LMFDB - Embedded newform 384.2.n.a.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(49,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("384.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.n (of order $8$, degree $4$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.2
Character	$\chi$	$=$	384.145
Dual form			384.2.n.a.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-2.14608 - 5.18109i) q^{11} +(-0.984096 - 0.407626i) q^{13} -1.30330i q^{15} -0.979053i q^{17} +(-5.68961 - 2.35671i) q^{19} +(-1.40398 - 3.38951i) q^{21} +(3.70206 + 3.70206i) q^{23} +(-2.33445 + 2.33445i) q^{25} +(0.923880 - 0.382683i) q^{27} +(-1.17302 + 2.83193i) q^{29} -1.54469 q^{31} +5.60797 q^{33} +(1.82981 - 4.41756i) q^{35} +(-8.23352 + 3.41044i) q^{37} +(0.753195 - 0.753195i) q^{39} +(-1.10862 - 1.10862i) q^{41} +(3.47106 + 8.37989i) q^{43} +(1.20409 + 0.498752i) q^{45} -3.15582i q^{47} -6.45997i q^{49} +(0.904527 + 0.374667i) q^{51} +(-2.55252 - 6.16232i) q^{53} +(5.16815 + 5.16815i) q^{55} +(4.35464 - 4.35464i) q^{57} +(8.95423 - 3.70896i) q^{59} +(-2.00717 + 4.84573i) q^{61} +3.66878 q^{63} +1.38825 q^{65} +(-1.14380 + 2.76138i) q^{67} +(-4.83697 + 2.00354i) q^{69} +(-10.0373 + 10.0373i) q^{71} +(8.11103 + 8.11103i) q^{73} +(-1.26339 - 3.05010i) q^{75} +(19.0083 + 7.87349i) q^{77} -0.155459i q^{79} +1.00000i q^{81} +(-5.13862 - 2.12849i) q^{83} +(0.488304 + 1.17887i) q^{85} +(-2.16747 - 2.16747i) q^{87} +(-6.15303 + 6.15303i) q^{89} +(3.61044 - 1.49549i) q^{91} +(0.591127 - 1.42711i) q^{93} +8.02623 q^{95} +14.3852 q^{97} +(-2.14608 + 5.18109i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) $ 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		0			0
$5$	−1.20409	+	0.498752i	−0.538487	+	0.223048i	−0.635316	−	0.772253i	$-0.719130\pi$
$5$	−1.20409	+	0.498752i	−0.538487	+	0.223048i	0.0968290	+	0.995301i	$0.469130\pi$
$6$		0			0
$7$	−2.59422	+	2.59422i	−0.980524	+	0.980524i	−0.999814	−	0.0192902i	$-0.993859\pi$
$7$	−2.59422	+	2.59422i	−0.980524	+	0.980524i	0.0192902	+	0.999814i	$0.493859\pi$
$8$		0			0
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$		0			0
$11$	−2.14608	−	5.18109i	−0.647066	−	1.56216i	−0.816960	−	0.576694i	$-0.804342\pi$
$11$	−2.14608	−	5.18109i	−0.647066	−	1.56216i	0.169894	−	0.985462i	$-0.445658\pi$
$12$		0			0
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	0.242016	−	0.970272i	$-0.422191\pi$
$13$	−0.984096	−	0.407626i	−0.272939	−	0.113055i	−0.514955	+	0.857217i	$0.672191\pi$
$14$		0			0
$15$		−	1.30330i		−	0.336511i
$16$		0			0
$17$		−	0.979053i		−	0.237455i	−0.992927	−	0.118728i	$-0.962118\pi$
$17$		−	0.979053i		−	0.237455i	0.992927	−	0.118728i	$-0.0378815\pi$
$18$		0			0
$19$	−5.68961	−	2.35671i	−1.30529	−	0.540667i	−0.381781	−	0.924253i	$-0.624689\pi$
$19$	−5.68961	−	2.35671i	−1.30529	−	0.540667i	−0.923505	+	0.383586i	$0.874689\pi$
$20$		0			0
$21$	−1.40398	−	3.38951i	−0.306374	−	0.739653i
$22$		0			0
