LMFDB - Embedded newform 3784.1.em.b.2259.1

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			2259.1
Root			$-0.251587 - 0.967835i$ of defining polynomial
Character	$\chi$	$=$	3784.2259
Dual form			3784.1.em.b.531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0448648 - 0.998993i) q^{2} +(-0.784643 + 0.0470091i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(0.0821646 + 0.781744i) q^{6} +(0.134233 + 0.990950i) q^{8} +(-0.379392 + 0.0456236i) q^{9} +O(q^{10})$	\(q+(-0.0448648 - 0.998993i) q^{2} +(-0.784643 + 0.0470091i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(0.0821646 + 0.781744i) q^{6} +(0.134233 + 0.990950i) q^{8} +(-0.379392 + 0.0456236i) q^{9} +(0.998210 - 0.0598042i) q^{11} +(0.777271 - 0.117155i) q^{12} +(0.983930 - 0.178557i) q^{16} +(-0.543606 - 0.641322i) q^{17} +(0.0625990 + 0.376963i) q^{18} +(-1.00550 + 0.560638i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-0.151909 - 0.771232i) q^{24} +(-0.447313 + 0.894377i) q^{25} +(1.06896 - 0.193988i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(-0.780427 + 0.0938498i) q^{33} +(-0.616287 + 0.571831i) q^{34} +(0.373775 - 0.0794483i) q^{36} +(0.605185 + 0.979332i) q^{38} +(-1.87163 + 0.702435i) q^{41} +(0.251587 + 0.967835i) q^{43} +(-0.988831 + 0.149042i) q^{44} +(-0.763640 + 0.186357i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(0.456684 + 0.477654i) q^{51} +(-0.241751 - 1.05918i) q^{54} +(0.762602 - 0.487168i) q^{57} +(-0.207368 + 1.53085i) q^{59} +(-0.963963 + 0.266037i) q^{64} +(0.128769 + 0.775431i) q^{66} +(1.43407 + 1.33062i) q^{67} +(0.598905 + 0.590012i) q^{68} +(-0.0961377 - 0.369834i) q^{72} +(-0.512366 + 1.75378i) q^{73} +(0.308937 - 0.722795i) q^{75} +(0.951194 - 0.648513i) q^{76} +(-0.458402 + 0.111868i) q^{81} +(0.785698 + 1.83823i) q^{82} +(0.0756171 + 0.0483060i) q^{83} +(0.955573 - 0.294755i) q^{86} +(0.193256 + 0.981148i) q^{88} +(-0.246481 - 0.628023i) q^{89} +(0.220430 + 0.754510i) q^{96} +(-0.197760 + 0.462682i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(-0.375984 + 0.0682311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$2$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$3$	−0.784643	+	0.0470091i	−0.784643	+	0.0470091i	−0.447313	−	0.894377i	$-0.647619\pi$
$3$	−0.784643	+	0.0470091i	−0.784643	+	0.0470091i	−0.337330	+	0.941386i	$0.609524\pi$
$4$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$5$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$5$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$6$	0.0821646	+	0.781744i	0.0821646	+	0.781744i
$7$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$7$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$8$	0.134233	+	0.990950i	0.134233	+	0.990950i
$9$	−0.379392	+	0.0456236i	−0.379392	+	0.0456236i
$10$		0			0
$11$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$11$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$12$	0.777271	−	0.117155i	0.777271	−	0.117155i
$13$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$13$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$14$		0			0
$15$		0			0
$16$	0.983930	−	0.178557i	0.983930	−	0.178557i
$17$	−0.543606	−	0.641322i	−0.543606	−	0.641322i	0.420357	−	0.907359i	$-0.361905\pi$
$17$	−0.543606	−	0.641322i	−0.543606	−	0.641322i	−0.963963	+	0.266037i	$0.914286\pi$
$18$	0.0625990	+	0.376963i	0.0625990	+	0.376963i
$19$	−1.00550	+	0.560638i	−1.00550	+	0.560638i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	−1.00550	+	0.560638i	−1.00550	+	0.560638i	−0.104528	+	0.994522i	$0.533333\pi$
$20$		0			0
$21$		0			0
$22$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$23$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$23$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$24$	−0.151909	−	0.771232i	−0.151909	−	0.771232i
$25$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$26$		0			0
$27$	1.06896	−	0.193988i	1.06896	−	0.193988i
$28$		0			0
$29$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$29$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$30$		0			0
$31$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$31$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$	−0.780427	+	0.0938498i	−0.780427	+	0.0938498i
$34$	−0.616287	+	0.571831i	−0.616287	+	0.571831i
$35$		0			0
$36$	0.373775	−	0.0794483i	0.373775	−	0.0794483i
$37$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$37$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$38$	0.605185	+	0.979332i	0.605185	+	0.979332i
$39$		0			0
$40$		0			0
$41$	−1.87163	+	0.702435i	−1.87163	+	0.702435i	−0.925304	+	0.379225i	$0.876190\pi$
$41$	−1.87163	+	0.702435i	−1.87163	+	0.702435i	−0.946327	+	0.323210i	$0.895238\pi$
$42$		0			0
$43$	0.251587	+	0.967835i	0.251587	+	0.967835i
$43$	0.251587	+	0.967835i	0.251587	+	0.967835i
$44$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$45$		0			0
$46$		0			0
$47$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$47$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$48$	−0.763640	+	0.186357i	−0.763640	+	0.186357i
$49$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$50$	0.913545	+	0.406737i	0.913545	+	0.406737i
$51$	0.456684	+	0.477654i	0.456684	+	0.477654i
$52$		0			0
$53$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$53$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$54$	−0.241751	−	1.05918i	−0.241751	−	1.05918i
$55$		0			0
$56$		0			0
$57$	0.762602	−	0.487168i	0.762602	−	0.487168i
$58$		0			0
$59$	−0.207368	+	1.53085i	−0.207368	+	1.53085i	0.525684	+	0.850680i	$0.323810\pi$
$59$	−0.207368	+	1.53085i	−0.207368	+	1.53085i	−0.733052	+	0.680173i	$0.761905\pi$
$60$		0			0
$61$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$61$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$62$		0			0
$63$		0			0
$64$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$65$		0			0
