LMFDB - Embedded newform 3784.1.em.b.1219.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3784,1,Mod(203,3784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3784, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 105, 84, 170]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3784.203");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3784 = 2^{3} \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3784.em (of order $210$, degree $48$, 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:	$1.88846200780$
Analytic rank:	$0$
Dimension:	$48$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{105}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{105} - \cdots)$

Embedding invariants

Embedding label			1219.1
Root			$0.772417 - 0.635116i$ of defining polynomial
Character	$\chi$	$=$	3784.1219
Dual form			3784.1.em.b.3635.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.550897 - 0.834573i) q^{2} +(0.431949 + 1.66167i) q^{3} +(-0.393025 + 0.919528i) q^{4} +(1.14883 - 1.27590i) q^{6} +(0.983930 - 0.178557i) q^{8} +(-1.70117 + 0.948526i) q^{9} +O(q^{10})$	\(q+(-0.550897 - 0.834573i) q^{2} +(0.431949 + 1.66167i) q^{3} +(-0.393025 + 0.919528i) q^{4} +(1.14883 - 1.27590i) q^{6} +(0.983930 - 0.178557i) q^{8} +(-1.70117 + 0.948526i) q^{9} +(0.251587 + 0.967835i) q^{11} +(-1.69772 - 0.255890i) q^{12} +(-0.691063 - 0.722795i) q^{16} +(1.92908 - 0.470769i) q^{17} +(1.72878 + 0.897210i) q^{18} +(-0.231838 + 1.17703i) q^{19} +(0.669131 - 0.743145i) q^{22} +(0.721710 + 1.55784i) q^{24} +(0.712376 - 0.701798i) q^{25} +(-1.12447 - 1.17611i) q^{27} +(-0.222521 + 0.974928i) q^{32} +(-1.49955 + 0.836110i) q^{33} +(-1.45562 - 1.35061i) q^{34} +(-0.203594 - 1.93707i) q^{36} +(1.11004 - 0.454935i) q^{38} +(-0.0709825 + 1.58055i) q^{41} +(-0.772417 + 0.635116i) q^{43} +(-0.988831 - 0.149042i) q^{44} +(0.902545 - 1.46053i) q^{48} +(0.669131 - 0.743145i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(1.61553 + 3.00216i) q^{51} +(-0.362079 + 1.58637i) q^{54} +(-2.05598 + 0.123177i) q^{57} +(-1.65836 - 0.300947i) q^{59} +(0.936235 - 0.351375i) q^{64} +(1.52389 + 0.790876i) q^{66} +(0.153250 - 0.142195i) q^{67} +(-0.325292 + 1.95887i) q^{68} +(-1.50447 + 1.23704i) q^{72} +(1.95542 + 0.0585235i) q^{73} +(1.47387 + 0.880596i) q^{75} +(-0.991192 - 0.675783i) q^{76} +(0.444699 - 0.719627i) q^{81} +(1.35819 - 0.811480i) q^{82} +(-1.09982 - 0.0658919i) q^{83} +(0.955573 + 0.294755i) q^{86} +(0.420357 + 0.907359i) q^{88} +(-0.204903 + 0.522085i) q^{89} +(-1.71613 + 0.0513618i) q^{96} +(-1.32616 - 0.792344i) q^{97} +(-0.988831 - 0.149042i) q^{98} +(-1.34601 - 1.40781i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

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 $

$2$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$2$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$3$	0.431949	+	1.66167i	0.431949	+	1.66167i	0.712376	+	0.701798i	$0.247619\pi$
$3$	0.431949	+	1.66167i	0.431949	+	1.66167i	−0.280427	+	0.959875i	$0.590476\pi$
$4$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$5$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$5$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$6$	1.14883	−	1.27590i	1.14883	−	1.27590i
$7$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$7$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$8$	0.983930	−	0.178557i	0.983930	−	0.178557i
$9$	−1.70117	+	0.948526i	−1.70117	+	0.948526i
$10$		0			0
$11$	0.251587	+	0.967835i	0.251587	+	0.967835i
$11$	0.251587	+	0.967835i	0.251587	+	0.967835i
$12$	−1.69772	−	0.255890i	−1.69772	−	0.255890i
$13$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$13$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$14$		0			0
$15$		0			0
$16$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$17$	1.92908	−	0.470769i	1.92908	−	0.470769i	0.936235	−	0.351375i	$-0.114286\pi$
$17$	1.92908	−	0.470769i	1.92908	−	0.470769i	0.992847	−	0.119394i	$-0.0380952\pi$
$18$	1.72878	+	0.897210i	1.72878	+	0.897210i
$19$	−0.231838	+	1.17703i	−0.231838	+	1.17703i	0.669131	+	0.743145i	$0.266667\pi$
$19$	−0.231838	+	1.17703i	−0.231838	+	1.17703i	−0.900969	+	0.433884i	$0.857143\pi$
$20$		0			0
$21$		0			0
$22$	0.669131	−	0.743145i	0.669131	−	0.743145i
$23$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$23$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$24$	0.721710	+	1.55784i	0.721710	+	1.55784i
$25$	0.712376	−	0.701798i	0.712376	−	0.701798i
$26$		0			0
$27$	−1.12447	−	1.17611i	−1.12447	−	1.17611i
$28$		0			0
$29$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$29$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$30$		0			0
$31$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$31$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$32$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$33$	−1.49955	+	0.836110i	−1.49955	+	0.836110i
$34$	−1.45562	−	1.35061i	−1.45562	−	1.35061i
$35$		0			0
$36$	−0.203594	−	1.93707i	−0.203594	−	1.93707i
$37$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$37$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$38$	1.11004	−	0.454935i	1.11004	−	0.454935i
$39$		0			0
$40$		0			0
$41$	−0.0709825	+	1.58055i	−0.0709825	+	1.58055i	0.575617	+	0.817719i	$0.304762\pi$
$41$	−0.0709825	+	1.58055i	−0.0709825	+	1.58055i	−0.646600	+	0.762830i	$0.723810\pi$
$42$		0			0
$43$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$43$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$44$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$45$		0			0
$46$		0			0
$47$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$47$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$48$	0.902545	−	1.46053i	0.902545	−	1.46053i
$49$	0.669131	−	0.743145i	0.669131	−	0.743145i
$50$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$51$	1.61553	+	3.00216i	1.61553	+	3.00216i
$52$		0			0
