131369i	−0.717702	+	0.696350i	$0.754806\pi$
$168$		0			0
$169$	8.93211	+	3.25102i	0.687085	+	0.250079i
$170$		0			0
$171$	−3.07492	−	0.705034i	−0.235145	−	0.0539153i
$172$		0			0
$173$	11.3682	+	4.13769i	0.864309	+	0.314583i	0.735860	−	0.677133i	$-0.236778\pi$
$173$	11.3682	+	4.13769i	0.864309	+	0.314583i	0.128449	+	0.991716i	$0.459000\pi$
$174$		0			0
$175$	−2.56701	−	2.15398i	−0.194048	−	0.162825i
$176$		0			0
$177$	3.15300	−	17.8815i	0.236994	−	1.34406i
$178$		0			0
$179$	9.09890	+	15.7598i	0.680084	+	1.17794i	0.974955	+	0.222403i	$0.0713900\pi$
$179$	9.09890	+	15.7598i	0.680084	+	1.17794i	−0.294871	+	0.955537i	$0.595277\pi$
$180$		0			0
$181$	19.2341	−	7.00064i	1.42966	−	0.520353i	0.492825	−	0.870128i	$-0.335964\pi$
$181$	19.2341	−	7.00064i	1.42966	−	0.520353i	0.936834	+	0.349775i	$0.113742\pi$
$182$		0			0
$183$	8.54578	−	14.8017i	0.631722	−	1.09417i
$184$		0			0
$185$	2.56537	−	2.15260i	0.188610	−	0.158262i
$186$		0			0
$187$	0.156404	+	0.887008i	0.0114374	+	0.0648645i
$188$		0			0
$189$	18.8262			1.36941
$190$		0			0
$191$	6.70464			0.485131			0.242565	−	0.970135i	$-0.422011\pi$
$191$	6.70464			0.485131			0.242565	+	0.970135i	$0.422011\pi$
$192$		0			0
$193$	−1.82646	−	10.3584i	−0.131471	−	0.745612i	−0.977252	−	0.212081i	$-0.931976\pi$
$193$	−1.82646	−	10.3584i	−0.131471	−	0.745612i	0.845781	−	0.533531i	$-0.179135\pi$
$194$		0			0
$195$	2.16056	−	1.81293i	0.154721	−	0.129826i
$196$		0			0
$197$	−6.09112	+	10.5501i	−0.433975	+	0.751666i	−0.997211	−	0.0746295i	$-0.976223\pi$
$197$	−6.09112	+	10.5501i	−0.433975	+	0.751666i	0.563237	+	0.826296i	$0.309556\pi$
$198$		0			0
$199$	−16.6310	+	6.05321i	−1.17894	+	0.429100i	−0.855829	−	0.517259i	$-0.826952\pi$
$199$	−16.6310	+	6.05321i	−1.17894	+	0.429100i	−0.323115	+	0.946360i	$0.604730\pi$
$200$		0			0
$201$	−1.85469	−	3.21241i	−0.130820	−	0.226586i
$202$		0			0
$203$	−1.88442	+	10.6871i	−0.132260	+	0.750086i
$204$		0			0
$205$	−6.58000	−	5.52128i	−0.459567	−	0.385623i
$206$		0			0
$207$	5.07796	+	1.84823i	0.352943	+	0.128461i
$208$		0			0
$209$	0.548482	−	10.7756i	0.0379393	−	0.745364i
$210$		0			0
$211$	−18.9353	−	6.89188i	−1.30356	−	0.474457i	−0.405405	−	0.914137i	$-0.632869\pi$
$211$	−18.9353	−	6.89188i	−1.30356	−	0.474457i	−0.898154	+	0.439681i	$0.855092\pi$
$212$		0			0
$213$	−0.121150	−	0.101657i	−0.00830107	−	0.00696543i
$214$		0			0
$215$	−1.82940	+	10.3751i	−0.124764	+	0.707573i
$216$		0			0
$217$	12.6815	+	21.9650i	0.860876	+	1.49108i
$218$		0			0
$219$	10.9891	−	3.99972i	0.742578	−	0.270276i
$220$		0			0
$221$	0.340112	−	0.589091i	0.0228784	−	0.0396265i
$222$		0			0
$223$	14.8141	−	12.4305i	0.992028	−	0.832411i	0.00616830	−	0.999981i	$-0.498037\pi$
$223$	14.8141	−	12.4305i	0.992028	−	0.832411i	0.985860	+	0.167570i	$0.0535921\pi$
$224$		0			0
$225$	−0.125676	−	0.712746i	−0.00837842	−	0.0475164i
$226$		0			0
$227$	5.01480			0.332844			0.166422	−	0.986055i	$-0.446779\pi$
$227$	5.01480			0.332844			0.166422	+	0.986055i	$0.446779\pi$
$228$		0			0
$229$	15.4150			1.01865			0.509325	−	0.860574i	$-0.329895\pi$
$229$	15.4150			1.01865			0.509325	+	0.860574i	$0.329895\pi$
$230$		0			0
$231$	2.17311	+	12.3243i	0.142980	+	0.810879i
$232$		0			0
$233$	−6.63763	+	5.56963i	−0.434845	+	0.364879i	−0.833776	−	0.552102i	$-0.813826\pi$
$233$	−6.63763	+	5.56963i	−0.434845	+	0.364879i	0.398931	+	0.916981i	$0.369381\pi$
$234$		0			0
$235$	5.89096	−	10.2034i	0.384284	−	0.665600i
$236$		0			0
$237$	−7.74291	+	2.81819i	−0.502956	+	0.183061i
$238$		0			0
$239$	−6.11195	−	10.5862i	−0.395349	−	0.684765i	0.597796	−	0.801648i	$-0.296043\pi$
$239$	−6.11195	−	10.5862i	−0.395349	−	0.684765i	−0.993146	+	0.116883i	$0.962710\pi$
$240$		0			0
$241$	−0.270059	+	1.53158i	−0.0173960	+	0.0986577i	−0.992270	−	0.124101i	$-0.960395\pi$
$241$	−0.270059	+	1.53158i	−0.0173960	+	0.0986577i	0.974874	+	0.222759i	$0.0715063\pi$
$242$		0			0
$243$	5.62418	+	4.71924i	0.360791	+	0.302740i
$244$		0			0
$245$	−3.97410	−	1.44646i	−0.253896	−	0.0924106i
$246$		0			0
$247$	−5.54831	+	5.96780i	−0.353030	+	0.379722i
$248$		0			0
$249$	1.31068	+	0.477050i	0.0830612	+	0.0302318i
$250$		0			0
$251$	−5.05420	−	4.24098i	−0.319018	−	0.267688i	0.469189	−	0.883098i	$-0.344546\pi$
$251$	−5.05420	−	4.24098i	−0.319018	−	0.267688i	−0.788208	+	0.615410i	$0.788991\pi$
$252$		0			0
$253$	−3.20935	+	18.2011i	−0.201770	+	1.14430i
$254$		0			0
$255$	0.274493	+	0.475435i	0.0171894	+	0.0297729i
$256$		0			0
$257$	27.4725	−	9.99916i	1.71368	−	0.623730i	0.716422	−	0.697667i	$-0.245779\pi$
$257$	27.4725	−	9.99916i	1.71368	−	0.623730i	0.997263	+	0.0739369i	$0.0235563\pi$
$258$		0			0
$259$	5.61099	−	9.71852i	0.348650	−	0.603879i
$260$		0			0
$261$	−1.79544	+	1.50655i	−0.111135	+	0.0932533i
$262$		0			0
$263$	3.62948	+	20.5838i	0.223804	+	1.26925i	0.864959	+	0.501842i	$0.167344\pi$
$263$	3.62948	+	20.5838i	0.223804	+	1.26925i	−0.641156	+	0.767411i	$0.721545\pi$
$264$		0			0
$265$	−2.63135			−0.161642
$266$		0			0
$267$	−12.0474			−0.737288
$268$		0			0
$269$	4.36839	+	24.7744i	0.266345	+	1.51052i	0.765176	+	0.643821i	$0.222652\pi$
$269$	4.36839	+	24.7744i	0.266345	+	1.51052i	−0.498831	+	0.866699i	$0.666237\pi$
$270$		0			0
$271$	−17.1970	+	14.4300i	−1.04464	+	0.876559i	−0.992520	−	0.122081i	$-0.961043\pi$
$271$	−17.1970	+	14.4300i	−1.04464	+	0.876559i	−0.0521227	+	0.998641i	$0.516599\pi$
$272$		0			0
$273$	4.72559	−	8.18496i	0.286006	−	0.495376i
