LMFDB - Embedded newform 380.2.u.b.61.2

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			61.2
Root			$-0.478554 + 0.828880i$ of defining polynomial
Character	$\chi$	$=$	380.61
Dual form			380.2.u.b.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.166200 + 0.942568i) q^{3} +(0.766044 - 0.642788i) q^{5} +(-2.28066 + 3.95023i) q^{7} +(1.95827 - 0.712751i) q^{9} +O(q^{10})$	\(q+(0.166200 + 0.942568i) q^{3} +(0.766044 - 0.642788i) q^{5} +(-2.28066 + 3.95023i) q^{7} +(1.95827 - 0.712751i) q^{9} +(-0.558879 - 0.968007i) q^{11} +(-0.897380 + 5.08930i) q^{13} +(0.733187 + 0.615217i) q^{15} +(6.80290 + 2.47605i) q^{17} +(-3.68742 + 2.32442i) q^{19} +(-4.10240 - 1.49315i) q^{21} +(-3.31875 - 2.78477i) q^{23} +(0.173648 - 0.984808i) q^{25} +(2.43294 + 4.21398i) q^{27} +(2.51115 - 0.913983i) q^{29} +(1.37022 - 2.37328i) q^{31} +(0.819526 - 0.687664i) q^{33} +(0.792067 + 4.49203i) q^{35} -0.491893 q^{37} -4.94615 q^{39} +(1.45408 + 8.24648i) q^{41} +(3.16372 - 2.65467i) q^{43} +(1.04197 - 1.80475i) q^{45} +(2.48547 - 0.904639i) q^{47} +(-6.90286 - 11.9561i) q^{49} +(-1.20320 + 6.82371i) q^{51} +(-10.4500 - 8.76856i) q^{53} +(-1.05035 - 0.382296i) q^{55} +(-2.80377 - 3.08933i) q^{57} +(2.45313 + 0.892868i) q^{59} +(3.64703 + 3.06022i) q^{61} +(-1.65062 + 9.36114i) q^{63} +(2.58390 + 4.47545i) q^{65} +(11.9079 - 4.33411i) q^{67} +(2.07325 - 3.59098i) q^{69} +(0.524118 - 0.439787i) q^{71} +(-2.28024 - 12.9319i) q^{73} +0.957108 q^{75} +5.09846 q^{77} +(-2.75095 - 15.6014i) q^{79} +(1.22158 - 1.02502i) q^{81} +(1.88033 - 3.25683i) q^{83} +(6.80290 - 2.47605i) q^{85} +(1.27884 + 2.21502i) q^{87} +(2.04379 - 11.5909i) q^{89} +(-18.0573 - 15.1518i) q^{91} +(2.46471 + 0.897081i) q^{93} +(-1.33063 + 4.15084i) q^{95} +(3.27804 + 1.19311i) q^{97} +(-1.78438 - 1.49727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.166200	+	0.942568i	0.0959557	+	0.544192i	0.994450	+	0.105207i	$0.0335506\pi$
$3$	0.166200	+	0.942568i	0.0959557	+	0.544192i	−0.898495	+	0.438984i	$0.855338\pi$
$4$		0			0
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$		0			0
$7$	−2.28066	+	3.95023i	−0.862010	+	1.49305i	0.00797511	+	0.999968i	$0.497461\pi$
$7$	−2.28066	+	3.95023i	−0.862010	+	1.49305i	−0.869985	+	0.493077i	$0.835872\pi$
$8$		0			0
$9$	1.95827	−	0.712751i	0.652756	−	0.237584i
$10$		0			0
$11$	−0.558879	−	0.968007i	−0.168508	−	0.291865i	0.769387	−	0.638783i	$-0.220562\pi$
$11$	−0.558879	−	0.968007i	−0.168508	−	0.291865i	−0.937896	+	0.346918i	$0.887228\pi$
$12$		0			0
$13$	−0.897380	+	5.08930i	−0.248889	+	1.41152i	0.562397	+	0.826867i	$0.309879\pi$
$13$	−0.897380	+	5.08930i	−0.248889	+	1.41152i	−0.811286	+	0.584650i	$0.801232\pi$
$14$		0			0
$15$	0.733187	+	0.615217i	0.189308	+	0.158848i
$16$		0			0
$17$	6.80290	+	2.47605i	1.64994	+	0.600531i	0.988736	−	0.149671i	$-0.0478216\pi$
$17$	6.80290	+	2.47605i	1.64994	+	0.600531i	0.661209	+	0.750202i	$0.270044\pi$
$18$		0			0
$19$	−3.68742	+	2.32442i	−0.845953	+	0.533257i
$19$	−3.68742	+	2.32442i	−0.845953	+	0.533257i
$20$		0			0
$21$	−4.10240	−	1.49315i	−0.895218	−	0.325833i
$22$		0			0
$23$	−3.31875	−	2.78477i	−0.692008	−	0.580664i	0.227480	−	0.973783i	$-0.426952\pi$
$23$	−3.31875	−	2.78477i	−0.692008	−	0.580664i	−0.919488	+	0.393119i	$0.871396\pi$
$24$		0			0
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$		0			0
$27$	2.43294	+	4.21398i	0.468220	+	0.810981i
$28$		0			0
$29$	2.51115	−	0.913983i	0.466308	−	0.169722i	−0.0981710	−	0.995170i	$-0.531299\pi$
$29$	2.51115	−	0.913983i	0.466308	−	0.169722i	0.564479	+	0.825447i	$0.309077\pi$
$30$		0			0
$31$	1.37022	−	2.37328i	0.246098	−	0.426254i	−0.716342	−	0.697750i	$-0.754185\pi$
$31$	1.37022	−	2.37328i	0.246098	−	0.426254i	0.962440	+	0.271495i	$0.0875181\pi$
$32$		0			0
$33$	0.819526	−	0.687664i	0.142661	−	0.119707i
$34$		0			0
$35$	0.792067	+	4.49203i	0.133884	+	0.759292i
$36$		0			0
$37$	−0.491893			−0.0808666			−0.0404333	−	0.999182i	$-0.512874\pi$
$37$	−0.491893			−0.0808666			−0.0404333	+	0.999182i	$0.512874\pi$
$38$		0			0
$39$	−4.94615			−0.792018
$40$		0			0
$41$	1.45408	+	8.24648i	0.227089	+	1.28788i	0.858652	+	0.512560i	$0.171303\pi$
$41$	1.45408	+	8.24648i	0.227089	+	1.28788i	−0.631563	+	0.775325i	$0.717586\pi$
$42$		0			0
$43$	3.16372	−	2.65467i	0.482462	−	0.404834i	−0.368853	−	0.929488i	$-0.620250\pi$
$43$	3.16372	−	2.65467i	0.482462	−	0.404834i	0.851316	+	0.524654i	$0.175805\pi$
$44$		0			0
$45$	1.04197	−	1.80475i	0.155328	−	0.269036i
$46$		0			0
$47$	2.48547	−	0.904639i	0.362544	−	0.131955i	−0.154324	−	0.988020i	$-0.549320\pi$
$47$	2.48547	−	0.904639i	0.362544	−	0.131955i	0.516868	+	0.856065i	$0.327098\pi$
$48$		0			0
$49$	−6.90286	−	11.9561i	−0.986124	−	1.70802i
$50$		0			0
$51$	−1.20320	+	6.82371i	−0.168482	+	0.955510i
$52$		0			0
$53$	−10.4500	−	8.76856i	−1.43541	−	1.20445i	−0.942425	−	0.334418i	$-0.891460\pi$
$53$	−10.4500	−	8.76856i	−1.43541	−	1.20445i	−0.492988	−	0.870036i	$-0.664095\pi$
$54$		0			0
$55$	−1.05035	−	0.382296i	−0.141629	−	0.0515488i
$56$		0			0
$57$	−2.80377	−	3.08933i	−0.371368	−	0.409192i
$58$		0			0
$59$	2.45313	+	0.892868i	0.319371	+	0.116241i	0.496731	−	0.867905i	$-0.334534\pi$
$59$	2.45313	+	0.892868i	0.319371	+	0.116241i	−0.177360	+	0.984146i	$0.556756\pi$
$60$		0			0
$61$	3.64703	+	3.06022i	0.466954	+	0.391821i	0.845682	−	0.533687i	$-0.179194\pi$
$61$	3.64703	+	3.06022i	0.466954	+	0.391821i	−0.378728	+	0.925508i	$0.623638\pi$
$62$		0			0
$63$	−1.65062	+	9.36114i	−0.207959	+	1.17939i
$64$		0			0
$65$	2.58390	+	4.47545i	0.320494	+	0.555112i
$66$		0			0
$67$	11.9079	−	4.33411i	1.45478	−	0.529495i	0.510855	−	0.859667i	$-0.329329\pi$
$67$	11.9079	−	4.33411i	1.45478	−	0.529495i	0.943921	+	0.330171i	$0.107107\pi$
$68$		0			0
$69$	2.07325	−	3.59098i	0.249590	−	0.432303i
$70$		0			0
$71$	0.524118	−	0.439787i	0.0622013	−	0.0521931i	−0.611157	−	0.791509i	$-0.709296\pi$
$71$	0.524118	−	0.439787i	0.0622013	−	0.0521931i	0.673358	+	0.739316i	$0.264851\pi$
$72$		0			0
$73$	−2.28024	−	12.9319i	−0.266882	−	1.51356i	−0.763623	−	0.645662i	$-0.776581\pi$
$73$	−2.28024	−	12.9319i	−0.266882	−	1.51356i	0.496741	−	0.867899i	$-0.334530\pi$
$74$		0			0
$75$	0.957108			0.110517
$76$		0			0
$77$	5.09846			0.581024
$78$		0			0
$79$	−2.75095	−	15.6014i	−0.309506	−	1.75529i	−0.601499	−	0.798874i	$-0.705430\pi$
$79$	−2.75095	−	15.6014i	−0.309506	−	1.75529i	0.291993	−	0.956420i	$-0.405681\pi$
$80$		0			0
$81$	1.22158	−	1.02502i	0.135731	−	0.113892i
$82$		0			0
$83$	1.88033	−	3.25683i	0.206393	−	0.357484i	−0.744182	−	0.667976i	$-0.767161\pi$
$83$	1.88033	−	3.25683i	0.206393	−	0.357484i	0.950576	+	0.310493i	$0.100494\pi$
$84$		0			0