$53$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$53$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$54$	−0.362079	+	1.58637i	−0.362079	+	1.58637i
$55$		0			0
$56$		0			0
$57$	−2.05598	+	0.123177i	−2.05598	+	0.123177i
$58$		0			0
$59$	−1.65836	−	0.300947i	−1.65836	−	0.300947i	−0.733052	−	0.680173i	$-0.761905\pi$
$59$	−1.65836	−	0.300947i	−1.65836	−	0.300947i	−0.925304	+	0.379225i	$0.876190\pi$
$60$		0			0
$61$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$61$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$62$		0			0
$63$		0			0
$64$	0.936235	−	0.351375i	0.936235	−	0.351375i
$65$		0			0
$66$	1.52389	+	0.790876i	1.52389	+	0.790876i
$67$	0.153250	−	0.142195i	0.153250	−	0.142195i	−0.599822	−	0.800134i	$-0.704762\pi$
$67$	0.153250	−	0.142195i	0.153250	−	0.142195i	0.753071	+	0.657939i	$0.228571\pi$
$68$	−0.325292	+	1.95887i	−0.325292	+	1.95887i
$69$		0			0
$70$		0			0
$71$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$71$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$72$	−1.50447	+	1.23704i	−1.50447	+	1.23704i
$73$	1.95542	+	0.0585235i	1.95542	+	0.0585235i	0.983930	−	0.178557i	$-0.0571429\pi$
$73$	1.95542	+	0.0585235i	1.95542	+	0.0585235i	0.971490	+	0.237080i	$0.0761905\pi$
$74$		0			0
$75$	1.47387	+	0.880596i	1.47387	+	0.880596i
$76$	−0.991192	−	0.675783i	−0.991192	−	0.675783i
$77$		0			0
$78$		0			0
$79$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$79$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$80$		0			0
$81$	0.444699	−	0.719627i	0.444699	−	0.719627i
$82$	1.35819	−	0.811480i	1.35819	−	0.811480i
$83$	−1.09982	−	0.0658919i	−1.09982	−	0.0658919i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−1.09982	−	0.0658919i	−1.09982	−	0.0658919i	−0.599822	+	0.800134i	$0.704762\pi$
$84$		0			0
$85$		0			0
$86$	0.955573	+	0.294755i	0.955573	+	0.294755i
$87$		0			0
$88$	0.420357	+	0.907359i	0.420357	+	0.907359i
$89$	−0.204903	+	0.522085i	−0.204903	+	0.522085i	−0.995974	−	0.0896393i	$-0.971429\pi$
$89$	−0.204903	+	0.522085i	−0.204903	+	0.522085i	0.791071	+	0.611724i	$0.209524\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.71613	+	0.0513618i	−1.71613	+	0.0513618i
$97$	−1.32616	−	0.792344i	−1.32616	−	0.792344i	−0.337330	−	0.941386i	$-0.609524\pi$
$97$	−1.32616	−	0.792344i	−1.32616	−	0.792344i	−0.988831	+	0.149042i	$0.952381\pi$
$98$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$99$	−1.34601	−	1.40781i	−1.34601	−	1.40781i
$100$	0.365341	+	0.930874i	0.365341	+	0.930874i
$101$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$101$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$102$	1.61553	−	3.00216i	1.61553	−	3.00216i
$103$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$103$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.87296	−	0.516904i	−1.87296	−	0.516904i	−0.999552	−	0.0299155i	$-0.990476\pi$
$107$	−1.87296	−	0.516904i	−1.87296	−	0.516904i	−0.873408	−	0.486989i	$-0.838095\pi$
$108$	1.52341	−	0.571746i	1.52341	−	0.571746i
$109$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$109$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.183156	−	0.340361i	0.183156	−	0.340361i	−0.772417	−	0.635116i	$-0.780952\pi$
$113$	0.183156	−	0.340361i	0.183156	−	0.340361i	0.955573	+	0.294755i	$0.0952381\pi$
$114$	1.23543	+	1.64801i	1.23543	+	1.64801i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.662421	+	1.54981i	0.662421	+	1.54981i
$119$		0			0
$120$		0			0
$121$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$122$		0			0
$123$	−2.65702	+	0.564766i	−2.65702	+	0.564766i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$127$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$	−1.38900	−	1.00917i	−1.38900	−	1.00917i
$130$		0			0
$131$	0.655517	−	0.821992i	0.655517	−	0.821992i	−0.337330	−	0.941386i	$-0.609524\pi$
$131$	0.655517	−	0.821992i	0.655517	−	0.821992i	0.992847	+	0.119394i	$0.0380952\pi$
$132$	−0.179465	−	1.70749i	−0.179465	−	1.70749i
$133$		0			0
$134$	−0.203097	−	0.0495633i	−0.203097	−	0.0495633i
$135$		0			0
$136$	1.81402	−	0.807654i	1.81402	−	0.807654i
$137$	0.251348	−	1.85552i	0.251348	−	1.85552i	−0.222521	−	0.974928i	$-0.571429\pi$
$137$	0.251348	−	1.85552i	0.251348	−	1.85552i	0.473869	−	0.880596i	$-0.342857\pi$
$138$		0			0
$139$	−0.0504174	−	0.140700i	−0.0504174	−	0.140700i	0.913545	−	0.406737i	$-0.133333\pi$
$139$	−0.0504174	−	0.140700i	−0.0504174	−	0.140700i	−0.963963	+	0.266037i	$0.914286\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.86120	+	0.574106i	1.86120	+	0.574106i
$145$		0			0
$146$	−1.02839	−	1.66418i	−1.02839	−	1.66418i
$147$	1.52389	+	0.790876i	1.52389	+	0.790876i
$148$		0			0
$149$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$149$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$150$	−0.0770283	−	1.71517i	−0.0770283	−	1.71517i
$151$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$151$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$152$	−0.0179460	+	1.19951i	−0.0179460	+	1.19951i
$153$	−2.83516	+	2.63064i	−2.83516	+	2.63064i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$157$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.845565	+	0.0253068i	−0.845565	+	0.0253068i
$163$	1.12949	−	0.629774i	1.12949	−	0.629774i	0.193256	−	0.981148i	$-0.438095\pi$
$163$	1.12949	−	0.629774i	1.12949	−	0.629774i	0.936235	+	0.351375i	$0.114286\pi$
$164$	−1.42546	−	0.686466i	−1.42546	−	0.686466i
$165$		0			0
$166$	0.550897	+	0.954182i	0.550897	+	0.954182i
$167$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$167$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$168$		0			0
$169$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$170$		0			0
$171$	−0.722046	−	2.22223i	−0.722046	−	2.22223i
$172$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$		0			0
$176$	0.525684	−	0.850680i	0.525684	−	0.850680i
$177$	−0.216249	−	2.88564i	−0.216249	−	2.88564i
$178$	0.548599	−	0.116608i	0.548599	−	0.116608i
$179$	0.176177	+	1.67621i	0.176177	+	1.67621i	0.623490	+	0.781831i	$0.285714\pi$