$274$		0			0
$275$	2.32601	−	0.846600i	0.140264	−	0.0510519i
$276$		0			0
$277$	−1.31202	−	2.27248i	−0.0788314	−	0.136540i	0.823915	−	0.566714i	$-0.191786\pi$
$277$	−1.31202	−	2.27248i	−0.0788314	−	0.136540i	−0.902746	+	0.430174i	$0.858452\pi$
$278$		0			0
$279$	−0.951219	+	5.39463i	−0.0569480	+	0.322968i
$280$		0			0
$281$	−8.76242	−	7.35254i	−0.522722	−	0.438616i	0.342857	−	0.939387i	$-0.388605\pi$
$281$	−8.76242	−	7.35254i	−0.522722	−	0.438616i	−0.865580	+	0.500771i	$0.833050\pi$
$282$		0			0
$283$	−19.9029	−	7.24406i	−1.18310	−	0.430614i	−0.325806	−	0.945437i	$-0.605636\pi$
$283$	−19.9029	−	7.24406i	−1.18310	−	0.430614i	−0.857297	+	0.514822i	$0.827858\pi$
$284$		0			0
$285$	−1.93220	−	6.28614i	−0.114454	−	0.372359i
$286$		0			0
$287$	−27.0478	−	9.84458i	−1.59658	−	0.581107i
$288$		0			0
$289$	−12.9213	−	10.8423i	−0.760078	−	0.637781i
$290$		0			0
$291$	1.85127	−	10.4991i	0.108523	−	0.615465i
$292$		0			0
$293$	13.4334	+	23.2673i	0.784788	+	1.35929i	0.929126	+	0.369764i	$0.120561\pi$
$293$	13.4334	+	23.2673i	0.784788	+	1.35929i	−0.144338	+	0.989528i	$0.546105\pi$
$294$		0			0
$295$	−11.3091	+	4.11618i	−0.658442	+	0.239653i
$296$		0			0
$297$	−6.95323	+	12.0434i	−0.403468	+	0.698826i
$298$		0			0
$299$	10.6924	−	8.97201i	0.618359	−	0.518865i
$300$		0			0
$301$	6.13031	+	34.7667i	0.353345	+	2.00392i
$302$		0			0
$303$	−0.813281			−0.0467217
$304$		0			0
$305$	−11.3285			−0.648665
$306$		0			0
$307$	−0.736789	−	4.17854i	−0.0420508	−	0.238482i	0.956537	−	0.291612i	$-0.0941914\pi$
$307$	−0.736789	−	4.17854i	−0.0420508	−	0.238482i	−0.998588	+	0.0531297i	$0.983080\pi$
$308$		0			0
$309$	−8.81478	+	7.39648i	−0.501455	+	0.420771i
$310$		0			0
$311$	16.5037	−	28.5852i	0.935839	−	1.62092i	0.162707	−	0.986674i	$-0.447977\pi$
$311$	16.5037	−	28.5852i	0.935839	−	1.62092i	0.773131	−	0.634246i	$-0.218689\pi$
$312$		0			0
$313$	7.30450	−	2.65862i	0.412875	−	0.150274i	−0.127227	−	0.991874i	$-0.540608\pi$
$313$	7.30450	−	2.65862i	0.412875	−	0.150274i	0.540102	+	0.841599i	$0.318386\pi$
$314$		0			0
$315$	−1.21263	−	2.10033i	−0.0683237	−	0.118340i
$316$		0			0
$317$	−2.10897	+	11.9606i	−0.118452	+	0.671772i	0.866532	+	0.499122i	$0.166344\pi$
$317$	−2.10897	+	11.9606i	−0.118452	+	0.671772i	−0.984983	+	0.172650i	$0.944767\pi$
$318$		0			0
$319$	−6.14065	−	5.15262i	−0.343810	−	0.288491i
$320$		0			0
$321$	12.0669	+	4.39199i	0.673508	+	0.245137i
$322$		0			0
$323$	−0.956433	−	1.26527i	−0.0532174	−	0.0704014i
$324$		0			0
$325$	−1.75666	−	0.639372i	−0.0974419	−	0.0354660i
$326$		0			0
$327$	−15.1604	−	12.7211i	−0.838374	−	0.703479i
$328$		0			0
$329$	6.85583	−	38.8814i	0.377974	−	2.14360i
$330$		0			0
$331$	−14.9145	−	25.8326i	−0.819774	−	1.41989i	−0.905848	−	0.423602i	$-0.860766\pi$
$331$	−14.9145	−	25.8326i	−0.819774	−	1.41989i	0.0860741	−	0.996289i	$-0.472568\pi$
$332$		0			0
$333$	2.27753	−	0.828955i	0.124808	−	0.0454264i
$334$		0			0
$335$	−1.22931	+	2.12922i	−0.0671642	+	0.116332i
$336$		0			0
$337$	−17.4827	+	14.6697i	−0.952341	+	0.799109i	−0.979690	−	0.200517i	$-0.935738\pi$
$337$	−17.4827	+	14.6697i	−0.952341	+	0.799109i	0.0273495	+	0.999626i	$0.491293\pi$
$338$		0			0
$339$	−3.64207	−	20.6552i	−0.197810	−	1.12184i
$340$		0			0
$341$	−18.7350			−1.01456
$342$		0			0
$343$	9.28509			0.501348
$344$		0			0
$345$	1.95615	+	11.0939i	0.105315	+	0.597273i
$346$		0			0
$347$	−26.5831	+	22.3059i	−1.42706	+	1.19744i	−0.479630	+	0.877471i	$0.659229\pi$
$347$	−26.5831	+	22.3059i	−1.42706	+	1.19744i	−0.947427	+	0.319972i	$0.896327\pi$
$348$		0			0
$349$	6.05693	−	10.4909i	0.324220	−	0.561565i	−0.657134	−	0.753774i	$-0.728232\pi$
$349$	6.05693	−	10.4909i	0.324220	−	0.561565i	0.981354	+	0.192208i	$0.0615649\pi$
$350$		0			0
$351$	9.86911	−	3.59206i	0.526774	−	0.191730i
$352$		0			0
$353$	−15.8193	−	27.3998i	−0.841976	−	1.45835i	−0.888221	−	0.459416i	$-0.848059\pi$
$353$	−15.8193	−	27.3998i	−0.841976	−	1.45835i	0.0462448	−	0.998930i	$-0.485275\pi$
$354$		0			0
$355$	−0.0182024	+	0.103231i	−0.000966085	+	0.00547894i
$356$		0			0
$357$	1.40925	+	1.18250i	0.0745854	+	0.0625846i
$358$		0			0
$359$	0.327164	+	0.119078i	0.0172671	+	0.00628470i	0.350639	−	0.936511i	$-0.385964\pi$
$359$	0.327164	+	0.119078i	0.0172671	+	0.00628470i	−0.333372	+	0.942795i	$0.608187\pi$
$360$		0			0
$361$	7.78015	+	17.3340i	0.409482	+	0.912318i
$362$		0			0
$363$	6.90855	+	2.51450i	0.362605	+	0.131977i
$364$		0			0
$365$	−5.93774	−	4.98236i	−0.310796	−	0.260788i
$366$		0			0
$367$	0.812336	−	4.60699i	0.0424036	−	0.240483i	−0.956238	−	0.292590i	$-0.905483\pi$
$367$	0.812336	−	4.60699i	0.0424036	−	0.240483i	0.998641	+	0.0521076i	$0.0165939\pi$
$368$		0			0
$369$	−3.10832	−	5.38376i	−0.161813	−	0.280268i
$370$		0			0
$371$	−8.28586	+	3.01581i	−0.430180	+	0.156573i
$372$		0			0
$373$	8.99161	−	15.5739i	0.465568	−	0.806388i	−0.533659	−	0.845700i	$-0.679183\pi$
$373$	8.99161	−	15.5739i	0.465568	−	0.806388i	0.999227	+	0.0393123i	$0.0125167\pi$
$374$		0			0
$375$	1.15575	−	0.969791i	0.0596828	−	0.0500798i
$376$		0			0
$377$	1.05125	+	5.96193i	0.0541421	+	0.307055i
$378$		0			0
$379$	8.98539			0.461548			0.230774	−	0.973007i	$-0.425874\pi$
$379$	8.98539			0.461548			0.230774	+	0.973007i	$0.425874\pi$
$380$		0			0
$381$	2.56338			0.131326
$382$		0			0
$383$	−2.05099	−	11.6317i	−0.104801	−	0.594354i	−0.991300	−	0.131624i	$-0.957981\pi$