$23$	3.70206	+	3.70206i	0.771932	+	0.771932i	0.978444	−	0.206512i	$-0.0662113\pi$
$23$	3.70206	+	3.70206i	0.771932	+	0.771932i	−0.206512	+	0.978444i	$0.566211\pi$
$24$		0			0
$25$	−2.33445	+	2.33445i	−0.466890	+	0.466890i
$26$		0			0
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$		0			0
$29$	−1.17302	+	2.83193i	−0.217825	+	0.525876i	−0.994586	−	0.103920i	$-0.966861\pi$
$29$	−1.17302	+	2.83193i	−0.217825	+	0.525876i	0.776761	+	0.629796i	$0.216861\pi$
$30$		0			0
$31$	−1.54469			−0.277434			−0.138717	−	0.990332i	$-0.544298\pi$
$31$	−1.54469			−0.277434			−0.138717	+	0.990332i	$0.544298\pi$
$32$		0			0
$33$	5.60797			0.976222
$34$		0			0
$35$	1.82981	−	4.41756i	0.309295	−	0.746703i
$36$		0			0
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.937288	−	0.348557i	$-0.886672\pi$
$37$	−8.23352	+	3.41044i	−1.35358	+	0.560672i	−0.416295	+	0.909229i	$0.636672\pi$
$38$		0			0
$39$	0.753195	−	0.753195i	0.120608	−	0.120608i
$40$		0			0
$41$	−1.10862	−	1.10862i	−0.173138	−	0.173138i	0.615219	−	0.788357i	$-0.289068\pi$
$41$	−1.10862	−	1.10862i	−0.173138	−	0.173138i	−0.788357	+	0.615219i	$0.789068\pi$
$42$		0			0
$43$	3.47106	+	8.37989i	0.529332	+	1.27792i	0.931961	+	0.362558i	$0.118097\pi$
$43$	3.47106	+	8.37989i	0.529332	+	1.27792i	−0.402629	+	0.915363i	$0.631903\pi$
$44$		0			0
$45$	1.20409	+	0.498752i	0.179496	+	0.0743495i
$46$		0			0
$47$		−	3.15582i		−	0.460324i	−0.973152	−	0.230162i	$-0.926074\pi$
$47$		−	3.15582i		−	0.460324i	0.973152	−	0.230162i	$-0.0739256\pi$
$48$		0			0
$49$		−	6.45997i		−	0.922853i
$50$		0			0
$51$	0.904527	+	0.374667i	0.126659	+	0.0524639i
$52$		0			0
$53$	−2.55252	−	6.16232i	−0.350615	−	0.846460i	−0.996544	−	0.0830627i	$-0.973530\pi$
$53$	−2.55252	−	6.16232i	−0.350615	−	0.846460i	0.645929	−	0.763397i	$-0.276470\pi$
$54$		0			0
$55$	5.16815	+	5.16815i	0.696873	+	0.696873i
$56$		0			0
$57$	4.35464	−	4.35464i	0.576786	−	0.576786i
$58$		0			0
$59$	8.95423	−	3.70896i	1.16574	−	0.482866i	0.285958	−	0.958242i	$-0.407688\pi$
$59$	8.95423	−	3.70896i	1.16574	−	0.482866i	0.879783	+	0.475376i	$0.157688\pi$
$60$		0			0
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	−0.998737	−	0.0502499i	$-0.983998\pi$
$61$	−2.00717	+	4.84573i	−0.256991	+	0.620432i	0.741746	+	0.670681i	$0.233998\pi$
$62$		0			0
$63$	3.66878			0.462223
$64$		0			0
$65$	1.38825			0.172191
$66$		0			0
$67$	−1.14380	+	2.76138i	−0.139738	+	0.337357i	−0.978220	−	0.207573i	$-0.933444\pi$
$67$	−1.14380	+	2.76138i	−0.139738	+	0.337357i	0.838482	+	0.544930i	$0.183444\pi$
$68$		0			0
$69$	−4.83697	+	2.00354i	−0.582303	+	0.241198i
$70$		0			0
$71$	−10.0373	+	10.0373i	−1.19120	+	1.19120i	−0.214474	+	0.976730i	$0.568804\pi$
$71$	−10.0373	+	10.0373i	−1.19120	+	1.19120i	−0.976730	+	0.214474i	$0.931196\pi$
$72$		0			0
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	0.998776	−	0.0494525i	$-0.0157476\pi$
$73$	8.11103	+	8.11103i	0.949324	+	0.949324i	−0.0494525	+	0.998776i	$0.515748\pi$
$74$		0			0
