LMFDB - Embedded newform 896.2.bh.a.81.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, not 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			81.2
Character	$\chi$	$=$	896.81
Dual form			896.2.bh.a.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44576 + 1.87670i) q^{3} +(0.0746500 - 0.0972858i) q^{5} +(-1.07291 + 2.41844i) q^{7} +(1.68329 - 6.28212i) q^{9} +O(q^{10})$	\(q+(-2.44576 + 1.87670i) q^{3} +(0.0746500 - 0.0972858i) q^{5} +(-1.07291 + 2.41844i) q^{7} +(1.68329 - 6.28212i) q^{9} +(0.199204 - 1.51311i) q^{11} +(-2.54811 + 6.15169i) q^{13} +0.378033i q^{15} +(-3.30969 - 1.91085i) q^{17} +(-4.82378 + 0.635062i) q^{19} +(-1.91462 - 7.92845i) q^{21} +(1.27015 - 4.74027i) q^{23} +(1.29020 + 4.81510i) q^{25} +(4.13349 + 9.97912i) q^{27} +(0.576820 + 0.238927i) q^{29} +(2.06530 - 3.57721i) q^{31} +(2.35244 + 4.07454i) q^{33} +(0.155188 + 0.284915i) q^{35} +(1.36509 - 1.77902i) q^{37} +(-5.31279 - 19.8276i) q^{39} +(-4.05813 - 4.05813i) q^{41} +(-0.464012 + 0.192200i) q^{43} +(-0.485503 - 0.632720i) q^{45} +(7.70274 - 4.44718i) q^{47} +(-4.69775 - 5.18952i) q^{49} +(11.6808 - 1.53780i) q^{51} +(0.971468 - 7.37903i) q^{53} +(-0.132333 - 0.132333i) q^{55} +(10.6060 - 10.6060i) q^{57} +(0.171916 + 0.0226332i) q^{59} +(-0.731024 - 5.55268i) q^{61} +(13.3869 + 10.8111i) q^{63} +(0.408255 + 0.707119i) q^{65} +(-2.69764 + 2.06997i) q^{67} +(5.78957 + 13.9772i) q^{69} +(2.39694 - 2.39694i) q^{71} +(14.7474 - 3.95155i) q^{73} +(-12.1920 - 9.35526i) q^{75} +(3.44564 + 2.10519i) q^{77} +(-0.174648 + 0.100833i) q^{79} +(-11.9401 - 6.89363i) q^{81} +(-1.61043 + 3.88792i) q^{83} +(-0.432967 + 0.179341i) q^{85} +(-1.85915 + 0.498159i) q^{87} +(-13.5423 - 3.62866i) q^{89} +(-12.1436 - 12.7627i) q^{91} +(1.66211 + 12.6249i) q^{93} +(-0.298313 + 0.516692i) q^{95} -12.3233 q^{97} +(-9.17020 - 3.79842i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.44576	+	1.87670i	−1.41206	+	1.08351i	−0.428376	+	0.903600i	$0.640914\pi$
$3$	−2.44576	+	1.87670i	−1.41206	+	1.08351i	−0.983683	+	0.179911i	$0.942419\pi$
$4$		0			0
$5$	0.0746500	−	0.0972858i	0.0333845	−	0.0435075i	−0.776363	−	0.630286i	$-0.782938\pi$
$5$	0.0746500	−	0.0972858i	0.0333845	−	0.0435075i	0.809747	+	0.586779i	$0.199604\pi$
$6$		0			0
$7$	−1.07291	+	2.41844i	−0.405520	+	0.914086i
$7$	−1.07291	+	2.41844i	−0.405520	+	0.914086i
$8$		0			0
$9$	1.68329	−	6.28212i	0.561096	−	2.09404i
$10$		0			0
$11$	0.199204	−	1.51311i	0.0600624	−	0.456219i	−0.934815	−	0.355134i	$-0.884435\pi$
$11$	0.199204	−	1.51311i	0.0600624	−	0.456219i	0.994878	−	0.101085i	$-0.0322314\pi$
$12$		0			0
$13$	−2.54811	+	6.15169i	−0.706720	+	1.70617i	0.00131927	+	0.999999i	$0.499580\pi$
$13$	−2.54811	+	6.15169i	−0.706720	+	1.70617i	−0.708039	+	0.706173i	$0.750420\pi$
$14$		0			0
$15$			0.378033i			0.0976077i
$16$		0			0
$17$	−3.30969	−	1.91085i	−0.802717	−	0.463449i	0.0417031	−	0.999130i	$-0.486722\pi$
$17$	−3.30969	−	1.91085i	−0.802717	−	0.463449i	−0.844420	+	0.535681i	$0.820055\pi$
$18$		0			0
$19$	−4.82378	+	0.635062i	−1.10665	+	0.145693i	−0.661633	−	0.749828i	$-0.730136\pi$
$19$	−4.82378	+	0.635062i	−1.10665	+	0.145693i	−0.445018	+	0.895522i	$0.646803\pi$
$20$		0			0
$21$	−1.91462	−	7.92845i	−0.417804	−	1.73013i
$22$		0			0
$23$	1.27015	−	4.74027i	0.264845	−	0.988415i	−0.697500	−	0.716585i	$-0.745704\pi$
$23$	1.27015	−	4.74027i	0.264845	−	0.988415i	0.962345	−	0.271830i	$-0.0876290\pi$
$24$		0			0
$25$	1.29020	+	4.81510i	0.258041	+	0.963021i
$26$		0			0
$27$	4.13349	+	9.97912i	0.795490	+	1.92048i
$28$		0			0
$29$	0.576820	+	0.238927i	0.107113	+	0.0443676i	0.435596	−	0.900142i	$-0.356538\pi$
$29$	0.576820	+	0.238927i	0.107113	+	0.0443676i	−0.328484	+	0.944510i	$0.606538\pi$
$30$		0			0
$31$	2.06530	−	3.57721i	0.370939	−	0.642486i	−0.618771	−	0.785572i	$-0.712369\pi$
$31$	2.06530	−	3.57721i	0.370939	−	0.642486i	0.989710	+	0.143085i	$0.0457024\pi$
$32$		0			0
$33$	2.35244	+	4.07454i	0.409507	+	0.709286i
$34$		0			0
$35$	0.155188	+	0.284915i	0.0262315	+	0.0481595i
$36$		0			0
$37$	1.36509	−	1.77902i	0.224419	−	0.292468i	−0.667550	−	0.744565i	$-0.732657\pi$
$37$	1.36509	−	1.77902i	0.224419	−	0.292468i	0.891969	+	0.452096i	$0.149324\pi$
$38$		0			0
$39$	−5.31279	−	19.8276i	−0.850727	−	3.17496i
$40$		0			0
$41$	−4.05813	−	4.05813i	−0.633774	−	0.633774i	0.315239	−	0.949012i	$-0.397915\pi$
$41$	−4.05813	−	4.05813i	−0.633774	−	0.633774i	−0.949012	+	0.315239i	$0.897915\pi$
$42$		0			0
$43$	−0.464012	+	0.192200i	−0.0707612	+	0.0293103i	−0.417783	−	0.908547i	$-0.637193\pi$
$43$	−0.464012	+	0.192200i	−0.0707612	+	0.0293103i	0.347022	+	0.937857i	$0.387193\pi$
$44$		0			0
$45$	−0.485503	−	0.632720i	−0.0723745	−	0.0943203i
$46$		0			0
$47$	7.70274	−	4.44718i	1.12356	−	0.648688i	0.181253	−	0.983437i	$-0.441985\pi$
$47$	7.70274	−	4.44718i	1.12356	−	0.648688i	0.942307	+	0.334749i	$0.108651\pi$
$48$		0			0
$49$	−4.69775	−	5.18952i	−0.671107	−	0.741361i
$50$		0			0
$51$	11.6808	−	1.53780i	1.63564	−	0.215336i
$52$		0			0
$53$	0.971468	−	7.37903i	0.133441	−	1.01359i	−0.785408	−	0.618979i	$-0.787547\pi$
$53$	0.971468	−	7.37903i	0.133441	−	1.01359i	0.918849	−	0.394609i	$-0.129120\pi$
$54$		0			0
$55$	−0.132333	−	0.132333i	−0.0178438	−	0.0178438i
$56$		0			0
$57$	10.6060	−	10.6060i	1.40480	−	1.40480i
$58$		0			0
$59$	0.171916	+	0.0226332i	0.0223816	+	0.00294659i	0.141709	−	0.989908i	$-0.454740\pi$
$59$	0.171916	+	0.0226332i	0.0223816	+	0.00294659i	−0.119327	+	0.992855i	$0.538074\pi$
$60$		0			0
$61$	−0.731024	−	5.55268i	−0.0935980	−	0.710948i	−0.972327	−	0.233626i	$-0.924941\pi$
$61$	−0.731024	−	5.55268i	−0.0935980	−	0.710948i	0.878729	−	0.477322i	$-0.158392\pi$
$62$		0			0
$63$	13.3869	+	10.8111i	1.68660	+	1.36206i
$64$		0			0
$65$	0.408255	+	0.707119i	0.0506379	+	0.0877073i
$66$		0			0
$67$	−2.69764	+	2.06997i	−0.329570	+	0.252888i	−0.760270	−	0.649607i	$-0.774933\pi$
$67$	−2.69764	+	2.06997i	−0.329570	+	0.252888i	0.430700	+	0.902495i	$0.358267\pi$
$68$		0			0
$69$	5.78957	+	13.9772i	0.696982	+	1.68266i
$70$		0			0
$71$	2.39694	−	2.39694i	0.284465	−	0.284465i	−0.550422	−	0.834887i	$-0.685533\pi$
$71$	2.39694	−	2.39694i	0.284465	−	0.284465i	0.834887	+	0.550422i	$0.185533\pi$
$72$		0			0
$73$	14.7474	−	3.95155i	1.72605	−	0.462494i	0.746783	−	0.665068i	$-0.231597\pi$
$73$	14.7474	−	3.95155i	1.72605	−	0.462494i	0.979267	+	0.202574i	$0.0649307\pi$
$74$		0			0
$75$	−12.1920	−	9.35526i	−1.40781	−	1.08025i
$76$		0			0
$77$	3.44564	+	2.10519i	0.392667	+	0.239908i
$78$		0			0
$79$	−0.174648	+	0.100833i	−0.0196494	+	0.0113446i	−0.509793	−	0.860297i	$-0.670278\pi$
$79$	−0.174648	+	0.100833i	−0.0196494	+	0.0113446i	0.490143	+	0.871642i	$0.336945\pi$
$80$		0			0
$81$	−11.9401	−	6.89363i	−1.32668	−	0.765959i
$82$		0			0
$83$	−1.61043	+	3.88792i	−0.176767	+	0.426754i	−0.987285	−	0.158960i	$-0.949186\pi$