$383$	−2.05099	−	11.6317i	−0.104801	−	0.594354i	0.886499	−	0.462730i	$-0.153130\pi$
$384$		0			0
$385$	6.35410	−	5.33172i	0.323835	−	0.271730i
$386$		0			0
$387$	−3.81235	+	6.60318i	−0.193792	+	0.335658i
$388$		0			0
$389$	3.11727	−	1.13459i	0.158052	−	0.0575262i	−0.261783	−	0.965127i	$-0.584310\pi$
$389$	3.11727	−	1.13459i	0.158052	−	0.0575262i	0.419834	+	0.907601i	$0.362088\pi$
$390$		0			0
$391$	1.35844	+	2.35289i	0.0686992	+	0.118991i
$392$		0			0
$393$	−1.22942	+	6.97240i	−0.0620162	+	0.351711i
$394$		0			0
$395$	4.18371	+	3.51055i	0.210505	+	0.176635i
$396$		0			0
$397$	−28.3418	−	10.3156i	−1.42243	−	0.517723i	−0.487680	−	0.873022i	$-0.662157\pi$
$397$	−28.3418	−	10.3156i	−1.42243	−	0.517723i	−0.934753	+	0.355299i	$0.884379\pi$
$398$		0			0
$399$	−13.2889	−	17.5799i	−0.665277	−	0.880097i
$400$		0			0
$401$	12.9553	+	4.71536i	0.646959	+	0.235474i	0.644596	−	0.764524i	$-0.277026\pi$
$401$	12.9553	+	4.71536i	0.646959	+	0.235474i	0.00236276	+	0.999997i	$0.499248\pi$
$402$		0			0
$403$	10.8388	+	9.09486i	0.539921	+	0.453047i
$404$		0			0
$405$	−1.09485	+	6.20919i	−0.0544034	+	0.308537i
$406$		0			0
$407$	4.14469	+	7.17882i	0.205445	+	0.355841i
$408$		0			0
$409$	25.9524	−	9.44591i	1.28326	−	0.467070i	0.391754	−	0.920070i	$-0.371868\pi$
$409$	25.9524	−	9.44591i	1.28326	−	0.467070i	0.891511	+	0.453000i	$0.149646\pi$
$410$		0			0
$411$	−9.03304	+	15.6457i	−0.445567	+	0.771744i
$412$		0			0
$413$	−30.8937	+	25.9229i	−1.52018	+	1.27558i
$414$		0			0
$415$	−0.160536	−	0.910442i	−0.00788038	−	0.0446919i
$416$		0			0
$417$	−19.6947			−0.964456
$418$		0			0
$419$	21.2139			1.03637			0.518184	−	0.855269i	$-0.326608\pi$
$419$	21.2139			1.03637			0.518184	+	0.855269i	$0.326608\pi$
$420$		0			0
$421$	5.42288	+	30.7547i	0.264295	+	1.49889i	0.771036	+	0.636792i	$0.219739\pi$
$421$	5.42288	+	30.7547i	0.264295	+	1.49889i	−0.506741	+	0.862099i	$0.669150\pi$
$422$		0			0
$423$	6.53211	−	5.48109i	0.317602	−	0.266500i
$424$		0			0
$425$	0.181936	−	0.315123i	0.00882521	−	0.0152857i
$426$		0			0
$427$	−35.6722	+	12.9836i	−1.72630	+	0.628322i
$428$		0			0
$429$	3.49067	+	6.04602i	0.168531	+	0.291905i
$430$		0			0
$431$	1.69732	−	9.62595i	0.0817568	−	0.463666i	−0.916253	−	0.400601i	$-0.868801\pi$
$431$	1.69732	−	9.62595i	0.0817568	−	0.463666i	0.998009	−	0.0630649i	$-0.0200875\pi$
$432$		0			0
$433$	15.1630	+	12.7233i	0.728690	+	0.611443i	0.929774	−	0.368131i	$-0.120002\pi$
$433$	15.1630	+	12.7233i	0.728690	+	0.611443i	−0.201084	+	0.979574i	$0.564447\pi$
$434$		0			0
$435$	−4.59125	−	1.67108i	−0.220133	−	0.0801220i
$436$		0			0
$437$	−9.56230	−	31.1095i	−0.457427	−	1.48817i
$438$		0			0
$439$	−21.4219	−	7.79694i	−1.02241	−	0.372128i	−0.224225	−	0.974537i	$-0.571985\pi$
$439$	−21.4219	−	7.79694i	−1.02241	−	0.372128i	−0.798187	+	0.602410i	$0.794207\pi$
$440$		0			0
$441$	−2.34472	−	1.96745i	−0.111653	−	0.0936882i
$442$		0			0
$443$	−2.22149	+	12.5987i	−0.105546	+	0.598581i	0.885455	+	0.464725i	$0.153847\pi$
$443$	−2.22149	+	12.5987i	−0.105546	+	0.598581i	−0.991001	+	0.133856i	$0.957264\pi$
$444$		0			0
$445$	3.99257	+	6.91533i	0.189266	+	0.327818i
$446$		0			0
$447$	7.57717	−	2.75786i	0.358388	−	0.130443i
$448$		0			0
$449$	−7.14276	+	12.3716i	−0.337088	+	0.583853i	−0.983884	−	0.178810i	$-0.942775\pi$
$449$	−7.14276	+	12.3716i	−0.337088	+	0.583853i	0.646796	+	0.762663i	$0.276109\pi$
$450$		0			0
$451$	16.2874	−	13.6668i	0.766945	−	0.643544i
$452$		0			0
$453$	−5.18017	−	29.3782i	−0.243386	−	1.38031i
$454$		0			0
$455$	−6.26434			−0.293677
$456$		0			0
$457$	29.7160			1.39005			0.695027	−	0.718984i	$-0.255392\pi$
$457$	29.7160			1.39005			0.695027	+	0.718984i	$0.255392\pi$
$458$		0			0
$459$	0.354985	+	2.01322i	0.0165693	+	0.0939691i
$460$		0			0
$461$	17.1209	−	14.3662i	0.797402	−	0.669099i	−0.150164	−	0.988661i	$-0.547980\pi$
$461$	17.1209	−	14.3662i	0.797402	−	0.669099i	0.947565	+	0.319562i	$0.103536\pi$
$462$		0			0
$463$	19.2984	−	33.4259i	0.896874	−	1.55343i	0.0654067	−	0.997859i	$-0.479166\pi$
$463$	19.2984	−	33.4259i	0.896874	−	1.55343i	0.831468	−	0.555573i	$-0.187501\pi$
$464$		0			0
$465$	−10.7306	+	3.90562i	−0.497619	+	0.181119i
$466$		0			0
$467$	−7.24255	−	12.5445i	−0.335145	−	0.580489i	0.648367	−	0.761328i	$-0.275452\pi$
$467$	−7.24255	−	12.5445i	−0.335145	−	0.580489i	−0.983513	+	0.180839i	$0.942119\pi$
$468$		0			0
$469$	−1.43065	+	8.11363i	−0.0660613	+	0.374653i
$470$		0			0
$471$	−3.49626	−	2.93371i	−0.161099	−	0.135178i
$472$		0			0
$473$	−24.5048	−	8.91902i	−1.12673	−	0.410097i
$474$		0			0
$475$	−2.96797	+	3.19236i	−0.136180	+	0.146476i
$476$		0			0
$477$	−1.78956	−	0.651348i	−0.0819385	−	0.0298232i
$478$		0			0
$479$	11.5193	+	9.66583i	0.526330	+	0.441643i	0.866832	−	0.498601i	$-0.166153\pi$
$479$	11.5193	+	9.66583i	0.526330	+	0.441643i	−0.340502	+	0.940244i	$0.610597\pi$
$480$		0			0
$481$	1.08710	−	6.16523i	0.0495673	−	0.281110i
$482$		0			0
$483$	18.8745	+	32.6915i	0.858818	+	1.48752i
$484$		0			0
$485$	−6.64008	+	2.41679i	−0.301511	+	0.109741i
$486$		0			0
$487$	−0.424122	+	0.734601i	−0.0192188	+	0.0332879i	−0.875475	−	0.483264i	$-0.839451\pi$
$487$	−0.424122	+	0.734601i	−0.0192188	+	0.0332879i	0.856256	+	0.516552i	$0.172785\pi$
$488$		0			0
$489$	8.38648	−	7.03709i	0.379250	−	0.318228i
$490$		0			0
$491$	4.71762	+	26.7549i	0.212903	+	1.20743i	0.884508	+	0.466525i	$0.154494\pi$
$491$	4.71762	+	26.7549i	0.212903	+	1.20743i	−0.671605	+	0.740909i	$0.734395\pi$