$179$	0.176177	+	1.67621i	0.176177	+	1.67621i	−0.447313	+	0.894377i	$0.647619\pi$
$180$		0			0
$181$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$181$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.940958	+	1.74859i	0.940958	+	1.74859i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$191$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$192$	0.988276	+	1.40394i	0.988276	+	1.40394i
$193$	−0.686957	+	1.04070i	−0.686957	+	1.04070i	0.309017	+	0.951057i	$0.400000\pi$
$193$	−0.686957	+	1.04070i	−0.686957	+	1.04070i	−0.995974	+	0.0896393i	$0.971429\pi$
$194$	0.0693087	+	1.54328i	0.0693087	+	1.54328i
$195$		0			0
$196$	0.420357	+	0.907359i	0.420357	+	0.907359i
$197$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$197$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$198$	−0.433412	+	1.89890i	−0.433412	+	1.89890i
$199$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$199$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$200$	0.575617	−	0.817719i	0.575617	−	0.817719i
$201$	0.302477	+	0.193230i	0.302477	+	0.193230i
$202$		0			0
$203$		0			0
$204$	−3.39551	+	0.305601i	−3.39551	+	0.305601i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.19750	+	0.0717437i	−1.19750	+	0.0717437i
$210$		0			0
$211$	1.37656	+	0.123893i	1.37656	+	0.123893i	0.753071	−	0.657939i	$-0.228571\pi$
$211$	1.37656	+	0.123893i	1.37656	+	0.123893i	0.623490	+	0.781831i	$0.285714\pi$
$212$		0			0
$213$		0			0
$214$	0.600414	+	1.84788i	0.600414	+	1.84788i
$215$		0			0
$216$	−1.31641	−	0.956425i	−1.31641	−	0.956425i
$217$		0			0
$218$		0			0
$219$	0.747394	+	3.27455i	0.747394	+	3.27455i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$223$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$224$		0			0
$225$	−0.546199	+	1.86958i	−0.546199	+	1.86958i
$226$	−0.384956	+	0.0346467i	−0.384956	+	0.0346467i
$227$	1.26459	+	1.24581i	1.26459	+	1.24581i	0.955573	+	0.294755i	$0.0952381\pi$
$227$	1.26459	+	1.24581i	1.26459	+	1.24581i	0.309017	+	0.951057i	$0.400000\pi$
$228$	0.694787	−	1.93894i	0.694787	−	1.93894i
$229$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$229$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.00490124	+	0.0295146i	−0.00490124	+	0.0295146i	−0.988831	−	0.149042i	$-0.952381\pi$
$233$	−0.00490124	+	0.0295146i	−0.00490124	+	0.0295146i	0.983930	+	0.178557i	$0.0571429\pi$
$234$		0			0
$235$		0			0
$236$	0.928505	−	1.40662i	0.928505	−	1.40662i
$237$		0			0
$238$		0			0
$239$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$239$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$240$		0			0
$241$	−0.144074	+	1.92253i	−0.144074	+	1.92253i	0.193256	+	0.981148i	$0.438095\pi$
$241$	−0.144074	+	1.92253i	−0.144074	+	1.92253i	−0.337330	+	0.941386i	$0.609524\pi$
$242$	0.887586	+	0.460642i	0.887586	+	0.460642i
$243$	−0.167005	−	0.0515143i	−0.167005	−	0.0515143i
$244$		0			0
$245$		0			0
$246$	1.93508	+	1.90635i	1.93508	+	1.90635i
$247$		0			0
$248$		0			0
$249$	−0.365576	−	1.85601i	−0.365576	−	1.85601i
$250$		0			0
$251$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.104528	−	0.994522i	$-0.533333\pi$
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.978148	+	0.207912i	$0.933333\pi$
$258$	−0.0770283	+	1.71517i	−0.0770283	+	1.71517i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.04714	−	0.0942439i	−1.04714	−	0.0942439i
$263$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$263$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$264$	−1.32616	+	1.09043i	−1.32616	+	1.09043i
$265$		0			0
$266$		0			0
$267$	−0.956042	−	0.114968i	−0.956042	−	0.114968i
$268$	0.0705212	+	0.196803i	0.0705212	+	0.196803i
$269$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$269$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$270$		0			0
$271$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$271$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$272$	−1.67339	−	1.06900i	−1.67339	−	1.06900i
$273$		0			0
$274$	−1.68704	+	0.812434i	−1.68704	+	0.812434i
$275$	0.858449	+	0.512899i	0.858449	+	0.512899i
$276$		0			0
$277$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$277$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$278$	−0.0896495	+	0.119588i	−0.0896495	+	0.119588i
$279$		0			0
$280$		0			0
$281$	−1.12608	−	1.59970i	−1.12608	−	1.59970i	−0.733052	−	0.680173i	$-0.761905\pi$
$281$	−1.12608	−	1.59970i	−1.12608	−	1.59970i	−0.393025	−	0.919528i	$-0.628571\pi$
$282$		0			0
$283$	1.36145	−	1.34124i	1.36145	−	1.34124i	0.473869	−	0.880596i	$-0.342857\pi$
$283$	1.36145	−	1.34124i	1.36145	−	1.34124i	0.887586	−	0.460642i	$-0.152381\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.546199	−	1.86958i	−0.546199	−	1.86958i
$289$	2.61215	−	1.35566i	2.61215	−	1.35566i
$290$		0			0
$291$	0.743784	−	2.54590i	0.743784	−	2.54590i
$292$	−0.822343	+	1.77506i	−0.822343	+	1.77506i
$293$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$293$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$294$	−0.179465	−	1.70749i	−0.179465	−	1.70749i
$295$		0			0
$296$		0			0
$297$	0.855376	−	1.38420i	0.855376	−	1.38420i
$298$		0			0
$299$		0			0
$300$	−1.38900	+	1.00917i	−1.38900	+	1.00917i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.01096	−	0.645829i	1.01096	−	0.645829i
$305$		0			0
$306$	3.75734	+	0.916934i	3.75734	+	0.916934i
$307$	0.873408	+	1.51279i	0.873408	+	1.51279i	0.858449	+	0.512899i	$0.171429\pi$
$307$	0.873408	+	1.51279i	0.873408	+	1.51279i	0.0149594	+	0.999888i	$0.495238\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$311$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$312$		0			0
$313$	−0.155256	−	0.934934i	−0.155256	−	0.934934i	−0.946327	−	0.323210i	$-0.895238\pi$
$313$	−0.155256	−	0.934934i	−0.155256	−	0.934934i	0.791071	−	0.611724i	$-0.209524\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$317$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.0499031	−	3.33552i	0.0499031	−	3.33552i