$66$	0.128769	+	0.775431i	0.128769	+	0.775431i
$67$	1.43407	+	1.33062i	1.43407	+	1.33062i	0.858449	+	0.512899i	$0.171429\pi$
$67$	1.43407	+	1.33062i	1.43407	+	1.33062i	0.575617	+	0.817719i	$0.304762\pi$
$68$	0.598905	+	0.590012i	0.598905	+	0.590012i
$69$		0			0
$70$		0			0
$71$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$71$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$72$	−0.0961377	−	0.369834i	−0.0961377	−	0.369834i
$73$	−0.512366	+	1.75378i	−0.512366	+	1.75378i	0.134233	+	0.990950i	$0.457143\pi$
$73$	−0.512366	+	1.75378i	−0.512366	+	1.75378i	−0.646600	+	0.762830i	$0.723810\pi$
$74$		0			0
$75$	0.308937	−	0.722795i	0.308937	−	0.722795i
$76$	0.951194	−	0.648513i	0.951194	−	0.648513i
$77$		0			0
$78$		0			0
$79$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$79$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$80$		0			0
$81$	−0.458402	+	0.111868i	−0.458402	+	0.111868i
$82$	0.785698	+	1.83823i	0.785698	+	1.83823i
$83$	0.0756171	+	0.0483060i	0.0756171	+	0.0483060i	0.575617	−	0.817719i	$-0.304762\pi$
$83$	0.0756171	+	0.0483060i	0.0756171	+	0.0483060i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.955573	−	0.294755i	0.955573	−	0.294755i
$87$		0			0
$88$	0.193256	+	0.981148i	0.193256	+	0.981148i
$89$	−0.246481	−	0.628023i	−0.246481	−	0.628023i	0.753071	−	0.657939i	$-0.228571\pi$
$89$	−0.246481	−	0.628023i	−0.246481	−	0.628023i	−0.999552	+	0.0299155i	$0.990476\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.220430	+	0.754510i	0.220430	+	0.754510i
$97$	−0.197760	+	0.462682i	−0.197760	+	0.462682i	−0.988831	−	0.149042i	$-0.952381\pi$
$97$	−0.197760	+	0.462682i	−0.197760	+	0.462682i	0.791071	+	0.611724i	$0.209524\pi$
$98$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$99$	−0.375984	+	0.0682311i	−0.375984	+	0.0682311i
$100$	0.365341	−	0.930874i	0.365341	−	0.930874i
$101$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$101$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$102$	0.456684	−	0.477654i	0.456684	−	0.477654i
$103$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$103$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.712420	+	1.07927i	0.712420	+	1.07927i	0.992847	+	0.119394i	$0.0380952\pi$
$107$	0.712420	+	1.07927i	0.712420	+	1.07927i	−0.280427	+	0.959875i	$0.590476\pi$
$108$	−1.04727	+	0.289028i	−1.04727	+	0.289028i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.20716	−	1.26259i	1.20716	−	1.26259i	0.251587	−	0.967835i	$-0.419048\pi$
$113$	1.20716	−	1.26259i	1.20716	−	1.26259i	0.955573	−	0.294755i	$-0.0952381\pi$
$114$	−0.520892	−	0.739977i	−0.520892	−	0.739977i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.53861	+	0.138478i	1.53861	+	0.138478i
$119$		0			0
$120$		0			0
$121$	0.992847	−	0.119394i	0.992847	−	0.119394i
$122$		0			0
$123$	1.43554	−	0.639145i	1.43554	−	0.639145i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$127$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$128$	0.309017	+	0.951057i	0.309017	+	0.951057i
$129$	−0.242903	−	0.747578i	−0.242903	−	0.747578i
$130$		0			0
$131$	1.21143	+	1.51908i	1.21143	+	1.51908i	0.791071	+	0.611724i	$0.209524\pi$
$131$	1.21143	+	1.51908i	1.21143	+	1.51908i	0.420357	+	0.907359i	$0.361905\pi$
$132$	0.768873	−	0.163429i	0.768873	−	0.163429i
$133$		0			0
$134$	1.26494	−	1.49232i	1.26494	−	1.49232i
$135$		0			0
$136$	0.562548	−	0.624773i	0.562548	−	0.624773i
$137$	−0.913584	+	1.69772i	−0.913584	+	1.69772i	−0.222521	+	0.974928i	$0.571429\pi$
$137$	−0.913584	+	1.69772i	−0.913584	+	1.69772i	−0.691063	+	0.722795i	$0.742857\pi$
$138$		0			0
$139$	0.118234	+	0.0914284i	0.118234	+	0.0914284i	0.669131	−	0.743145i	$-0.266667\pi$
$139$	0.118234	+	0.0914284i	0.118234	+	0.0914284i	−0.550897	+	0.834573i	$0.685714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.365149	+	0.112633i	−0.365149	+	0.112633i
$145$		0			0
$146$	1.77500	+	0.433167i	1.77500	+	0.433167i
$147$	0.128769	+	0.775431i	0.128769	+	0.775431i
$148$		0			0
$149$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$149$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$150$	−0.735927	−	0.276198i	−0.735927	−	0.276198i
$151$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$151$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$152$	−0.690535	−	0.921141i	−0.690535	−	0.921141i
$153$	0.235499	+	0.218511i	0.235499	+	0.218511i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$157$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.132321	+	0.452922i	0.132321	+	0.452922i
$163$	−1.83737	+	0.220952i	−1.83737	+	0.220952i	−0.963963	−	0.266037i	$-0.914286\pi$
$163$	−1.83737	+	0.220952i	−1.83737	+	0.220952i	−0.873408	+	0.486989i	$0.838095\pi$
$164$	1.80113	−	0.867379i	1.80113	−	0.867379i
$165$		0			0
$166$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i
$167$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$167$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$168$		0			0
$169$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$170$		0			0
$171$	0.355899	−	0.258576i	0.355899	−	0.258576i
$172$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$173$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$173$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$174$		0			0
$175$		0			0
$176$	0.971490	−	0.237080i	0.971490	−	0.237080i
$177$	0.0907460	−	1.21092i	0.0907460	−	1.21092i
$178$	−0.616333	+	0.274409i	−0.616333	+	0.274409i
$179$	1.51108	−	0.321189i	1.51108	−	0.321189i	0.623490	−	0.781831i	$-0.285714\pi$
$179$	1.51108	−	0.321189i	1.51108	−	0.321189i	0.887586	+	0.460642i	$0.152381\pi$
$180$		0			0
$181$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$181$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.580986	−	0.607664i	−0.580986	−	0.607664i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$191$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$192$	0.743861	−	0.254059i	0.743861	−	0.254059i