$83$	−1.61043	+	3.88792i	−0.176767	+	0.426754i	0.810518	+	0.585714i	$0.199186\pi$
$84$		0			0
$85$	−0.432967	+	0.179341i	−0.0469618	+	0.0194522i
$86$		0			0
$87$	−1.85915	+	0.498159i	−0.199322	+	0.0534083i
$88$		0			0
$89$	−13.5423	−	3.62866i	−1.43549	−	0.384637i	−0.544535	−	0.838738i	$-0.683294\pi$
$89$	−13.5423	−	3.62866i	−1.43549	−	0.384637i	−0.890950	+	0.454101i	$0.849961\pi$
$90$		0			0
$91$	−12.1436	−	12.7627i	−1.27300	−	1.33789i
$92$		0			0
$93$	1.66211	+	12.6249i	0.172352	+	1.30915i
$94$		0			0
$95$	−0.298313	+	0.516692i	−0.0306062	+	0.0530115i
$96$		0			0
$97$	−12.3233			−1.25124			−0.625619	−	0.780129i	$-0.715153\pi$
$97$	−12.3233			−1.25124			−0.625619	+	0.780129i	$0.715153\pi$
$98$		0			0
$99$	−9.17020	−	3.79842i	−0.921639	−	0.381756i
$100$		0			0
$101$	1.86438	+	0.245450i	0.185513	+	0.0244232i	0.222710	−	0.974885i	$-0.428510\pi$
$101$	1.86438	+	0.245450i	0.185513	+	0.0244232i	−0.0371973	+	0.999308i	$0.511843\pi$
$102$		0			0
$103$	−3.32276	−	0.890332i	−0.327402	−	0.0877270i	0.0913742	−	0.995817i	$-0.470874\pi$
$103$	−3.32276	−	0.890332i	−0.327402	−	0.0877270i	−0.418776	+	0.908090i	$0.637541\pi$
$104$		0			0
$105$	−0.914252	−	0.405594i	−0.0892218	−	0.0395819i
$106$		0			0
$107$	−5.81946	−	4.46543i	−0.562588	−	0.431689i	0.287917	−	0.957655i	$-0.407037\pi$
$107$	−5.81946	−	4.46543i	−0.562588	−	0.431689i	−0.850505	+	0.525966i	$0.823704\pi$
$108$		0			0
$109$	−7.79338	−	10.1565i	−0.746470	−	0.972819i	−0.999985	−	0.00548736i	$-0.998253\pi$
$109$	−7.79338	−	10.1565i	−0.746470	−	0.972819i	0.253515	−	0.967332i	$-0.418413\pi$
$110$		0			0
$111$			6.91290i			0.656143i
$112$		0			0
$113$			19.0835i			1.79523i	0.440784	+	0.897613i	$0.354701\pi$
$113$			19.0835i			1.79523i	−0.440784	+	0.897613i	$0.645299\pi$
$114$		0			0
$115$	−0.366344	−	0.477429i	−0.0341618	−	0.0445205i
$116$		0			0
$117$	34.3564	+	26.3626i	3.17625	+	2.43723i
$118$		0			0
$119$	8.17227	−	5.95414i	0.749150	−	0.545815i
$120$		0			0
$121$	8.37537	+	2.24417i	0.761398	+	0.204016i
$122$		0			0
$123$	17.5411	+	2.30933i	1.58163	+	0.208225i
$124$		0			0
$125$	1.13121	+	0.468564i	0.101179	+	0.0419096i
$126$		0			0
$127$	−6.27038			−0.556406			−0.278203	−	0.960522i	$-0.589739\pi$
$127$	−6.27038			−0.556406			−0.278203	+	0.960522i	$0.589739\pi$
$128$		0			0
$129$	0.774161	−	1.34089i	0.0681611	−	0.118058i
$130$		0			0
$131$	−0.0562693	−	0.427408i	−0.00491628	−	0.0373428i	0.988811	−	0.149174i	$-0.0476616\pi$
$131$	−0.0562693	−	0.427408i	−0.00491628	−	0.0373428i	−0.993727	+	0.111832i	$0.964328\pi$
$132$		0			0
$133$	3.63959	−	12.3474i	0.315593	−	1.07066i
$134$		0			0
$135$	1.27939	+	0.342812i	0.110112	+	0.0295046i
$136$		0			0
$137$	−12.0106	+	3.21823i	−1.02613	+	0.274952i	−0.732356	−	0.680922i	$-0.761579\pi$
$137$	−12.0106	+	3.21823i	−1.02613	+	0.274952i	−0.293778	+	0.955874i	$0.594913\pi$
$138$		0			0
$139$	−5.36721	+	2.22317i	−0.455241	+	0.188567i	−0.598507	−	0.801117i	$-0.704239\pi$
$139$	−5.36721	+	2.22317i	−0.455241	+	0.188567i	0.143267	+	0.989684i	$0.454239\pi$
$140$		0			0
$141$	−10.4930	+	25.3324i	−0.883673	+	2.13338i
$142$		0			0
$143$	8.80057	+	5.08101i	0.735941	+	0.424896i
$144$		0			0
$145$	0.0663038	−	0.0382805i	0.00550623	−	0.00317902i
$146$		0			0
$147$	21.2287	+	3.87608i	1.75092	+	0.319693i
$148$		0			0
$149$	−0.154554	−	0.118593i	−0.0126615	−	0.00971555i	0.602411	−	0.798186i	$-0.294207\pi$
$149$	−0.154554	−	0.118593i	−0.0126615	−	0.00971555i	−0.615073	+	0.788470i	$0.710873\pi$
$150$		0			0
$151$	−17.8925	+	4.79429i	−1.45607	+	0.390153i	−0.898131	−	0.439727i	$-0.855075\pi$
$151$	−17.8925	+	4.79429i	−1.45607	+	0.390153i	−0.557941	+	0.829881i	$0.688408\pi$
$152$		0			0
$153$	−17.5753	+	17.5753i	−1.42088	+	1.42088i
$154$		0			0
$155$	−0.193837	−	0.467964i	−0.0155693	−	0.0375877i
$156$		0			0
$157$	12.3159	−	9.45029i	0.982913	−	0.754216i	0.0135650	−	0.999908i	$-0.495682\pi$
$157$	12.3159	−	9.45029i	0.982913	−	0.754216i	0.969348	+	0.245692i	$0.0790153\pi$
$158$		0			0
$159$	11.4722	+	19.8705i	0.909806	+	1.57583i
$160$		0			0
$161$	10.1013	+	8.15765i	0.796096	+	0.642913i
$162$		0			0
$163$	−1.67742	−	12.7413i	−0.131386	−	0.997974i	−0.922416	−	0.386197i	$-0.873788\pi$
$163$	−1.67742	−	12.7413i	−0.131386	−	0.997974i	0.791030	−	0.611777i	$-0.209545\pi$
$164$		0			0
$165$	0.572004	+	0.0753058i	0.0445305	+	0.00586255i
$166$		0			0
$167$	−8.06897	+	8.06897i	−0.624396	+	0.624396i	−0.946652	−	0.322257i	$-0.895559\pi$
$167$	−8.06897	+	8.06897i	−0.624396	+	0.624396i	0.322257	+	0.946652i	$0.395559\pi$
$168$		0			0
$169$	−22.1580	−	22.1580i	−1.70446	−	1.70446i
$170$		0			0
$171$	−4.13027	+	31.3725i	−0.315850	+	2.39912i
$172$		0			0
$173$	1.78969	−	0.235618i	0.136068	−	0.0179137i	−0.0621846	−	0.998065i	$-0.519807\pi$
$173$	1.78969	−	0.235618i	0.136068	−	0.0179137i	0.198252	+	0.980151i	$0.436473\pi$
$174$		0			0
$175$	−13.0293	−	2.04587i	−0.984925	−	0.154653i
$176$		0			0
$177$	−0.462941	+	0.267279i	−0.0347968	+	0.0200899i
$178$		0			0
$179$	−3.83032	−	4.99177i	−0.286292	−	0.373103i	0.627963	−	0.778244i	$-0.283889\pi$
$179$	−3.83032	−	4.99177i	−0.286292	−	0.373103i	−0.914254	+	0.405141i	$0.867222\pi$
$180$		0			0
$181$	−8.02607	+	3.32451i	−0.596573	+	0.247109i	−0.660476	−	0.750847i	$-0.729645\pi$
$181$	−8.02607	+	3.32451i	−0.596573	+	0.247109i	0.0639024	+	0.997956i	$0.479645\pi$
$182$		0			0
$183$	12.2086	+	12.2086i	0.902486	+	0.902486i
$184$		0			0
$185$	−0.0711692	−	0.265607i	−0.00523246	−	0.0195278i
$186$		0			0
$187$	−3.55062	+	4.62726i	−0.259647	+	0.338379i
$188$		0			0
$189$	−28.5688	−	0.710043i	−2.07807	−	0.0516480i
$190$		0			0
$191$	0.0869346	+	0.150575i	0.00629037	+	0.0108952i	0.869153	−	0.494542i	$-0.164664\pi$
$191$	0.0869346	+	0.150575i	0.00629037	+	0.0108952i	−0.862863	+	0.505438i	$0.831331\pi$
$192$		0			0
$193$	−8.43448	+	14.6089i	−0.607127	+	1.05157i	0.384585	+	0.923090i	$0.374345\pi$
$193$	−8.43448	+	14.6089i	−0.607127	+	1.05157i	−0.991711	+	0.128485i	$0.958989\pi$
$194$		0			0
$195$	−2.32554	−	0.963271i	−0.166536	−	0.0689813i
$196$		0			0
$197$	−4.64197	−	11.2067i	−0.330727	−	0.798445i	−0.998535	−	0.0541116i	$-0.982767\pi$
$197$	−4.64197	−	11.2067i	−0.330727	−	0.798445i	0.667808	−	0.744333i	$-0.267233\pi$
$198$		0			0
$199$	5.47864	+	20.4466i	0.388370	+	1.44942i	0.832785	+	0.553597i	$0.186745\pi$
$199$	5.47864	+	20.4466i	0.388370	+	1.44942i	−0.444415	+	0.895821i	$0.646588\pi$
$200$		0			0
$201$	2.71307	−	10.1253i	0.191365	−	0.714185i
$202$		0			0
$203$	−1.19670	+	1.13866i	−0.0839921	+	0.0799183i
$204$		0			0
$205$	−0.697738	+	0.0918590i	−0.0487321	+	0.00641571i
$206$		0			0
$207$	−27.6409	−	15.9585i	−1.92118	−	1.10919i
$208$		0			0
$209$			7.42540i			0.513626i
$210$		0			0
$211$	1.68083	−	4.05787i	0.115713	−	0.279355i	−0.855403	−	0.517962i	$-0.826691\pi$