$85$	6.80290	−	2.47605i	0.737878	−	0.268565i
$86$		0			0
$87$	1.27884	+	2.21502i	0.137106	+	0.237475i
$88$		0			0
$89$	2.04379	−	11.5909i	0.216642	−	1.22864i	−0.661393	−	0.750039i	$-0.730035\pi$
$89$	2.04379	−	11.5909i	0.216642	−	1.22864i	0.878035	−	0.478597i	$-0.158854\pi$
$90$		0			0
$91$	−18.0573	−	15.1518i	−1.89292	−	1.58834i
$92$		0			0
$93$	2.46471	+	0.897081i	0.255579	+	0.0930230i
$94$		0			0
$95$	−1.33063	+	4.15084i	−0.136519	+	0.425867i
$96$		0			0
$97$	3.27804	+	1.19311i	0.332835	+	0.121142i	0.503031	−	0.864268i	$-0.332218\pi$
$97$	3.27804	+	1.19311i	0.332835	+	0.121142i	−0.170197	+	0.985410i	$0.554440\pi$
$98$		0			0
$99$	−1.78438	−	1.49727i	−0.179337	−	0.150482i
$100$		0			0
$101$	1.83378	−	10.3999i	0.182468	−	1.03483i	−0.746697	−	0.665164i	$-0.768362\pi$
$101$	1.83378	−	10.3999i	0.182468	−	1.03483i	0.929165	−	0.369665i	$-0.120527\pi$
$102$		0			0
$103$	5.77623	+	10.0047i	0.569149	+	0.985794i	0.996650	+	0.0817799i	$0.0260605\pi$
$103$	5.77623	+	10.0047i	0.569149	+	0.985794i	−0.427502	+	0.904015i	$0.640606\pi$
$104$		0			0
$105$	−4.10240	+	1.49315i	−0.400354	+	0.145717i
$106$		0			0
$107$	−3.88420	+	6.72763i	−0.375499	+	0.650384i	−0.990402	−	0.138219i	$-0.955862\pi$
$107$	−3.88420	+	6.72763i	−0.375499	+	0.650384i	0.614902	+	0.788603i	$0.289195\pi$
$108$		0			0
$109$	−10.1216	+	8.49299i	−0.969469	+	0.813481i	−0.982467	−	0.186435i	$-0.940307\pi$
$109$	−10.1216	+	8.49299i	−0.969469	+	0.813481i	0.0129986	+	0.999916i	$0.495862\pi$
$110$		0			0
$111$	−0.0817526	−	0.463642i	−0.00775961	−	0.0440070i
$112$		0			0
$113$	−1.84103			−0.173190			−0.0865950	−	0.996244i	$-0.527599\pi$
$113$	−1.84103			−0.173190			−0.0865950	+	0.996244i	$0.527599\pi$
$114$		0			0
$115$	−4.33233			−0.403991
$116$		0			0
$117$	1.87009	+	10.6058i	0.172890	+	0.980507i
$118$		0			0
$119$	−25.2961	+	21.2259i	−2.31889	+	1.94578i
$120$		0			0
$121$	4.87531	−	8.44428i	0.443210	−	0.767662i
$122$		0			0
$123$	−7.53120	+	2.74113i	−0.679066	+	0.247160i
$124$		0			0
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$		0			0
$127$	−0.731989	+	4.15132i	−0.0649536	+	0.368370i	0.934954	+	0.354769i	$0.115441\pi$
$127$	−0.731989	+	4.15132i	−0.0649536	+	0.368370i	−0.999908	+	0.0136008i	$0.995671\pi$
$128$		0			0
$129$	3.02802	+	2.54081i	0.266602	+	0.223706i
$130$		0			0
$131$	−2.58430	−	0.940609i	−0.225791	−	0.0821814i	0.226647	−	0.973977i	$-0.427224\pi$
$131$	−2.58430	−	0.940609i	−0.225791	−	0.0821814i	−0.452439	+	0.891796i	$0.649446\pi$
$132$		0			0
$133$	−0.772191	−	19.8674i	−0.0669574	−	1.72272i
$134$		0			0
$135$	4.57244	+	1.66423i	0.393533	+	0.143234i
$136$		0			0
$137$	1.69224	+	1.41996i	0.144578	+	0.121315i	0.712208	−	0.701968i	$-0.247695\pi$
$137$	1.69224	+	1.41996i	0.144578	+	0.121315i	−0.567630	+	0.823284i	$0.692140\pi$
$138$		0			0
$139$	1.53264	−	8.69203i	0.129997	−	0.737248i	−0.848217	−	0.529649i	$-0.822324\pi$
$139$	1.53264	−	8.69203i	0.129997	−	0.737248i	0.978214	−	0.207600i	$-0.0665651\pi$
$140$		0			0
$141$	1.26577	+	2.19238i	0.106597	+	0.184631i
$142$		0			0
$143$	5.42800	−	1.97563i	0.453912	−	0.165211i
$144$		0			0
$145$	1.33615	−	2.31429i	0.110962	−	0.192191i
$146$		0			0
$147$	10.1222	−	8.49352i	0.834864	−	0.700534i
$148$		0			0
$149$	3.62671	+	20.5681i	0.297111	+	1.68500i	0.658495	+	0.752585i	$0.271194\pi$
$149$	3.62671	+	20.5681i	0.297111	+	1.68500i	−0.361383	+	0.932417i	$0.617695\pi$
$150$		0			0
$151$	5.73130			0.466407			0.233203	−	0.972428i	$-0.425079\pi$
$151$	5.73130			0.466407			0.233203	+	0.972428i	$0.425079\pi$
$152$		0			0
$153$	15.0867			1.21969
$154$		0			0
$155$	−0.475871	−	2.69880i	−0.0382229	−	0.216773i
$156$		0			0
$157$	−14.1251	+	11.8523i	−1.12730	+	0.945919i	−0.998950	−	0.0458101i	$-0.985413\pi$
$157$	−14.1251	+	11.8523i	−1.12730	+	0.945919i	−0.128352	+	0.991729i	$0.540969\pi$
$158$		0			0
$159$	6.52818	−	11.3071i	0.517718	−	0.896714i
$160$		0			0
$161$	18.5694	−	6.75872i	1.46348	−	0.532661i
$162$		0			0
$163$	−1.74094	−	3.01540i	−0.136361	−	0.236185i	0.789755	−	0.613422i	$-0.210207\pi$
$163$	−1.74094	−	3.01540i	−0.136361	−	0.236185i	−0.926117	+	0.377237i	$0.876874\pi$
$164$		0			0
$165$	0.185772	−	1.05356i	0.0144623	−	0.0820198i
$166$		0			0
$167$	16.4620	+	13.8132i	1.27387	+	1.06890i	0.994059	+	0.108843i	$0.0347147\pi$
$167$	16.4620	+	13.8132i	1.27387	+	1.06890i	0.279806	+	0.960056i	$0.409730\pi$
$168$		0			0
$169$	−12.8797	−	4.68781i	−0.990742	−	0.360601i
$170$		0			0
$171$	−5.56423	+	7.18004i	−0.425507	+	0.549071i
$172$		0			0
$173$	−10.3262	−	3.75842i	−0.785084	−	0.285747i	−0.0817929	−	0.996649i	$-0.526065\pi$
$173$	−10.3262	−	3.75842i	−0.785084	−	0.285747i	−0.703291	+	0.710902i	$0.748287\pi$
$174$		0			0
$175$	3.49418	+	2.93197i	0.264135	+	0.221636i
$176$		0			0
$177$	−0.433877	+	2.46064i	−0.0326122	+	0.184953i
$178$		0			0
$179$	8.54852	+	14.8065i	0.638946	+	1.10669i	0.985664	+	0.168718i	$0.0539627\pi$
$179$	8.54852	+	14.8065i	0.638946	+	1.10669i	−0.346718	+	0.937969i	$0.612704\pi$
$180$		0			0
$181$	−10.8910	+	3.96399i	−0.809519	+	0.294641i	−0.713425	−	0.700732i	$-0.752857\pi$
$181$	−10.8910	+	3.96399i	−0.809519	+	0.294641i	−0.0960938	+	0.995372i	$0.530635\pi$
$182$		0			0
$183$	−2.27833	+	3.94618i	−0.168419	+	0.291710i
$184$		0			0
$185$	−0.376812	+	0.316182i	−0.0277037	+	0.0232462i
$186$		0			0
$187$	−1.40516	−	7.96907i	−0.102756	−	0.582756i
$188$		0			0
$189$	−22.1949			−1.61444
$190$		0			0
$191$	25.8688			1.87180			0.935901	−	0.352262i	$-0.114587\pi$
$191$	25.8688			1.87180			0.935901	+	0.352262i	$0.114587\pi$
$192$		0			0
$193$	2.44272	+	13.8534i	0.175831	+	0.997187i	0.937180	+	0.348845i	$0.113426\pi$
$193$	2.44272	+	13.8534i	0.175831	+	0.997187i	−0.761349	+	0.648342i	$0.775463\pi$
$194$		0			0
$195$	−3.78897	+	3.17932i	−0.271334	+	0.227676i
$196$		0			0
$197$	−1.70220	+	2.94830i	−0.121277	+	0.210057i	−0.920271	−	0.391281i	$-0.872032\pi$
$197$	−1.70220	+	2.94830i	−0.121277	+	0.210057i	0.798995	+	0.601338i	$0.205365\pi$
$198$		0			0
$199$	17.3891	−	6.32911i	1.23268	−	0.448659i	0.358166	−	0.933658i	$-0.383402\pi$
$199$	17.3891	−	6.32911i	1.23268	−	0.448659i	0.874515	+	0.484999i	$0.161180\pi$
$200$		0			0
$201$	6.06427	+	10.5036i	0.427741	+	0.740869i
$202$		0			0
$203$	−2.11665	+	12.0041i	−0.148559	+	0.842522i
$204$		0			0
$205$	6.41463	+	5.38251i	0.448017	+	0.375931i
$206$		0			0
$207$	−8.48385	−	3.08787i	−0.589668	−	0.214622i
$208$		0			0
$209$	4.31087	+	2.27039i	0.298189	+	0.157046i
$210$		0			0
$211$	−14.8432	−	5.40250i	−1.02185	−	0.371923i	−0.223878	−	0.974617i	$-0.571872\pi$
$211$	−14.8432	−	5.40250i	−1.02185	−	0.371923i	−0.797972	+	0.602694i	$0.794094\pi$
$212$		0			0
$213$	0.501638	+	0.420924i	0.0343716	+	0.0288412i