$193$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	0.753071	+	0.657939i	$0.228571\pi$
$193$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	−0.809017	+	0.587785i	$0.800000\pi$
$194$	0.471089	+	0.176803i	0.471089	+	0.176803i
$195$		0			0
$196$	0.193256	+	0.981148i	0.193256	+	0.981148i
$197$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$197$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$198$	0.0850309	+	0.372545i	0.0850309	+	0.372545i
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$201$	−1.18778	−	0.976647i	−1.18778	−	0.976647i
$202$		0			0
$203$		0			0
$204$	−0.497662	−	0.434795i	−0.497662	−	0.434795i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.970169	+	0.619768i	−0.970169	+	0.619768i
$210$		0			0
$211$	1.48194	−	1.29473i	1.48194	−	1.29473i	0.623490	−	0.781831i	$-0.285714\pi$
$211$	1.48194	−	1.29473i	1.48194	−	1.29473i	0.858449	−	0.512899i	$-0.171429\pi$
$212$		0			0
$213$		0			0
$214$	1.04622	−	0.760123i	1.04622	−	0.760123i
$215$		0			0
$216$	0.335722	+	1.03325i	0.335722	+	1.03325i
$217$		0			0
$218$		0			0
$219$	0.319581	−	1.40018i	0.319581	−	1.40018i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$223$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$224$		0			0
$225$	0.128902	−	0.359728i	0.128902	−	0.359728i
$226$	−1.31548	−	1.14930i	−1.31548	−	1.14930i
$227$	0.146556	+	0.293030i	0.146556	+	0.293030i	0.955573	−	0.294755i	$-0.0952381\pi$
$227$	0.146556	+	0.293030i	0.146556	+	0.293030i	−0.809017	+	0.587785i	$0.800000\pi$
$228$	−0.715862	+	0.553566i	−0.715862	+	0.553566i
$229$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$229$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.854598	−	0.841907i	−0.854598	−	0.841907i	0.134233	−	0.990950i	$-0.457143\pi$
$233$	−0.854598	−	0.841907i	−0.854598	−	0.841907i	−0.988831	+	0.149042i	$0.952381\pi$
$234$		0			0
$235$		0			0
$236$	0.0693087	−	1.54328i	0.0693087	−	1.54328i
$237$		0			0
$238$		0			0
$239$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$239$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$240$		0			0
$241$	−0.0823372	−	1.09871i	−0.0823372	−	1.09871i	−0.873408	−	0.486989i	$-0.838095\pi$
$241$	−0.0823372	−	1.09871i	−0.0823372	−	1.09871i	0.791071	−	0.611724i	$-0.209524\pi$
$242$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$243$	−0.683730	+	0.210903i	−0.683730	+	0.210903i
$244$		0			0
$245$		0			0
$246$	−0.702906	−	1.40542i	−0.702906	−	1.40542i
$247$		0			0
$248$		0			0
$249$	−0.0616032	−	0.0343483i	−0.0616032	−	0.0343483i
$250$		0			0
$251$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$251$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.936235	−	0.351375i	0.936235	−	0.351375i
$257$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$257$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$258$	−0.735927	+	0.276198i	−0.735927	+	0.276198i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.46320	−	1.27836i	1.46320	−	1.27836i
$263$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$263$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$264$	−0.197760	−	0.760767i	−0.197760	−	0.760767i
$265$		0			0
$266$		0			0
$267$	0.222922	+	0.481187i	0.222922	+	0.481187i
$268$	−1.54757	−	1.19671i	−1.54757	−	1.19671i
$269$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$269$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$270$		0			0
$271$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$271$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$272$	−0.649382	−	0.533951i	−0.649382	−	0.533951i
$273$		0			0
$274$	1.73700	+	0.836496i	1.73700	+	0.836496i
$275$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$276$		0			0
$277$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$277$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$278$	0.0860318	−	0.122216i	0.0860318	−	0.122216i
$279$		0			0
$280$		0			0
$281$	−1.72903	+	0.590533i	−1.72903	+	0.590533i	−0.995974	−	0.0896393i	$-0.971429\pi$
$281$	−1.72903	+	0.590533i	−1.72903	+	0.590533i	−0.733052	+	0.680173i	$0.761905\pi$
$282$		0			0
$283$	−0.854881	+	1.70929i	−0.854881	+	1.70929i	−0.163818	+	0.986491i	$0.552381\pi$
$283$	−0.854881	+	1.70929i	−0.854881	+	1.70929i	−0.691063	+	0.722795i	$0.742857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.128902	+	0.359728i	0.128902	+	0.359728i
$289$	0.0480313	−	0.289238i	0.0480313	−	0.289238i
$290$		0			0
$291$	0.133421	−	0.372337i	0.133421	−	0.372337i
$292$	0.353096	−	1.79265i	0.353096	−	1.79265i
$293$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$293$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$294$	0.768873	−	0.163429i	0.768873	−	0.163429i
$295$		0			0
$296$		0			0
$297$	1.05545	−	0.257569i	1.05545	−	0.257569i
$298$		0			0
$299$		0			0
$300$	−0.242903	+	0.747578i	−0.242903	+	0.747578i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.889233	+	0.731167i	−0.889233	+	0.731167i
$305$		0			0
$306$	0.207725	−	0.245065i	0.207725	−	0.245065i
$307$	−0.992847	+	1.71966i	−0.992847	+	1.71966i	−0.393025	+	0.919528i	$0.628571\pi$
$307$	−0.992847	+	1.71966i	−0.992847	+	1.71966i	−0.599822	+	0.800134i	$0.704762\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$311$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$312$		0			0
$313$	−0.984593	+	0.969973i	−0.984593	+	0.969973i	−0.999552	−	0.0299155i	$-0.990476\pi$
$313$	−0.984593	+	0.969973i	−0.984593	+	0.969973i	0.0149594	+	0.999888i	$0.495238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$317$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.609731	−	0.813351i	−0.609731	−	0.813351i
$322$		0			0
$323$	0.906144	+	0.340081i	0.906144	+	0.340081i
$324$	0.446529	−	0.152508i	0.446529	−	0.152508i
$325$		0			0
$326$	0.303163	+	1.82561i	0.303163	+	1.82561i
$327$		0			0
$328$	−0.947313	−	1.76040i	−0.947313	−	1.76040i