$211$	1.68083	−	4.05787i	0.115713	−	0.279355i	0.971116	+	0.238607i	$0.0766907\pi$
$212$		0			0
$213$	−1.36401	+	10.3607i	−0.0934603	+	0.709902i
$214$		0			0
$215$	−0.0159402	+	0.0594896i	−0.00108711	+	0.00405715i
$216$		0			0
$217$	6.43541	+	8.83283i	0.436864	+	0.599612i
$218$		0			0
$219$	−28.6527	+	37.3409i	−1.93617	+	2.52326i
$220$		0			0
$221$	20.1884	−	15.4911i	1.35802	−	1.04205i
$222$		0			0
$223$	17.8395			1.19462			0.597311	−	0.802010i	$-0.296236\pi$
$223$	17.8395			1.19462			0.597311	+	0.802010i	$0.296236\pi$
$224$		0			0
$225$	32.4208			2.16139
$226$		0			0
$227$	−1.59768	+	1.22594i	−0.106042	+	0.0813686i	−0.660421	−	0.750895i	$-0.729622\pi$
$227$	−1.59768	+	1.22594i	−0.106042	+	0.0813686i	0.554380	+	0.832264i	$0.312956\pi$
$228$		0			0
$229$	−1.62373	+	2.11608i	−0.107299	+	0.139835i	−0.843916	−	0.536475i	$-0.819755\pi$
$229$	−1.62373	+	2.11608i	−0.107299	+	0.139835i	0.736617	+	0.676310i	$0.236422\pi$
$230$		0			0
$231$	−12.3780	+	1.31764i	−0.814412	+	0.0866945i
$232$		0			0
$233$	−4.16758	+	15.5536i	−0.273027	+	1.01895i	0.684125	+	0.729365i	$0.260184\pi$
$233$	−4.16758	+	15.5536i	−0.273027	+	1.01895i	−0.957152	+	0.289586i	$0.906482\pi$
$234$		0			0
$235$	0.142362	−	1.08135i	0.00928669	−	0.0705394i
$236$		0			0
$237$	0.237914	−	0.574374i	0.0154541	−	0.0373096i
$238$		0			0
$239$			1.80626i			0.116837i	0.998292	+	0.0584186i	$0.0186058\pi$
$239$			1.80626i			0.116837i	−0.998292	+	0.0584186i	$0.981394\pi$
$240$		0			0
$241$	−4.50083	−	2.59856i	−0.289924	−	0.167388i	0.347984	−	0.937501i	$-0.386867\pi$
$241$	−4.50083	−	2.59856i	−0.289924	−	0.167388i	−0.637908	+	0.770113i	$0.720200\pi$
$242$		0			0
$243$	10.0132	−	1.31826i	0.642345	−	0.0845663i
$244$		0			0
$245$	−0.855554	+	0.0696261i	−0.0546593	+	0.00444825i
$246$		0			0
$247$	8.38483	−	31.2926i	0.533514	−	1.99110i
$248$		0			0
$249$	−3.35772	−	12.5312i	−0.212787	−	0.794132i
$250$		0			0
$251$	5.10587	+	12.3267i	0.322280	+	0.778053i	0.999121	+	0.0419232i	$0.0133485\pi$
$251$	5.10587	+	12.3267i	0.322280	+	0.778053i	−0.676841	+	0.736129i	$0.736652\pi$
$252$		0			0
$253$	−6.91952	−	2.86616i	−0.435026	−	0.180194i
$254$		0			0
$255$	0.722364	−	1.25117i	0.0452362	−	0.0783514i
$256$		0			0
$257$	−10.7199	−	18.5675i	−0.668692	−	1.15821i	−0.978270	−	0.207334i	$-0.933521\pi$
$257$	−10.7199	−	18.5675i	−0.668692	−	1.15821i	0.309578	−	0.950874i	$-0.399812\pi$
$258$		0			0
$259$	2.83784	+	5.21010i	0.176335	+	0.323740i
$260$		0			0
$261$	2.47192	−	3.22147i	0.153008	−	0.199404i
$262$		0			0
$263$	5.71539	+	21.3301i	0.352426	+	1.31527i	0.883693	+	0.468067i	$0.155050\pi$
$263$	5.71539	+	21.3301i	0.352426	+	1.31527i	−0.531267	+	0.847205i	$0.678284\pi$
$264$		0			0
$265$	−0.645354	−	0.645354i	−0.0396438	−	0.0396438i
$266$		0			0
$267$	39.9312	−	16.5400i	2.44375	−	1.01223i
$268$		0			0
$269$	−15.3948	−	20.0628i	−0.938635	−	1.22325i	−0.974612	−	0.223900i	$-0.928121\pi$
$269$	−15.3948	−	20.0628i	−0.938635	−	1.22325i	0.0359776	−	0.999353i	$-0.488545\pi$
$270$		0			0
$271$	9.11627	−	5.26328i	0.553774	−	0.319721i	−0.196869	−	0.980430i	$-0.563077\pi$
$271$	9.11627	−	5.26328i	0.553774	−	0.319721i	0.750643	+	0.660708i	$0.229744\pi$
$272$		0			0
$273$	53.6520	+	8.42445i	3.24717	+	0.509871i
$274$		0			0
$275$	7.54278	−	0.993026i	0.454847	−	0.0598817i
$276$		0			0
$277$	−2.30720	+	17.5250i	−0.138626	+	1.05297i	0.770791	+	0.637088i	$0.219861\pi$
$277$	−2.30720	+	17.5250i	−0.138626	+	1.05297i	−0.909417	+	0.415885i	$0.863472\pi$
$278$		0			0
$279$	−18.9960	−	18.9960i	−1.13726	−	1.13726i
$280$		0			0
$281$	22.4872	−	22.4872i	1.34148	−	1.34148i	0.446884	−	0.894592i	$-0.352534\pi$
$281$	22.4872	−	22.4872i	1.34148	−	1.34148i	0.894592	−	0.446884i	$-0.147466\pi$
$282$		0			0
$283$	−21.0612	−	2.77276i	−1.25196	−	0.164824i	−0.524760	−	0.851250i	$-0.675845\pi$
$283$	−21.0612	−	2.77276i	−1.25196	−	0.164824i	−0.727199	+	0.686427i	$0.759178\pi$
$284$		0			0
$285$	−0.240075	−	1.82355i	−0.0142208	−	0.108018i
$286$		0			0
$287$	14.1684	−	5.46038i	0.836332	−	0.322316i
$288$		0			0
$289$	−1.19731	−	2.07380i	−0.0704300	−	0.121988i
$290$		0			0
$291$	30.1397	−	23.1270i	1.76682	−	1.35573i
$292$		0			0
$293$	−4.96186	−	11.9790i	−0.289875	−	0.699820i	0.710116	−	0.704085i	$-0.248642\pi$
$293$	−4.96186	−	11.9790i	−0.289875	−	0.699820i	−0.999991	+	0.00426496i	$0.998642\pi$
$294$		0			0
$295$	0.0150354	−	0.0150354i	0.000875397	−	0.000875397i
$296$		0			0
$297$	15.9229	−	4.26652i	0.923940	−	0.247569i
$298$		0			0
$299$	25.9242	+	19.8923i	1.49924	+	1.15040i
$300$		0			0
$301$	0.0330158	−	1.32840i	0.00190300	−	0.0765677i
$302$		0			0
$303$	−5.02046	+	2.89856i	−0.288418	+	0.166518i
$304$		0			0
$305$	−0.594768	−	0.343389i	−0.0340563	−	0.0196624i
$306$		0			0
$307$	−3.58579	+	8.65687i	−0.204652	+	0.494073i	−0.992565	−	0.121712i	$-0.961161\pi$
$307$	−3.58579	+	8.65687i	−0.204652	+	0.494073i	0.787913	+	0.615786i	$0.211161\pi$
$308$		0			0
$309$	9.79756	−	4.05828i	0.557364	−	0.230868i
$310$		0			0
$311$	8.40723	−	2.25271i	0.476730	−	0.127740i	−0.0124494	−	0.999923i	$-0.503963\pi$
$311$	8.40723	−	2.25271i	0.476730	−	0.127740i	0.489180	+	0.872183i	$0.337296\pi$
$312$		0			0
$313$	7.26621	+	1.94697i	0.410710	+	0.110050i	0.458257	−	0.888819i	$-0.348474\pi$
$313$	7.26621	+	1.94697i	0.410710	+	0.110050i	−0.0475471	+	0.998869i	$0.515140\pi$
$314$		0			0
$315$	2.05110	−	0.495314i	0.115566	−	0.0279078i
$316$		0			0
$317$	0.382669	+	2.90666i	0.0214928	+	0.163254i	0.998825	−	0.0484559i	$-0.0154300\pi$
$317$	0.382669	+	2.90666i	0.0214928	+	0.163254i	−0.977332	+	0.211710i	$0.932097\pi$
$318$		0			0
$319$	0.476427	−	0.825195i	0.0266748	−	0.0462020i
$320$		0			0
$321$	22.6132			1.26215
$322$		0			0
$323$	17.1787	+	7.11565i	0.955849	+	0.395926i
$324$		0			0
$325$	−32.9086	−	4.33250i	−1.82544	−	0.240324i
$326$		0			0
$327$	38.1214	+	10.2146i	2.10812	+	0.564869i
$328$		0			0
$329$	2.49094	+	23.4001i	0.137330	+	1.29009i
$330$		0			0
$331$	−21.9637	−	16.8533i	−1.20723	−	0.926344i	−0.208570	−	0.978007i	$-0.566881\pi$
$331$	−21.9637	−	16.8533i	−1.20723	−	0.926344i	−0.998665	+	0.0516640i	$0.983548\pi$
$332$		0			0
$333$	−8.87815	−	11.5702i	−0.486520	−	0.634045i
$334$		0			0
$335$			0.416966i			0.0227813i
$336$		0			0
$337$		−	1.09614i		−	0.0597105i	−0.999554	−	0.0298552i	$-0.990495\pi$
$337$		−	1.09614i		−	0.0597105i	0.999554	−	0.0298552i	$-0.00950463\pi$
$338$		0			0
$339$	−35.8140	−	46.6737i	−1.94515	−	2.53497i
$340$		0			0
$341$	−5.00129	−	3.83762i	−0.270835	−	0.207819i
$342$		0			0
$343$	17.5908	−	5.79338i	0.949815	−	0.312813i
$344$		0			0
$345$	1.79198	+	0.480159i	0.0964769	+	0.0258509i
$346$		0			0
$347$	−20.3411	−	2.67796i	−1.09197	−	0.143761i	−0.437034	−	0.899445i	$-0.643971\pi$
$347$	−20.3411	−	2.67796i	−1.09197	−	0.143761i	−0.654936	+	0.755684i	$0.727304\pi$
$348$		0			0