$214$		0			0
$215$	0.717156	−	4.06720i	0.0489097	−	0.277380i
$216$		0			0
$217$	6.25001	+	10.8253i	0.424278	+	0.734871i
$218$		0			0
$219$	11.8102	−	4.29856i	0.798058	−	0.290469i
$220$		0			0
$221$	−18.7061	+	32.4000i	−1.25831	+	2.17946i
$222$		0			0
$223$	−17.0138	+	14.2763i	−1.13933	+	0.956008i	−0.999417	−	0.0341558i	$-0.989126\pi$
$223$	−17.0138	+	14.2763i	−1.13933	+	0.956008i	−0.139910	+	0.990164i	$0.544681\pi$
$224$		0			0
$225$	−0.361873	−	2.05228i	−0.0241249	−	0.136819i
$226$		0			0
$227$	−5.60932			−0.372304			−0.186152	−	0.982521i	$-0.559602\pi$
$227$	−5.60932			−0.372304			−0.186152	+	0.982521i	$0.559602\pi$
$228$		0			0
$229$	1.04017			0.0687366			0.0343683	−	0.999409i	$-0.489058\pi$
$229$	1.04017			0.0687366			0.0343683	+	0.999409i	$0.489058\pi$
$230$		0			0
$231$	0.847365	+	4.80565i	0.0557525	+	0.316188i
$232$		0			0
$233$	9.15779	−	7.68430i	0.599947	−	0.503415i	−0.291482	−	0.956576i	$-0.594148\pi$
$233$	9.15779	−	7.68430i	0.599947	−	0.503415i	0.891428	+	0.453161i	$0.149704\pi$
$234$		0			0
$235$	1.32249	−	2.29063i	0.0862699	−	0.149424i
$236$		0			0
$237$	14.2482	−	5.18591i	0.925517	−	0.336861i
$238$		0			0
$239$	4.50416	+	7.80144i	0.291350	+	0.504633i	0.974129	−	0.225992i	$-0.0725622\pi$
$239$	4.50416	+	7.80144i	0.291350	+	0.504633i	−0.682779	+	0.730625i	$0.739229\pi$
$240$		0			0
$241$	−2.31012	+	13.1014i	−0.148808	+	0.843933i	0.815422	+	0.578867i	$0.196505\pi$
$241$	−2.31012	+	13.1014i	−0.148808	+	0.843933i	−0.964230	+	0.265066i	$0.914606\pi$
$242$		0			0
$243$	12.3516	+	10.3642i	0.792358	+	0.664867i
$244$		0			0
$245$	−12.9731	−	4.72184i	−0.828824	−	0.301667i
$246$		0			0
$247$	−8.52062	−	20.8523i	−0.542154	−	1.32680i
$248$		0			0
$249$	3.38230	+	1.23105i	0.214344	+	0.0780149i
$250$		0			0
$251$	−17.0043	−	14.2683i	−1.07330	−	0.900609i	−0.0779560	−	0.996957i	$-0.524839\pi$
$251$	−17.0043	−	14.2683i	−1.07330	−	0.900609i	−0.995348	+	0.0963480i	$0.969284\pi$
$252$		0			0
$253$	−0.840890	+	4.76892i	−0.0528663	+	0.299820i
$254$		0			0
$255$	3.46449	+	6.00067i	0.216955	+	0.375776i
$256$		0			0
$257$	2.37388	−	0.864022i	0.148079	−	0.0538962i	−0.266918	−	0.963719i	$-0.586005\pi$
$257$	2.37388	−	0.864022i	0.148079	−	0.0538962i	0.414996	+	0.909823i	$0.363783\pi$
$258$		0			0
$259$	1.12184	−	1.94309i	0.0697079	−	0.120738i
$260$		0			0
$261$	4.26605	−	3.57964i	0.264062	−	0.221574i
$262$		0			0
$263$	−2.18211	−	12.3753i	−0.134554	−	0.763096i	−0.975169	−	0.221462i	$-0.928917\pi$
$263$	−2.18211	−	12.3753i	−0.134554	−	0.763096i	0.840615	−	0.541634i	$-0.182194\pi$
$264$		0			0
$265$	−13.6415			−0.837988
$266$		0			0
$267$	11.2649			0.689401
$268$		0			0
$269$	−3.59540	−	20.3905i	−0.219216	−	1.24323i	−0.873439	−	0.486933i	$-0.838116\pi$
$269$	−3.59540	−	20.3905i	−0.219216	−	1.24323i	0.654224	−	0.756301i	$-0.272995\pi$
$270$		0			0
$271$	−1.02160	+	0.857226i	−0.0620579	+	0.0520728i	−0.673289	−	0.739379i	$-0.735119\pi$
$271$	−1.02160	+	0.857226i	−0.0620579	+	0.0520728i	0.611231	+	0.791452i	$0.290675\pi$
$272$		0			0
$273$	11.2805	−	19.5384i	0.682728	−	1.18252i
$274$		0			0
$275$	−1.05035	+	0.382296i	−0.0633384	+	0.0230533i
$276$		0			0
$277$	−14.1070	−	24.4340i	−0.847606	−	1.46810i	−0.883338	−	0.468736i	$-0.844710\pi$
$277$	−14.1070	−	24.4340i	−0.847606	−	1.46810i	0.0357322	−	0.999361i	$-0.488624\pi$
$278$		0			0
$279$	0.991688	−	5.62414i	0.0593708	−	0.336709i
$280$		0			0
$281$	9.31199	+	7.81369i	0.555507	+	0.466126i	0.876801	−	0.480854i	$-0.159673\pi$
$281$	9.31199	+	7.81369i	0.555507	+	0.466126i	−0.321294	+	0.946980i	$0.604118\pi$
$282$		0			0
$283$	−1.65082	−	0.600850i	−0.0981312	−	0.0357168i	0.292488	−	0.956269i	$-0.405517\pi$
$283$	−1.65082	−	0.600850i	−0.0981312	−	0.0357168i	−0.390619	+	0.920552i	$0.627739\pi$
$284$		0			0
$285$	−4.13359	−	0.564335i	−0.244853	−	0.0334283i
$286$		0			0
$287$	−35.8918	−	13.0635i	−2.11862	−	0.771116i
$288$		0			0
$289$	27.1258	+	22.7612i	1.59564	+	1.33890i
$290$		0			0
$291$	−0.579775	+	3.28807i	−0.0339870	+	0.192750i
$292$		0			0
$293$	3.85056	+	6.66937i	0.224952	+	0.389629i	0.956305	−	0.292370i	$-0.0944440\pi$
$293$	3.85056	+	6.66937i	0.224952	+	0.389629i	−0.731353	+	0.681999i	$0.761111\pi$
$294$		0			0
$295$	2.45313	−	0.892868i	0.142827	−	0.0519848i
$296$		0			0
$297$	2.71944	−	4.71021i	0.157798	−	0.273314i
$298$		0			0
$299$	17.1507	−	14.3911i	0.991850	−	0.832261i
$300$		0			0
$301$	3.27119	+	18.5518i	0.188548	+	1.06931i
$302$		0			0
$303$	10.1074			0.580654
$304$		0			0
$305$	4.76086			0.272606
$306$		0			0
$307$	−1.11720	−	6.33598i	−0.0637623	−	0.361614i	−0.999949	−	0.0101104i	$-0.996782\pi$
$307$	−1.11720	−	6.33598i	−0.0637623	−	0.361614i	0.936187	−	0.351503i	$-0.114329\pi$
$308$		0			0
$309$	−8.47012	+	7.10727i	−0.481848	+	0.404319i
$310$		0			0
$311$	14.5028	−	25.1196i	0.822379	−	1.42440i	−0.0815274	−	0.996671i	$-0.525980\pi$
$311$	14.5028	−	25.1196i	0.822379	−	1.42440i	0.903906	−	0.427731i	$-0.140687\pi$
$312$		0			0
$313$	−12.8655	+	4.68265i	−0.727200	+	0.264679i	−0.678979	−	0.734158i	$-0.737577\pi$
$313$	−12.8655	+	4.68265i	−0.727200	+	0.264679i	−0.0482209	+	0.998837i	$0.515355\pi$
$314$		0			0
$315$	4.75278	+	8.23205i	0.267789	+	0.463824i
$316$		0			0
$317$	−0.782232	+	4.43626i	−0.0439345	+	0.249165i	−0.998863	−	0.0476705i	$-0.984820\pi$
$317$	−0.782232	+	4.43626i	−0.0439345	+	0.249165i	0.954929	+	0.296836i	$0.0959314\pi$
$318$		0			0
$319$	−2.28817	−	1.92000i	−0.128113	−	0.107500i
$320$		0			0
$321$	−6.98680	−	2.54299i	−0.389965	−	0.141936i
$322$		0			0
$323$	−30.8405	+	6.68250i	−1.71601	+	0.371824i
$324$		0			0
$325$	4.85615	+	1.76749i	0.269371	+	0.0980430i
$326$		0			0
$327$	−9.68742	−	8.12871i	−0.535715	−	0.449519i
$328$		0			0
$329$	−2.09501	+	11.8814i	−0.115501	+	0.655041i
$330$		0			0
$331$	−7.72326	−	13.3771i	−0.424509	−	0.735271i	0.571866	−	0.820347i	$-0.306220\pi$
$331$	−7.72326	−	13.3771i	−0.424509	−	0.735271i	−0.996374	+	0.0850767i	$0.972886\pi$
$332$		0			0
$333$	−0.963257	+	0.350597i	−0.0527862	+	0.0192126i
$334$		0			0
$335$	6.33604	−	10.9743i	0.346175	−	0.599592i
$336$		0			0
$337$	−16.3175	+	13.6920i	−0.888869	+	0.745850i	−0.967983	−	0.251016i	$-0.919235\pi$
$337$	−16.3175	+	13.6920i	−0.888869	+	0.745850i	0.0791136	+	0.996866i	$0.474791\pi$
$338$		0			0
$339$	−0.305980	−	1.73530i	−0.0166186	−	0.0942485i
$340$		0			0
$341$	−3.06314			−0.165878
$342$		0			0
$343$	31.0432			1.67617
$344$		0			0
$345$	−0.720033	−	4.08351i	−0.0387653	−	0.219849i
$346$		0			0
$347$	2.69463	−	2.26106i	0.144655	−	0.121380i	−0.567588	−	0.823312i	$-0.692124\pi$
$347$	2.69463	−	2.26106i	0.144655	−	0.121380i	0.712244	+	0.701932i	$0.247679\pi$
$348$		0			0