$75$	−1.26339	−	3.05010i	−0.145884	−	0.352196i
$76$		0			0
$77$	19.0083	+	7.87349i	2.16620	+	0.897268i
$78$		0			0
$79$		−	0.155459i		−	0.0174905i	−0.999962	−	0.00874523i	$-0.997216\pi$
$79$		−	0.155459i		−	0.0174905i	0.999962	−	0.00874523i	$-0.00278373\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	−5.13862	−	2.12849i	−0.564037	−	0.233632i	0.0823997	−	0.996599i	$-0.473742\pi$
$83$	−5.13862	−	2.12849i	−0.564037	−	0.233632i	−0.646437	+	0.762968i	$0.723742\pi$
$84$		0			0
$85$	0.488304	+	1.17887i	0.0529640	+	0.127866i
$86$		0			0
$87$	−2.16747	−	2.16747i	−0.232377	−	0.232377i
$88$		0			0
$89$	−6.15303	+	6.15303i	−0.652220	+	0.652220i	−0.953527	−	0.301307i	$-0.902577\pi$
$89$	−6.15303	+	6.15303i	−0.652220	+	0.652220i	0.301307	+	0.953527i	$0.402577\pi$
$90$		0			0
$91$	3.61044	−	1.49549i	0.378477	−	0.156770i
$92$		0			0
$93$	0.591127	−	1.42711i	0.0612970	−	0.147984i
$94$		0			0
$95$	8.02623			0.823474
$96$		0			0
$97$	14.3852			1.46059			0.730296	−	0.683131i	$-0.239382\pi$
$97$	14.3852			1.46059			0.730296	+	0.683131i	$0.239382\pi$
$98$		0			0
$99$	−2.14608	+	5.18109i	−0.215689	+	0.520719i
$100$		0			0
$101$	12.1198	−	5.02020i	1.20597	−	0.499528i	0.313045	−	0.949738i	$-0.398651\pi$
$101$	12.1198	−	5.02020i	1.20597	−	0.499528i	0.892923	+	0.450210i	$0.148651\pi$
$102$		0			0
$103$	10.3057	−	10.3057i	1.01545	−	1.01545i	0.0155752	−	0.999879i	$-0.495042\pi$
$103$	10.3057	−	10.3057i	1.01545	−	1.01545i	0.999879	−	0.0155752i	$-0.00495796\pi$
$104$		0			0
$105$	3.38105	+	3.38105i	0.329957	+	0.329957i
$106$		0			0
$107$	0.576841	+	1.39262i	0.0557653	+	0.134629i	0.949307	−	0.314352i	$-0.101787\pi$
$107$	0.576841	+	1.39262i	0.0557653	+	0.134629i	−0.893541	+	0.448981i	$0.851787\pi$
$108$		0			0
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.216987	−	0.976174i	$-0.569623\pi$
$109$	−11.0738	−	4.58693i	−1.06068	−	0.439348i	−0.843693	+	0.536826i	$0.819623\pi$
$110$		0			0
$111$		−	8.91190i		−	0.845880i
$112$		0			0
$113$		−	9.41139i		−	0.885349i	−0.896682	−	0.442675i	$-0.854030\pi$
$113$		−	9.41139i		−	0.885349i	0.896682	−	0.442675i	$-0.145970\pi$
$114$		0			0
$115$	−6.30402	−	2.61121i	−0.587853	−	0.243497i
$116$		0			0
$117$	0.407626	+	0.984096i	0.0376850	+	0.0909797i
$118$		0			0
$119$	2.53988	+	2.53988i	0.232831	+	0.232831i
$120$		0			0
$121$	−14.4598	+	14.4598i	−1.31453	+	1.31453i
$122$		0			0
$123$	1.44849	−	0.599983i	0.130606	−	0.0540986i
$124$		0			0
$125$	4.14034	−	9.99566i	0.370323	−	0.894039i
$126$		0			0
$127$	−16.0219			−1.42171			−0.710855	−	0.703338i	$-0.751692\pi$
$127$	−16.0219			−1.42171			−0.710855	+	0.703338i	$0.751692\pi$
$128$		0			0
$129$	−9.07033			−0.798598
$130$		0			0
$131$	−2.18619	+	5.27794i	−0.191009	+	0.461135i	−0.990151	−	0.140007i	$-0.955288\pi$
$131$	−2.18619	+	5.27794i	−0.191009	+	0.461135i	0.799142	+	0.601142i	$0.205288\pi$
$132$		0			0
$133$	20.8739	−	8.64627i	1.81000	−	0.749727i
$134$		0			0
$135$	−0.921573	+	0.921573i	−0.0793163	+	0.0793163i