$349$	−8.25989	−	3.42136i	−0.442142	−	0.183141i	0.150495	−	0.988611i	$-0.451913\pi$
$349$	−8.25989	−	3.42136i	−0.442142	−	0.183141i	−0.592637	+	0.805470i	$0.701913\pi$
$350$		0			0
$351$	−71.9211			−3.83886
$352$		0			0
$353$	−13.1282	+	22.7388i	−0.698746	+	1.21026i	0.270156	+	0.962817i	$0.412925\pi$
$353$	−13.1282	+	22.7388i	−0.698746	+	1.21026i	−0.968902	+	0.247446i	$0.920409\pi$
$354$		0			0
$355$	−0.0542566	−	0.412120i	−0.00287964	−	0.0218731i
$356$		0			0
$357$	−8.81328	+	29.8992i	−0.466448	+	1.58244i
$358$		0			0
$359$	−22.5422	−	6.04016i	−1.18973	−	0.318788i	−0.390952	−	0.920411i	$-0.627854\pi$
$359$	−22.5422	−	6.04016i	−1.18973	−	0.318788i	−0.798780	+	0.601623i	$0.794521\pi$
$360$		0			0
$361$	4.51294	−	1.20924i	0.237523	−	0.0636441i
$362$		0			0
$363$	−24.6958	+	10.2293i	−1.29619	+	0.536900i
$364$		0			0
$365$	0.716462	−	1.72969i	0.0375014	−	0.0905363i
$366$		0			0
$367$	−10.9201	−	6.30473i	−0.570025	−	0.329104i	0.187134	−	0.982334i	$-0.440080\pi$
$367$	−10.9201	−	6.30473i	−0.570025	−	0.329104i	−0.757159	+	0.653230i	$0.773413\pi$
$368$		0			0
$369$	−32.3247	+	18.6627i	−1.68275	+	0.971539i
$370$		0			0
$371$	16.8035	+	10.2664i	0.872393	+	0.533007i
$372$		0			0
$373$	−14.9844	−	11.4979i	−0.775861	−	0.595339i	0.143091	−	0.989710i	$-0.454296\pi$
$373$	−14.9844	−	11.4979i	−0.775861	−	0.595339i	−0.918951	+	0.394371i	$0.870963\pi$
$374$		0			0
$375$	−3.64603	+	0.976950i	−0.188280	+	0.0504495i
$376$		0			0
$377$	−2.93961	+	2.93961i	−0.151397	+	0.151397i
$378$		0			0
$379$	−5.99418	−	14.4712i	−0.307901	−	0.743338i	−0.999773	−	0.0213177i	$-0.993214\pi$
$379$	−5.99418	−	14.4712i	−0.307901	−	0.743338i	0.691872	−	0.722020i	$-0.256786\pi$
$380$		0			0
$381$	15.3358	−	11.7676i	0.785679	−	0.602873i
$382$		0			0
$383$	−14.4135	−	24.9650i	−0.736497	−	1.27565i	−0.954063	−	0.299605i	$-0.903145\pi$
$383$	−14.4135	−	24.9650i	−0.736497	−	1.27565i	0.217566	−	0.976046i	$-0.430188\pi$
$384$		0			0
$385$	0.462022	−	0.178060i	0.0235468	−	0.00907475i
$386$		0			0
$387$	0.426358	+	3.23851i	0.0216730	+	0.164623i
$388$		0			0
$389$	22.0785	+	2.90669i	1.11942	+	0.147375i	0.667449	−	0.744655i	$-0.267386\pi$
$389$	22.0785	+	2.90669i	1.11942	+	0.147375i	0.451975	+	0.892030i	$0.350719\pi$
$390$		0			0
$391$	−13.2618	+	13.2618i	−0.670676	+	0.670676i
$392$		0			0
$393$	0.939737	+	0.939737i	0.0474034	+	0.0474034i
$394$		0			0
$395$	−0.00322785	+	0.0245179i	−0.000162411	+	0.00123363i
$396$		0			0
$397$	7.07370	−	0.931270i	0.355019	−	0.0467391i	0.0490923	−	0.998794i	$-0.484367\pi$
$397$	7.07370	−	0.931270i	0.355019	−	0.0467391i	0.305927	+	0.952055i	$0.401034\pi$
$398$		0			0
$399$	14.2708	+	37.0292i	0.714432	+	1.85378i
$400$		0			0
$401$	6.77195	−	3.90979i	0.338175	−	0.195245i	−0.321290	−	0.946981i	$-0.604116\pi$
$401$	6.77195	−	3.90979i	0.338175	−	0.195245i	0.659465	+	0.751736i	$0.270783\pi$
$402$		0			0
$403$	16.7433	+	21.8203i	0.834042	+	1.08694i
$404$		0			0
$405$	−1.56198	+	0.646994i	−0.0776155	+	0.0321494i
$406$		0			0
$407$	−2.41991	−	2.41991i	−0.119951	−	0.119951i
$408$		0			0
$409$	−2.08678	−	7.78797i	−0.103185	−	0.385090i	0.894948	−	0.446170i	$-0.147212\pi$
$409$	−2.08678	−	7.78797i	−0.103185	−	0.385090i	−0.998133	+	0.0610796i	$0.980546\pi$
$410$		0			0
$411$	23.3354	−	30.4112i	1.15105	−	1.50008i
$412$		0			0
$413$	−0.239187	+	0.391487i	−0.0117696	+	0.0192638i
$414$		0			0
$415$	0.258021	+	0.446905i	0.0126657	+	0.0219377i
$416$		0			0
$417$	8.95468	−	15.5100i	0.438513	−	0.759526i
$418$		0			0
$419$	30.7670	+	12.7441i	1.50307	+	0.622591i	0.974113	−	0.226060i	$-0.0725847\pi$
$419$	30.7670	+	12.7441i	1.50307	+	0.622591i	0.528953	+	0.848651i	$0.322585\pi$
$420$		0			0
$421$	9.04483	+	21.8361i	0.440818	+	1.06423i	0.975662	+	0.219278i	$0.0703702\pi$
$421$	9.04483	+	21.8361i	0.440818	+	1.06423i	−0.534845	+	0.844950i	$0.679630\pi$
$422$		0			0
$423$	−14.9718	−	55.8754i	−0.727952	−	2.71675i
$424$		0			0
$425$	4.93077	−	18.4019i	0.239177	−	0.892622i
$426$		0			0
$427$	14.2132	+	4.18956i	0.687823	+	0.202747i
$428$		0			0
$429$	−31.0596	+	4.08907i	−1.49957	+	0.197422i
$430$		0			0
$431$	22.1475	+	12.7869i	1.06681	+	0.615921i	0.927307	−	0.374301i	$-0.122117\pi$
$431$	22.1475	+	12.7869i	1.06681	+	0.615921i	0.139499	+	0.990222i	$0.455451\pi$
$432$		0			0
$433$			2.13990i			0.102837i	0.998677	+	0.0514184i	$0.0163742\pi$
$433$			2.13990i			0.102837i	−0.998677	+	0.0514184i	$0.983626\pi$
$434$		0			0
$435$	−0.0903221	+	0.218057i	−0.00433061	+	0.0104550i
$436$		0			0
$437$	−3.11656	+	23.6726i	−0.149085	+	1.13242i
$438$		0			0
$439$	−3.25022	+	12.1300i	−0.155125	+	0.578933i	0.843970	+	0.536390i	$0.180213\pi$
$439$	−3.25022	+	12.1300i	−0.155125	+	0.578933i	−0.999095	+	0.0425428i	$0.986454\pi$
$440$		0			0
$441$	−40.5089	+	20.7763i	−1.92899	+	0.989349i
$442$		0			0
$443$	4.23055	−	5.51336i	0.200999	−	0.261947i	−0.681968	−	0.731382i	$-0.738876\pi$
$443$	4.23055	−	5.51336i	0.200999	−	0.261947i	0.882967	+	0.469435i	$0.155542\pi$
$444$		0			0
$445$	−1.36395	+	1.04660i	−0.0646576	+	0.0496135i
$446$		0			0
$447$	0.600565			0.0284058
$448$		0			0
$449$	−16.2595			−0.767331			−0.383666	−	0.923472i	$-0.625338\pi$
$449$	−16.2595			−0.767331			−0.383666	+	0.923472i	$0.625338\pi$
$450$		0			0
$451$	−6.94879	+	5.33199i	−0.327206	+	0.251074i
$452$		0			0
$453$	34.7634	−	45.3045i	1.63332	−	2.12859i
$454$		0			0
$455$	−2.14815	+	0.228671i	−0.100707	+	0.0107203i
$456$		0			0
$457$	−5.41360	+	20.2038i	−0.253238	+	0.945096i	0.715825	+	0.698280i	$0.246051\pi$
$457$	−5.41360	+	20.2038i	−0.253238	+	0.945096i	−0.969062	+	0.246816i	$0.920616\pi$
$458$		0			0
$459$	5.38804	−	40.9263i	0.251492	−	1.91027i
$460$		0			0
$461$	6.20645	−	14.9837i	0.289063	−	0.697861i	−0.710922	−	0.703271i	$-0.751722\pi$
$461$	6.20645	−	14.9837i	0.289063	−	0.697861i	0.999985	+	0.00541027i	$0.00172215\pi$
$462$		0			0
$463$		−	27.2689i		−	1.26729i	−0.773623	−	0.633646i	$-0.781557\pi$
$463$		−	27.2689i		−	1.26729i	0.773623	−	0.633646i	$-0.218443\pi$
$464$		0			0
$465$	1.35230	+	0.780753i	0.0627116	+	0.0362065i
$466$		0			0
$467$	−26.2301	+	3.45325i	−1.21378	+	0.159798i	−0.710106	−	0.704095i	$-0.751353\pi$
$467$	−26.2301	+	3.45325i	−1.21378	+	0.159798i	−0.503677	+	0.863892i	$0.668020\pi$
$468$		0			0
$469$	−2.11180	−	8.74499i	−0.0975140	−	0.403806i
$470$		0			0
$471$	−12.3863	+	46.2263i	−0.570730	+	2.12999i
$472$		0			0
$473$	0.198386	+	0.740387i	0.00912181	+	0.0340431i
$474$		0			0
$475$	−9.28155	−	22.4076i	−0.425867	−	1.02813i
$476$		0			0
$477$	−44.7207	−	18.5239i	−2.04762	−	0.848151i
$478$		0			0
$479$	8.05963	−	13.9597i	0.368254	−	0.637835i	−0.621039	−	0.783780i	$-0.713289\pi$
$479$	8.05963	−	13.9597i	0.368254	−	0.637835i	0.989293	+	0.145945i	$0.0466223\pi$
$480$		0			0
$481$	7.46556	+	12.9307i	0.340400	+	0.589591i
$482$		0			0
$483$	−40.0149	−	0.994521i	−1.82074	−	0.0452523i
$484$		0			0