$349$	−4.55638	+	7.89188i	−0.243897	+	0.422443i	−0.961821	−	0.273679i	$-0.911759\pi$
$349$	−4.55638	+	7.89188i	−0.243897	+	0.422443i	0.717924	+	0.696122i	$0.245093\pi$
$350$		0			0
$351$	−23.6295	+	8.60042i	−1.26125	+	0.459057i
$352$		0			0
$353$	−12.4350	−	21.5381i	−0.661850	−	1.14636i	−0.980129	−	0.198361i	$-0.936438\pi$
$353$	−12.4350	−	21.5381i	−0.661850	−	1.14636i	0.318279	−	0.947997i	$-0.396895\pi$
$354$		0			0
$355$	0.118808	−	0.673793i	0.00630567	−	0.0357612i
$356$		0			0
$357$	−24.2111	−	20.3155i	−1.28139	−	1.07521i
$358$		0			0
$359$	−18.2882	−	6.65634i	−0.965212	−	0.351308i	−0.189138	−	0.981951i	$-0.560569\pi$
$359$	−18.2882	−	6.65634i	−0.965212	−	0.351308i	−0.776074	+	0.630642i	$0.782792\pi$
$360$		0			0
$361$	8.19419	−	17.1422i	0.431273	−	0.902221i
$362$		0			0
$363$	8.76958	+	3.19187i	0.460284	+	0.167530i
$364$		0			0
$365$	−10.0592	−	8.44068i	−0.526523	−	0.441805i
$366$		0			0
$367$	3.57276	−	20.2622i	0.186497	−	1.05768i	−0.737520	−	0.675325i	$-0.764003\pi$
$367$	3.57276	−	20.2622i	0.186497	−	1.05768i	0.924017	−	0.382351i	$-0.124885\pi$
$368$		0			0
$369$	8.72516	+	15.1124i	0.454214	+	0.786721i
$370$		0			0
$371$	58.4707	−	21.2816i	3.03565	−	1.10488i
$372$		0			0
$373$	1.84938	−	3.20322i	0.0957572	−	0.165856i	−0.814167	−	0.580630i	$-0.802806\pi$
$373$	1.84938	−	3.20322i	0.0957572	−	0.165856i	0.909924	+	0.414774i	$0.136139\pi$
$374$		0			0
$375$	0.733187	−	0.615217i	0.0378616	−	0.0317697i
$376$		0			0
$377$	2.39808	+	13.6002i	0.123507	+	0.700444i
$378$		0			0
$379$	−6.68304			−0.343285			−0.171642	−	0.985159i	$-0.554907\pi$
$379$	−6.68304			−0.343285			−0.171642	+	0.985159i	$0.554907\pi$
$380$		0			0
$381$	−4.03456			−0.206697
$382$		0			0
$383$	5.39114	+	30.5747i	0.275474	+	1.56229i	0.737451	+	0.675400i	$0.236029\pi$
$383$	5.39114	+	30.5747i	0.275474	+	1.56229i	−0.461977	+	0.886892i	$0.652860\pi$
$384$		0			0
$385$	3.90565	−	3.27723i	0.199050	−	0.167023i
$386$		0			0
$387$	4.30328	−	7.45350i	0.218748	−	0.378883i
$388$		0			0
$389$	11.2323	−	4.08822i	0.569500	−	0.207281i	−0.0411892	−	0.999151i	$-0.513115\pi$
$389$	11.2323	−	4.08822i	0.569500	−	0.207281i	0.610689	+	0.791870i	$0.290892\pi$
$390$		0			0
$391$	−15.6819	−	27.1619i	−0.793068	−	1.37363i
$392$		0			0
$393$	0.457076	−	2.59221i	0.0230564	−	0.130760i
$394$		0			0
$395$	−12.1357	−	10.1831i	−0.610615	−	0.512367i
$396$		0			0
$397$	4.00480	+	1.45763i	0.200995	+	0.0731562i	0.440556	−	0.897725i	$-0.354781\pi$
$397$	4.00480	+	1.45763i	0.200995	+	0.0731562i	−0.239561	+	0.970881i	$0.577004\pi$
$398$		0			0
$399$	18.5980	−	4.02980i	0.931065	−	0.201742i
$400$		0			0
$401$	0.433821	+	0.157898i	0.0216640	+	0.00788506i	0.352829	−	0.935688i	$-0.385220\pi$
$401$	0.433821	+	0.157898i	0.0216640	+	0.00788506i	−0.331165	+	0.943573i	$0.607442\pi$
$402$		0			0
$403$	10.8487	+	9.10317i	0.540414	+	0.453461i
$404$		0			0
$405$	0.276909	−	1.57043i	0.0137597	−	0.0780352i
$406$		0			0
$407$	0.274909	+	0.476156i	0.0136267	+	0.0236022i
$408$		0			0
$409$	29.7422	−	10.8253i	1.47066	−	0.535276i	0.522378	−	0.852714i	$-0.325045\pi$
$409$	29.7422	−	10.8253i	1.47066	−	0.535276i	0.948279	+	0.317438i	$0.102823\pi$
$410$		0			0
$411$	−1.05715	+	1.83104i	−0.0521456	+	0.0903188i
$412$		0			0
$413$	−9.12181	+	7.65411i	−0.448855	+	0.376634i
$414$		0			0
$415$	−0.653033	−	3.70353i	−0.0320561	−	0.181799i
$416$		0			0
$417$	8.44755			0.413678
$418$		0			0
$419$	23.8430			1.16481			0.582403	−	0.812900i	$-0.302112\pi$
$419$	23.8430			1.16481			0.582403	+	0.812900i	$0.302112\pi$
$420$		0			0
$421$	1.32252	+	7.50041i	0.0644559	+	0.365547i	0.999926	+	0.0121424i	$0.00386514\pi$
$421$	1.32252	+	7.50041i	0.0644559	+	0.365547i	−0.935470	+	0.353405i	$0.885024\pi$
$422$		0			0
$423$	4.22244	−	3.54305i	0.205302	−	0.172269i
$424$		0			0
$425$	3.61975	−	6.26958i	0.175583	−	0.304119i
$426$		0			0
$427$	−20.4062	+	7.42726i	−0.987526	+	0.359430i
$428$		0			0
$429$	2.76430	+	4.78791i	0.133462	+	0.231162i
$430$		0			0
$431$	−1.04802	+	5.94360i	−0.0504812	+	0.286293i	−0.999589	−	0.0286575i	$-0.990877\pi$
$431$	−1.04802	+	5.94360i	−0.0504812	+	0.286293i	0.949108	+	0.314950i	$0.101988\pi$
$432$		0			0
$433$	−14.2376	−	11.9468i	−0.684216	−	0.574126i	0.233019	−	0.972472i	$-0.425140\pi$
$433$	−14.2376	−	11.9468i	−0.684216	−	0.574126i	−0.917235	+	0.398347i	$0.869584\pi$
$434$		0			0
$435$	2.40344	+	0.874781i	0.115236	+	0.0419425i
$436$		0			0
$437$	18.7106	+	2.55445i	0.895049	+	0.122196i
$438$		0			0
$439$	−13.0999	−	4.76797i	−0.625223	−	0.227563i	0.00992755	−	0.999951i	$-0.496840\pi$
$439$	−13.0999	−	4.76797i	−0.625223	−	0.227563i	−0.635151	+	0.772388i	$0.719062\pi$
$440$		0			0
$441$	−22.0394	−	18.4932i	−1.04949	−	0.880630i
$442$		0			0
$443$	−2.65351	+	15.0488i	−0.126072	+	0.714991i	0.854593	+	0.519298i	$0.173807\pi$
$443$	−2.65351	+	15.0488i	−0.126072	+	0.714991i	−0.980665	+	0.195692i	$0.937305\pi$
$444$		0			0
$445$	−5.88487	−	10.1929i	−0.278970	−	0.483189i
$446$		0			0
$447$	−18.7840	+	6.83683i	−0.888455	+	0.323371i
$448$		0			0
$449$	16.3149	−	28.2582i	0.769947	−	1.33359i	−0.167645	−	0.985847i	$-0.553616\pi$
$449$	16.3149	−	28.2582i	0.769947	−	1.33359i	0.937591	−	0.347739i	$-0.113051\pi$
$450$		0			0
$451$	7.17000	−	6.01635i	0.337622	−	0.283299i
$452$		0			0
$453$	0.952543	+	5.40214i	0.0447544	+	0.253815i
$454$		0			0
$455$	−23.5721			−1.10508
$456$		0			0
$457$	−19.5721			−0.915546			−0.457773	−	0.889069i	$-0.651353\pi$
$457$	−19.5721			−0.915546			−0.457773	+	0.889069i	$0.651353\pi$
$458$		0			0
$459$	6.11702	+	34.6914i	0.285518	+	1.61925i
$460$		0			0
$461$	−24.0645	+	20.1925i	−1.12079	+	0.940457i	−0.998644	−	0.0520545i	$-0.983423\pi$
$461$	−24.0645	+	20.1925i	−1.12079	+	0.940457i	−0.122149	+	0.992512i	$0.538979\pi$
$462$		0			0
$463$	15.2496	−	26.4132i	0.708711	−	1.22752i	−0.256624	−	0.966511i	$-0.582610\pi$
$463$	15.2496	−	26.4132i	0.708711	−	1.22752i	0.965335	−	0.261012i	$-0.0840563\pi$
$464$		0			0
$465$	2.46471	−	0.897081i	0.114298	−	0.0416011i
$466$		0			0
$467$	3.74239	+	6.48201i	0.173177	+	0.299952i	0.939529	−	0.342469i	$-0.111263\pi$
$467$	3.74239	+	6.48201i	0.173177	+	0.299952i	−0.766352	+	0.642421i	$0.777930\pi$
$468$		0			0
$469$	−10.0371	+	56.9234i	−0.463472	+	2.62848i
$470$		0			0
$471$	−13.5192	−	11.3440i	−0.622932	−	0.522702i
$472$		0			0
$473$	−4.33788	−	1.57886i	−0.199456	−	0.0725960i
$474$		0			0
$475$	1.64879	+	4.03503i	0.0756516	+	0.185140i
$476$		0			0
$477$	−26.7136	−	9.72296i	−1.22313	−	0.445184i
$478$		0			0
$479$	−4.59620	−	3.85667i	−0.210006	−	0.176216i	0.531718	−	0.846922i	$-0.321547\pi$
$479$	−4.59620	−	3.85667i	−0.210006	−	0.176216i	−0.741723	+	0.670706i	$0.765991\pi$
$480$		0			0