$322$		0			0
$323$	0.106874	+	2.37973i	0.106874	+	2.37973i
$324$	0.486939	+	0.691744i	0.486939	+	0.691744i
$325$		0			0
$326$	−1.14783	−	0.595702i	−1.14783	−	0.595702i
$327$		0			0
$328$	0.212376	+	1.56782i	0.212376	+	1.56782i
$329$		0			0
$330$		0			0
$331$	1.64952	−	1.12462i	1.64952	−	1.12462i	0.791071	−	0.611724i	$-0.209524\pi$
$331$	1.64952	−	1.12462i	1.64952	−	1.12462i	0.858449	−	0.512899i	$-0.171429\pi$
$332$	0.492847	−	0.985420i	0.492847	−	0.985420i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.30158	−	0.579499i	1.30158	−	0.579499i	0.365341	−	0.930874i	$-0.380952\pi$
$337$	1.30158	−	0.579499i	1.30158	−	0.579499i	0.936235	+	0.351375i	$0.114286\pi$
$338$	0.913545	+	0.406737i	0.913545	+	0.406737i
$339$	0.644682	+	0.157327i	0.644682	+	0.157327i
$340$		0			0
$341$		0			0
$342$	−1.45684	+	1.82682i	−1.45684	+	1.82682i
$343$		0			0
$344$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$345$		0			0
$346$		0			0
$347$	0.385820	+	0.0231150i	0.385820	+	0.0231150i	0.251587	−	0.967835i	$-0.419048\pi$
$347$	0.385820	+	0.0231150i	0.385820	+	0.0231150i	0.134233	+	0.990950i	$0.457143\pi$
$348$		0			0
$349$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$349$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$350$		0			0
$351$		0			0
$352$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$353$	0.947982	+	0.879599i	0.947982	+	0.879599i	0.992847	−	0.119394i	$-0.0380952\pi$
$353$	0.947982	+	0.879599i	0.947982	+	0.879599i	−0.0448648	+	0.998993i	$0.514286\pi$
$354$	−2.28915	+	1.77017i	−2.28915	+	1.77017i
$355$		0			0
$356$	−0.399540	−	0.393607i	−0.399540	−	0.393607i
$357$		0			0
$358$	1.30186	−	1.07045i	1.30186	−	1.07045i
$359$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$359$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$360$		0			0
$361$	−0.406343	−	0.166535i	−0.406343	−	0.166535i
$362$		0			0
$363$	−1.18648	−	1.24096i	−1.18648	−	1.24096i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$367$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$368$		0			0
$369$	−1.37844	−	2.75611i	−1.37844	−	2.75611i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$373$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$374$	0.940958	−	1.74859i	0.940958	−	1.74859i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.267986	−	1.97835i	0.267986	−	1.97835i	0.0747301	−	0.997204i	$-0.476190\pi$
$379$	0.267986	−	1.97835i	0.267986	−	1.97835i	0.193256	−	0.981148i	$-0.438095\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$383$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$384$	0.627253	−	1.59821i	0.627253	−	1.59821i
$385$		0			0
$386$	1.24698			1.24698
$387$	0.711588	−	1.81310i	0.711588	−	1.81310i
$388$	1.24980	−	0.908031i	1.24980	−	0.908031i
$389$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$389$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$390$		0			0
$391$		0			0
$392$	0.525684	−	0.850680i	0.525684	−	0.850680i
$393$	1.64903	+	0.734196i	1.64903	+	0.734196i
$394$		0			0
$395$		0			0
$396$	1.82354	−	0.684386i	1.82354	−	0.684386i
$397$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$397$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$398$		0			0
$399$		0			0
$400$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$401$	−1.44633	+	1.18924i	−1.44633	+	1.18924i	−0.500000	+	0.866025i	$0.666667\pi$
$401$	−1.44633	+	1.18924i	−1.44633	+	1.18924i	−0.946327	+	0.323210i	$0.895238\pi$
$402$	−0.00536937	−	0.358889i	−0.00536937	−	0.358889i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.12562	+	2.66545i	2.12562	+	2.66545i
$409$	1.54711	−	0.580639i	1.54711	−	0.580639i	0.575617	−	0.817719i	$-0.304762\pi$
$409$	1.54711	−	0.580639i	1.54711	−	0.580639i	0.971490	+	0.237080i	$0.0761905\pi$
$410$		0			0
$411$	3.19184	−	0.383833i	3.19184	−	0.383833i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.212019	−	0.144552i	0.212019	−	0.144552i
$418$	0.719573	+	0.959875i	0.719573	+	0.959875i
$419$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	−0.995974	−	0.0896393i	$-0.971429\pi$
$419$	−0.0597394	+	0.261736i	−0.0597394	+	0.261736i	0.936235	+	0.351375i	$0.114286\pi$
$420$		0			0
$421$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$421$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$422$	−0.654946	−	1.21709i	−0.654946	−	1.21709i
$423$		0			0
$424$		0			0
$425$	1.04385	−	1.68919i	1.04385	−	1.68919i
$426$		0			0
$427$		0			0
$428$	1.21143	−	1.51908i	1.21143	−	1.51908i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	−0.0730026	+	1.62553i	−0.0730026	+	1.62553i
$433$	−1.65836	+	1.05940i	−1.65836	+	1.05940i	−0.733052	+	0.680173i	$0.761905\pi$
$433$	−1.65836	+	1.05940i	−1.65836	+	1.05940i	−0.925304	+	0.379225i	$0.876190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	2.32111	−	2.42769i	2.32111	−	2.42769i
$439$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$439$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$440$		0			0
$441$	−0.433412	+	1.89890i	−0.433412	+	1.89890i
$442$		0			0
$443$	−0.0905618	+	0.252731i	−0.0905618	+	0.252731i	−0.978148	−	0.207912i	$-0.933333\pi$
$443$	−0.0905618	+	0.252731i	−0.0905618	+	0.252731i	0.887586	+	0.460642i	$0.152381\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.211513	+	0.456559i	0.211513	+	0.456559i	0.983930	−	0.178557i	$-0.0571429\pi$
$449$	0.211513	+	0.456559i	0.211513	+	0.456559i	−0.772417	+	0.635116i	$0.780952\pi$
$450$	1.86120	−	0.574106i	1.86120	−	0.574106i
$451$	−1.54757	+	0.328946i	−1.54757	+	0.328946i
$452$	0.240986	+	0.302187i	0.240986	+	0.302187i
$453$		0			0
$454$	0.343062	−	1.74171i	0.343062	−	1.74171i
$455$		0			0
$456$	−2.00094	+	0.488306i	−2.00094	+	0.488306i
$457$	1.27889	+	1.33761i	1.27889	+	1.33761i	0.913545	+	0.406737i	$0.133333\pi$
$457$	1.27889	+	1.33761i	1.27889	+	1.33761i	0.365341	+	0.930874i	$0.380952\pi$
$458$		0			0
$459$	−2.72288	−	1.73944i	−2.72288	−	1.73944i
$460$		0			0