$485$	−0.919932	+	1.19888i	−0.0417719	+	0.0544383i
$486$		0			0
$487$	5.15370	+	19.2339i	0.233537	+	0.871570i	0.978803	+	0.204804i	$0.0656556\pi$
$487$	5.15370	+	19.2339i	0.233537	+	0.871570i	−0.745266	+	0.666767i	$0.767678\pi$
$488$		0			0
$489$	28.0141	+	28.0141i	1.26684	+	1.26684i
$490$		0			0
$491$	2.69918	−	1.11804i	0.121812	−	0.0504562i	−0.320945	−	0.947098i	$-0.604000\pi$
$491$	2.69918	−	1.11804i	0.121812	−	0.0504562i	0.442757	+	0.896642i	$0.354000\pi$
$492$		0			0
$493$	−1.45254	−	1.89299i	−0.0654192	−	0.0852559i
$494$		0			0
$495$	−1.05409	+	0.608578i	−0.0473777	+	0.0273535i
$496$		0			0
$497$	3.22518	+	8.36856i	0.144669	+	0.375381i
$498$		0			0
$499$	10.5730	−	1.39197i	0.473314	−	0.0623130i	0.109904	−	0.993942i	$-0.464946\pi$
$499$	10.5730	−	1.39197i	0.473314	−	0.0623130i	0.363410	+	0.931629i	$0.381612\pi$
$500$		0			0
$501$	4.59175	−	34.8778i	0.205144	−	1.55822i
$502$		0			0
$503$	−8.98317	−	8.98317i	−0.400540	−	0.400540i	0.477884	−	0.878423i	$-0.341404\pi$
$503$	−8.98317	−	8.98317i	−0.400540	−	0.400540i	−0.878423	+	0.477884i	$0.841404\pi$
$504$		0			0
$505$	0.163055	−	0.163055i	0.00725585	−	0.00725585i
$506$		0			0
$507$	95.7771	+	12.6093i	4.25361	+	0.559999i
$508$		0			0
$509$	3.82715	+	29.0701i	0.169635	+	1.28851i	0.838409	+	0.545042i	$0.183486\pi$
$509$	3.82715	+	29.0701i	0.169635	+	1.28851i	−0.668774	+	0.743466i	$0.733180\pi$
$510$		0			0
$511$	−6.26594	+	39.9053i	−0.277189	+	1.76531i
$512$		0			0
$513$	−26.2764	−	45.5120i	−1.16013	−	2.00941i
$514$		0			0
$515$	−0.334661	+	0.256794i	−0.0147469	+	0.0113157i
$516$		0			0
$517$	−5.19464	−	12.5410i	−0.228460	−	0.551551i
$518$		0			0
$519$	−3.93498	+	3.93498i	−0.172726	+	0.172726i
$520$		0			0
$521$	7.86432	−	2.10724i	0.344542	−	0.0923197i	−0.0823985	−	0.996599i	$-0.526258\pi$
$521$	7.86432	−	2.10724i	0.344542	−	0.0923197i	0.426941	+	0.904280i	$0.359591\pi$
$522$		0			0
$523$	−22.0586	−	16.9262i	−0.964555	−	0.740129i	0.00108832	−	0.999999i	$-0.499654\pi$
$523$	−22.0586	−	16.9262i	−0.964555	−	0.740129i	−0.965644	+	0.259870i	$0.916320\pi$
$524$		0			0
$525$	35.7061	−	19.4484i	1.55834	−	0.848798i
$526$		0			0
$527$	−13.6710	+	7.89297i	−0.595519	+	0.343823i
$528$		0			0
$529$	−0.938305	−	0.541730i	−0.0407959	−	0.0235535i
$530$		0			0
$531$	0.431569	−	1.04190i	0.0187285	−	0.0452146i
$532$		0			0
$533$	35.3050	−	14.6238i	1.52923	−	0.633427i
$534$		0			0
$535$	−0.868845	+	0.232806i	−0.0375634	+	0.0100651i
$536$		0			0
$537$	18.7361	+	5.02032i	0.808522	+	0.216643i
$538$		0			0
$539$	−8.78812	+	6.07442i	−0.378531	+	0.261644i
$540$		0			0
$541$	4.97274	+	37.7717i	0.213795	+	1.62393i	0.675821	+	0.737066i	$0.263789\pi$
$541$	4.97274	+	37.7717i	0.213795	+	1.62393i	−0.462026	+	0.886866i	$0.652877\pi$
$542$		0			0
$543$	13.3907	−	23.1934i	0.574652	−	0.995326i
$544$		0			0
$545$	−1.56986			−0.0672455
$546$		0			0
$547$	−3.72389	−	1.54249i	−0.159222	−	0.0659520i	0.301649	−	0.953419i	$-0.402463\pi$
$547$	−3.72389	−	1.54249i	−0.159222	−	0.0659520i	−0.460871	+	0.887467i	$0.652463\pi$
$548$		0			0
$549$	−36.1131	−	4.75438i	−1.54127	−	0.202912i
$550$		0			0
$551$	−2.93418	−	0.786212i	−0.125000	−	0.0334938i
$552$		0			0
$553$	−0.0564784	−	0.530560i	−0.00240170	−	0.0225617i
$554$		0			0
$555$	0.672527	+	0.516048i	0.0285472	+	0.0219050i
$556$		0			0
$557$	27.5011	+	35.8402i	1.16526	+	1.51860i	0.812577	+	0.582854i	$0.198064\pi$
$557$	27.5011	+	35.8402i	1.16526	+	1.51860i	0.352683	+	0.935743i	$0.385269\pi$
$558$		0			0
$559$		−	3.34421i		−	0.141445i
$560$		0			0
$561$		−	17.9806i		−	0.759142i
$562$		0			0
$563$	−24.6335	−	32.1030i	−1.03818	−	1.35298i	−0.933541	−	0.358469i	$-0.883299\pi$
$563$	−24.6335	−	32.1030i	−1.03818	−	1.35298i	−0.104637	−	0.994511i	$-0.533368\pi$
$564$		0			0
$565$	1.85656	+	1.42459i	0.0781059	+	0.0599327i
$566$		0			0
$567$	29.4825	−	21.4803i	1.23815	−	0.902088i
$568$		0			0
$569$	−32.8330	−	8.79758i	−1.37643	−	0.368814i	−0.506608	−	0.862177i	$-0.669101\pi$
$569$	−32.8330	−	8.79758i	−1.37643	−	0.368814i	−0.869823	+	0.493363i	$0.835767\pi$
$570$		0			0
$571$	−10.8970	−	1.43461i	−0.456024	−	0.0600367i	−0.100984	−	0.994888i	$-0.532199\pi$
$571$	−10.8970	−	1.43461i	−0.456024	−	0.0600367i	−0.355039	+	0.934851i	$0.615533\pi$
$572$		0			0
$573$	−0.495205	−	0.205121i	−0.0206875	−	0.00856904i
$574$		0			0
$575$	24.4637			1.02021
$576$		0			0
$577$	2.43437	−	4.21645i	0.101344	−	0.175533i	−0.810895	−	0.585192i	$-0.801019\pi$
$577$	2.43437	−	4.21645i	0.101344	−	0.175533i	0.912239	+	0.409659i	$0.134352\pi$
$578$		0			0
$579$	−6.78786	−	51.5589i	−0.282094	−	2.14271i
$580$		0			0
$581$	−7.67488	−	8.06610i	−0.318407	−	0.334638i
$582$		0			0
$583$	−10.9717	−	2.93987i	−0.454403	−	0.121757i
$584$		0			0
$585$	5.12942	−	1.37442i	0.212075	−	0.0568254i
$586$		0			0
$587$	40.7302	−	16.8710i	1.68112	−	0.696341i	0.681737	−	0.731597i	$-0.261225\pi$
$587$	40.7302	−	16.8710i	1.68112	−	0.696341i	0.999378	+	0.0352564i	$0.0112248\pi$
$588$		0			0
$589$	−7.69081	+	18.5673i	−0.316894	+	0.765051i
$590$		0			0
$591$	32.3847	+	18.6973i	1.33213	+	0.769106i
$592$		0			0
$593$	−37.3410	+	21.5588i	−1.53341	+	0.885315i	−0.534209	+	0.845353i	$0.679390\pi$
$593$	−37.3410	+	21.5588i	−1.53341	+	0.885315i	−0.999201	+	0.0399620i	$0.987276\pi$
$594$		0			0
$595$	0.0308068	−	1.23952i	0.00126296	−	0.0508154i
$596$		0			0
$597$	−51.7714	−	39.7256i	−2.11886	−	1.62586i
$598$		0			0
$599$	−29.5451	+	7.91659i	−1.20718	+	0.323463i	−0.805655	−	0.592385i	$-0.798186\pi$
$599$	−29.5451	+	7.91659i	−1.20718	+	0.323463i	−0.401525	+	0.915848i	$0.631520\pi$
$600$		0			0
$601$	6.56768	−	6.56768i	0.267901	−	0.267901i	−0.560353	−	0.828254i	$-0.689334\pi$
$601$	6.56768	−	6.56768i	0.267901	−	0.267901i	0.828254	+	0.560353i	$0.189334\pi$
$602$		0			0
$603$	8.46291	+	20.4313i	0.344636	+	0.832026i
$604$		0			0
$605$	0.843548	−	0.647277i	0.0342951	−	0.0263156i
$606$		0			0
$607$	16.4364	+	28.4687i	0.667133	+	1.15551i	0.978702	+	0.205285i	$0.0658121\pi$
$607$	16.4364	+	28.4687i	0.667133	+	1.15551i	−0.311569	+	0.950223i	$0.600855\pi$
$608$		0			0
$609$	0.789927	−	5.03074i	0.0320095	−	0.203856i
$610$		0			0
$611$	7.73021	+	58.7168i	0.312731	+	2.37543i
$612$		0			0
$613$	−27.1330	−	3.57213i	−1.09589	−	0.144277i	−0.439166	−	0.898406i	$-0.644726\pi$
$613$	−27.1330	−	3.57213i	−1.09589	−	0.144277i	−0.656726	+	0.754129i	$0.728059\pi$
$614$		0			0
$615$	1.53411	−	1.53411i	0.0618612	−	0.0618612i
$616$		0			0
$617$	8.02312	+	8.02312i	0.322999	+	0.322999i	0.849916	−	0.526918i	$-0.176652\pi$
$617$	8.02312	+	8.02312i	0.322999	+	0.322999i	−0.526918	+	0.849916i	$0.676652\pi$
$618$		0			0
$619$	4.70972	−	35.7739i	0.189300	−	1.43787i	−0.588061	−	0.808817i	$-0.700108\pi$
$619$	4.70972	−	35.7739i	0.189300	−	1.43787i	0.777360	−	0.629056i	$-0.216558\pi$
$620$		0			0
$621$	52.5539	−	6.91885i	2.10892	−	0.277644i