$492$		0			0
$493$	−1.17838			−0.0530714
$494$		0			0
$495$	1.79147			0.0805206
$496$		0			0
$497$	0.0609962	+	0.345927i	0.00273605	+	0.0155169i
$498$		0			0
$499$	8.19888	−	6.87968i	0.367032	−	0.307977i	−0.440554	−	0.897726i	$-0.645218\pi$
$499$	8.19888	−	6.87968i	0.367032	−	0.307977i	0.807586	+	0.589749i	$0.200774\pi$
$500$		0			0
$501$	1.99234	−	3.45084i	0.0890113	−	0.154172i
$502$		0			0
$503$	−29.3209	+	10.6719i	−1.30736	+	0.475839i	−0.899385	−	0.437157i	$-0.855986\pi$
$503$	−29.3209	+	10.6719i	−1.30736	+	0.475839i	−0.407970	+	0.912995i	$0.633763\pi$
$504$		0			0
$505$	0.269525	+	0.466832i	0.0119937	+	0.0207737i
$506$		0			0
$507$	−2.49029	+	14.1231i	−0.110598	+	0.627230i
$508$		0			0
$509$	33.1668	+	27.8302i	1.47009	+	1.23355i	0.916051	+	0.401063i	$0.131359\pi$
$509$	33.1668	+	27.8302i	1.47009	+	1.23355i	0.554040	+	0.832490i	$0.313085\pi$
$510$		0			0
$511$	−24.4077	−	8.88367i	−1.07973	−	0.392990i
$512$		0			0
$513$	1.24488	−	24.4571i	0.0549626	−	1.07981i
$514$		0			0
$515$	7.16692	+	2.60855i	0.315812	+	0.114946i
$516$		0			0
$517$	22.3407	+	18.7461i	0.982543	+	0.824452i
$518$		0			0
$519$	−3.16948	+	17.9750i	−0.139125	+	0.789015i
$520$		0			0
$521$	−18.3439	−	31.7726i	−0.803663	−	1.39198i	−0.917190	−	0.398450i	$-0.869548\pi$
$521$	−18.3439	−	31.7726i	−0.803663	−	1.39198i	0.113527	−	0.993535i	$-0.463785\pi$
$522$		0			0
$523$	36.6256	−	13.3306i	1.60153	−	0.582908i	0.621787	−	0.783186i	$-0.286407\pi$
$523$	36.6256	−	13.3306i	1.60153	−	0.582908i	0.979739	+	0.200278i	$0.0641847\pi$
$524$		0			0
$525$	2.52787	−	4.37840i	0.110325	−	0.191089i
$526$		0			0
$527$	−2.10975	+	1.77029i	−0.0919021	+	0.0771150i
$528$		0			0
$529$	5.68689	+	32.2520i	0.247256	+	1.40226i
$530$		0			0
$531$	−8.71015			−0.377988
$532$		0			0
$533$	−16.0574			−0.695521
$534$		0			0
$535$	−1.47798	−	8.38205i	−0.0638987	−	0.362387i
$536$		0			0
$537$	−21.0322	+	17.6481i	−0.907605	+	0.761571i
$538$		0			0
$539$	5.23419	−	9.06589i	0.225453	−	0.390496i
$540$		0			0
$541$	23.2295	−	8.45486i	0.998716	−	0.363503i	0.209627	−	0.977781i	$-0.432775\pi$
$541$	23.2295	−	8.45486i	0.998716	−	0.363503i	0.789089	+	0.614279i	$0.210553\pi$
$542$		0			0
$543$	15.4407	+	26.7441i	0.662623	+	1.14770i
$544$		0			0
$545$	−2.27781	+	12.9181i	−0.0975706	+	0.553350i
$546$		0			0
$547$	11.9613	+	10.0368i	0.511430	+	0.429141i	0.861632	−	0.507533i	$-0.169443\pi$
$547$	11.9613	+	10.0368i	0.511430	+	0.429141i	−0.350202	+	0.936674i	$0.613887\pi$
$548$		0			0
$549$	−7.70442	−	2.80418i	−0.328816	−	0.119679i
$550$		0			0
$551$	13.7589	+	3.15472i	0.586150	+	0.134396i
$552$		0			0
$553$	17.1976	+	6.25940i	0.731314	+	0.266177i
$554$		0			0
$555$	3.87044	+	3.24769i	0.164291	+	0.137857i
$556$		0			0
$557$	0.785151	−	4.45281i	0.0332679	−	0.188672i	−0.963645	−	0.267185i	$-0.913906\pi$
$557$	0.785151	−	4.45281i	0.0332679	−	0.188672i	0.996913	+	0.0785138i	$0.0250175\pi$
$558$		0			0
$559$	9.84715	+	17.0558i	0.416490	+	0.721382i
$560$		0			0
$561$	−1.27695	+	0.464771i	−0.0539127	+	0.0196226i
$562$		0			0
$563$	7.56521	−	13.1033i	0.318835	−	0.552239i	−0.661410	−	0.750025i	$-0.730042\pi$
$563$	7.56521	−	13.1033i	0.318835	−	0.552239i	0.980245	+	0.197785i	$0.0633749\pi$
$564$		0			0
$565$	−10.6493	+	8.93583i	−0.448020	+	0.375933i
$566$		0			0
$567$	3.66883	+	20.8069i	0.154076	+	0.873810i
$568$		0			0
$569$	−2.59851			−0.108935			−0.0544676	−	0.998516i	$-0.517346\pi$
$569$	−2.59851			−0.108935			−0.0544676	+	0.998516i	$0.517346\pi$
$570$		0			0
$571$	39.1787			1.63958			0.819790	−	0.572665i	$-0.194090\pi$
$571$	39.1787			1.63958			0.819790	+	0.572665i	$0.194090\pi$
$572$		0			0
$573$	1.75653	+	9.96180i	0.0733802	+	0.416160i
$574$		0			0
$575$	5.71972	−	4.79941i	0.238529	−	0.200149i
$576$		0			0
$577$	−4.88434	+	8.45993i	−0.203338	+	0.352191i	−0.949602	−	0.313459i	$-0.898512\pi$
$577$	−4.88434	+	8.45993i	−0.203338	+	0.352191i	0.746264	+	0.665650i	$0.231846\pi$
$578$		0			0
$579$	14.9120	−	5.42753i	0.619723	−	0.225561i
$580$		0			0
$581$	−1.54898	−	2.68290i	−0.0642623	−	0.111306i
$582$		0			0
$583$	1.13103	−	6.41440i	0.0468426	−	0.265657i
$584$		0			0
$585$	−1.03643	−	0.869666i	−0.0428510	−	0.0359562i
$586$		0			0
$587$	5.08774	+	1.85178i	0.209993	+	0.0764313i	0.444875	−	0.895593i	$-0.353248\pi$
$587$	5.08774	+	1.85178i	0.209993	+	0.0764313i	−0.234882	+	0.972024i	$0.575470\pi$
$588$		0			0
$589$	29.3732	−	15.0221i	1.21030	−	0.618973i
$590$		0			0
$591$	−17.2713	−	6.28623i	−0.710445	−	0.258581i
$592$		0			0
$593$	−2.38413	−	2.00052i	−0.0979043	−	0.0821515i	0.592522	−	0.805555i	$-0.298132\pi$
$593$	−2.38413	−	2.00052i	−0.0979043	−	0.0821515i	−0.690426	+	0.723403i	$0.742577\pi$
$594$		0			0
$595$	0.211735	−	1.20081i	0.00868030	−	0.0492285i
$596$		0			0
$597$	−13.3510	−	23.1247i	−0.546421	−	0.946429i
$598$		0			0
$599$	16.8738	−	6.14155i	0.689444	−	0.250937i	0.0265467	−	0.999648i	$-0.491549\pi$
$599$	16.8738	−	6.14155i	0.689444	−	0.250937i	0.662897	+	0.748711i	$0.269327\pi$
$600$		0			0
$601$	−20.1403	+	34.8839i	−0.821538	+	1.42295i	0.0829986	+	0.996550i	$0.473550\pi$
$601$	−20.1403	+	34.8839i	−0.821538	+	1.42295i	−0.904537	+	0.426396i	$0.859783\pi$
$602$		0			0
$603$	−1.36310	+	1.14378i	−0.0555097	+	0.0465781i
$604$		0			0
$605$	−0.846175	−	4.79890i	−0.0344019	−	0.195103i
$606$		0			0
$607$	30.5465			1.23984			0.619922	−	0.784663i	$-0.287164\pi$
$607$	30.5465			1.23984			0.619922	+	0.784663i	$0.287164\pi$