$136$		0			0
$137$	−8.63573	−	8.63573i	−0.737801	−	0.737801i	0.234351	−	0.972152i	$-0.424703\pi$
$137$	−8.63573	−	8.63573i	−0.737801	−	0.737801i	−0.972152	+	0.234351i	$0.924703\pi$
$138$		0			0
$139$	4.05369	+	9.78647i	0.343829	+	0.830078i	0.997321	+	0.0731441i	$0.0233033\pi$
$139$	4.05369	+	9.78647i	0.343829	+	0.830078i	−0.653492	+	0.756933i	$0.726697\pi$
$140$		0			0
$141$	2.91560	+	1.20768i	0.245538	+	0.101705i
$142$		0			0
$143$			5.97348i			0.499528i
$144$		0			0
$145$		−	3.99495i		−	0.331763i
$146$		0			0
$147$	5.96824	+	2.47213i	0.492252	+	0.203897i
$148$		0			0
$149$	1.10547	+	2.66884i	0.0905637	+	0.218640i	0.962671	−	0.270675i	$-0.0872468\pi$
$149$	1.10547	+	2.66884i	0.0905637	+	0.218640i	−0.872107	+	0.489315i	$0.837247\pi$
$150$		0			0
$151$	−6.40487	−	6.40487i	−0.521221	−	0.521221i	0.396719	−	0.917940i	$-0.370149\pi$
$151$	−6.40487	−	6.40487i	−0.521221	−	0.521221i	−0.917940	+	0.396719i	$0.870149\pi$
$152$		0			0
$153$	−0.692295	+	0.692295i	−0.0559687	+	0.0559687i
$154$		0			0
$155$	1.85995	−	0.770416i	0.149395	−	0.0618813i
$156$		0			0
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	−0.995938	−	0.0900446i	$-0.971299\pi$
$157$	−2.85724	+	6.89798i	−0.228032	+	0.550519i	0.767905	+	0.640563i	$0.221299\pi$
$158$		0			0
$159$	6.67005			0.528969
$160$		0			0
$161$	−19.2079			−1.51379
$162$		0			0
$163$	−0.958379	+	2.31373i	−0.0750661	+	0.181225i	−0.956958	−	0.290226i	$-0.906270\pi$
$163$	−0.958379	+	2.31373i	−0.0750661	+	0.181225i	0.881892	+	0.471451i	$0.156270\pi$
$164$		0			0
$165$	−6.75251	+	2.79698i	−0.525683	+	0.217745i
$166$		0			0
$167$	−3.60896	+	3.60896i	−0.279270	+	0.279270i	−0.832817	−	0.553548i	$-0.813274\pi$
$167$	−3.60896	+	3.60896i	−0.279270	+	0.279270i	0.553548	+	0.832817i	$0.313274\pi$
$168$		0			0
$169$	−8.39010	−	8.39010i	−0.645392	−	0.645392i
$170$		0			0
$171$	2.35671	+	5.68961i	0.180222	+	0.435095i
$172$		0			0
$173$	−2.16959	−	0.898673i	−0.164951	−	0.0683248i	0.298680	−	0.954353i	$-0.403454\pi$
$173$	−2.16959	−	0.898673i	−0.164951	−	0.0683248i	−0.463631	+	0.886028i	$0.653454\pi$
$174$		0			0
$175$		−	12.1122i		−	0.915593i
$176$		0			0
$177$			9.69199i			0.728494i
$178$		0			0
$179$	2.66481	+	1.10380i	0.199177	+	0.0825020i	0.480042	−	0.877245i	$-0.340621\pi$
$179$	2.66481	+	1.10380i	0.199177	+	0.0825020i	−0.280865	+	0.959747i	$0.590621\pi$
$180$		0			0
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	0.877298	−	0.479947i	$-0.159344\pi$
$181$	−1.10884	−	2.67697i	−0.0824191	−	0.198977i	−0.959717	+	0.280969i	$0.909344\pi$
$182$		0			0
$183$	−3.70876	−	3.70876i	−0.274159	−	0.274159i
$184$		0			0
$185$	8.21296	−	8.21296i	0.603829	−	0.603829i
$186$		0			0
$187$	−5.07256	+	2.10112i	−0.370942	+	0.153649i
$188$		0			0
$189$	−1.40398	+	3.38951i	−0.102125	+	0.246551i
$190$		0			0
$191$	−8.35300			−0.604402			−0.302201	−	0.953244i	$-0.597721\pi$
$191$	−8.35300			−0.604402			−0.302201	+	0.953244i	$0.597721\pi$
$192$		0			0