$622$		0			0
$623$	23.3054	−	28.8582i	0.933710	−	1.15618i
$624$		0			0
$625$	−21.4555	+	12.3873i	−0.858220	+	0.495493i
$626$		0			0
$627$	−13.9352	−	18.1607i	−0.556519	−	0.725270i
$628$		0			0
$629$	−7.91744	+	3.27951i	−0.315689	+	0.130763i
$630$		0			0
$631$	16.7532	+	16.7532i	0.666936	+	0.666936i	0.957005	−	0.290070i	$-0.0936785\pi$
$631$	16.7532	+	16.7532i	0.666936	+	0.666936i	−0.290070	+	0.957005i	$0.593679\pi$
$632$		0			0
$633$	3.50450	+	13.0790i	0.139291	+	0.519843i
$634$		0			0
$635$	−0.468084	+	0.610019i	−0.0185753	+	0.0242079i
$636$		0			0
$637$	43.8948	−	15.6756i	1.73917	−	0.621090i
$638$		0			0
$639$	−11.0231	−	19.0926i	−0.436068	−	0.755292i
$640$		0			0
$641$	15.5398	−	26.9158i	0.613786	−	1.06311i	−0.376810	−	0.926291i	$-0.622979\pi$
$641$	15.5398	−	26.9158i	0.613786	−	1.06311i	0.990596	−	0.136818i	$-0.0436877\pi$
$642$		0			0
$643$	−20.4285	−	8.46178i	−0.805623	−	0.333700i	−0.0584169	−	0.998292i	$-0.518605\pi$
$643$	−20.4285	−	8.46178i	−0.805623	−	0.333700i	−0.747206	+	0.664592i	$0.768605\pi$
$644$		0			0
$645$	−0.0726580	−	0.175412i	−0.00286091	−	0.00690684i
$646$		0			0
$647$	−3.79811	−	14.1747i	−0.149319	−	0.557266i	−0.999525	−	0.0308162i	$-0.990189\pi$
$647$	−3.79811	−	14.1747i	−0.149319	−	0.557266i	0.850206	−	0.526450i	$-0.176477\pi$
$648$		0			0
$649$	0.0684929	−	0.255619i	0.00268858	−	0.0100339i
$650$		0			0
$651$	−32.3160	−	9.52566i	−1.26656	−	0.373340i
$652$		0			0
$653$	34.3865	−	4.52707i	1.34565	−	0.177158i	0.576955	−	0.816776i	$-0.304241\pi$
$653$	34.3865	−	4.52707i	1.34565	−	0.177158i	0.768693	+	0.639618i	$0.220907\pi$
$654$		0			0
$655$	−0.0457812	−	0.0264318i	−0.00178882	−	0.00103278i
$656$		0			0
$657$		−	99.2963i		−	3.87392i
$658$		0			0
$659$	−14.7136	+	35.5218i	−0.573162	+	1.38373i	0.325688	+	0.945477i	$0.394404\pi$
$659$	−14.7136	+	35.5218i	−0.573162	+	1.38373i	−0.898850	+	0.438257i	$0.855596\pi$
$660$		0			0
$661$	−1.02858	+	7.81285i	−0.0400072	+	0.303885i	0.959729	+	0.280927i	$0.0906417\pi$
$661$	−1.02858	+	7.81285i	−0.0400072	+	0.303885i	−0.999736	+	0.0229580i	$0.992692\pi$
$662$		0			0
$663$	−20.3039	+	75.7751i	−0.788537	+	2.94286i
$664$		0			0
$665$	−0.929531	−	1.27581i	−0.0360457	−	0.0494740i
$666$		0			0
$667$	1.86523	−	2.43081i	0.0722218	−	0.0941213i
$668$		0			0
$669$	−43.6311	+	33.4793i	−1.68688	+	1.29439i
$670$		0			0
$671$	−8.54742			−0.329970
$672$		0			0
$673$	11.5940			0.446916			0.223458	−	0.974714i	$-0.428265\pi$
$673$	11.5940			0.446916			0.223458	+	0.974714i	$0.428265\pi$
$674$		0			0
$675$	−42.7175	+	32.7783i	−1.64420	+	1.26164i
$676$		0			0
$677$	3.61669	−	4.71336i	0.139001	−	0.181149i	−0.718666	−	0.695356i	$-0.755247\pi$
$677$	3.61669	−	4.71336i	0.139001	−	0.181149i	0.857666	+	0.514206i	$0.171913\pi$
$678$		0			0
$679$	13.2217	−	29.8031i	0.507402	−	1.14374i
$680$		0			0
$681$	1.60681	−	5.99671i	0.0615733	−	0.229795i
$682$		0			0
$683$	−6.76146	+	51.3584i	−0.258720	+	1.96517i	0.00287261	+	0.999996i	$0.499086\pi$
$683$	−6.76146	+	51.3584i	−0.258720	+	1.96517i	−0.261593	+	0.965178i	$0.584248\pi$
$684$		0			0
$685$	−0.583503	+	1.40870i	−0.0222945	+	0.0538237i
$686$		0			0
$687$		−	8.22268i		−	0.313715i
$688$		0			0
$689$	42.9181	+	24.7788i	1.63505	+	0.943996i
$690$		0			0
$691$	19.2320	−	2.53194i	0.731620	−	0.0963196i	0.244493	−	0.969651i	$-0.421378\pi$
$691$	19.2320	−	2.53194i	0.731620	−	0.0963196i	0.487127	+	0.873331i	$0.338045\pi$
$692$		0			0
$693$	19.0250	−	18.1023i	0.722701	−	0.687648i
$694$		0			0
$695$	−0.184379	+	0.688113i	−0.00699390	+	0.0261016i
$696$		0			0
$697$	5.67667	+	21.1856i	0.215019	+	0.802463i
$698$		0			0
$699$	−18.9965	−	45.8616i	−0.718514	−	1.73465i
$700$		0			0
$701$	31.5656	+	13.0749i	1.19222	+	0.493832i	0.888476	−	0.458923i	$-0.151765\pi$
$701$	31.5656	+	13.0749i	1.19222	+	0.493832i	0.303739	+	0.952755i	$0.401765\pi$
$702$		0			0
$703$	−5.45509	+	9.44849i	−0.205743	+	0.356357i
$704$		0			0
$705$	1.68118	+	2.91189i	0.0633169	+	0.109668i
$706$		0			0
$707$	−2.59391	+	4.24556i	−0.0975541	+	0.159671i
$708$		0			0
$709$	12.3531	−	16.0988i	0.463929	−	0.604604i	−0.501536	−	0.865137i	$-0.667231\pi$
$709$	12.3531	−	16.0988i	0.463929	−	0.604604i	0.965465	+	0.260533i	$0.0838981\pi$
$710$		0			0
$711$	0.339462	+	1.26689i	0.0127308	+	0.0475121i
$712$		0			0
$713$	−14.3337	−	14.3337i	−0.536801	−	0.536801i
$714$		0			0
$715$	1.15127	−	0.476873i	0.0430552	−	0.0178340i
$716$		0			0
$717$	−3.38980	−	4.41768i	−0.126595	−	0.164981i
$718$		0			0
$719$	−19.8525	+	11.4618i	−0.740373	+	0.427455i	−0.822205	−	0.569191i	$-0.807256\pi$
$719$	−19.8525	+	11.4618i	−0.740373	+	0.427455i	0.0818317	+	0.996646i	$0.473923\pi$
$720$		0			0
$721$	5.71823	−	7.08068i	0.212958	−	0.263698i
$722$		0			0
$723$	15.8847	−	2.09125i	0.590757	−	0.0777746i
$724$		0			0
$725$	−0.406242	+	3.08571i	−0.0150874	+	0.114600i
$726$		0			0
$727$	−2.05933	−	2.05933i	−0.0763765	−	0.0763765i	0.667887	−	0.744263i	$-0.267199\pi$
$727$	−2.05933	−	2.05933i	−0.0763765	−	0.0763765i	−0.744263	+	0.667887i	$0.767199\pi$
$728$		0			0
$729$	7.23139	−	7.23139i	0.267829	−	0.267829i
$730$		0			0
$731$	1.90300	+	0.250535i	0.0703851	+	0.00926637i
$732$		0			0
$733$	−2.24400	−	17.0449i	−0.0828841	−	0.629567i	−0.981588	−	0.191011i	$-0.938823\pi$
$733$	−2.24400	−	17.0449i	−0.0828841	−	0.629567i	0.898704	−	0.438556i	$-0.144510\pi$
$734$		0			0
$735$	1.96181	−	1.77590i	0.0723625	−	0.0655052i
$736$		0			0
$737$	2.59471	+	4.49417i	0.0955774	+	0.165545i
$738$		0			0
$739$	−15.3313	+	11.7641i	−0.563972	+	0.432751i	−0.850996	−	0.525173i	$-0.824001\pi$
$739$	−15.3313	+	11.7641i	−0.563972	+	0.432751i	0.287024	+	0.957923i	$0.407334\pi$
$740$		0			0
$741$	38.2195	+	92.2700i	1.40403	+	3.38962i
$742$		0			0
$743$	17.4644	−	17.4644i	0.640708	−	0.640708i	−0.310022	−	0.950729i	$-0.600336\pi$
$743$	17.4644	−	17.4644i	0.640708	−	0.640708i	0.950729	+	0.310022i	$0.100336\pi$
$744$		0			0
$745$	−0.0230749	+	0.00618290i	−0.000845399	+	0.000226524i
$746$		0			0
$747$	21.7135	+	16.6614i	0.794457	+	0.609608i
$748$		0			0
$749$	17.0431	−	9.28305i	0.622742	−	0.339195i
$750$		0			0
$751$	−23.0021	+	13.2803i	−0.839360	+	0.484605i	−0.857047	−	0.515239i	$-0.827703\pi$
$751$	−23.0021	+	13.2803i	−0.839360	+	0.484605i	0.0176867	+	0.999844i	$0.494370\pi$
$752$		0			0
$753$	−35.6212	−	20.5659i	−1.29811	−	0.749462i
$754$		0			0
$755$	−0.869261	+	2.09858i	−0.0316356	+	0.0763752i
$756$		0			0
$757$	2.27095	−	0.940657i	0.0825390	−	0.0341888i	−0.341032	−	0.940052i	$-0.610776\pi$
$757$	2.27095	−	0.940657i	0.0825390	−	0.0341888i	0.423571	+	0.905863i	$0.360776\pi$
$758$		0			0
$759$	22.3024	−	5.97591i	0.809525	−	0.216912i
$760$		0			0
$761$	11.7955	+	3.16059i	0.427587	+	0.114571i	0.466193	−	0.884683i	$-0.345625\pi$
$761$	11.7955	+	3.16059i	0.427587	+	0.114571i	−0.0386065	+	0.999254i	$0.512292\pi$