$608$		0			0
$609$	−16.3726			−0.663452
$610$		0			0
$611$	−3.82462	−	21.6905i	−0.154728	−	0.877504i
$612$		0			0
$613$	24.0219	−	20.1568i	0.970235	−	0.814124i	−0.0123524	−	0.999924i	$-0.503932\pi$
$613$	24.0219	−	20.1568i	0.970235	−	0.814124i	0.982588	+	0.185800i	$0.0594876\pi$
$614$		0			0
$615$	6.47967	−	11.2231i	0.261286	−	0.452560i
$616$		0			0
$617$	41.0154	−	14.9284i	1.65122	−	0.600994i	0.662271	−	0.749264i	$-0.269593\pi$
$617$	41.0154	−	14.9284i	1.65122	−	0.600994i	0.988947	+	0.148270i	$0.0473703\pi$
$618$		0			0
$619$	−1.34573	−	2.33087i	−0.0540895	−	0.0936857i	0.837713	−	0.546111i	$-0.183892\pi$
$619$	−1.34573	−	2.33087i	−0.0540895	−	0.0936857i	−0.891802	+	0.452425i	$0.850559\pi$
$620$		0			0
$621$	−7.28419	+	41.3107i	−0.292304	+	1.65774i
$622$		0			0
$623$	20.4979	+	17.1998i	0.821231	+	0.689095i
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$		0			0
$627$	16.1542	−	2.00814i	0.645135	−	0.0801973i
$628$		0			0
$629$	1.14507	+	0.416771i	0.0456569	+	0.0166177i
$630$		0			0
$631$	−17.9778	−	15.0852i	−0.715685	−	0.600531i	0.210503	−	0.977593i	$-0.432490\pi$
$631$	−17.9778	−	15.0852i	−0.715685	−	0.600531i	−0.926188	+	0.377062i	$0.876934\pi$
$632$		0			0
$633$	5.27919	−	29.9398i	0.209829	−	1.19000i
$634$		0			0
$635$	−0.849517	−	1.47141i	−0.0337121	−	0.0583910i
$636$		0			0
$637$	−7.42918	+	2.70400i	−0.294355	+	0.107136i
$638$		0			0
$639$	−0.0379326	+	0.0657011i	−0.00150059	+	0.00259910i
$640$		0			0
$641$	29.5691	−	24.8114i	1.16791	−	0.979991i	0.167924	−	0.985800i	$-0.446294\pi$
$641$	29.5691	−	24.8114i	1.16791	−	0.979991i	0.999983	+	0.00580901i	$0.00184908\pi$
$642$		0			0
$643$	−4.94981	−	28.0718i	−0.195201	−	1.10704i	−0.912132	−	0.409897i	$-0.865564\pi$
$643$	−4.94981	−	28.0718i	−0.195201	−	1.10704i	0.716930	−	0.697145i	$-0.245547\pi$
$644$		0			0
$645$	−15.8946			−0.625850
$646$		0			0
$647$	−8.39487			−0.330036			−0.165018	−	0.986291i	$-0.552768\pi$
$647$	−8.39487			−0.330036			−0.165018	+	0.986291i	$0.552768\pi$
$648$		0			0
$649$	−5.17296	−	29.3373i	−0.203057	−	1.15159i
$650$		0			0
$651$	−29.3133	+	24.5968i	−1.14888	+	0.964025i
$652$		0			0
$653$	−2.14161	+	3.70938i	−0.0838077	+	0.145159i	−0.904883	−	0.425661i	$-0.860041\pi$
$653$	−2.14161	+	3.70938i	−0.0838077	+	0.145159i	0.821075	+	0.570821i	$0.193375\pi$
$654$		0			0
$655$	4.40967	−	1.60499i	0.172300	−	0.0627121i
$656$		0			0
$657$	−2.80492	−	4.85826i	−0.109430	−	0.189539i
$658$		0			0
$659$	−2.57762	+	14.6184i	−0.100410	+	0.569453i	0.892545	+	0.450959i	$0.148918\pi$
$659$	−2.57762	+	14.6184i	−0.100410	+	0.569453i	−0.992955	+	0.118494i	$0.962193\pi$
$660$		0			0
$661$	−32.4321	−	27.2137i	−1.26146	−	1.05849i	−0.995525	−	0.0945016i	$-0.969874\pi$
$661$	−32.4321	−	27.2137i	−1.26146	−	1.05849i	−0.265937	−	0.963990i	$-0.585681\pi$
$662$		0			0
$663$	0.964380	+	0.351006i	0.0374534	+	0.0136319i
$664$		0			0
$665$	−5.68705	+	13.4540i	−0.220534	+	0.521726i
$666$		0			0
$667$	−22.7217	−	8.27001i	−0.879787	−	0.320216i
$668$		0			0
$669$	22.3505	+	18.7543i	0.864121	+	0.725083i
$670$		0			0
$671$	4.86931	−	27.6152i	0.187978	−	1.06607i
$672$		0			0
$673$	−2.96569	−	5.13672i	−0.114319	−	0.198006i	0.803188	−	0.595725i	$-0.203135\pi$
$673$	−2.96569	−	5.13672i	−0.114319	−	0.198006i	−0.917507	+	0.397719i	$0.869802\pi$
$674$		0			0
$675$	5.27930	−	1.92151i	0.203200	−	0.0739588i
$676$		0			0
$677$	4.02585	−	6.97297i	0.154726	−	0.267993i	−0.778233	−	0.627975i	$-0.783884\pi$
$677$	4.02585	−	6.97297i	0.154726	−	0.267993i	0.932959	+	0.359982i	$0.117217\pi$
$678$		0			0
$679$	−18.1391	+	15.2205i	−0.696114	+	0.584109i
$680$		0			0
$681$	1.31382	+	7.45102i	0.0503456	+	0.285524i
$682$		0			0
$683$	−42.4980			−1.62614			−0.813071	−	0.582164i	$-0.802206\pi$
$683$	−42.4980			−1.62614			−0.813071	+	0.582164i	$0.802206\pi$
$684$		0			0
$685$	11.9744			0.457517
$686$		0			0
$687$	4.03854	+	22.9037i	0.154080	+	0.873830i
$688$		0			0
$689$	−3.76820	+	3.16190i	−0.143557	+	0.120459i
$690$		0			0
$691$	12.1536	−	21.0507i	0.462345	−	0.800805i	−0.536733	−	0.843752i	$-0.680342\pi$
$691$	12.1536	−	21.0507i	0.462345	−	0.800805i	0.999077	+	0.0429478i	$0.0136749\pi$
$692$		0			0
$693$	5.64117	−	2.05322i	0.214290	−	0.0779953i
$694$		0			0
$695$	6.52694	+	11.3050i	0.247581	+	0.428823i
$696$		0			0
$697$	0.542740	−	3.07803i	0.0205578	−	0.116589i
$698$		0			0
$699$	−10.0144	−	8.40305i	−0.378778	−	0.317833i
$700$		0			0
$701$	16.0317	+	5.83508i	0.605511	+	0.220388i	0.626538	−	0.779391i	$-0.284471\pi$
$701$	16.0317	+	5.83508i	0.605511	+	0.220388i	−0.0210272	+	0.999779i	$0.506694\pi$
$702$		0			0
$703$	−12.2543	−	7.93185i	−0.462179	−	0.299155i
$704$		0			0
$705$	16.7037	+	6.07965i	0.629098	+	0.228973i
$706$		0			0
$707$	1.38375	+	1.16110i	0.0520412	+	0.0436678i
$708$		0			0
$709$	−2.01281	+	11.4152i	−0.0755928	+	0.428708i	0.923400	+	0.383839i	$0.125398\pi$
$709$	−2.01281	+	11.4152i	−0.0755928	+	0.428708i	−0.998993	+	0.0448691i	$0.985713\pi$
$710$		0			0
$711$	1.97633	+	3.42311i	0.0741184	+	0.128377i
$712$		0			0
$713$	−53.1047	+	19.3285i	−1.98879	+	0.723860i
$714$		0			0
$715$	2.31365	−	4.00736i	0.0865257	−	0.149867i
$716$		0			0
$717$	14.1278	−	11.8546i	0.527613	−	0.442719i
$718$		0			0
$719$	2.09646	+	11.8896i	0.0781848	+	0.443408i	0.998620	+	0.0525135i	$0.0167232\pi$
$719$	2.09646	+	11.8896i	0.0781848	+	0.443408i	−0.920435	+	0.390895i	$0.872166\pi$
$720$		0			0