$329$		0			0
$330$		0			0
$331$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.999552	−	0.0299155i	$-0.990476\pi$
$331$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.393025	−	0.919528i	$-0.628571\pi$
$332$	−0.0796428	−	0.0413333i	−0.0796428	−	0.0413333i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.598622	+	0.664837i	−0.598622	+	0.664837i	−0.963963	−	0.266037i	$-0.914286\pi$
$337$	−0.598622	+	0.664837i	−0.598622	+	0.664837i	0.365341	+	0.930874i	$0.380952\pi$
$338$	0.669131	+	0.743145i	0.669131	+	0.743145i
$339$	−0.887836	+	1.04743i	−0.887836	+	1.04743i
$340$		0			0
$341$		0			0
$342$	−0.274283	−	0.343940i	−0.274283	−	0.343940i
$343$		0			0
$344$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$345$		0			0
$346$		0			0
$347$	1.47208	+	0.940400i	1.47208	+	0.940400i	0.998210	+	0.0598042i	$0.0190476\pi$
$347$	1.47208	+	0.940400i	1.47208	+	0.940400i	0.473869	+	0.880596i	$0.342857\pi$
$348$		0			0
$349$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$349$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$350$		0			0
$351$		0			0
$352$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$353$	1.35659	−	1.25873i	1.35659	−	1.25873i	0.420357	−	0.907359i	$-0.361905\pi$
$353$	1.35659	−	1.25873i	1.35659	−	1.25873i	0.936235	−	0.351375i	$-0.114286\pi$
$354$	−1.21377	−	0.0363269i	−1.21377	−	0.0363269i
$355$		0			0
$356$	0.301784	+	0.603401i	0.301784	+	0.603401i
$357$		0			0
$358$	−0.388660	−	1.49514i	−0.388660	−	1.49514i
$359$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$359$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$360$		0			0
$361$	0.171026	−	0.276760i	0.171026	−	0.276760i
$362$		0			0
$363$	−0.773418	+	0.140355i	−0.773418	+	0.140355i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$367$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$368$		0			0
$369$	0.678034	−	0.351889i	0.678034	−	0.351889i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$373$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$374$	−0.580986	+	0.607664i	−0.580986	+	0.607664i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.798678	+	1.48419i	−0.798678	+	1.48419i	0.0747301	+	0.997204i	$0.476190\pi$
$379$	−0.798678	+	1.48419i	−0.798678	+	1.48419i	−0.873408	+	0.486989i	$0.838095\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$383$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$384$	−0.287176	−	0.731713i	−0.287176	−	0.731713i
$385$		0			0
$386$	1.24698			1.24698
$387$	−0.139606	−	0.355710i	−0.139606	−	0.355710i
$388$	0.155489	−	0.478546i	0.155489	−	0.478546i
$389$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$389$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$390$		0			0
$391$		0			0
$392$	0.971490	−	0.237080i	0.971490	−	0.237080i
$393$	−1.02195	−	1.13499i	−1.02195	−	1.13499i
$394$		0			0
$395$		0			0
$396$	0.368355	−	0.101659i	0.368355	−	0.101659i
$397$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$397$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$398$		0			0
$399$		0			0
$400$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$401$	−0.485041	−	1.86591i	−0.485041	−	1.86591i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.485041	−	1.86591i	−0.485041	−	1.86591i	0.0149594	−	0.999888i	$-0.495238\pi$
$402$	−0.922374	+	1.23040i	−0.922374	+	1.23040i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.412029	+	0.516668i	−0.412029	+	0.516668i
$409$	−1.59293	+	0.439620i	−1.59293	+	0.439620i	−0.946327	−	0.323210i	$-0.895238\pi$
$409$	−1.59293	+	0.439620i	−1.59293	+	0.439620i	−0.646600	+	0.762830i	$0.723810\pi$
$410$		0			0
$411$	0.637029	−	1.37505i	0.637029	−	1.37505i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0970692	−	0.0661806i	−0.0970692	−	0.0661806i
$418$	0.662670	+	0.941386i	0.662670	+	0.941386i
$419$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	−0.963963	−	0.266037i	$-0.914286\pi$
$419$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$420$		0			0
$421$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$421$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$422$	−1.35991	−	1.42236i	−1.35991	−	1.42236i
$423$		0			0
$424$		0			0
$425$	0.816746	−	0.199317i	0.816746	−	0.199317i
$426$		0			0
$427$		0			0
$428$	−0.806297	−	1.01106i	−0.806297	−	1.01106i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	1.01714	−	0.381741i	1.01714	−	0.381741i
$433$	−0.207368	+	0.170507i	−0.207368	+	0.170507i	−0.733052	−	0.680173i	$-0.761905\pi$
$433$	−0.207368	+	0.170507i	−0.207368	+	0.170507i	0.525684	+	0.850680i	$0.323810\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.41310	−	0.256441i	−1.41310	−	0.256441i
$439$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$439$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$440$		0			0
$441$	0.0850309	+	0.372545i	0.0850309	+	0.372545i
$442$		0			0
$443$	0.749728	−	0.579754i	0.749728	−	0.579754i	−0.163818	−	0.986491i	$-0.552381\pi$
$443$	0.749728	−	0.579754i	0.749728	−	0.579754i	0.913545	+	0.406737i	$0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.385820	+	1.95878i	0.385820	+	1.95878i	0.251587	+	0.967835i	$0.419048\pi$
$449$	0.385820	+	1.95878i	0.385820	+	1.95878i	0.134233	+	0.990950i	$0.457143\pi$
$450$	−0.365149	−	0.112633i	−0.365149	−	0.112633i
$451$	−1.82627	+	0.813109i	−1.82627	+	0.813109i
$452$	−1.08912	+	1.36572i	−1.08912	+	1.36572i
$453$		0			0
$454$	0.286160	−	0.159555i	0.286160	−	0.159555i
$455$		0			0
$456$	0.585126	+	0.690306i	0.585126	+	0.690306i
$457$	1.03447	−	0.187729i	1.03447	−	0.187729i	0.365341	−	0.930874i	$-0.380952\pi$
$457$	1.03447	−	0.187729i	1.03447	−	0.187729i	0.669131	+	0.743145i	$0.266667\pi$
$458$		0			0
$459$	−0.705501	−	0.580095i	−0.705501	−	0.580095i
$460$		0			0
$461$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$461$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$462$		0			0