$481$	0.441415	−	2.50339i	0.0201268	−	0.114145i
$482$		0			0
$483$	9.45679	+	16.3796i	0.430299	+	0.745299i
$484$		0			0
$485$	3.27804	−	1.19311i	0.148848	−	0.0541763i
$486$		0			0
$487$	−3.24803	+	5.62576i	−0.147182	+	0.254927i	−0.930185	−	0.367091i	$-0.880354\pi$
$487$	−3.24803	+	5.62576i	−0.147182	+	0.254927i	0.783003	+	0.622018i	$0.213687\pi$
$488$		0			0
$489$	2.55288	−	2.14212i	0.115445	−	0.0968699i
$490$		0			0
$491$	5.01124	+	28.4202i	0.226154	+	1.28258i	0.860467	+	0.509507i	$0.170172\pi$
$491$	5.01124	+	28.4202i	0.226154	+	1.28258i	−0.634312	+	0.773077i	$0.718717\pi$
$492$		0			0
$493$	19.3461			0.871306
$494$		0			0
$495$	−2.32935			−0.104696
$496$		0			0
$497$	0.541922	+	3.07339i	0.0243085	+	0.137860i
$498$		0			0
$499$	−9.63514	+	8.08484i	−0.431328	+	0.361927i	−0.832453	−	0.554096i	$-0.813064\pi$
$499$	−9.63514	+	8.08484i	−0.431328	+	0.361927i	0.401124	+	0.916024i	$0.368619\pi$
$500$		0			0
$501$	−10.2839	+	17.8123i	−0.459452	+	0.795794i
$502$		0			0
$503$	−14.4854	+	5.27226i	−0.645872	+	0.235078i	−0.644125	−	0.764920i	$-0.722778\pi$
$503$	−14.4854	+	5.27226i	−0.645872	+	0.235078i	−0.00174715	+	0.999998i	$0.500556\pi$
$504$		0			0
$505$	−5.28017	−	9.14552i	−0.234964	−	0.406970i
$506$		0			0
$507$	2.27798	−	12.9191i	0.101169	−	0.573755i
$508$		0			0
$509$	−4.58561	−	3.84778i	−0.203254	−	0.170550i	0.535479	−	0.844548i	$-0.320131\pi$
$509$	−4.58561	−	3.84778i	−0.203254	−	0.170550i	−0.738733	+	0.673998i	$0.764575\pi$
$510$		0			0
$511$	56.2843	+	20.4858i	2.48987	+	0.906239i
$512$		0			0
$513$	−18.7663	−	9.88356i	−0.828554	−	0.436370i
$514$		0			0
$515$	10.8558	+	3.95117i	0.478362	+	0.174109i
$516$		0			0
$517$	−2.26478	−	1.90037i	−0.0996047	−	0.0835783i
$518$		0			0
$519$	1.82635	−	10.3578i	0.0801680	−	0.454655i
$520$		0			0
$521$	8.62104	+	14.9321i	0.377695	+	0.654187i	0.990726	−	0.135872i	$-0.0433835\pi$
$521$	8.62104	+	14.9321i	0.377695	+	0.654187i	−0.613032	+	0.790058i	$0.710050\pi$
$522$		0			0
$523$	0.113607	−	0.0413496i	0.00496770	−	0.00180809i	−0.339535	−	0.940593i	$-0.610270\pi$
$523$	0.113607	−	0.0413496i	0.00496770	−	0.00180809i	0.344503	+	0.938785i	$0.388048\pi$
$524$		0			0
$525$	−2.18284	+	3.78080i	−0.0952671	+	0.165007i
$526$		0			0
$527$	15.1978	−	12.7525i	0.662027	−	0.555507i
$528$		0			0
$529$	−0.734698	−	4.16668i	−0.0319434	−	0.181160i
$530$		0			0
$531$	5.44028			0.236088
$532$		0			0
$533$	−43.2737			−1.87439
$534$		0			0
$535$	1.34897	+	7.65037i	0.0583209	+	0.330754i
$536$		0			0
$537$	−12.5353	+	10.5184i	−0.540940	+	0.453902i
$538$		0			0
$539$	−7.71574	+	13.3640i	−0.332340	+	0.575630i
$540$		0			0
$541$	36.3600	−	13.2340i	1.56324	−	0.568973i	0.591764	−	0.806112i	$-0.298432\pi$
$541$	36.3600	−	13.2340i	1.56324	−	0.568973i	0.971476	+	0.237139i	$0.0762097\pi$
$542$		0			0
$543$	−5.54640	−	9.60665i	−0.238019	−	0.412261i
$544$		0			0
$545$	−2.29437	+	13.0120i	−0.0982800	+	0.557373i
$546$		0			0
$547$	−7.34449	−	6.16276i	−0.314028	−	0.263501i	0.472127	−	0.881531i	$-0.343486\pi$
$547$	−7.34449	−	6.16276i	−0.314028	−	0.263501i	−0.786154	+	0.618030i	$0.787931\pi$
$548$		0			0
$549$	9.32303	+	3.39331i	0.397897	+	0.144823i
$550$		0			0
$551$	−7.13519	+	9.20719i	−0.303969	+	0.392240i
$552$		0			0
$553$	67.9030	+	24.7147i	2.88753	+	1.05098i
$554$		0			0
$555$	−0.360649	−	0.302621i	−0.0153087	−	0.0128455i
$556$		0			0
$557$	5.99528	−	34.0009i	0.254028	−	1.44067i	−0.544527	−	0.838744i	$-0.683291\pi$
$557$	5.99528	−	34.0009i	0.254028	−	1.44067i	0.798555	−	0.601922i	$-0.205598\pi$
$558$		0			0
$559$	10.6714	+	18.4834i	0.451351	+	0.781762i
$560$		0			0
$561$	7.27784	−	2.64892i	0.307271	−	0.111837i
$562$		0			0
$563$	21.6196	−	37.4463i	0.911158	−	1.57817i	0.0987270	−	0.995115i	$-0.468523\pi$
$563$	21.6196	−	37.4463i	0.911158	−	1.57817i	0.812431	−	0.583057i	$-0.198144\pi$
$564$		0			0
$565$	−1.41031	+	1.18339i	−0.0593324	+	0.0497858i
$566$		0			0
$567$	1.26307	+	7.16324i	0.0530440	+	0.300828i
$568$		0			0
$569$	−0.172138			−0.00721638			−0.00360819	−	0.999993i	$-0.501149\pi$
$569$	−0.172138			−0.00721638			−0.00360819	+	0.999993i	$0.501149\pi$
$570$		0			0
$571$	−28.8203			−1.20609			−0.603046	−	0.797706i	$-0.706046\pi$
$571$	−28.8203			−1.20609			−0.603046	+	0.797706i	$0.706046\pi$
$572$		0			0
$573$	4.29940	+	24.3831i	0.179610	+	1.01862i
$574$		0			0
$575$	−3.31875	+	2.78477i	−0.138402	+	0.116133i
$576$		0			0
$577$	−1.03745	+	1.79692i	−0.0431898	+	0.0748069i	−0.886812	−	0.462130i	$-0.847085\pi$
$577$	−1.03745	+	1.79692i	−0.0431898	+	0.0748069i	0.843622	+	0.536937i	$0.180419\pi$
$578$		0			0
$579$	−12.6517	+	4.60486i	−0.525789	+	0.191371i
$580$		0			0
$581$	8.57682	+	14.8555i	0.355826	+	0.616309i
$582$		0			0
$583$	−2.64776	+	15.0162i	−0.109659	+	0.621908i
$584$		0			0
$585$	8.24986	+	6.92245i	0.341090	+	0.286208i
$586$		0			0
$587$	−28.5583	−	10.3944i	−1.17873	−	0.429022i	−0.322975	−	0.946407i	$-0.604683\pi$
$587$	−28.5583	−	10.3944i	−1.17873	−	0.429022i	−0.855752	+	0.517385i	$0.826905\pi$
$588$		0			0
$589$	0.463930	+	11.9363i	0.0191159	+	0.491825i
$590$		0			0
$591$	−3.06187	−	1.11443i	−0.125949	−	0.0458416i
$592$		0			0
$593$	−8.44741	−	7.08822i	−0.346894	−	0.291078i	0.452648	−	0.891689i	$-0.350480\pi$
$593$	−8.44741	−	7.08822i	−0.346894	−	0.291078i	−0.799541	+	0.600611i	$0.794924\pi$
$594$		0			0
$595$	−5.73416	+	32.5200i	−0.235078	+	1.33319i
$596$		0			0
$597$	8.85569	+	15.3385i	0.362439	+	0.627763i
$598$		0			0
$599$	−23.2641	+	8.46746i	−0.950547	+	0.345971i	−0.770322	−	0.637655i	$-0.779905\pi$
$599$	−23.2641	+	8.46746i	−0.950547	+	0.345971i	−0.180225	+	0.983625i	$0.557683\pi$
$600$		0			0
$601$	−20.6916	+	35.8388i	−0.844026	+	1.46190i	0.0424380	+	0.999099i	$0.486487\pi$
$601$	−20.6916	+	35.8388i	−0.844026	+	1.46190i	−0.886464	+	0.462797i	$0.846846\pi$
$602$		0			0
$603$	20.2296	−	16.9747i	0.823814	−	0.691262i
$604$		0			0
$605$	−1.69318	−	9.60248i	−0.0688374	−	0.390396i
$606$		0			0
$607$	27.0263			1.09696			0.548481	−	0.836163i	$-0.315206\pi$
$607$	27.0263			1.09696			0.548481	+	0.836163i	$0.315206\pi$
$608$		0			0
$609$	−11.6665			−0.472749
$610$		0			0
$611$	2.37356	+	13.4611i	0.0960239	+	0.544579i
$612$		0			0
$613$	5.62519	−	4.72010i	0.227199	−	0.190643i	−0.522081	−	0.852896i	$-0.674844\pi$
$613$	5.62519	−	4.72010i	0.227199	−	0.190643i	0.749280	+	0.662253i	$0.230400\pi$
$614$		0			0
$615$	−4.00727	+	6.94079i	−0.161589	+	0.279880i
$616$		0			0
$617$	−15.4866	+	5.63667i	−0.623468	+	0.226924i	−0.634386	−	0.773017i	$-0.718747\pi$
$617$	−15.4866	+	5.63667i	−0.623468	+	0.226924i	0.0109180	+	0.999940i	$0.496525\pi$
$618$		0			0
$619$	5.27186	+	9.13112i	0.211894	+	0.367011i	0.952307	−	0.305141i	$-0.0987036\pi$