$461$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$461$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$462$		0			0
$463$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$463$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$464$		0			0
$465$		0			0
$466$	0.0273322	−	0.0121691i	0.0273322	−	0.0121691i
$467$	1.10572	−	1.22803i	1.10572	−	1.22803i	0.134233	−	0.990950i	$-0.457143\pi$
$467$	1.10572	−	1.22803i	1.10572	−	1.22803i	0.971490	−	0.237080i	$-0.0761905\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.68544			−1.68544
$473$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$474$		0			0
$475$	0.660880	+	1.00119i	0.660880	+	1.00119i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$479$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$480$		0			0
$481$		0			0
$482$	1.68387	−	0.938878i	1.68387	−	0.938878i
$483$		0			0
$484$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$485$		0			0
$486$	0.0490102	+	0.167757i	0.0490102	+	0.167757i
$487$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$487$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$488$		0			0
$489$	1.53436	+	1.60481i	1.53436	+	1.60481i
$490$		0			0
$491$	−1.55045	−	0.804658i	−1.55045	−	0.804658i	−0.550897	−	0.834573i	$-0.685714\pi$
$491$	−1.55045	−	0.804658i	−1.55045	−	0.804658i	−0.999552	+	0.0299155i	$0.990476\pi$
$492$	0.524956	−	2.66517i	0.524956	−	2.66517i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.34758	+	1.32757i	−1.34758	+	1.32757i
$499$	0.998889	−	1.17844i	0.998889	−	1.17844i	0.0149594	−	0.999888i	$-0.495238\pi$
$499$	0.998889	−	1.17844i	0.998889	−	1.17844i	0.983930	−	0.178557i	$-0.0571429\pi$
$500$		0			0
$501$		0			0
$502$	−0.251587	+	0.967835i	−0.251587	+	0.967835i
$503$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$503$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.25857	−	1.16779i	−1.25857	−	1.16779i
$508$		0			0
$509$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$509$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$510$		0			0
$511$		0			0
$512$	0.858449	−	0.512899i	0.858449	−	0.512899i
$513$	1.64501	−	1.05087i	1.64501	−	1.05087i
$514$	−0.0600409	+	1.33691i	−0.0600409	+	1.33691i
$515$		0			0
$516$	1.47387	−	0.880596i	1.47387	−	0.880596i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.552687	−	0.894377i	0.552687	−	0.894377i	−0.447313	−	0.894377i	$-0.647619\pi$
$521$	0.552687	−	0.894377i	0.552687	−	0.894377i	1.00000			$0$
$522$		0			0
$523$	1.95542	+	0.415637i	1.95542	+	0.415637i	0.983930	+	0.178557i	$0.0571429\pi$
$523$	1.95542	+	0.415637i	1.95542	+	0.415637i	0.971490	+	0.237080i	$0.0761905\pi$
$524$	0.498210	+	0.925830i	0.498210	+	0.925830i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.64062	+	0.506064i	1.64062	+	0.506064i
$529$	0.826239	−	0.563320i	0.826239	−	0.563320i
$530$		0			0
$531$	3.10660	−	1.06103i	3.10660	−	1.06103i
$532$		0			0
$533$		0			0
$534$	0.430731	+	0.861223i	0.430731	+	0.861223i
$535$		0			0
$536$	0.125397	−	0.167273i	0.125397	−	0.167273i
$537$	−2.70921	+	1.01678i	−2.70921	+	1.01678i
$538$		0			0
$539$	0.887586	+	0.460642i	0.887586	+	0.460642i
$540$		0			0
$541$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$541$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$542$		0			0
$543$		0			0
$544$	0.0297048	+	1.98547i	0.0297048	+	1.98547i
$545$		0			0
$546$		0			0
$547$	1.74664	−	0.906479i	1.74664	−	0.906479i	0.791071	−	0.611724i	$-0.209524\pi$
$547$	1.74664	−	0.906479i	1.74664	−	0.906479i	0.955573	−	0.294755i	$-0.0952381\pi$
$548$	1.60742	+	0.960388i	1.60742	+	0.960388i
$549$		0			0
$550$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.149193	+	0.00893834i	0.149193	+	0.00893834i
$557$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$557$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.49914	+	2.31887i	−2.49914	+	2.31887i
$562$	−0.714715	+	1.82106i	−0.714715	+	1.82106i
$563$	−0.267386	−	0.0240652i	−0.267386	−	0.0240652i	−0.0448648	−	0.998993i	$-0.514286\pi$
$563$	−0.267386	−	0.0240652i	−0.267386	−	0.0240652i	−0.222521	+	0.974928i	$0.571429\pi$
$564$		0			0
$565$		0			0
$566$	−1.86938	−	0.397350i	−1.86938	−	0.397350i
$567$		0			0
$568$		0			0
$569$	−0.502948	+	0.0150527i	−0.502948	+	0.0150527i	−0.280427	−	0.959875i	$-0.590476\pi$
$569$	−0.502948	+	0.0150527i	−0.502948	+	0.0150527i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$	−1.23305	−	0.185853i	−1.23305	−	0.185853i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.23305	−	0.185853i	−1.23305	−	0.185853i	−0.733052	+	0.680173i	$0.761905\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.25941	+	1.48579i	−1.25941	+	1.48579i
$577$	0.862387	+	1.72429i	0.862387	+	1.72429i	0.669131	+	0.743145i	$0.266667\pi$
$577$	0.862387	+	1.72429i	0.862387	+	1.72429i	0.193256	+	0.981148i	$0.438095\pi$
$578$	−2.57042	−	1.43320i	−2.57042	−	1.43320i
$579$	−2.02603	−	0.691971i	−2.02603	−	0.691971i
$580$		0			0
$581$		0			0
$582$	−2.53449	+	0.781786i	−2.53449	+	0.781786i
$583$		0			0
$584$	1.93445	−	0.291571i	1.93445	−	0.291571i
$585$		0			0
$586$		0			0
$587$	−1.06479	−	1.42037i	−1.06479	−	1.42037i	−0.900969	−	0.433884i	$-0.857143\pi$
$587$	−1.06479	−	1.42037i	−1.06479	−	1.42037i	−0.163818	−	0.986491i	$-0.552381\pi$
$588$	−1.32616	+	1.09043i	−1.32616	+	1.09043i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.38741	+	1.28733i	1.38741	+	1.28733i	0.913545	+	0.406737i	$0.133333\pi$
$593$	1.38741	+	1.28733i	1.38741	+	1.28733i	0.473869	+	0.880596i	$0.342857\pi$
$594$	−1.62644	+	0.0486775i	−1.62644	+	0.0486775i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$599$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$600$	1.60742	+	0.603275i	1.60742	+	0.603275i
$601$	−1.61514	−	1.17347i	−1.61514	−	1.17347i	−0.842721	−	0.538351i	$-0.819048\pi$
$601$	−1.61514	−	1.17347i	−1.61514	−	1.17347i	−0.772417	−	0.635116i	$-0.780952\pi$
$602$		0			0