$721$	25.5576			0.951815
$722$		0			0
$723$	−2.34638			−0.0872629
$724$		0			0
$725$	0.562347	+	3.18923i	0.0208850	+	0.118445i
$726$		0			0
$727$	−2.84897	+	2.39057i	−0.105662	+	0.0886612i	−0.694088	−	0.719890i	$-0.744192\pi$
$727$	−2.84897	+	2.39057i	−0.105662	+	0.0886612i	0.588426	+	0.808551i	$0.299748\pi$
$728$		0			0
$729$	−14.9959	+	25.9736i	−0.555403	+	0.961986i
$730$		0			0
$731$	−3.60226	+	1.31111i	−0.133234	+	0.0484933i
$732$		0			0
$733$	−4.28268	−	7.41782i	−0.158184	−	0.273984i	0.776030	−	0.630697i	$-0.217231\pi$
$733$	−4.28268	−	7.41782i	−0.158184	−	0.273984i	−0.934214	+	0.356713i	$0.883897\pi$
$734$		0			0
$735$	1.10799	−	6.28370i	0.0408687	−	0.231778i
$736$		0			0
$737$	−4.66198	−	3.91187i	−0.171726	−	0.144095i
$738$		0			0
$739$	2.60103	+	0.946697i	0.0956804	+	0.0348248i	0.389417	−	0.921062i	$-0.372677\pi$
$739$	2.60103	+	0.946697i	0.0956804	+	0.0348248i	−0.293736	+	0.955886i	$0.594899\pi$
$740$		0			0
$741$	−10.3206	−	6.68022i	−0.379136	−	0.245404i
$742$		0			0
$743$	20.3640	+	7.41189i	0.747083	+	0.271916i	0.687378	−	0.726300i	$-0.258762\pi$
$743$	20.3640	+	7.41189i	0.747083	+	0.271916i	0.0597050	+	0.998216i	$0.480984\pi$
$744$		0			0
$745$	−4.09416	−	3.43540i	−0.149998	−	0.125863i
$746$		0			0
$747$	0.116186	−	0.658924i	0.00425103	−	0.0241088i
$748$		0			0
$749$	−14.2607	−	24.7003i	−0.521076	−	0.902530i
$750$		0			0
$751$	32.8421	−	11.9535i	1.19843	−	0.436191i	0.335751	−	0.941951i	$-0.391010\pi$
$751$	32.8421	−	11.9535i	1.19843	−	0.436191i	0.862674	+	0.505760i	$0.168788\pi$
$752$		0			0
$753$	4.97713	−	8.62065i	0.181377	−	0.314154i
$754$		0			0
$755$	−15.1467	+	12.7096i	−0.551243	+	0.462548i
$756$		0			0
$757$	−4.00158	−	22.6941i	−0.145440	−	0.824831i	−0.967013	−	0.254727i	$-0.918014\pi$
$757$	−4.00158	−	22.6941i	−0.145440	−	0.824831i	0.821573	−	0.570103i	$-0.193097\pi$
$758$		0			0
$759$	−27.8842			−1.01213
$760$		0			0
$761$	−27.9096			−1.01172			−0.505862	−	0.862615i	$-0.668825\pi$
$761$	−27.9096			−1.01172			−0.505862	+	0.862615i	$0.668825\pi$
$762$		0			0
$763$	7.63292	+	43.2884i	0.276330	+	1.56715i
$764$		0			0
$765$	0.201738	−	0.169278i	0.00729384	−	0.00612026i
$766$		0			0
$767$	−11.2490	+	19.4839i	−0.406178	+	0.703521i
$768$		0			0
$769$	−24.7790	+	9.01883i	−0.893554	+	0.325227i	−0.747667	−	0.664074i	$-0.768826\pi$
$769$	−24.7790	+	9.01883i	−0.893554	+	0.325227i	−0.145888	+	0.989301i	$0.546604\pi$
$770$		0			0
$771$	22.0543	+	38.1991i	0.794265	+	1.37571i
$772$		0			0
$773$	−1.47221	+	8.34931i	−0.0529516	+	0.300304i	−0.999770	−	0.0214661i	$-0.993167\pi$
$773$	−1.47221	+	8.34931i	−0.0529516	+	0.300304i	0.946818	+	0.321770i	$0.104278\pi$
$774$		0			0
$775$	5.79804	+	4.86513i	0.208272	+	0.174761i
$776$		0			0
$777$	15.9099	+	5.79071i	0.570763	+	0.207741i
$778$		0			0
$779$	−14.5776	+	34.4867i	−0.522296	+	1.23561i
$780$		0			0
$781$	−0.243821	−	0.0887437i	−0.00872461	−	0.00317550i
$782$		0			0
$783$	−13.9373	−	11.6948i	−0.498078	−	0.417937i
$784$		0			0
$785$	−0.525302	+	2.97914i	−0.0187488	+	0.106330i
$786$		0			0
$787$	−12.0148	−	20.8103i	−0.428283	−	0.741807i	0.568438	−	0.822726i	$-0.307548\pi$
$787$	−12.0148	−	20.8103i	−0.428283	−	0.741807i	−0.996721	+	0.0809188i	$0.974215\pi$
$788$		0			0
$789$	−29.6327	+	10.7854i	−1.05495	+	0.383971i
$790$		0			0
$791$	−23.2922	+	40.3433i	−0.828176	+	1.43444i
$792$		0			0
$793$	−16.2228	+	13.6126i	−0.576089	+	0.483396i
$794$		0			0
$795$	−0.689381	−	3.90967i	−0.0244498	−	0.138662i
$796$		0			0
$797$	6.63639			0.235073			0.117537	−	0.993069i	$-0.462500\pi$
$797$	6.63639			0.235073			0.117537	+	0.993069i	$0.462500\pi$
$798$		0			0
$799$	4.28712			0.151668
$800$		0			0
$801$	1.00354	+	5.69137i	0.0354584	+	0.201095i
$802$		0			0
$803$	14.6976	−	12.3328i	0.518669	−	0.435215i
$804$		0			0
$805$	12.5102	−	21.6683i	0.440926	−	0.763707i
$806$		0			0
$807$	−35.6655	+	12.9812i	−1.25548	+	0.456959i
$808$		0			0
$809$	−19.3684	−	33.5470i	−0.680956	−	1.17945i	−0.974689	−	0.223564i	$-0.928231\pi$
$809$	−19.3684	−	33.5470i	−0.680956	−	1.17945i	0.293733	−	0.955888i	$-0.405102\pi$
$810$		0			0
$811$	−3.57509	+	20.2754i	−0.125538	+	0.711964i	0.855448	+	0.517888i	$0.173282\pi$
$811$	−3.57509	+	20.2754i	−0.125538	+	0.711964i	−0.980987	+	0.194075i	$0.937829\pi$
$812$		0			0
$813$	−25.9456	−	21.7709i	−0.909951	−	0.763540i
$814$		0			0
$815$	−6.81869	−	2.48180i	−0.238848	−	0.0869336i
$816$		0			0
$817$	45.5707	−	5.66494i	1.59432	−	0.198191i
$818$		0			0
$819$	−4.26034	−	1.55064i	−0.148868	−	0.0541836i
$820$		0			0
$821$	−23.1458	−	19.4216i	−0.807793	−	0.677819i	0.142287	−	0.989825i	$-0.454554\pi$
$821$	−23.1458	−	19.4216i	−0.807793	−	0.677819i	−0.950080	+	0.312007i	$0.898999\pi$
$822$		0			0
$823$	−7.02026	+	39.8139i	−0.244711	+	1.38782i	0.576453	+	0.817131i	$0.304437\pi$
$823$	−7.02026	+	39.8139i	−0.244711	+	1.38782i	−0.821163	+	0.570693i	$0.806675\pi$
$824$		0			0
$825$	1.86727	+	3.23421i	0.0650100	+	0.112601i
$826$		0			0
$827$	24.4203	−	8.88826i	0.849177	−	0.309075i	0.119472	−	0.992838i	$-0.461880\pi$
$827$	24.4203	−	8.88826i	0.849177	−	0.309075i	0.729705	+	0.683763i	$0.239658\pi$
$828$		0			0
$829$	21.1425	−	36.6199i	0.734309	−	1.27186i	−0.220717	−	0.975338i	$-0.570840\pi$
$829$	21.1425	−	36.6199i	0.734309	−	1.27186i	0.955026	−	0.296523i	$-0.0958270\pi$
$830$		0			0
$831$	3.03273	−	2.54476i	0.105204	−	0.0882768i
$832$		0			0
$833$	−0.267223	−	1.51550i	−0.00925872	−	0.0525088i