$619$	5.27186	+	9.13112i	0.211894	+	0.367011i	−0.740413	+	0.672152i	$0.765370\pi$
$620$		0			0
$621$	3.66061	−	20.7603i	0.146895	−	0.833083i
$622$		0			0
$623$	41.1256	+	34.5085i	1.64766	+	1.38255i
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$		0			0
$627$	−1.42352	+	4.44063i	−0.0568501	+	0.177342i
$628$		0			0
$629$	−3.34629	−	1.21795i	−0.133425	−	0.0485629i
$630$		0			0
$631$	−12.0300	−	10.0944i	−0.478907	−	0.401850i	0.371124	−	0.928583i	$-0.378972\pi$
$631$	−12.0300	−	10.0944i	−0.478907	−	0.401850i	−0.850031	+	0.526733i	$0.823417\pi$
$632$		0			0
$633$	2.62527	−	14.8886i	0.104345	−	0.591771i
$634$		0			0
$635$	2.10768	+	3.65061i	0.0836407	+	0.144870i
$636$		0			0
$637$	67.0427	−	24.4016i	2.65633	−	0.966825i
$638$		0			0
$639$	0.712904	−	1.23479i	0.0282020	−	0.0488474i
$640$		0			0
$641$	2.38617	−	2.00224i	0.0942481	−	0.0790836i	−0.594446	−	0.804135i	$-0.702629\pi$
$641$	2.38617	−	2.00224i	0.0942481	−	0.0790836i	0.688694	+	0.725052i	$0.258184\pi$
$642$		0			0
$643$	3.53665	+	20.0573i	0.139472	+	0.790983i	0.971641	+	0.236462i	$0.0759877\pi$
$643$	3.53665	+	20.0573i	0.139472	+	0.790983i	−0.832169	+	0.554522i	$0.812901\pi$
$644$		0			0
$645$	3.95280			0.155641
$646$		0			0
$647$	−2.01187			−0.0790946			−0.0395473	−	0.999218i	$-0.512592\pi$
$647$	−2.01187			−0.0790946			−0.0395473	+	0.999218i	$0.512592\pi$
$648$		0			0
$649$	−0.506703	−	2.87366i	−0.0198898	−	0.112801i
$650$		0			0
$651$	−9.16485	+	7.69022i	−0.359199	+	0.301404i
$652$		0			0
$653$	−0.326876	+	0.566166i	−0.0127916	+	0.0221558i	−0.872350	−	0.488881i	$-0.837405\pi$
$653$	−0.326876	+	0.566166i	−0.0127916	+	0.0221558i	0.859559	+	0.511037i	$0.170738\pi$
$654$		0			0
$655$	−2.58430	+	0.940609i	−0.100977	+	0.0367526i
$656$		0			0
$657$	−13.6825	−	23.6988i	−0.533806	−	0.924579i
$658$		0			0
$659$	−0.256516	+	1.45477i	−0.00999243	+	0.0566699i	−0.989396	−	0.145241i	$-0.953604\pi$
$659$	−0.256516	+	1.45477i	−0.00999243	+	0.0566699i	0.979404	+	0.201911i	$0.0647153\pi$
$660$		0			0
$661$	−1.31742	−	1.10545i	−0.0512418	−	0.0429970i	0.616807	−	0.787114i	$-0.288426\pi$
$661$	−1.31742	−	1.10545i	−0.0512418	−	0.0429970i	−0.668049	+	0.744117i	$0.732870\pi$
$662$		0			0
$663$	−33.6482	−	12.2469i	−1.30679	−	0.475631i
$664$		0			0
$665$	−13.3620	−	14.7229i	−0.518157	−	0.570931i
$666$		0			0
$667$	−10.8791	−	3.95967i	−0.421241	−	0.153319i
$668$		0			0
$669$	−16.2840	−	13.6639i	−0.629577	−	0.528278i
$670$		0			0
$671$	0.924067	−	5.24064i	0.0356732	−	0.202313i
$672$		0			0
$673$	15.1537	+	26.2469i	0.584130	+	1.01174i	0.994983	+	0.100042i	$0.0318977\pi$
$673$	15.1537	+	26.2469i	0.584130	+	1.01174i	−0.410853	+	0.911702i	$0.634769\pi$
$674$		0			0
$675$	4.57244	−	1.66423i	0.175993	−	0.0640563i
$676$		0			0
$677$	13.5349	−	23.4432i	0.520190	−	0.900995i	−0.479535	−	0.877523i	$-0.659195\pi$
$677$	13.5349	−	23.4432i	0.520190	−	0.900995i	0.999724	−	0.0234721i	$-0.00747210\pi$
$678$		0			0
$679$	−12.1892	+	10.2279i	−0.467777	+	0.392512i
$680$		0			0
$681$	−0.932270	−	5.28717i	−0.0357247	−	0.202605i
$682$		0			0
$683$	−49.3960			−1.89008			−0.945042	−	0.326948i	$-0.893980\pi$
$683$	−49.3960			−1.89008			−0.945042	+	0.326948i	$0.893980\pi$
$684$		0			0
$685$	2.20906			0.0844038
$686$		0			0
$687$	0.172877	+	0.980433i	0.00659566	+	0.0374059i
$688$		0			0
$689$	54.0034	−	45.3142i	2.05737	−	1.72633i
$690$		0			0
$691$	2.99171	−	5.18179i	0.113810	−	0.197125i	−0.803493	−	0.595314i	$-0.797028\pi$
$691$	2.99171	−	5.18179i	0.113810	−	0.197125i	0.917303	+	0.398189i	$0.130361\pi$
$692$		0			0
$693$	9.98415	−	3.63393i	0.379267	−	0.138042i
$694$		0			0
$695$	−4.41306	−	7.64364i	−0.167397	−	0.289940i
$696$		0			0
$697$	−10.5268	+	59.7003i	−0.398730	+	2.26131i
$698$		0			0
$699$	8.76499	+	7.35470i	0.331522	+	0.278180i
$700$		0			0
$701$	11.2185	+	4.08320i	0.423717	+	0.154220i	0.545073	−	0.838389i	$-0.316502\pi$
$701$	11.2185	+	4.08320i	0.423717	+	0.154220i	−0.121356	+	0.992609i	$0.538724\pi$
$702$		0			0
$703$	1.81382	−	1.14336i	0.0684094	−	0.0431227i
$704$		0			0
$705$	2.37887	+	0.865837i	0.0895933	+	0.0326093i
$706$		0			0
$707$	36.8997	+	30.9625i	1.38776	+	1.16447i
$708$		0			0
$709$	4.35271	−	24.6854i	0.163469	−	0.927080i	−0.787159	−	0.616750i	$-0.788449\pi$
$709$	4.35271	−	24.6854i	0.163469	−	0.927080i	0.950629	−	0.310331i	$-0.100440\pi$
$710$		0			0
$711$	−16.5070	−	28.5909i	−0.619061	−	1.07224i
$712$		0			0
$713$	−11.1564	+	4.06061i	−0.417812	+	0.152071i
$714$		0			0
$715$	2.88818	−	5.00248i	0.108012	−	0.187082i
$716$		0			0
$717$	−6.60479	+	5.54208i	−0.246660	+	0.206973i
$718$		0			0
$719$	3.32244	+	18.8425i	0.123906	+	0.702706i	0.981952	+	0.189132i	$0.0605676\pi$
$719$	3.32244	+	18.8425i	0.123906	+	0.702706i	−0.858046	+	0.513574i	$0.828321\pi$
$720$		0			0
$721$	−52.6946			−1.96245
$722$		0			0
$723$	−12.7329			−0.473540
$724$		0			0
$725$	−0.464041	−	2.63171i	−0.0172341	−	0.0977392i
$726$		0			0
$727$	−5.68566	+	4.77084i	−0.210870	+	0.176941i	−0.742105	−	0.670284i	$-0.766172\pi$
$727$	−5.68566	+	4.77084i	−0.210870	+	0.176941i	0.531235	+	0.847224i	$0.321728\pi$
$728$		0			0
$729$	−5.32418	+	9.22175i	−0.197192	+	0.341546i
$730$		0			0
$731$	28.0955	−	10.2259i	1.03915	−	0.378220i
$732$		0			0
$733$	−1.59766	−	2.76722i	−0.0590108	−	0.102210i	0.835011	−	0.550234i	$-0.185461\pi$
$733$	−1.59766	−	2.76722i	−0.0590108	−	0.102210i	−0.894022	+	0.448024i	$0.852128\pi$
$734$		0			0
$735$	2.29451	−	13.0128i	0.0846344	−	0.479986i
$736$		0			0
$737$	−10.8505	−	9.10465i	−0.399683	−	0.335374i
$738$		0			0
$739$	1.47844	+	0.538109i	0.0543853	+	0.0197946i	0.369070	−	0.929402i	$-0.379676\pi$
$739$	1.47844	+	0.538109i	0.0543853	+	0.0197946i	−0.314684	+	0.949196i	$0.601899\pi$
$740$		0			0
$741$	18.2386	−	11.4969i	0.670010	−	0.422350i
$742$		0			0
$743$	−10.6647	−	3.88164i	−0.391251	−	0.142404i	0.138901	−	0.990306i	$-0.455643\pi$
$743$	−10.6647	−	3.88164i	−0.391251	−	0.142404i	−0.530152	+	0.847903i	$0.677865\pi$
$744$		0			0
$745$	15.9991	+	13.4249i	0.586163	+	0.491849i
$746$		0			0
$747$	1.36088	−	7.71795i	0.0497921	−	0.282385i
$748$		0			0
$749$	−17.7171	−	30.6869i	−0.647369	−	1.12128i
$750$		0			0
$751$	−27.5103	+	10.0129i	−1.00386	+	0.365377i	−0.791074	−	0.611721i	$-0.790478\pi$
$751$	−27.5103	+	10.0129i	−1.00386	+	0.365377i	−0.212791	+	0.977098i	$0.568255\pi$
$752$		0			0
$753$	10.6227	−	18.3991i	0.387114	−	0.670501i
$754$		0			0
$755$	4.39043	−	3.68401i	0.159784	−	0.134075i
$756$		0			0
$757$	6.71567	+	38.0865i	0.244085	+	1.38428i	0.822607	+	0.568610i	$0.192519\pi$
$757$	6.71567	+	38.0865i	0.244085	+	1.38428i	−0.578522	+	0.815667i	$0.696370\pi$
$758$		0			0
$759$	−4.63479			−0.168232
$760$		0			0