$463$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$463$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$464$		0			0
$465$		0			0
$466$	−0.802718	+	0.891509i	−0.802718	+	0.891509i
$467$	−0.172731	−	1.64343i	−0.172731	−	1.64343i	−0.646600	−	0.762830i	$-0.723810\pi$
$467$	−0.172731	−	1.64343i	−0.172731	−	1.64343i	0.473869	−	0.880596i	$-0.342857\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.54483			−1.54483
$473$	0.309017	+	0.951057i	0.309017	+	0.951057i
$474$		0			0
$475$	−0.0516499	−	1.15007i	−0.0516499	−	1.15007i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$479$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$480$		0			0
$481$		0			0
$482$	−1.09391	+	0.131548i	−1.09391	+	0.131548i
$483$		0			0
$484$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$485$		0			0
$486$	0.241366	+	0.673579i	0.241366	+	0.673579i
$487$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$487$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$488$		0			0
$489$	1.43129	−	0.259742i	1.43129	−	0.259742i
$490$		0			0
$491$	−0.325292	−	1.95887i	−0.325292	−	1.95887i	−0.280427	−	0.959875i	$-0.590476\pi$
$491$	−0.325292	−	1.95887i	−0.325292	−	1.95887i	−0.0448648	−	0.998993i	$-0.514286\pi$
$492$	−1.37247	+	0.765253i	−1.37247	+	0.765253i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.0315499	+	0.0630822i	−0.0315499	+	0.0630822i
$499$	−0.465589	+	0.190816i	−0.465589	+	0.190816i	−0.599822	−	0.800134i	$-0.704762\pi$
$499$	−0.465589	+	0.190816i	−0.465589	+	0.190816i	0.134233	+	0.990950i	$0.457143\pi$
$500$		0			0
$501$		0			0
$502$	−0.998210	−	0.0598042i	−0.998210	−	0.0598042i
$503$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$503$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.576215	−	0.534650i	0.576215	−	0.534650i
$508$		0			0
$509$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$509$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$510$		0			0
$511$		0			0
$512$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$513$	−0.966080	+	0.794354i	−0.966080	+	0.794354i
$514$	−0.195726	+	0.0734573i	−0.195726	+	0.0734573i
$515$		0			0
$516$	0.308937	+	0.722795i	0.308937	+	0.722795i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.88759	−	0.460642i	1.88759	−	0.460642i	0.887586	−	0.460642i	$-0.152381\pi$
$521$	1.88759	−	0.460642i	1.88759	−	0.460642i	1.00000			$0$
$522$		0			0
$523$	−0.512366	−	0.228120i	−0.512366	−	0.228120i	0.134233	−	0.990950i	$-0.457143\pi$
$523$	−0.512366	−	0.228120i	−0.512366	−	0.228120i	−0.646600	+	0.762830i	$0.723810\pi$
$524$	−1.34272	−	1.40438i	−1.34272	−	1.40438i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.751128	+	0.231692i	−0.751128	+	0.231692i
$529$	0.826239	+	0.563320i	0.826239	+	0.563320i
$530$		0			0
$531$	0.00883084	−	0.590254i	0.00883084	−	0.590254i
$532$		0			0
$533$		0			0
$534$	0.470701	−	0.244286i	0.470701	−	0.244286i
$535$		0			0
$536$	−1.12608	+	1.59970i	−1.12608	+	1.59970i
$537$	−1.17056	+	0.323053i	−1.17056	+	0.323053i
$538$		0			0
$539$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$540$		0			0
$541$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$541$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$542$		0			0
$543$		0			0
$544$	−0.504279	+	0.672684i	−0.504279	+	0.672684i
$545$		0			0
$546$		0			0
$547$	−0.0439796	+	0.264840i	−0.0439796	+	0.264840i	−0.999552	−	0.0299155i	$-0.990476\pi$
$547$	−0.0439796	+	0.264840i	−0.0439796	+	0.264840i	0.955573	+	0.294755i	$0.0952381\pi$
$548$	0.757723	−	1.77278i	0.757723	−	1.77278i
$549$		0			0
$550$	0.936235	+	0.351375i	0.936235	+	0.351375i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.125953	−	0.0804620i	−0.125953	−	0.0804620i
$557$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$557$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.484433	+	0.449488i	0.484433	+	0.449488i
$562$	0.667511	+	1.70079i	0.667511	+	1.70079i
$563$	0.713714	−	0.623553i	0.713714	−	0.623553i	−0.222521	−	0.974928i	$-0.571429\pi$
$563$	0.713714	−	0.623553i	0.713714	−	0.623553i	0.936235	+	0.351375i	$0.114286\pi$
$564$		0			0
$565$		0			0
$566$	1.74592	+	0.777333i	1.74592	+	0.777333i
$567$		0			0
$568$		0			0
$569$	−0.559851	−	1.91631i	−0.559851	−	1.91631i	−0.337330	−	0.941386i	$-0.609524\pi$
$569$	−0.559851	−	1.91631i	−0.559851	−	1.91631i	−0.222521	−	0.974928i	$-0.571429\pi$
$570$		0			0
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.353582	−	0.144912i	0.353582	−	0.144912i
$577$	−0.977937	+	0.507533i	−0.977937	+	0.507533i	−0.873408	−	0.486989i	$-0.838095\pi$
$577$	−0.977937	+	0.507533i	−0.977937	+	0.507533i	−0.104528	+	0.994522i	$0.533333\pi$
$578$	−0.291102	−	0.0350063i	−0.291102	−	0.0350063i
$579$	−0.0146630	−	0.980079i	−0.0146630	−	0.980079i
$580$		0			0
$581$		0			0
$582$	−0.377948	−	0.116581i	−0.377948	−	0.116581i
$583$		0			0
$584$	−1.80668	−	0.272314i	−1.80668	−	0.272314i
$585$		0			0
$586$		0			0
$587$	−0.188593	−	0.267914i	−0.188593	−	0.267914i	0.712376	−	0.701798i	$-0.247619\pi$
$587$	−0.188593	−	0.267914i	−0.188593	−	0.267914i	−0.900969	+	0.433884i	$0.857143\pi$
$588$	−0.197760	−	0.760767i	−0.197760	−	0.760767i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.0219320	+	0.0203500i	−0.0219320	+	0.0203500i	−0.691063	−	0.722795i	$-0.742857\pi$
$593$	−0.0219320	+	0.0203500i	−0.0219320	+	0.0203500i	0.669131	+	0.743145i	$0.266667\pi$
$594$	−0.304662	−	1.04283i	−0.304662	−	1.04283i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$599$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$600$	0.757723	+	0.209118i	0.757723	+	0.209118i
$601$	−0.520830	−	1.60295i	−0.520830	−	1.60295i	−0.772417	−	0.635116i	$-0.780952\pi$
$601$	−0.520830	−	1.60295i	−0.520830	−	1.60295i	0.251587	−	0.967835i	$-0.419048\pi$
$602$		0			0