$834$		0			0
$835$	−2.64109			−0.0913986
$836$		0			0
$837$	−42.5224			−1.46979
$838$		0			0
$839$	−4.17152	−	23.6578i	−0.144017	−	0.816760i	−0.968151	−	0.250366i	$-0.919449\pi$
$839$	−4.17152	−	23.6578i	−0.144017	−	0.816760i	0.824135	−	0.566394i	$-0.191662\pi$
$840$		0			0
$841$	−14.1815	+	11.8997i	−0.489016	+	0.410333i
$842$		0			0
$843$	8.62881	−	14.9455i	0.297192	−	0.514752i
$844$		0			0
$845$	8.93211	−	3.25102i	0.307274	−	0.111839i
$846$		0			0
$847$	−8.16457	−	14.1415i	−0.280538	−	0.485906i
$848$		0			0
$849$	5.54895	−	31.4697i	0.190440	−	1.08004i
$850$		0			0
$851$	19.1545	+	16.0725i	0.656607	+	0.550959i
$852$		0			0
$853$	32.0196	+	11.6542i	1.09633	+	0.399031i	0.825962	−	0.563726i	$-0.190633\pi$
$853$	32.0196	+	11.6542i	1.09633	+	0.399031i	0.270367	+	0.962757i	$0.412855\pi$
$854$		0			0
$855$	−2.80871	+	1.43643i	−0.0960560	+	0.0491250i
$856$		0			0
$857$	−22.0477	−	8.02471i	−0.753136	−	0.274119i	−0.0632110	−	0.998000i	$-0.520134\pi$
$857$	−22.0477	−	8.02471i	−0.753136	−	0.274119i	−0.689925	+	0.723881i	$0.742356\pi$
$858$		0			0
$859$	−11.1208	−	9.33148i	−0.379437	−	0.318386i	0.433044	−	0.901373i	$-0.357439\pi$
$859$	−11.1208	−	9.33148i	−0.379437	−	0.318386i	−0.812482	+	0.582987i	$0.801884\pi$
$860$		0			0
$861$	7.54096	−	42.7669i	0.256995	−	1.45749i
$862$		0			0
$863$	9.90294	+	17.1524i	0.337100	+	0.583874i	0.983886	−	0.178797i	$-0.0572206\pi$
$863$	9.90294	+	17.1524i	0.337100	+	0.583874i	−0.646786	+	0.762672i	$0.723887\pi$
$864$		0			0
$865$	11.3682	−	4.13769i	0.386531	−	0.140686i
$866$		0			0
$867$	12.7243	−	22.0391i	0.432140	−	0.748488i
$868$		0			0
$869$	−10.3559	+	8.68963i	−0.351300	+	0.294776i
$870$		0			0
$871$	0.798109	+	4.52630i	0.0270429	+	0.153368i
$872$		0			0
$873$	−5.11412			−0.173087
$874$		0			0
$875$	−3.35099			−0.113284
$876$		0			0
$877$	−6.81493	−	38.6494i	−0.230124	−	1.30510i	−0.852644	−	0.522493i	$-0.825002\pi$
$877$	−6.81493	−	38.6494i	−0.230124	−	1.30510i	0.622520	−	0.782604i	$-0.286109\pi$
$878$		0			0
$879$	−31.0514	+	26.0552i	−1.04734	+	0.878820i
$880$		0			0
$881$	−25.8323	+	44.7429i	−0.870313	+	1.50743i	−0.00864008	+	0.999963i	$0.502750\pi$
$881$	−25.8323	+	44.7429i	−0.870313	+	1.50743i	−0.861673	+	0.507464i	$0.830583\pi$
$882$		0			0
$883$	−54.1502	+	19.7091i	−1.82230	+	0.663263i	−0.827495	+	0.561473i	$0.810235\pi$
$883$	−54.1502	+	19.7091i	−1.82230	+	0.663263i	−0.994806	+	0.101790i	$0.967543\pi$
$884$		0			0
$885$	−9.07870	−	15.7248i	−0.305177	−	0.528582i
$886$		0			0
$887$	5.37729	−	30.4962i	0.180552	−	1.02396i	−0.750986	−	0.660318i	$-0.770422\pi$
$887$	5.37729	−	30.4962i	0.180552	−	1.02396i	0.931538	−	0.363643i	$-0.118467\pi$
$888$		0			0
$889$	−4.36144	−	3.65968i	−0.146278	−	0.122742i
$890$		0			0
$891$	−14.6655	−	5.33779i	−0.491312	−	0.178823i
$892$		0			0
$893$	−50.0573	−	11.4774i	−1.67510	−	0.384076i
$894$		0			0
$895$	17.1003	+	6.22402i	0.571601	+	0.208046i
$896$		0			0
$897$	16.1320	+	13.5363i	0.538630	+	0.451964i
$898$		0			0
$899$	4.25629	−	24.1386i	0.141955	−	0.805068i
$900$		0			0
$901$	−0.478738	−	0.829199i	−0.0159491	−	0.0276246i
$902$		0			0
$903$	−50.0506	+	18.2169i	−1.66558	+	0.606221i
$904$		0			0
$905$	10.2342	−	17.7262i	0.340198	−	0.589240i
$906$		0			0
$907$	23.1502	−	19.4254i	0.768691	−	0.645008i	−0.171682	−	0.985152i	$-0.554920\pi$
$907$	23.1502	−	19.4254i	0.768691	−	0.645008i	0.940373	+	0.340144i	$0.110476\pi$
$908$		0			0
$909$	0.0677459	+	0.384206i	0.00224699	+	0.0127433i
$910$		0			0
$911$	40.6832			1.34789			0.673947	−	0.738780i	$-0.264598\pi$
$911$	40.6832			1.34789			0.673947	+	0.738780i	$0.264598\pi$
$912$		0			0
$913$	2.28838			0.0757342
$914$		0			0
$915$	−2.96792	−	16.8319i	−0.0981163	−	0.556445i
$916$		0			0
$917$	12.0461	−	10.1079i	0.397798	−	0.333792i
$918$		0			0
$919$	−21.3480	+	36.9759i	−0.704207	+	1.21972i	0.262771	+	0.964858i	$0.415364\pi$
$919$	−21.3480	+	36.9759i	−0.704207	+	1.21972i	−0.966977	+	0.254863i	$0.917970\pi$
$920$		0			0
$921$	6.01547	−	2.18945i	0.198217	−	0.0721449i
$922$		0			0
$923$	0.0979785	+	0.169704i	0.00322500	+	0.00558587i
$924$		0			0
$925$	0.581522	−	3.29798i	0.0191203	−	0.108437i
$926$		0			0
$927$	4.22848	+	3.54811i	0.138881	+	0.116535i
$928$		0			0
$929$	−40.4831	−	14.7346i	−1.32821	−	0.483428i	−0.422128	−	0.906536i	$-0.638717\pi$
$929$	−40.4831	−	14.7346i	−1.32821	−	0.483428i	−0.906079	+	0.423109i	$0.860939\pi$
$930$		0			0
$931$	−0.937107	+	18.4106i	−0.0307124	+	0.603384i
$932$		0			0
$933$	46.7959	+	17.0323i	1.53203	+	0.557613i
$934$		0			0
$935$	0.689970	+	0.578954i	0.0225644	+	0.0189338i
$936$		0			0
$937$	−2.16684	+	12.2888i	−0.0707877	+	0.401457i	0.928740	+	0.370731i	$0.120893\pi$
$937$	−2.16684	+	12.2888i	−0.0707877	+	0.401457i	−0.999528	+	0.0307255i	$0.990218\pi$
$938$		0			0
$939$	5.86389	+	10.1566i	0.191361	+	0.331447i
$940$		0			0
$941$	32.7107	−	11.9057i	1.06634	−	0.388116i	0.251533	−	0.967849i	$-0.419065\pi$
$941$	32.7107	−	11.9057i	1.06634	−	0.388116i	0.814806	+	0.579733i	$0.196843\pi$
$942$		0			0
$943$	32.0673	−	55.5422i	1.04426	−	1.80870i
$944$		0			0
$945$	14.4217	−	12.1013i	0.469139	−	0.393655i
$946$		0			0
$947$	0.467236	+	2.64983i	0.0151831	+	0.0861079i	0.991458	−	0.130428i	$-0.0416352\pi$
$947$	0.467236	+	2.64983i	0.0151831	+	0.0861079i	−0.976275	+	0.216536i	$0.930524\pi$
$948$		0			0
$949$	−14.4900			−0.470366
$950$		0			0
$951$	−18.3236			−0.594184
$952$		0			0