$603$	−0.125828	+	0.387259i	−0.125828	+	0.387259i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$607$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$608$	−1.09593	−	0.487939i	−1.09593	−	0.487939i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.30466	−	3.64092i	−1.30466	−	3.64092i
$613$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$613$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$614$	0.781374	−	1.56231i	0.781374	−	1.56231i
$615$		0			0
$616$		0			0
$617$	1.43923	+	0.443943i	1.43923	+	0.443943i	0.913545	−	0.406737i	$-0.133333\pi$
$617$	1.43923	+	0.443943i	1.43923	+	0.443943i	0.525684	+	0.850680i	$0.323810\pi$
$618$		0			0
$619$	−0.413214	−	0.668677i	−0.413214	−	0.668677i	0.575617	−	0.817719i	$-0.304762\pi$
$619$	−0.413214	−	0.668677i	−0.413214	−	0.668677i	−0.988831	+	0.149042i	$0.952381\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.0149594	−	0.999888i	0.0149594	−	0.999888i
$626$	−0.694741	+	0.644625i	−0.694741	+	0.644625i
$627$	−0.636472	−	1.95886i	−0.636472	−	1.95886i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$631$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$632$		0			0
$633$	0.388735	+	2.34091i	0.388735	+	2.34091i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.246733	−	0.215564i	−0.246733	−	0.215564i	0.525684	−	0.850680i	$-0.323810\pi$
$641$	−0.246733	−	0.215564i	−0.246733	−	0.215564i	−0.772417	+	0.635116i	$0.780952\pi$
$642$	−2.81123	+	1.79588i	−2.81123	+	1.79588i
$643$	1.07783	+	0.404515i	1.07783	+	0.404515i	0.826239	−	0.563320i	$-0.190476\pi$
$643$	1.07783	+	0.404515i	1.07783	+	0.404515i	0.251587	+	0.967835i	$0.419048\pi$
$644$		0			0
$645$		0			0
$646$	1.92718	−	1.40018i	1.92718	−	1.40018i
$647$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$647$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$648$	0.309058	−	0.787466i	0.309058	−	0.787466i
$649$	−0.125953	−	1.68073i	−0.125953	−	1.68073i
$650$		0			0
$651$		0			0
$652$	0.135176	+	1.28611i	0.135176	+	1.28611i
$653$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$653$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$654$		0			0
$655$		0			0
$656$	1.19147	−	1.04095i	1.19147	−	1.04095i
$657$	−3.38201	+	1.75521i	−3.38201	+	1.75521i
$658$		0			0
$659$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	−0.999552	−	0.0299155i	$-0.990476\pi$
$659$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	0.712376	−	0.701798i	$-0.247619\pi$
$660$		0			0
$661$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$661$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$662$	−1.84730	−	0.757093i	−1.84730	−	0.757093i
$663$		0			0
$664$	−1.09391	+	0.131548i	−1.09391	+	0.131548i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.388346	+	0.551683i	−0.388346	+	0.551683i	−0.963963	−	0.266037i	$-0.914286\pi$
$673$	−0.388346	+	0.551683i	−0.388346	+	0.551683i	0.575617	+	0.817719i	$0.304762\pi$
$674$	−1.20067	−	0.767016i	−1.20067	−	0.767016i
$675$	−1.62644	−	0.0486775i	−1.62644	−	0.0486775i
$676$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$677$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$677$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$678$	−0.223853	−	0.624705i	−0.223853	−	0.624705i
$679$		0			0
$680$		0			0
$681$	−1.52389	+	2.63946i	−1.52389	+	2.63946i
$682$		0			0
$683$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	−0.988831	−	0.149042i	$-0.952381\pi$
$683$	−0.0332580	−	0.443797i	−0.0332580	−	0.443797i	0.955573	−	0.294755i	$-0.0952381\pi$
$684$	2.32718	+	0.209450i	2.32718	+	0.209450i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.992847	+	0.119394i	0.992847	+	0.119394i
$689$		0			0
$690$		0			0
$691$	−1.41128	−	1.16041i	−1.41128	−	1.16041i	−0.963963	−	0.266037i	$-0.914286\pi$
$691$	−1.41128	−	1.16041i	−1.41128	−	1.16041i	−0.447313	−	0.894377i	$-0.647619\pi$
$692$		0			0
$693$		0			0
$694$	−0.193256	−	0.334729i	−0.193256	−	0.334729i
$695$		0			0
$696$		0			0
$697$	0.607142	+	3.08242i	0.607142	+	3.08242i
$698$		0			0
$699$	−0.0511607	+	0.00460455i	−0.0511607	+	0.00460455i
$700$		0			0
$701$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$701$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$702$		0			0
$703$		0			0
$704$	0.575617	+	0.817719i	0.575617	+	0.817719i
$705$		0			0
$706$	0.211849	−	1.27573i	0.211849	−	1.27573i
$707$		0			0
$708$	2.73842	+	0.935282i	2.73842	+	0.935282i
$709$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$709$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$710$		0			0
$711$		0			0
$712$	−0.108389	+	0.550282i	−0.108389	+	0.550282i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.61056	−	0.496793i	−1.61056	−	0.496793i
$717$		0			0
$718$		0			0
$719$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$719$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$720$		0			0
$721$		0			0
$722$	0.0848674	+	0.430867i	0.0848674	+	0.430867i
$723$	−3.25686	+	0.591032i	−3.25686	+	0.591032i
$724$		0			0
$725$		0			0
$726$	−0.382046	+	1.67385i	−0.382046	+	1.67385i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$	0.0514153	−	1.14485i	0.0514153	−	1.14485i
$730$		0			0
$731$	−1.19106	+	1.58882i	−1.19106	+	1.58882i
$732$		0			0
$733$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$733$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.176177	+	0.112546i	0.176177	+	0.112546i
$738$	−1.54080	+	2.66874i	−1.54080	+	2.66874i
$739$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.550897	+	0.834573i	$0.685714\pi$
$739$	−1.35991	+	1.42236i	−1.35991	+	1.42236i	−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$743$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.93348	−	0.931117i	1.93348	−	0.931117i
$748$	−1.97770	+	0.177996i	−1.97770	+	0.177996i
$749$		0			0
$750$		0			0
$751$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$751$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$752$		0			0
$753$	0.945834	−	1.43288i	0.945834	−	1.43288i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$757$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$758$	−1.79871	+	0.866214i	−1.79871	+	0.866214i