$603$	−0.604781	−	0.439399i	−0.604781	−	0.439399i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$607$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$608$	0.770326	+	0.855534i	0.770326	+	0.855534i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.254138	−	0.196521i	−0.254138	−	0.196521i
$613$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$613$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$614$	1.76247	+	0.914695i	1.76247	+	0.914695i
$615$		0			0
$616$		0			0
$617$	1.64062	−	0.506064i	1.64062	−	0.506064i	0.669131	−	0.743145i	$-0.266667\pi$
$617$	1.64062	−	0.506064i	1.64062	−	0.506064i	0.971490	+	0.237080i	$0.0761905\pi$
$618$		0			0
$619$	−1.93516	−	0.472252i	−1.93516	−	0.472252i	−0.988831	−	0.149042i	$-0.952381\pi$
$619$	−1.93516	−	0.472252i	−1.93516	−	0.472252i	−0.946327	−	0.323210i	$-0.895238\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$626$	1.01317	+	0.940084i	1.01317	+	0.940084i
$627$	0.732102	−	0.531903i	0.732102	−	0.531903i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$631$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$632$		0			0
$633$	−1.10193	+	1.08557i	−1.10193	+	1.08557i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.22308	+	0.730754i	1.22308	+	0.730754i	0.971490	−	0.237080i	$-0.0761905\pi$
$641$	1.22308	+	0.730754i	1.22308	+	0.730754i	0.251587	+	0.967835i	$0.419048\pi$
$642$	−0.785177	+	0.645607i	−0.785177	+	0.645607i
$643$	1.82445	+	0.503516i	1.82445	+	0.503516i	0.998210	−	0.0598042i	$-0.0190476\pi$
$643$	1.82445	+	0.503516i	1.82445	+	0.503516i	0.826239	+	0.563320i	$0.190476\pi$
$644$		0			0
$645$		0			0
$646$	0.299085	−	0.920489i	0.299085	−	0.920489i
$647$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$647$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$648$	−0.172388	−	0.439237i	−0.172388	−	0.439237i
$649$	−0.115446	+	1.54051i	−0.115446	+	1.54051i
$650$		0			0
$651$		0			0
$652$	1.81017	−	0.384763i	1.81017	−	0.384763i
$653$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$653$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$654$		0			0
$655$		0			0
$656$	−1.71613	+	1.02534i	−1.71613	+	1.02534i
$657$	0.114374	−	0.688746i	0.114374	−	0.688746i
$658$		0			0
$659$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.280427	+	0.959875i	$0.590476\pi$
$659$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.447313	+	0.894377i	$0.647619\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	−0.886009	+	1.43377i	−0.886009	+	1.43377i
$663$		0			0
$664$	−0.0377185	+	0.0814170i	−0.0377185	+	0.0814170i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.49722	−	0.511364i	−1.49722	−	0.511364i	−0.550897	−	0.834573i	$-0.685714\pi$
$673$	−1.49722	−	0.511364i	−1.49722	−	0.511364i	−0.946327	+	0.323210i	$0.895238\pi$
$674$	0.691025	+	0.568191i	0.691025	+	0.568191i
$675$	−0.304662	+	1.04283i	−0.304662	+	1.04283i
$676$	0.712376	−	0.701798i	0.712376	−	0.701798i
$677$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$677$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$678$	1.08621	+	0.839950i	1.08621	+	0.839950i
$679$		0			0
$680$		0			0
$681$	−0.128769	−	0.223035i	−0.128769	−	0.223035i
$682$		0			0
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$684$	−0.331288	+	0.289438i	−0.331288	+	0.289438i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.420357	+	0.907359i	0.420357	+	0.907359i
$689$		0			0
$690$		0			0
$691$	0.336689	−	1.29522i	0.336689	−	1.29522i	−0.550897	−	0.834573i	$-0.685714\pi$
$691$	0.336689	−	1.29522i	0.336689	−	1.29522i	0.887586	−	0.460642i	$-0.152381\pi$
$692$		0			0
$693$		0			0
$694$	0.873408	−	1.51279i	0.873408	−	1.51279i
$695$		0			0
$696$		0			0
$697$	1.46792	+	0.818471i	1.46792	+	0.818471i
$698$		0			0
$699$	0.710131	+	0.620423i	0.710131	+	0.620423i
$700$		0			0
$701$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$701$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$702$		0			0
$703$		0			0
$704$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$705$		0			0
$706$	−1.31833	−	1.29875i	−1.31833	−	1.29875i
$707$		0			0
$708$	0.0181655	+	1.21418i	0.0181655	+	1.21418i
$709$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$709$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$710$		0			0
$711$		0			0
$712$	0.589254	−	0.328552i	0.589254	−	0.328552i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.47620	+	0.455348i	−1.47620	+	0.455348i
$717$		0			0
$718$		0			0
$719$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$719$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$720$		0			0
$721$		0			0
$722$	−0.284155	−	0.158437i	−0.284155	−	0.158437i
$723$	0.116255	+	0.858227i	0.116255	+	0.858227i
$724$		0			0
$725$		0			0
$726$	0.174913	+	0.766342i	0.174913	+	0.766342i
$727$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$727$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	0.968336	−	0.363423i	0.968336	−	0.363423i
$730$		0			0
$731$	0.483930	−	0.687469i	0.483930	−	0.687469i
$732$		0			0
$733$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$733$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.51108	+	1.24247i	1.51108	+	1.24247i
$738$	−0.381954	−	0.661564i	−0.381954	−	0.661564i
$739$	0.264152	+	0.0479366i	0.264152	+	0.0479366i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.264152	+	0.0479366i	0.264152	+	0.0479366i	−0.0448648	+	0.998993i	$0.514286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$743$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0308924	−	0.0148770i	−0.0308924	−	0.0148770i
$748$	0.633118	+	0.553139i	0.633118	+	0.553139i
$749$		0			0
$750$		0			0
$751$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$751$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$752$		0			0
$753$	−0.0352660	+	0.785259i	−0.0352660	+	0.785259i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$757$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$758$	1.51853	+	0.731286i	1.51853	+	0.731286i