$953$	4.99262	+	28.3145i	0.161727	+	0.917198i	0.952375	+	0.304928i	$0.0986324\pi$
$953$	4.99262	+	28.3145i	0.161727	+	0.917198i	−0.790649	+	0.612270i	$0.790257\pi$
$954$		0			0
$955$	5.13605	−	4.30966i	0.166199	−	0.139457i
$956$		0			0
$957$	6.04702	−	10.4737i	0.195472	−	0.338568i
$958$		0			0
$959$	37.7061	−	13.7239i	1.21759	−	0.443168i
$960$		0			0
$961$	−13.1434	−	22.7650i	−0.423979	−	0.734354i
$962$		0			0
$963$	1.06968	−	6.06643i	0.0344698	−	0.195488i
$964$		0			0
$965$	−8.05738	−	6.76094i	−0.259376	−	0.217643i
$966$		0			0
$967$	50.6219	+	18.4249i	1.62789	+	0.592504i	0.984862	−	0.173338i	$-0.0554554\pi$
$967$	50.6219	+	18.4249i	1.62789	+	0.592504i	0.643029	+	0.765842i	$0.277678\pi$
$968$		0			0
$969$	1.62937	−	1.75256i	0.0523429	−	0.0563003i
$970$		0			0
$971$	−14.2905	−	5.20131i	−0.458604	−	0.166918i	0.102379	−	0.994745i	$-0.467354\pi$
$971$	−14.2905	−	5.20131i	−0.458604	−	0.166918i	−0.560983	+	0.827827i	$0.689577\pi$
$972$		0			0
$973$	33.5094	+	28.1177i	1.07426	+	0.901413i
$974$		0			0
$975$	0.489759	−	2.77756i	0.0156849	−	0.0889532i
$976$		0			0
$977$	20.7994	+	36.0255i	0.665430	+	1.15256i	0.979168	+	0.203049i	$0.0650852\pi$
$977$	20.7994	+	36.0255i	0.665430	+	1.15256i	−0.313738	+	0.949510i	$0.601581\pi$
$978$		0			0
$979$	−18.5735	+	6.76021i	−0.593613	+	0.216057i
$980$		0			0
$981$	−4.74679	+	8.22168i	−0.151553	+	0.262498i
$982$		0			0
$983$	−17.5169	+	14.6984i	−0.558701	+	0.468806i	−0.877875	−	0.478890i	$-0.841039\pi$
$983$	−17.5169	+	14.6984i	−0.558701	+	0.468806i	0.319173	+	0.947696i	$0.396595\pi$
$984$		0			0
$985$	2.11543	+	11.9972i	0.0674030	+	0.382262i
$986$		0			0
$987$	59.5663			1.89602
$988$		0			0
$989$	−78.6610			−2.50127
$990$		0			0
$991$	−1.32528	−	7.51606i	−0.0420991	−	0.238756i	0.956496	−	0.291745i	$-0.0942360\pi$
$991$	−1.32528	−	7.51606i	−0.0420991	−	0.238756i	−0.998595	+	0.0529898i	$0.983125\pi$
$992$		0			0
$993$	34.4749	−	28.9279i	1.09403	−	0.917999i
$994$		0			0
$995$	−8.84920	+	15.3273i	−0.280538	+	0.485907i
$996$		0			0
$997$	44.2704	−	16.1131i	1.40206	−	0.510307i	0.473268	−	0.880918i	$-0.343074\pi$
$997$	44.2704	−	16.1131i	1.40206	−	0.510307i	0.928788	+	0.370612i	$0.120852\pi$
$998$		0			0
$999$	9.40711	+	16.2936i	0.297628	+	0.515507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.61.3	✓	18
19.5	even	9	inner	380.2.u.b.81.3	yes	18
19.9	even	9		7220.2.a.w.1.7		9
19.10	odd	18		7220.2.a.y.1.3		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.61.3	✓	18	1.1	even	1	trivial
380.2.u.b.81.3	yes	18	19.5	even	9	inner
7220.2.a.w.1.7		9	19.9	even	9
7220.2.a.y.1.3		9	19.10	odd	18

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.261988 + 1.48581i) q^{3} +(0.766044 - 0.642788i) q^{5} +(1.67550 - 2.90204i) q^{7} +(0.680094 - 0.247534i) q^{9} +O(q^{10})\)	\(q+(0.261988 + 1.48581i) q^{3} +(0.766044 - 0.642788i) q^{5} +(1.67550 - 2.90204i) q^{7} +(0.680094 - 0.247534i) q^{9} +(1.23765 + 2.14367i) q^{11} +(0.324617 - 1.84100i) q^{13} +(1.15575 + 0.969791i) q^{15} +(0.341929 + 0.124452i) q^{17} +(-3.65925 - 2.36853i) q^{19} +(4.75084 + 1.72916i) q^{21} +(5.71972 + 4.79941i) q^{23} +(0.173648 - 0.984808i) q^{25} +(2.80906 + 4.86543i) q^{27} +(-3.04312 + 1.10761i) q^{29} +(-3.78440 + 6.55477i) q^{31} +(-2.86083 + 2.40052i) q^{33} +(-0.581894 - 3.30008i) q^{35} +3.34885 q^{37} +2.82041 q^{39} +(-1.49157 - 8.45909i) q^{41} +(-8.07036 + 6.77184i) q^{43} +(0.361870 - 0.626778i) q^{45} +(11.0714 - 4.02966i) q^{47} +(-2.11458 - 3.66255i) q^{49} +(-0.0953303 + 0.540645i) q^{51} +(-2.01573 - 1.69140i) q^{53} +(2.32601 + 0.846600i) q^{55} +(2.56050 - 6.05746i) q^{57} +(-11.3091 - 4.11618i) q^{59} +(-8.67810 - 7.28179i) q^{61} +(0.421140 - 2.38841i) q^{63} +(-0.934699 - 1.61895i) q^{65} +(-2.31034 + 0.840895i) q^{67} +(-5.63250 + 9.75578i) q^{69} +(-0.0802996 + 0.0673793i) q^{71} +(-1.34598 - 7.63341i) q^{73} +1.50873 q^{75} +8.29469 q^{77} +(0.948370 + 5.37847i) q^{79} +(-4.82989 + 4.05276i) q^{81} +(0.462244 - 0.800630i) q^{83} +(0.341929 - 0.124452i) q^{85} +(-2.44295 - 4.23132i) q^{87} +(-1.38660 + 7.86382i) q^{89} +(-4.79876 - 4.02664i) q^{91} +(-10.7306 - 3.90562i) q^{93} +(-4.32560 + 0.537720i) q^{95} +(-6.64008 - 2.41679i) q^{97} +(1.37235 + 1.15154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 15 * q^9	\( 18 q + 3 q^{3} + 15 q^{9} + 9 q^{13} + 3 q^{15} + 12 q^{17} - 18 q^{19} - 9 q^{21} + 21 q^{23} + 18 q^{27} - 9 q^{29} + 6 q^{31} - 21 q^{33} - 6 q^{35} - 36 q^{37} - 12 q^{39} + 6 q^{41} - 12 q^{43} - 6 q^{45} + 21 q^{47} - 3 q^{49} - 9 q^{51} + 36 q^{53} - 3 q^{55} - 24 q^{57} - 6 q^{61} + 36 q^{63} + 15 q^{65} + 60 q^{67} + 27 q^{69} - 36 q^{71} - 60 q^{73} - 6 q^{75} - 36 q^{77} - 3 q^{79} + 3 q^{81} - 6 q^{83} + 12 q^{85} + 21 q^{87} + 6 q^{89} - 30 q^{91} - 48 q^{93} - 21 q^{95} - 57 q^{97} + 3 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 15 * q^9 + 9 * q^13 + 3 * q^15 + 12 * q^17 - 18 * q^19 - 9 * q^21 + 21 * q^23 + 18 * q^27 - 9 * q^29 + 6 * q^31 - 21 * q^33 - 6 * q^35 - 36 * q^37 - 12 * q^39 + 6 * q^41 - 12 * q^43 - 6 * q^45 + 21 * q^47 - 3 * q^49 - 9 * q^51 + 36 * q^53 - 3 * q^55 - 24 * q^57 - 6 * q^61 + 36 * q^63 + 15 * q^65 + 60 * q^67 + 27 * q^69 - 36 * q^71 - 60 * q^73 - 6 * q^75 - 36 * q^77 - 3 * q^79 + 3 * q^81 - 6 * q^83 + 12 * q^85 + 21 * q^87 + 6 * q^89 - 30 * q^91 - 48 * q^93 - 21 * q^95 - 57 * q^97 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more