$759$		0			0
$760$		0			0
$761$	−0.551842	−	1.88890i	−0.551842	−	1.88890i	−0.447313	−	0.894377i	$-0.647619\pi$
$761$	−0.551842	−	1.88890i	−0.551842	−	1.88890i	−0.104528	−	0.994522i	$-0.533333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.67938	+	0.356963i	−1.67938	+	0.356963i
$769$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	−0.222521	−	0.974928i	$-0.571429\pi$
$769$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	0.0747301	−	0.997204i	$-0.476190\pi$
$770$		0			0
$771$	0.839429	−	2.13883i	0.839429	−	2.13883i
$772$	−0.686957	−	1.04070i	−0.686957	−	1.04070i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−1.90517	+	0.404957i	−1.90517	+	0.404957i
$775$		0			0
$776$	−1.44633	−	0.542816i	−1.44633	−	0.542816i
$777$		0			0
$778$		0			0
$779$	−1.84389	−	0.449980i	−1.84389	−	0.449980i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$785$		0			0
$786$	−0.295706	−	1.78070i	−0.295706	−	1.78070i
$787$	1.19147	+	0.921344i	1.19147	+	0.921344i	0.998210	−	0.0598042i	$-0.0190476\pi$
$787$	1.19147	+	0.921344i	1.19147	+	0.921344i	0.193256	+	0.981148i	$0.438095\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−1.57575	−	1.14485i	−1.57575	−	1.14485i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$797$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$798$		0			0
$799$		0			0
$800$	0.525684	+	0.850680i	0.525684	+	0.850680i
$801$	−0.146636	−	1.08251i	−0.146636	−	1.08251i
$802$	1.78928	+	0.551920i	1.78928	+	0.551920i
$803$	0.435317	+	1.90725i	0.435317	+	1.90725i
$804$	−0.296561	+	0.202192i	−0.296561	+	0.202192i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.202174	−	1.49251i	0.202174	−	1.49251i	−0.550897	−	0.834573i	$-0.685714\pi$
$809$	0.202174	−	1.49251i	0.202174	−	1.49251i	0.753071	−	0.657939i	$-0.228571\pi$
$810$		0			0
$811$	1.22256	+	0.544320i	1.22256	+	0.544320i	0.913545	−	0.406737i	$-0.133333\pi$
$811$	1.22256	+	0.544320i	1.22256	+	0.544320i	0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.05351	−	3.24237i	1.05351	−	3.24237i
$817$	−0.568474	−	1.05640i	−0.568474	−	1.05640i
$818$	−1.33688	−	0.971302i	−1.33688	−	0.971302i
$819$		0			0
$820$		0			0
$821$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$821$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$822$	−2.07871	−	2.45237i	−2.07871	−	2.45237i
$823$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$823$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$824$		0			0
$825$	−0.481465	+	1.64801i	−0.481465	+	1.64801i
$826$		0			0
$827$	−0.533704	+	0.412706i	−0.533704	+	0.412706i	−0.842721	−	0.538351i	$-0.819048\pi$
$827$	−0.533704	+	0.412706i	−0.533704	+	0.412706i	0.309017	+	0.951057i	$0.400000\pi$
$828$		0			0
$829$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$829$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.940958	−	1.74859i	0.940958	−	1.74859i
$834$	−0.237440	−	0.0973122i	−0.237440	−	0.0973122i
$835$		0			0
$836$	0.404676	−	1.12933i	0.404676	−	1.12933i
$837$		0			0
$838$	0.251348	−	0.0943324i	0.251348	−	0.0943324i
$839$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$839$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$840$		0			0
$841$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$842$		0			0
$843$	2.17177	−	2.56216i	2.17177	−	2.56216i
$844$	−0.654946	+	1.21709i	−0.654946	+	1.21709i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.81678	+	1.68295i	2.81678	+	1.68295i
$850$	−1.98481	+	0.0594030i	−1.98481	+	0.0594030i
$851$		0			0
$852$		0			0
$853$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$853$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$854$		0			0
$855$		0			0
$856$	−1.93516	−	0.174167i	−1.93516	−	0.174167i
$857$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.280427	+	0.959875i	$0.590476\pi$
$857$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.447313	+	0.894377i	$0.647619\pi$
$858$		0			0
$859$	1.05137			1.05137			0.525684	−	0.850680i	$-0.323810\pi$
$859$	1.05137			1.05137			0.525684	+	0.850680i	$0.323810\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$863$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$864$	1.39684	−	0.834573i	1.39684	−	0.834573i
$865$		0			0
$866$	1.79773	+	0.800400i	1.79773	+	0.800400i
$867$	3.38098	+	3.75496i	3.38098	+	3.75496i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.00758	+	0.0900136i	3.00758	+	0.0900136i
$874$		0			0
$875$		0			0
$876$	−3.30478	−	0.599729i	−3.30478	−	0.599729i
$877$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$877$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.717783	+	0.900071i	0.717783	+	0.900071i	0.998210	−	0.0598042i	$-0.0190476\pi$
$881$	0.717783	+	0.900071i	0.717783	+	0.900071i	−0.280427	+	0.959875i	$0.590476\pi$
$882$	1.82354	−	0.684386i	1.82354	−	0.684386i
$883$	1.19481	−	1.59382i	1.19481	−	1.59382i	0.525684	−	0.850680i	$-0.323810\pi$
$883$	1.19481	−	1.59382i	1.19481	−	1.59382i	0.669131	−	0.743145i	$-0.266667\pi$
$884$		0			0
$885$		0			0
$886$	0.260813	−	0.0636481i	0.260813	−	0.0636481i
$887$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$887$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.808360	+	0.249346i	0.808360	+	0.249346i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.264510	−	0.428040i	0.264510	−	0.428040i
$899$		0			0
$900$	−1.50447	−	1.23704i	−1.50447	−	1.23704i
$901$		0			0
$902$	1.12708	+	1.11034i	1.12708	+	1.11034i
$903$		0			0
$904$	0.119439	−	0.367595i	0.119439	−	0.367595i
$905$		0			0
$906$		0			0
$907$	−1.71613	+	1.02534i	−1.71613	+	1.02534i	−0.842721	+	0.538351i	$0.819048\pi$
$907$	−1.71613	+	1.02534i	−1.71613	+	1.02534i	−0.873408	+	0.486989i	$0.838095\pi$
$908$	−1.64257	+	0.673190i	−1.64257	+	0.673190i
$909$		0			0
$910$		0			0
$911$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$911$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$912$	1.50984	+	1.40093i	1.50984	+	1.40093i