$759$		0			0
$760$		0			0
$761$	−0.0905618	−	0.252731i	−0.0905618	−	0.252731i	0.887586	−	0.460642i	$-0.152381\pi$
$761$	−0.0905618	−	0.252731i	−0.0905618	−	0.252731i	−0.978148	+	0.207912i	$0.933333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.718092	+	0.319715i	−0.718092	+	0.319715i
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	0.0600362	+	0.152970i	0.0600362	+	0.152970i
$772$	−0.0559455	−	1.24572i	−0.0559455	−	1.24572i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	−0.349089	+	0.155424i	−0.349089	+	0.155424i
$775$		0			0
$776$	−0.485041	−	0.133863i	−0.485041	−	0.133863i
$777$		0			0
$778$		0			0
$779$	1.48811	−	1.75560i	1.48811	−	1.75560i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$785$		0			0
$786$	−1.08800	+	1.07184i	−1.08800	+	1.07184i
$787$	−1.71613	+	0.0513618i	−1.71613	+	0.0513618i	−0.873408	−	0.486989i	$-0.838095\pi$
$787$	−1.71613	+	0.0513618i	−1.71613	+	0.0513618i	−0.842721	+	0.538351i	$0.819048\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.118083	−	0.363423i	−0.118083	−	0.363423i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$797$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$798$		0			0
$799$		0			0
$800$	0.971490	+	0.237080i	0.971490	+	0.237080i
$801$	0.122166	+	0.227022i	0.122166	+	0.227022i
$802$	−1.84227	+	0.568266i	−1.84227	+	0.568266i
$803$	−0.406566	+	1.78128i	−0.406566	+	1.78128i
$804$	1.27055	+	0.866243i	1.27055	+	0.866243i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.813584	−	1.51189i	0.813584	−	1.51189i	−0.0448648	−	0.998993i	$-0.514286\pi$
$809$	0.813584	−	1.51189i	0.813584	−	1.51189i	0.858449	−	0.512899i	$-0.171429\pi$
$810$		0			0
$811$	−0.139886	−	0.155360i	−0.139886	−	0.155360i	0.669131	−	0.743145i	$-0.266667\pi$
$811$	−0.139886	−	0.155360i	−0.139886	−	0.155360i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.534634	+	0.388434i	0.534634	+	0.388434i
$817$	−0.795575	−	0.832106i	−0.795575	−	0.832106i
$818$	0.510644	+	1.57160i	0.510644	+	1.57160i
$819$		0			0
$820$		0			0
$821$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$821$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$822$	−1.40225	−	0.574696i	−1.40225	−	0.574696i
$823$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$823$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$824$		0			0
$825$	0.265158	−	0.739977i	0.265158	−	0.739977i
$826$		0			0
$827$	−1.58143	−	0.0473305i	−1.58143	−	0.0473305i	−0.772417	−	0.635116i	$-0.780952\pi$
$827$	−1.58143	−	0.0473305i	−1.58143	−	0.0473305i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$829$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.580986	+	0.607664i	−0.580986	+	0.607664i
$834$	−0.0617590	+	0.0999406i	−0.0617590	+	0.0999406i
$835$		0			0
$836$	0.910708	−	0.704238i	0.910708	−	0.704238i
$837$		0			0
$838$	−0.913584	+	0.252133i	−0.913584	+	0.252133i
$839$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$839$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$840$		0			0
$841$	0.992847	+	0.119394i	0.992847	+	0.119394i
$842$		0			0
$843$	1.32891	−	0.544638i	1.32891	−	0.544638i
$844$	−1.35991	+	1.42236i	−1.35991	+	1.42236i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.590424	−	1.38137i	0.590424	−	1.38137i
$850$	−0.235759	−	0.806981i	−0.235759	−	0.806981i
$851$		0			0
$852$		0			0
$853$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$853$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$854$		0			0
$855$		0			0
$856$	−0.973871	+	0.850846i	−0.973871	+	0.850846i
$857$	0.550256	+	1.40203i	0.550256	+	1.40203i	0.887586	+	0.460642i	$0.152381\pi$
$857$	0.550256	+	1.40203i	0.550256	+	1.40203i	−0.337330	+	0.941386i	$0.609524\pi$
$858$		0			0
$859$	1.94298			1.94298			0.971490	−	0.237080i	$-0.0761905\pi$
$859$	1.94298			1.94298			0.971490	+	0.237080i	$0.0761905\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$863$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$864$	−0.426990	−	0.998993i	−0.426990	−	0.998993i
$865$		0			0
$866$	0.179639	+	0.199510i	0.179639	+	0.199510i
$867$	−0.0240906	+	0.229207i	−0.0240906	+	0.229207i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.0539193	−	0.184560i	0.0539193	−	0.184560i
$874$		0			0
$875$		0			0
$876$	−0.192784	+	1.42319i	−0.192784	+	1.42319i
$877$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$877$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.18005	+	1.47974i	−1.18005	+	1.47974i	−0.337330	+	0.941386i	$0.609524\pi$
$881$	−1.18005	+	1.47974i	−1.18005	+	1.47974i	−0.842721	+	0.538351i	$0.819048\pi$
$882$	0.368355	−	0.101659i	0.368355	−	0.101659i
$883$	0.866962	−	1.23160i	0.866962	−	1.23160i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	0.866962	−	1.23160i	0.866962	−	1.23160i	0.971490	−	0.237080i	$-0.0761905\pi$
$884$		0			0
$885$		0			0
$886$	−0.612807	−	0.722962i	−0.612807	−	0.722962i
$887$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$887$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.450892	+	0.139082i	−0.450892	+	0.139082i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.93950	−	0.473312i	1.93950	−	0.473312i
$899$		0			0
$900$	−0.0961377	+	0.369834i	−0.0961377	+	0.369834i
$901$		0			0
$902$	0.894226	+	1.78795i	0.894226	+	1.78795i
$903$		0			0
$904$	1.41320	+	1.02675i	1.41320	+	1.02675i
$905$		0			0
$906$		0			0
$907$	0.220430	+	0.515722i	0.220430	+	0.515722i	0.992847	−	0.119394i	$-0.0380952\pi$
$907$	0.220430	+	0.515722i	0.220430	+	0.515722i	−0.772417	+	0.635116i	$0.780952\pi$
$908$	−0.172233	−	0.278713i	−0.172233	−	0.278713i
$909$		0			0
$910$		0			0
$911$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$911$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$912$	0.663359	−	0.615507i	0.663359	−	0.615507i
$913$	0.0783706	+	0.0436973i	0.0783706	+	0.0436973i