$762$		0			0
$763$	32.9246	−	7.95086i	1.19195	−	0.287840i
$764$		0			0
$765$	0.397831	+	3.02183i	0.0143836	+	0.109254i
$766$		0			0
$767$	−0.577295	+	0.999904i	−0.0208449	+	0.0361044i
$768$		0			0
$769$	−27.7647			−1.00122			−0.500611	−	0.865672i	$-0.666891\pi$
$769$	−27.7647			−1.00122			−0.500611	+	0.865672i	$0.666891\pi$
$770$		0			0
$771$	61.0639	+	25.2935i	2.19916	+	0.910924i
$772$		0			0
$773$	−2.43184	−	0.320158i	−0.0874672	−	0.0115153i	0.0866656	−	0.996237i	$-0.472379\pi$
$773$	−2.43184	−	0.320158i	−0.0874672	−	0.0115153i	−0.174133	+	0.984722i	$0.555712\pi$
$774$		0			0
$775$	19.8893	+	5.32932i	0.714445	+	0.191435i
$776$		0			0
$777$	−16.7185	−	7.41689i	−0.599771	−	0.266079i
$778$		0			0
$779$	22.1527	+	16.9984i	0.793703	+	0.609029i
$780$		0			0
$781$	−3.14935	−	4.10431i	−0.112693	−	0.146864i
$782$		0			0
$783$			6.74376i			0.241002i
$784$		0			0
$785$		−	1.90362i		−	0.0679432i
$786$		0			0
$787$	19.8054	+	25.8109i	0.705986	+	0.920058i	0.999354	−	0.0359412i	$-0.0114429\pi$
$787$	19.8054	+	25.8109i	0.705986	+	0.920058i	−0.293368	+	0.955999i	$0.594776\pi$
$788$		0			0
$789$	−54.0086	−	41.4423i	−1.92276	−	1.47538i
$790$		0			0
$791$	−46.1524	−	20.4748i	−1.64099	−	0.728001i
$792$		0			0
$793$	36.0211	+	9.65183i	1.27915	+	0.342746i
$794$		0			0
$795$	2.78952	+	0.367247i	0.0989339	+	0.0130249i
$796$		0			0
$797$	−3.28995	−	1.36274i	−0.116536	−	0.0482708i	0.323654	−	0.946176i	$-0.395089\pi$
$797$	−3.28995	−	1.36274i	−0.116536	−	0.0482708i	−0.440190	+	0.897905i	$0.645089\pi$
$798$		0			0
$799$	−33.9916			−1.20253
$800$		0			0
$801$	−45.5913	+	78.9665i	−1.61089	+	2.79014i
$802$		0			0
$803$	−3.04137	−	23.1015i	−0.107328	−	0.815235i
$804$		0			0
$805$	1.54769	−	0.373747i	0.0545488	−	0.0131728i
$806$		0			0
$807$	75.3037	+	20.1776i	2.65082	+	0.710284i
$808$		0			0
$809$	34.0941	−	9.13548i	1.19868	−	0.321186i	0.396371	−	0.918090i	$-0.370269\pi$
$809$	34.0941	−	9.13548i	1.19868	−	0.321186i	0.802313	+	0.596904i	$0.203603\pi$
$810$		0			0
$811$	10.7263	−	4.44297i	0.376651	−	0.156014i	−0.186323	−	0.982489i	$-0.559657\pi$
$811$	10.7263	−	4.44297i	0.376651	−	0.156014i	0.562974	+	0.826475i	$0.309657\pi$
$812$		0			0
$813$	−12.4186	+	29.9812i	−0.435540	+	1.05149i
$814$		0			0
$815$	−1.36477	−	0.787948i	−0.0478056	−	0.0276006i
$816$		0			0
$817$	2.11623	−	1.22181i	0.0740376	−	0.0427457i
$818$		0			0
$819$	−100.618	+	54.8045i	−3.51587	+	1.91503i
$820$		0			0
$821$	0.559941	+	0.429658i	0.0195421	+	0.0149952i	0.618486	−	0.785796i	$-0.287746\pi$
$821$	0.559941	+	0.429658i	0.0195421	+	0.0149952i	−0.598944	+	0.800791i	$0.704413\pi$
$822$		0			0
$823$	26.0594	−	6.98260i	0.908374	−	0.243398i	0.225765	−	0.974182i	$-0.427512\pi$
$823$	26.0594	−	6.98260i	0.908374	−	0.243398i	0.682609	+	0.730784i	$0.260845\pi$
$824$		0			0
$825$	−16.5842	+	16.5842i	−0.577388	+	0.577388i
$826$		0			0
$827$	−9.55713	−	23.0729i	−0.332334	−	0.802325i	−0.998406	−	0.0564377i	$-0.982026\pi$
$827$	−9.55713	−	23.0729i	−0.332334	−	0.802325i	0.666072	−	0.745887i	$-0.267974\pi$
$828$		0			0
$829$	21.5966	−	16.5716i	0.750079	−	0.575556i	−0.161406	−	0.986888i	$-0.551603\pi$
$829$	21.5966	−	16.5716i	0.750079	−	0.575556i	0.911486	+	0.411332i	$0.134936\pi$
$830$		0			0
$831$	−27.2462	−	47.1917i	−0.945159	−	1.63706i
$832$		0			0
$833$	5.63168	+	26.1524i	0.195126	+	0.906127i
$834$		0			0
$835$	0.182647	+	1.38735i	0.00632078	+	0.0480111i
$836$		0			0
$837$	44.2343	+	5.82356i	1.52896	+	0.201292i
$838$		0			0
$839$	−18.0711	+	18.0711i	−0.623885	+	0.623885i	−0.946523	−	0.322638i	$-0.895430\pi$
$839$	−18.0711	+	18.0711i	−0.623885	+	0.623885i	0.322638	+	0.946523i	$0.395430\pi$
$840$		0			0
$841$	−20.2305	−	20.2305i	−0.697602	−	0.697602i
$842$		0			0
$843$	−12.7966	+	97.2001i	−0.440739	+	3.34775i
$844$		0			0
$845$	−3.80976	+	0.501564i	−0.131060	+	0.0172543i
$846$		0			0
$847$	−14.4134	+	17.8476i	−0.495250	+	0.613250i
$848$		0			0
$849$	56.7143	−	32.7440i	1.94643	−	1.12377i
$850$		0			0
$851$	−6.69915	−	8.73050i	−0.229644	−	0.299278i
$852$		0			0
$853$	−26.1271	+	10.8222i	−0.894574	+	0.370545i	−0.782131	−	0.623114i	$-0.785867\pi$
$853$	−26.1271	+	10.8222i	−0.894574	+	0.370545i	−0.112442	+	0.993658i	$0.535867\pi$
$854$		0			0
$855$	2.74378	+	2.74378i	0.0938352	+	0.0938352i
$856$		0			0
$857$	−6.09140	−	22.7334i	−0.208078	−	0.776559i	−0.988489	−	0.151292i	$-0.951657\pi$
$857$	−6.09140	−	22.7334i	−0.208078	−	0.776559i	0.780411	−	0.625267i	$-0.215010\pi$
$858$		0			0
$859$	2.43440	−	3.17257i	0.0830605	−	0.108247i	−0.749975	−	0.661466i	$-0.769934\pi$
$859$	2.43440	−	3.17257i	0.0830605	−	0.108247i	0.833035	+	0.553220i	$0.186601\pi$
$860$		0			0
$861$	−24.4049	+	39.9445i	−0.831717	+	1.36130i
$862$		0			0
$863$	−16.2763	−	28.1913i	−0.554051	−	0.959644i	−0.997977	−	0.0635805i	$-0.979748\pi$
$863$	−16.2763	−	28.1913i	−0.554051	−	0.959644i	0.443926	−	0.896063i	$-0.353585\pi$
$864$		0			0
$865$	0.110678	−	0.191701i	0.00376318	−	0.00651802i
$866$		0			0
$867$	6.82022	+	2.82503i	0.231627	+	0.0959430i
$868$		0			0
$869$	0.117781	+	0.284347i	0.00399543	+	0.00964582i
$870$		0			0
$871$	−5.85994	−	21.8696i	−0.198557	−	0.741023i
$872$		0			0
$873$	−20.7436	+	77.4162i	−0.702064	+	2.62014i
$874$		0			0
$875$	−2.34688	+	2.23305i	−0.0793391	+	0.0754909i
$876$		0			0
$877$	−43.1937	+	5.68656i	−1.45855	+	0.192022i	−0.817700	−	0.575645i	$-0.804751\pi$
$877$	−43.1937	+	5.68656i	−1.45855	+	0.192022i	−0.640849	+	0.767667i	$0.721418\pi$
$878$		0			0
$879$	34.6164	+	19.9858i	1.16758	+	0.674104i
$880$		0			0
$881$			31.6488i			1.06628i	0.846029	+	0.533138i	$0.178987\pi$
$881$			31.6488i			1.06628i	−0.846029	+	0.533138i	$0.821013\pi$
$882$		0			0
$883$	−15.0521	+	36.3389i	−0.506542	+	1.22290i	0.439320	+	0.898331i	$0.355220\pi$
$883$	−15.0521	+	36.3389i	−0.506542	+	1.22290i	−0.945862	+	0.324570i	$0.894780\pi$
$884$		0			0
$885$	−0.00855610	+	0.0649900i	−0.000287610	+	0.00218462i
$886$		0			0
$887$	−2.67870	+	9.99703i	−0.0899418	+	0.335667i	−0.996204	−	0.0870485i	$-0.972256\pi$
$887$	−2.67870	+	9.99703i	−0.0899418	+	0.335667i	0.906262	+	0.422716i	$0.138923\pi$
$888$		0			0
$889$	6.72753	−	15.1646i	0.225634	−	0.508603i
$890$		0			0
$891$	−12.8093	+	16.6934i	−0.429129	+	0.559251i
$892$		0			0
$893$	−34.3321	+	26.3439i	−1.14888	+	0.881566i
$894$		0			0
$895$	−0.771562			−0.0257905
$896$		0			0
$897$	−100.736			−3.36348
$898$		0			0
$899$	2.04600	−	1.56995i	0.0682379	−	0.0523608i
$900$		0			0
$901$	−17.3155	+	22.5660i	−0.576862	+	0.751781i
$902$		0			0
$903$	2.41226	+	3.31091i	0.0802749	+	0.110180i
$904$		0			0
$905$	−0.275719	+	1.02900i	−0.00916521	+	0.0342050i
$906$		0			0
$907$	1.57396	−	11.9554i	0.0522624	−	0.396973i	−0.945242	−	0.326370i	$-0.894174\pi$
$907$	1.57396	−	11.9554i	0.0522624	−	0.396973i	0.997505	−	0.0706025i	$-0.0224922\pi$
$908$		0			0