$913$	−0.212928	−	1.08102i	−0.212928	−	1.08102i
$914$	0.411799	−	1.80421i	0.411799	−	1.80421i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.0483347	+	3.23070i	0.0483347	+	3.23070i
$919$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$919$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$920$		0			0
$921$	−2.13649	+	2.10477i	−2.13649	+	2.10477i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.77500	−	0.433167i	1.77500	−	0.433167i	0.791071	−	0.611724i	$-0.209524\pi$
$929$	1.77500	−	0.433167i	1.77500	−	0.433167i	0.983930	+	0.178557i	$0.0571429\pi$
$930$		0			0
$931$	0.719573	+	0.959875i	0.719573	+	0.959875i
$932$	−0.0252132	−	0.0161068i	−0.0252132	−	0.0161068i
$933$		0			0
$934$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$935$		0			0
$936$		0			0
$937$	−0.439476	+	0.245040i	−0.439476	+	0.245040i	−0.691063	−	0.722795i	$-0.742857\pi$
$937$	−0.439476	+	0.245040i	−0.439476	+	0.245040i	0.251587	+	0.967835i	$0.419048\pi$
$938$		0			0
$939$	1.48649	−	0.661829i	1.48649	−	0.661829i
$940$		0			0
$941$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$941$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$942$		0			0
$943$		0			0
$944$	0.928505	+	1.40662i	0.928505	+	1.40662i
$945$		0			0
$946$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$947$	−1.89265			−1.89265			−0.946327	−	0.323210i	$-0.895238\pi$
$947$	−1.89265			−1.89265			−0.946327	+	0.323210i	$0.895238\pi$
$948$		0			0
$949$		0			0
$950$	0.471490	−	1.10311i	0.471490	−	1.10311i
$951$		0			0
$952$		0			0
$953$	0.245256	−	0.109195i	0.245256	−	0.109195i	−0.280427	−	0.959875i	$-0.590476\pi$
$953$	0.245256	−	0.109195i	0.245256	−	0.109195i	0.525684	+	0.850680i	$0.323810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$962$		0			0
$963$	3.67652	−	0.897210i	3.67652	−	0.897210i
$964$	−1.71120	−	0.888084i	−1.71120	−	0.888084i
$965$		0			0
$966$		0			0
$967$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$967$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$968$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$969$	−3.90816	+	1.20551i	−3.90816	+	1.20551i
$970$		0			0
$971$	−1.28366	+	1.26460i	−1.28366	+	1.26460i	−0.337330	+	0.941386i	$0.609524\pi$
$971$	−1.28366	+	1.26460i	−1.28366	+	1.26460i	−0.946327	+	0.323210i	$0.895238\pi$
$972$	0.113006	−	0.133320i	0.113006	−	0.133320i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.854881	+	1.70929i	−0.854881	+	1.70929i	−0.163818	+	0.986491i	$0.552381\pi$
$977$	−0.854881	+	1.70929i	−0.854881	+	1.70929i	−0.691063	+	0.722795i	$0.742857\pi$
$978$	0.494061	−	2.16462i	0.494061	−	2.16462i
$979$	−0.556843	−	0.0669628i	−0.556843	−	0.0669628i
$980$		0			0
$981$		0			0
$982$	0.182592	+	1.73725i	0.182592	+	1.73725i
$983$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$983$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$984$	−2.51347	+	1.03012i	−2.51347	+	1.03012i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$991$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$992$		0			0
$993$	2.58126	+	2.25518i	2.58126	+	2.25518i
$994$		0			0
$995$		0			0
$996$	1.85033	+	0.393300i	1.85033	+	0.393300i
$997$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$997$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$998$	−1.53378	−	0.184444i	−1.53378	−	0.184444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.1219.1	yes	48
8.3	odd	2	CM	3784.1.em.b.1219.1	yes	48
11.5	even	5		3784.1.em.a.3283.1	yes	48
43.23	even	21		3784.1.em.a.1571.1	✓	48
88.27	odd	10		3784.1.em.a.3283.1	yes	48
344.195	odd	42		3784.1.em.a.1571.1	✓	48
473.324	even	105	inner	3784.1.em.b.3635.1	yes	48
3784.3635	odd	210	inner	3784.1.em.b.3635.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1571.1	✓	48	43.23	even	21
3784.1.em.a.1571.1	✓	48	344.195	odd	42
3784.1.em.a.3283.1	yes	48	11.5	even	5
3784.1.em.a.3283.1	yes	48	88.27	odd	10
3784.1.em.b.1219.1	yes	48	1.1	even	1	trivial
3784.1.em.b.1219.1	yes	48	8.3	odd	2	CM
3784.1.em.b.3635.1	yes	48	473.324	even	105	inner
3784.1.em.b.3635.1	yes	48	3784.3635	odd	210	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.550897 - 0.834573i) q^{2} +(0.431949 + 1.66167i) q^{3} +(-0.393025 + 0.919528i) q^{4} +(1.14883 - 1.27590i) q^{6} +(0.983930 - 0.178557i) q^{8} +(-1.70117 + 0.948526i) q^{9} +O(q^{10})\)	\(q+(-0.550897 - 0.834573i) q^{2} +(0.431949 + 1.66167i) q^{3} +(-0.393025 + 0.919528i) q^{4} +(1.14883 - 1.27590i) q^{6} +(0.983930 - 0.178557i) q^{8} +(-1.70117 + 0.948526i) q^{9} +(0.251587 + 0.967835i) q^{11} +(-1.69772 - 0.255890i) q^{12} +(-0.691063 - 0.722795i) q^{16} +(1.92908 - 0.470769i) q^{17} +(1.72878 + 0.897210i) q^{18} +(-0.231838 + 1.17703i) q^{19} +(0.669131 - 0.743145i) q^{22} +(0.721710 + 1.55784i) q^{24} +(0.712376 - 0.701798i) q^{25} +(-1.12447 - 1.17611i) q^{27} +(-0.222521 + 0.974928i) q^{32} +(-1.49955 + 0.836110i) q^{33} +(-1.45562 - 1.35061i) q^{34} +(-0.203594 - 1.93707i) q^{36} +(1.11004 - 0.454935i) q^{38} +(-0.0709825 + 1.58055i) q^{41} +(-0.772417 + 0.635116i) q^{43} +(-0.988831 - 0.149042i) q^{44} +(0.902545 - 1.46053i) q^{48} +(0.669131 - 0.743145i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(1.61553 + 3.00216i) q^{51} +(-0.362079 + 1.58637i) q^{54} +(-2.05598 + 0.123177i) q^{57} +(-1.65836 - 0.300947i) q^{59} +(0.936235 - 0.351375i) q^{64} +(1.52389 + 0.790876i) q^{66} +(0.153250 - 0.142195i) q^{67} +(-0.325292 + 1.95887i) q^{68} +(-1.50447 + 1.23704i) q^{72} +(1.95542 + 0.0585235i) q^{73} +(1.47387 + 0.880596i) q^{75} +(-0.991192 - 0.675783i) q^{76} +(0.444699 - 0.719627i) q^{81} +(1.35819 - 0.811480i) q^{82} +(-1.09982 - 0.0658919i) q^{83} +(0.955573 + 0.294755i) q^{86} +(0.420357 + 0.907359i) q^{88} +(-0.204903 + 0.522085i) q^{89} +(-1.71613 + 0.0513618i) q^{96} +(-1.32616 - 0.792344i) q^{97} +(-0.988831 - 0.149042i) q^{98} +(-1.34601 - 1.40781i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

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