$914$	−0.233951	−	1.02501i	−0.233951	−	1.02501i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.547859	+	0.730817i	−0.547859	+	0.730817i
$919$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$919$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$920$		0			0
$921$	0.698191	−	1.39599i	0.698191	−	1.39599i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.865319	−	1.02087i	−0.865319	−	1.02087i	−0.999552	−	0.0299155i	$-0.990476\pi$
$929$	−0.865319	−	1.02087i	−0.865319	−	1.02087i	0.134233	−	0.990950i	$-0.457143\pi$
$930$		0			0
$931$	0.662670	+	0.941386i	0.662670	+	0.941386i
$932$	0.926625	+	0.761913i	0.926625	+	0.761913i
$933$		0			0
$934$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$935$		0			0
$936$		0			0
$937$	1.98214	−	0.238361i	1.98214	−	0.238361i	0.983930	−	0.178557i	$-0.0571429\pi$
$937$	1.98214	−	0.238361i	1.98214	−	0.238361i	0.998210	−	0.0598042i	$-0.0190476\pi$
$938$		0			0
$939$	0.726957	−	0.807367i	0.726957	−	0.807367i
$940$		0			0
$941$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$941$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$942$		0			0
$943$		0			0
$944$	0.0693087	+	1.54328i	0.0693087	+	1.54328i
$945$		0			0
$946$	0.936235	−	0.351375i	0.936235	−	0.351375i
$947$	0.0299188			0.0299188			0.0149594	−	0.999888i	$-0.495238\pi$
$947$	0.0299188			0.0299188			0.0149594	+	0.999888i	$0.495238\pi$
$948$		0			0
$949$		0			0
$950$	−1.14660	+	0.103196i	−1.14660	+	0.103196i
$951$		0			0
$952$		0			0
$953$	0.634160	−	0.704306i	0.634160	−	0.704306i	−0.337330	−	0.941386i	$-0.609524\pi$
$953$	0.634160	−	0.704306i	0.634160	−	0.704306i	0.971490	+	0.237080i	$0.0761905\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.575617	+	0.817719i	0.575617	+	0.817719i
$962$		0			0
$963$	−0.319526	−	0.376963i	−0.319526	−	0.376963i
$964$	0.180494	+	1.08691i	0.180494	+	1.08691i
$965$		0			0
$966$		0			0
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	0.251587	+	0.967835i	0.251587	+	0.967835i
$969$	−0.726986	−	0.224246i	−0.726986	−	0.224246i
$970$		0			0
$971$	0.806030	−	1.61161i	0.806030	−	1.61161i	0.0149594	−	0.999888i	$-0.495238\pi$
$971$	0.806030	−	1.61161i	0.806030	−	1.61161i	0.791071	−	0.611724i	$-0.209524\pi$
$972$	0.662072	−	0.271343i	0.662072	−	0.271343i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.69631	+	0.880355i	1.69631	+	0.880355i	0.983930	+	0.178557i	$0.0571429\pi$
$977$	1.69631	+	0.880355i	1.69631	+	0.880355i	0.712376	+	0.701798i	$0.247619\pi$
$978$	−0.323695	−	1.41820i	−0.323695	−	1.41820i
$979$	−0.283598	−	0.612159i	−0.283598	−	0.612159i
$980$		0			0
$981$		0			0
$982$	−1.94230	+	0.412849i	−1.94230	+	0.412849i
$983$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$983$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$984$	0.826058	+	1.33676i	0.826058	+	1.33676i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$991$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$	1.13731	+	0.679510i	1.13731	+	0.679510i
$994$		0			0
$995$		0			0
$996$	0.0644342	+	0.0286880i	0.0644342	+	0.0286880i
$997$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$997$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$998$	0.211513	+	0.456559i	0.211513	+	0.456559i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.2259.1	yes	48
8.3	odd	2	CM	3784.1.em.b.2259.1	yes	48
11.3	even	5		3784.1.em.a.883.1	✓	48
43.15	even	21		3784.1.em.a.1907.1	yes	48
88.3	odd	10		3784.1.em.a.883.1	✓	48
344.187	odd	42		3784.1.em.a.1907.1	yes	48
473.58	even	105	inner	3784.1.em.b.531.1	yes	48
3784.531	odd	210	inner	3784.1.em.b.531.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.883.1	✓	48	11.3	even	5
3784.1.em.a.883.1	✓	48	88.3	odd	10
3784.1.em.a.1907.1	yes	48	43.15	even	21
3784.1.em.a.1907.1	yes	48	344.187	odd	42
3784.1.em.b.531.1	yes	48	473.58	even	105	inner
3784.1.em.b.531.1	yes	48	3784.531	odd	210	inner
3784.1.em.b.2259.1	yes	48	1.1	even	1	trivial
3784.1.em.b.2259.1	yes	48	8.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(-0.0448648 - 0.998993i) q^{2} +(-0.784643 + 0.0470091i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(0.0821646 + 0.781744i) q^{6} +(0.134233 + 0.990950i) q^{8} +(-0.379392 + 0.0456236i) q^{9} +O(q^{10})\)	\(q+(-0.0448648 - 0.998993i) q^{2} +(-0.784643 + 0.0470091i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(0.0821646 + 0.781744i) q^{6} +(0.134233 + 0.990950i) q^{8} +(-0.379392 + 0.0456236i) q^{9} +(0.998210 - 0.0598042i) q^{11} +(0.777271 - 0.117155i) q^{12} +(0.983930 - 0.178557i) q^{16} +(-0.543606 - 0.641322i) q^{17} +(0.0625990 + 0.376963i) q^{18} +(-1.00550 + 0.560638i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-0.151909 - 0.771232i) q^{24} +(-0.447313 + 0.894377i) q^{25} +(1.06896 - 0.193988i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(-0.780427 + 0.0938498i) q^{33} +(-0.616287 + 0.571831i) q^{34} +(0.373775 - 0.0794483i) q^{36} +(0.605185 + 0.979332i) q^{38} +(-1.87163 + 0.702435i) q^{41} +(0.251587 + 0.967835i) q^{43} +(-0.988831 + 0.149042i) q^{44} +(-0.763640 + 0.186357i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(0.456684 + 0.477654i) q^{51} +(-0.241751 - 1.05918i) q^{54} +(0.762602 - 0.487168i) q^{57} +(-0.207368 + 1.53085i) q^{59} +(-0.963963 + 0.266037i) q^{64} +(0.128769 + 0.775431i) q^{66} +(1.43407 + 1.33062i) q^{67} +(0.598905 + 0.590012i) q^{68} +(-0.0961377 - 0.369834i) q^{72} +(-0.512366 + 1.75378i) q^{73} +(0.308937 - 0.722795i) q^{75} +(0.951194 - 0.648513i) q^{76} +(-0.458402 + 0.111868i) q^{81} +(0.785698 + 1.83823i) q^{82} +(0.0756171 + 0.0483060i) q^{83} +(0.955573 - 0.294755i) q^{86} +(0.193256 + 0.981148i) q^{88} +(-0.246481 - 0.628023i) q^{89} +(0.220430 + 0.754510i) q^{96} +(-0.197760 + 0.462682i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(-0.375984 + 0.0682311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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