$761$	31.8253			1.15367			0.576833	−	0.816862i	$-0.304288\pi$
$761$	31.8253			1.15367			0.576833	+	0.816862i	$0.304288\pi$
$762$		0			0
$763$	−10.4654	−	59.3521i	−0.378872	−	2.14869i
$764$		0			0
$765$	11.5571	−	9.69754i	0.417847	−	0.350615i
$766$		0			0
$767$	−6.74546	+	11.6835i	−0.243565	+	0.421866i
$768$		0			0
$769$	−8.83346	+	3.21512i	−0.318543	+	0.115940i	−0.496343	−	0.868127i	$-0.665324\pi$
$769$	−8.83346	+	3.21512i	−0.318543	+	0.115940i	0.177800	+	0.984067i	$0.443102\pi$
$770$		0			0
$771$	1.20894	+	2.09394i	0.0435388	+	0.0754115i
$772$		0			0
$773$	2.61084	−	14.8068i	0.0939054	−	0.532564i	−0.901172	−	0.433462i	$-0.857292\pi$
$773$	2.61084	−	14.8068i	0.0939054	−	0.532564i	0.995077	−	0.0991019i	$-0.0315970\pi$
$774$		0			0
$775$	−2.09929	−	1.76152i	−0.0754088	−	0.0632755i
$776$		0			0
$777$	2.01794	+	0.734471i	0.0723933	+	0.0263490i
$778$		0			0
$779$	−24.5301	−	27.0284i	−0.878880	−	0.968393i
$780$		0			0
$781$	−0.718636	−	0.261562i	−0.0257148	−	0.00935942i
$782$		0			0
$783$	9.96098	+	8.35826i	0.355976	+	0.298700i
$784$		0			0
$785$	−3.20189	+	18.1588i	−0.114280	+	0.648116i
$786$		0			0
$787$	−13.6930	−	23.7170i	−0.488104	−	0.845421i	0.511803	−	0.859103i	$-0.328978\pi$
$787$	−13.6930	−	23.7170i	−0.488104	−	0.845421i	−0.999906	+	0.0136825i	$0.995645\pi$
$788$		0			0
$789$	11.3019	−	4.11356i	0.402359	−	0.146447i
$790$		0			0
$791$	4.19878	−	7.27251i	0.149292	−	0.258581i
$792$		0			0
$793$	−18.8471	+	15.8146i	−0.669282	+	0.561594i
$794$		0			0
$795$	−2.26721	−	12.8580i	−0.0804097	−	0.456026i
$796$		0			0
$797$	20.1496			0.713736			0.356868	−	0.934155i	$-0.383845\pi$
$797$	20.1496			0.713736			0.356868	+	0.934155i	$0.383845\pi$
$798$		0			0
$799$	19.1484			0.677420
$800$		0			0
$801$	−4.25915	−	24.1548i	−0.150490	−	0.853470i
$802$		0			0
$803$	−11.2438	+	9.43464i	−0.396784	+	0.332941i
$804$		0			0
$805$	9.88058	−	17.1137i	0.348245	−	0.603178i
$806$		0			0
$807$	18.6219	−	6.77782i	0.655522	−	0.238591i
$808$		0			0
$809$	−19.1867	−	33.2323i	−0.674568	−	1.16839i	−0.976595	−	0.215087i	$-0.930997\pi$
$809$	−19.1867	−	33.2323i	−0.674568	−	1.16839i	0.302027	−	0.953299i	$-0.402337\pi$
$810$		0			0
$811$	6.88099	−	39.0241i	0.241624	−	1.37032i	−0.586579	−	0.809892i	$-0.699526\pi$
$811$	6.88099	−	39.0241i	0.241624	−	1.37032i	0.828203	−	0.560428i	$-0.189363\pi$
$812$		0			0
$813$	−0.977784	−	0.820458i	−0.0342924	−	0.0287747i
$814$		0			0
$815$	−3.27191	−	1.19088i	−0.114610	−	0.0417146i
$816$		0			0
$817$	−5.49540	+	17.1427i	−0.192260	+	0.599747i
$818$		0			0
$819$	−46.1604	−	16.8010i	−1.61298	−	0.587075i
$820$		0			0
$821$	9.94984	+	8.34891i	0.347252	+	0.291379i	0.799685	−	0.600419i	$-0.205000\pi$
$821$	9.94984	+	8.34891i	0.347252	+	0.291379i	−0.452434	+	0.891798i	$0.649444\pi$
$822$		0			0
$823$	−6.71731	+	38.0958i	−0.234151	+	1.32793i	0.610244	+	0.792213i	$0.291071\pi$
$823$	−6.71731	+	38.0958i	−0.234151	+	1.32793i	−0.844395	+	0.535721i	$0.820040\pi$
$824$		0			0
$825$	−0.534908	−	0.926488i	−0.0186231	−	0.0322562i
$826$		0			0
$827$	−37.2916	+	13.5730i	−1.29675	+	0.471980i	−0.895938	−	0.444178i	$-0.853496\pi$
$827$	−37.2916	+	13.5730i	−1.29675	+	0.471980i	−0.400816	+	0.916158i	$0.631273\pi$
$828$		0			0
$829$	−26.8732	+	46.5457i	−0.933344	+	1.61660i	−0.155783	+	0.987791i	$0.549790\pi$
$829$	−26.8732	+	46.5457i	−0.933344	+	1.61660i	−0.777561	+	0.628807i	$0.783543\pi$
$830$		0			0
$831$	20.6861	−	17.3577i	0.717594	−	0.602132i
$832$		0			0
$833$	−17.3555	−	98.4280i	−0.601333	−	3.41033i
$834$		0			0
$835$	21.4896			0.743677
$836$		0			0
$837$	13.3346			0.460912
$838$		0			0
$839$	−0.947486	−	5.37346i	−0.0327109	−	0.185512i	0.964074	−	0.265632i	$-0.0855808\pi$
$839$	−0.947486	−	5.37346i	−0.0327109	−	0.185512i	−0.996785	+	0.0801200i	$0.974470\pi$
$840$		0			0
$841$	−16.7448	+	14.0505i	−0.577407	+	0.484502i
$842$		0			0
$843$	−5.81728	+	10.0758i	−0.200358	+	0.347030i
$844$		0			0
$845$	−12.8797	+	4.68781i	−0.443073	+	0.161266i
$846$		0			0
$847$	22.2379	+	38.5172i	0.764103	+	1.32347i
$848$		0			0
$849$	0.291975	−	1.65587i	0.0100206	−	0.0568294i
$850$		0			0
$851$	1.63247	+	1.36981i	0.0559604	+	0.0469563i
$852$		0			0
$853$	−28.6665	−	10.4338i	−0.981524	−	0.357245i	−0.199091	−	0.979981i	$-0.563799\pi$
$853$	−28.6665	−	10.4338i	−0.981524	−	0.357245i	−0.782432	+	0.622736i	$0.786021\pi$
$854$		0			0
$855$	0.352792	+	9.07685i	0.0120652	+	0.310422i
$856$		0			0
$857$	42.6050	+	15.5070i	1.45536	+	0.529707i	0.944083	−	0.329709i	$-0.106951\pi$
$857$	42.6050	+	15.5070i	1.45536	+	0.529707i	0.511276	+	0.859416i	$0.329173\pi$
$858$		0			0
$859$	−4.97862	−	4.17756i	−0.169868	−	0.142536i	0.553890	−	0.832590i	$-0.313143\pi$
$859$	−4.97862	−	4.17756i	−0.169868	−	0.142536i	−0.723759	+	0.690053i	$0.757587\pi$
$860$		0			0
$861$	6.34805	−	36.0016i	0.216341	−	1.22693i
$862$		0			0
$863$	10.8754	+	18.8367i	0.370203	+	0.641210i	0.989597	−	0.143871i	$-0.0459549\pi$
$863$	10.8754	+	18.8367i	0.370203	+	0.641210i	−0.619394	+	0.785080i	$0.712622\pi$
$864$		0			0
$865$	−10.3262	+	3.75842i	−0.351100	+	0.127790i
$866$		0			0
$867$	−16.9457	+	29.3508i	−0.575506	+	0.996806i
$868$		0			0
$869$	−13.5648	+	11.3822i	−0.460155	+	0.386116i
$870$		0			0
$871$	11.3717	+	64.4920i	0.385314	+	2.18523i
$872$		0			0
$873$	7.26967			0.246041
$874$		0			0
$875$	4.56133			0.154201
$876$		0			0
$877$	−7.34817	−	41.6736i	−0.248130	−	1.40722i	−0.813109	−	0.582111i	$-0.802227\pi$
$877$	−7.34817	−	41.6736i	−0.248130	−	1.40722i	0.564979	−	0.825105i	$-0.308884\pi$
$878$		0			0
$879$	−5.64637	+	4.73787i	−0.190447	+	0.159804i
$880$		0			0
$881$	5.18932	−	8.98817i	0.174833	−	0.302819i	−0.765271	−	0.643709i	$-0.777395\pi$
$881$	5.18932	−	8.98817i	0.174833	−	0.302819i	0.940103	+	0.340890i	$0.110728\pi$
$882$		0			0
$883$	17.3004	−	6.29684i	0.582206	−	0.211906i	−0.0340920	−	0.999419i	$-0.510854\pi$
$883$	17.3004	−	6.29684i	0.582206	−	0.211906i	0.616298	+	0.787513i	$0.288632\pi$
$884$		0			0
$885$	1.24930	+	2.16385i	0.0419947	+	0.0727370i
$886$		0			0
$887$	6.62268	−	37.5591i	0.222368	−	1.26111i	−0.645285	−	0.763942i	$-0.723262\pi$
$887$	6.62268	−	37.5591i	0.222368	−	1.26111i	0.867653	−	0.497170i	$-0.165627\pi$
$888$		0			0
$889$	−14.7292	−	12.3593i	−0.494003	−	0.414517i
$890$		0			0
$891$	−1.67494	−	0.609630i	−0.0561127	−	0.0204234i
$892$		0			0
$893$	−7.06224	+	9.11306i	−0.236329	+	0.304957i
$894$		0			0
$895$	16.0660	+	5.84753i	0.537026	+	0.195461i
$896$		0			0
$897$	16.4151	+	13.7739i	0.548083	+	0.459896i
$898$		0			0
$899$	1.27167	−	7.21202i	0.0424127	−	0.240534i
$900$		0			0
$901$	−49.3786	−	85.5262i	−1.64504	−	2.84929i
$902$		0			0
$903$	−16.9427	+	6.16663i	−0.563817	+	0.205213i
$904$		0			0