$909$	4.68024	−	11.2991i	0.155234	−	0.374767i
$910$		0			0
$911$		−	58.9763i		−	1.95397i	−0.213306	−	0.976985i	$-0.568423\pi$
$911$		−	58.9763i		−	1.95397i	0.213306	−	0.976985i	$-0.431577\pi$
$912$		0			0
$913$	5.56203	+	3.21124i	0.184076	+	0.106277i
$914$		0			0
$915$	2.09910	−	0.276351i	0.0693940	−	0.00913589i
$916$		0			0
$917$	1.09403	+	0.322484i	0.0361282	+	0.0106494i
$918$		0			0
$919$	3.74933	−	13.9927i	0.123679	−	0.461576i	−0.876110	−	0.482111i	$-0.839870\pi$
$919$	3.74933	−	13.9927i	0.123679	−	0.461576i	0.999789	+	0.0205349i	$0.00653692\pi$
$920$		0			0
$921$	−7.47633	−	27.9021i	−0.246354	−	0.919404i
$922$		0			0
$923$	8.63757	+	20.8529i	0.284309	+	0.686383i
$924$		0			0
$925$	10.3274	+	4.27774i	0.339562	+	0.140651i
$926$		0			0
$927$	−11.1863	+	19.3753i	−0.367408	+	0.636369i
$928$		0			0
$929$	−8.58803	−	14.8749i	−0.281764	−	0.488030i	0.690055	−	0.723757i	$-0.257586\pi$
$929$	−8.58803	−	14.8749i	−0.281764	−	0.488030i	−0.971819	+	0.235727i	$0.924253\pi$
$930$		0			0
$931$	25.9566	+	22.0498i	0.850692	+	0.722651i
$932$		0			0
$933$	−16.3344	+	21.2874i	−0.534764	+	0.696919i
$934$		0			0
$935$	0.185113	+	0.690850i	0.00605384	+	0.0225932i
$936$		0			0
$937$	3.73099	+	3.73099i	0.121886	+	0.121886i	0.765419	−	0.643533i	$-0.222532\pi$
$937$	3.73099	+	3.73099i	0.121886	+	0.121886i	−0.643533	+	0.765419i	$0.722532\pi$
$938$		0			0
$939$	−21.4253	+	8.87464i	−0.699187	+	0.289613i
$940$		0			0
$941$	11.7743	+	15.3446i	0.383832	+	0.500220i	0.944814	−	0.327608i	$-0.106243\pi$
$941$	11.7743	+	15.3446i	0.383832	+	0.500220i	−0.560981	+	0.827829i	$0.689576\pi$
$942$		0			0
$943$	−24.3911	+	14.0822i	−0.794283	+	0.458580i
$944$		0			0
$945$	−2.20174	+	2.72633i	−0.0716225	+	0.0886876i
$946$		0			0
$947$	22.8879	−	3.01325i	0.743756	−	0.0979173i	0.250882	−	0.968018i	$-0.419280\pi$
$947$	22.8879	−	3.01325i	0.743756	−	0.0979173i	0.492874	+	0.870100i	$0.335946\pi$
$948$		0			0
$949$	−13.2693	+	100.790i	−0.430740	+	3.27179i
$950$		0			0
$951$	−6.39083	−	6.39083i	−0.207237	−	0.207237i
$952$		0			0
$953$	−17.4881	+	17.4881i	−0.566494	+	0.566494i	−0.931144	−	0.364651i	$-0.881188\pi$
$953$	−17.4881	+	17.4881i	−0.566494	+	0.566494i	0.364651	+	0.931144i	$0.381188\pi$
$954$		0			0
$955$	0.0211385	+	0.00278294i	0.000684026	+	9.00537e-5i
$956$		0			0
$957$	0.383416	+	2.91234i	0.0123941	+	0.0941424i
$958$		0			0
$959$	5.10312	−	32.4998i	0.164788	−	1.04947i
$960$		0			0
$961$	6.96904	+	12.0707i	0.224808	+	0.389378i
$962$		0			0
$963$	−37.8482	+	29.0419i	−1.21964	+	0.935862i
$964$		0			0
$965$	0.791609	+	1.91111i	0.0254828	+	0.0615209i
$966$		0			0
$967$	18.2657	−	18.2657i	0.587384	−	0.587384i	−0.349538	−	0.936922i	$-0.613661\pi$
$967$	18.2657	−	18.2657i	0.587384	−	0.587384i	0.936922	+	0.349538i	$0.113661\pi$
$968$		0			0
$969$	−55.3689	+	14.8361i	−1.77871	+	0.476603i
$970$		0			0
$971$	−43.5338	−	33.4047i	−1.39707	−	1.07201i	−0.987135	−	0.159891i	$-0.948886\pi$
$971$	−43.5338	−	33.4047i	−1.39707	−	1.07201i	−0.409932	−	0.912116i	$-0.634448\pi$
$972$		0			0
$973$	0.381892	−	15.3655i	0.0122429	−	0.492597i
$974$		0			0
$975$	88.6173	−	51.1632i	2.83803	−	1.63854i
$976$		0			0
$977$	−0.272020	−	0.157051i	−0.00870269	−	0.00502450i	0.495642	−	0.868527i	$-0.334933\pi$
$977$	−0.272020	−	0.157051i	−0.00870269	−	0.00502450i	−0.504345	+	0.863502i	$0.668266\pi$
$978$		0			0
$979$	−8.18824	+	19.7682i	−0.261697	+	0.631793i
$980$		0			0
$981$	−76.9230	+	31.8625i	−2.45596	+	1.01729i
$982$		0			0
$983$	27.9908	−	7.50010i	0.892766	−	0.239216i	0.216859	−	0.976203i	$-0.430419\pi$
$983$	27.9908	−	7.50010i	0.892766	−	0.239216i	0.675907	+	0.736987i	$0.263752\pi$
$984$		0			0
$985$	−1.43678	−	0.384983i	−0.0457795	−	0.0122666i
$986$		0			0
$987$	−50.0070	−	52.5561i	−1.59174	−	1.67288i
$988$		0			0
$989$	0.321715	+	2.44367i	0.0102299	+	0.0777041i
$990$		0			0
$991$	−5.81462	+	10.0712i	−0.184707	+	0.319923i	−0.943478	−	0.331436i	$-0.892467\pi$
$991$	−5.81462	+	10.0712i	−0.184707	+	0.319923i	0.758771	+	0.651358i	$0.225800\pi$
$992$		0			0
$993$	85.3465			2.70839
$994$		0			0
$995$	2.39814	+	0.993342i	0.0760261	+	0.0314911i
$996$		0			0
$997$	−29.3652	−	3.86600i	−0.930005	−	0.122437i	−0.349723	−	0.936853i	$-0.613724\pi$
$997$	−29.3652	−	3.86600i	−0.930005	−	0.122437i	−0.580282	+	0.814416i	$0.697058\pi$
$998$		0			0
$999$	23.3956	+	6.26883i	0.740204	+	0.198337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.81.2		240
4.3	odd	2		224.2.bd.a.221.15	yes	240
7.2	even	3	inner	896.2.bh.a.849.2		240
28.23	odd	6		224.2.bd.a.93.26	yes	240
32.11	odd	8		224.2.bd.a.53.26	✓	240
32.21	even	8	inner	896.2.bh.a.305.2		240
224.107	odd	24		224.2.bd.a.149.15	yes	240
224.149	even	24	inner	896.2.bh.a.177.2		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.53.26	✓	240	32.11	odd	8
224.2.bd.a.93.26	yes	240	28.23	odd	6
224.2.bd.a.149.15	yes	240	224.107	odd	24
224.2.bd.a.221.15	yes	240	4.3	odd	2
896.2.bh.a.81.2		240	1.1	even	1	trivial
896.2.bh.a.177.2		240	224.149	even	24	inner
896.2.bh.a.305.2		240	32.21	even	8	inner
896.2.bh.a.849.2		240	7.2	even	3	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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44576 + 1.87670i) q^{3} +(0.0746500 - 0.0972858i) q^{5} +(-1.07291 + 2.41844i) q^{7} +(1.68329 - 6.28212i) q^{9} +O(q^{10})\)	\(q+(-2.44576 + 1.87670i) q^{3} +(0.0746500 - 0.0972858i) q^{5} +(-1.07291 + 2.41844i) q^{7} +(1.68329 - 6.28212i) q^{9} +(0.199204 - 1.51311i) q^{11} +(-2.54811 + 6.15169i) q^{13} +0.378033i q^{15} +(-3.30969 - 1.91085i) q^{17} +(-4.82378 + 0.635062i) q^{19} +(-1.91462 - 7.92845i) q^{21} +(1.27015 - 4.74027i) q^{23} +(1.29020 + 4.81510i) q^{25} +(4.13349 + 9.97912i) q^{27} +(0.576820 + 0.238927i) q^{29} +(2.06530 - 3.57721i) q^{31} +(2.35244 + 4.07454i) q^{33} +(0.155188 + 0.284915i) q^{35} +(1.36509 - 1.77902i) q^{37} +(-5.31279 - 19.8276i) q^{39} +(-4.05813 - 4.05813i) q^{41} +(-0.464012 + 0.192200i) q^{43} +(-0.485503 - 0.632720i) q^{45} +(7.70274 - 4.44718i) q^{47} +(-4.69775 - 5.18952i) q^{49} +(11.6808 - 1.53780i) q^{51} +(0.971468 - 7.37903i) q^{53} +(-0.132333 - 0.132333i) q^{55} +(10.6060 - 10.6060i) q^{57} +(0.171916 + 0.0226332i) q^{59} +(-0.731024 - 5.55268i) q^{61} +(13.3869 + 10.8111i) q^{63} +(0.408255 + 0.707119i) q^{65} +(-2.69764 + 2.06997i) q^{67} +(5.78957 + 13.9772i) q^{69} +(2.39694 - 2.39694i) q^{71} +(14.7474 - 3.95155i) q^{73} +(-12.1920 - 9.35526i) q^{75} +(3.44564 + 2.10519i) q^{77} +(-0.174648 + 0.100833i) q^{79} +(-11.9401 - 6.89363i) q^{81} +(-1.61043 + 3.88792i) q^{83} +(-0.432967 + 0.179341i) q^{85} +(-1.85915 + 0.498159i) q^{87} +(-13.5423 - 3.62866i) q^{89} +(-12.1436 - 12.7627i) q^{91} +(1.66211 + 12.6249i) q^{93} +(-0.298313 + 0.516692i) q^{95} -12.3233 q^{97} +(-9.17020 - 3.79842i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more