$905$	−5.79496	+	10.0372i	−0.192631	+	0.333647i
$906$		0			0
$907$	−33.7640	+	28.3314i	−1.12112	+	0.940728i	−0.998660	−	0.0517465i	$-0.983521\pi$
$907$	−33.7640	+	28.3314i	−1.12112	+	0.940728i	−0.122455	+	0.992474i	$0.539077\pi$
$908$		0			0
$909$	−3.82150	−	21.6728i	−0.126751	−	0.718842i
$910$		0			0
$911$	−30.0351			−0.995107			−0.497553	−	0.867433i	$-0.665768\pi$
$911$	−30.0351			−0.995107			−0.497553	+	0.867433i	$0.665768\pi$
$912$		0			0
$913$	−4.20352			−0.139116
$914$		0			0
$915$	0.791255	+	4.48743i	0.0261581	+	0.148350i
$916$		0			0
$917$	9.60955	−	8.06337i	0.317335	−	0.266276i
$918$		0			0
$919$	24.9301	−	43.1803i	0.822370	−	1.42439i	−0.0815433	−	0.996670i	$-0.525985\pi$
$919$	24.9301	−	43.1803i	0.822370	−	1.42439i	0.903913	−	0.427716i	$-0.140682\pi$
$920$		0			0
$921$	5.78641	−	2.10608i	0.190669	−	0.0693978i
$922$		0			0
$923$	1.76787	+	3.06205i	0.0581903	+	0.100789i
$924$		0			0
$925$	−0.0854163	+	0.484420i	−0.00280847	+	0.0159276i
$926$		0			0
$927$	18.4423	+	15.4749i	0.605724	+	0.508262i
$928$		0			0
$929$	32.3651	+	11.7799i	1.06187	+	0.386487i	0.813129	−	0.582084i	$-0.197762\pi$
$929$	32.3651	+	11.7799i	1.06187	+	0.386487i	0.248737	+	0.968571i	$0.419985\pi$
$930$		0			0
$931$	53.2448	+	28.0421i	1.74503	+	0.919044i
$932$		0			0
$933$	26.0873	+	9.49500i	0.854059	+	0.310852i
$934$		0			0
$935$	−6.19883	−	5.20144i	−0.202723	−	0.170105i
$936$		0			0
$937$	0.119594	−	0.678251i	0.00390696	−	0.0221575i	−0.982792	−	0.184716i	$-0.940863\pi$
$937$	0.119594	−	0.678251i	0.00390696	−	0.0221575i	0.986699	+	0.162558i	$0.0519746\pi$
$938$		0			0
$939$	−6.55196	−	11.3483i	−0.213815	−	0.370339i
$940$		0			0
$941$	17.2750	−	6.28758i	0.563148	−	0.204969i	−0.0447304	−	0.998999i	$-0.514243\pi$
$941$	17.2750	−	6.28758i	0.563148	−	0.204969i	0.607879	+	0.794030i	$0.292021\pi$
$942$		0			0
$943$	18.1388	−	31.4173i	0.590680	−	1.02309i
$944$		0			0
$945$	−17.0023	+	14.2666i	−0.553084	+	0.464093i
$946$		0			0
$947$	−3.93867	−	22.3373i	−0.127989	−	0.725864i	−0.979487	−	0.201506i	$-0.935416\pi$
$947$	−3.93867	−	22.3373i	−0.127989	−	0.725864i	0.851498	−	0.524358i	$-0.175695\pi$
$948$		0			0
$949$	67.8604			2.20284
$950$		0			0
$951$	−4.31148			−0.139809
$952$		0			0
$953$	−9.59020	−	54.3887i	−0.310657	−	1.76182i	−0.595602	−	0.803280i	$-0.703086\pi$
$953$	−9.59020	−	54.3887i	−0.310657	−	1.76182i	0.284945	−	0.958544i	$-0.408025\pi$
$954$		0			0
$955$	19.8167	−	16.6282i	0.641252	−	0.538075i
$956$		0			0
$957$	1.42944	−	2.47586i	0.0462072	−	0.0800332i
$958$		0			0
$959$	−9.46857	+	3.44628i	−0.305756	+	0.111286i
$960$		0			0
$961$	11.7450	+	20.3430i	0.378872	+	0.656225i
$962$		0			0
$963$	−2.81117	+	15.9429i	−0.0905888	+	0.513754i
$964$		0			0
$965$	10.7760	+	9.04214i	0.346892	+	0.291077i
$966$		0			0
$967$	33.4162	+	12.1625i	1.07459	+	0.391120i	0.817893	−	0.575371i	$-0.195142\pi$
$967$	33.4162	+	12.1625i	1.07459	+	0.391120i	0.256701	+	0.966491i	$0.417365\pi$
$968$		0			0
$969$	−11.4244	−	27.9587i	−0.367005	−	0.898161i
$970$		0			0
$971$	−49.8615	−	18.1481i	−1.60013	−	0.582400i	−0.620676	−	0.784067i	$-0.713142\pi$
$971$	−49.8615	−	18.1481i	−1.60013	−	0.582400i	−0.979454	+	0.201667i	$0.935364\pi$
$972$		0			0
$973$	30.8401	+	25.8779i	0.988687	+	0.829607i
$974$		0			0
$975$	−0.858890	+	4.87101i	−0.0275065	+	0.155997i
$976$		0			0
$977$	−1.62779	−	2.81942i	−0.0520777	−	0.0902012i	0.838811	−	0.544422i	$-0.183251\pi$
$977$	−1.62779	−	2.81942i	−0.0520777	−	0.0902012i	−0.890889	+	0.454221i	$0.849918\pi$
$978$		0			0
$979$	−12.3623	+	4.49952i	−0.395102	+	0.143805i
$980$		0			0
$981$	−13.7673	+	23.8457i	−0.439556	+	0.761334i
$982$		0			0
$983$	−15.4044	+	12.9258i	−0.491324	+	0.412270i	−0.854501	−	0.519450i	$-0.826137\pi$
$983$	−15.4044	+	12.9258i	−0.491324	+	0.412270i	0.363176	+	0.931720i	$0.381692\pi$
$984$		0			0
$985$	0.591168	+	3.35268i	0.0188362	+	0.106825i
$986$		0			0
$987$	−11.5472			−0.367551
$988$		0			0
$989$	−17.8922			−0.568940
$990$		0			0
$991$	0.942702	+	5.34633i	0.0299459	+	0.169832i	0.996113	−	0.0880856i	$-0.0280749\pi$
$991$	0.942702	+	5.34633i	0.0299459	+	0.169832i	−0.966167	+	0.257917i	$0.916964\pi$
$992$		0			0
$993$	11.3252	−	9.50296i	0.359394	−	0.301567i
$994$		0			0
$995$	9.25255	−	16.0259i	0.293325	−	0.508054i
$996$		0			0
$997$	7.85246	−	2.85806i	0.248690	−	0.0905157i	−0.214668	−	0.976687i	$-0.568867\pi$
$997$	7.85246	−	2.85806i	0.248690	−	0.0905157i	0.463358	+	0.886171i	$0.346645\pi$
$998$		0			0
$999$	−1.19675	−	2.07283i	−0.0378634	−	0.0655813i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.u.b.61.2	✓	18
19.5	even	9	inner	380.2.u.b.81.2	yes	18
19.9	even	9		7220.2.a.w.1.6		9
19.10	odd	18		7220.2.a.y.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.u.b.61.2	✓	18	1.1	even	1	trivial
380.2.u.b.81.2	yes	18	19.5	even	9	inner
7220.2.a.w.1.6		9	19.9	even	9
7220.2.a.y.1.4		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)

\(f(q)\)	\(=\)	\(q+(0.166200 + 0.942568i) q^{3} +(0.766044 - 0.642788i) q^{5} +(-2.28066 + 3.95023i) q^{7} +(1.95827 - 0.712751i) q^{9} +O(q^{10})\)	\(q+(0.166200 + 0.942568i) q^{3} +(0.766044 - 0.642788i) q^{5} +(-2.28066 + 3.95023i) q^{7} +(1.95827 - 0.712751i) q^{9} +(-0.558879 - 0.968007i) q^{11} +(-0.897380 + 5.08930i) q^{13} +(0.733187 + 0.615217i) q^{15} +(6.80290 + 2.47605i) q^{17} +(-3.68742 + 2.32442i) q^{19} +(-4.10240 - 1.49315i) q^{21} +(-3.31875 - 2.78477i) q^{23} +(0.173648 - 0.984808i) q^{25} +(2.43294 + 4.21398i) q^{27} +(2.51115 - 0.913983i) q^{29} +(1.37022 - 2.37328i) q^{31} +(0.819526 - 0.687664i) q^{33} +(0.792067 + 4.49203i) q^{35} -0.491893 q^{37} -4.94615 q^{39} +(1.45408 + 8.24648i) q^{41} +(3.16372 - 2.65467i) q^{43} +(1.04197 - 1.80475i) q^{45} +(2.48547 - 0.904639i) q^{47} +(-6.90286 - 11.9561i) q^{49} +(-1.20320 + 6.82371i) q^{51} +(-10.4500 - 8.76856i) q^{53} +(-1.05035 - 0.382296i) q^{55} +(-2.80377 - 3.08933i) q^{57} +(2.45313 + 0.892868i) q^{59} +(3.64703 + 3.06022i) q^{61} +(-1.65062 + 9.36114i) q^{63} +(2.58390 + 4.47545i) q^{65} +(11.9079 - 4.33411i) q^{67} +(2.07325 - 3.59098i) q^{69} +(0.524118 - 0.439787i) q^{71} +(-2.28024 - 12.9319i) q^{73} +0.957108 q^{75} +5.09846 q^{77} +(-2.75095 - 15.6014i) q^{79} +(1.22158 - 1.02502i) q^{81} +(1.88033 - 3.25683i) q^{83} +(6.80290 - 2.47605i) q^{85} +(1.27884 + 2.21502i) q^{87} +(2.04379 - 11.5909i) q^{89} +(-18.0573 - 15.1518i) q^{91} +(2.46471 + 0.897081i) q^{93} +(-1.33063 + 4.15084i) q^{95} +(3.27804 + 1.19311i) q^{97} +(-1.78438 - 1.49727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 15 q^{9}+O(q^{10}) \) 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

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