$193$	−12.3350			−0.887894			−0.443947	−	0.896053i	$-0.646422\pi$
$193$	−12.3350			−0.887894			−0.443947	+	0.896053i	$0.646422\pi$
$194$		0			0
$195$	−0.531259	+	1.28257i	−0.0380443	+	0.0918470i
$196$		0			0
$197$	−21.5154	+	8.91197i	−1.53291	+	0.634952i	−0.980126	−	0.198374i	$-0.936434\pi$
$197$	−21.5154	+	8.91197i	−1.53291	+	0.634952i	−0.552782	+	0.833326i	$0.686434\pi$
$198$		0			0
$199$	17.0334	−	17.0334i	1.20746	−	1.20746i	0.235616	−	0.971846i	$-0.424289\pi$
$199$	17.0334	−	17.0334i	1.20746	−	1.20746i	0.971846	−	0.235616i	$-0.0757109\pi$
$200$		0			0
$201$	−2.11347	−	2.11347i	−0.149073	−	0.149073i
$202$		0			0
$203$	−4.30357	−	10.3897i	−0.302051	−	0.729217i
$204$		0			0
$205$	1.88781	+	0.781958i	0.131851	+	0.0546143i
$206$		0			0
$207$		−	5.23550i		−	0.363892i
$208$		0			0
$209$			34.5360i			2.38891i
$210$		0			0
$211$	8.86549	+	3.67221i	0.610325	+	0.252805i	0.666368	−	0.745623i	$-0.267848\pi$
$211$	8.86549	+	3.67221i	0.610325	+	0.252805i	−0.0560422	+	0.998428i	$0.517848\pi$
$212$		0			0
$213$	−5.43213	−	13.1143i	−0.372203	−	0.898578i
$214$		0			0
$215$	−8.35897	−	8.35897i	−0.570077	−	0.570077i
$216$		0			0
$217$	4.00726	−	4.00726i	0.272031	−	0.272031i
$218$		0			0
$219$	−10.5976	+	4.38966i	−0.716117	+	0.296626i
$220$		0			0
$221$	−0.399087	+	0.963482i	−0.0268455	+	0.0648108i
$222$		0			0
$223$	−6.90976			−0.462712			−0.231356	−	0.972869i	$-0.574316\pi$
$223$	−6.90976			−0.462712			−0.231356	+	0.972869i	$0.574316\pi$
$224$		0			0
$225$	3.30141			0.220094
$226$		0			0
$227$	−1.65113	+	3.98617i	−0.109589	+	0.264572i	−0.969154	−	0.246454i	$-0.920734\pi$
$227$	−1.65113	+	3.98617i	−0.109589	+	0.264572i	0.859565	+	0.511026i	$0.170734\pi$
$228$		0			0
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	−0.135890	−	0.990724i	$-0.543389\pi$
$229$	7.09073	−	2.93708i	0.468568	−	0.194087i	0.604459	+	0.796636i	$0.293389\pi$
$230$		0			0
$231$	−14.5483	+	14.5483i	−0.957209	+	0.957209i
$232$		0			0
$233$	−1.49412	−	1.49412i	−0.0978831	−	0.0978831i	0.656470	−	0.754353i	$-0.272049\pi$
$233$	−1.49412	−	1.49412i	−0.0978831	−	0.0978831i	−0.754353	+	0.656470i	$0.772049\pi$
$234$		0			0
$235$	1.57397	+	3.79990i	0.102675	+	0.247878i
$236$		0			0
$237$	0.143625	+	0.0594914i	0.00932945	+	0.00386438i
$238$		0			0
$239$			5.41212i			0.350081i	0.984561	+	0.175041i	$0.0560057\pi$
$239$			5.41212i			0.350081i	−0.984561	+	0.175041i	$0.943994\pi$
$240$		0			0
$241$		−	19.6684i		−	1.26695i	−0.773762	−	0.633476i	$-0.781628\pi$
$241$		−	19.6684i		−	1.26695i	0.773762	−	0.633476i	$-0.218372\pi$
$242$		0			0
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$		0			0
$245$	3.22192	+	7.77841i	0.205841	+	0.496944i
$246$		0			0
$247$	4.63846	+	4.63846i	0.295138	+	0.295138i
$248$		0			0
$249$	3.93293	−	3.93293i	0.249239	−	0.249239i
$250$		0			0
$251$	−23.6647	+	9.80223i	−1.49370	+	0.618711i	−0.972119	−	0.234490i	$-0.924658\pi$
$251$	−23.6647	+	9.80223i	−1.49370	+	0.618711i	−0.521582	+	0.853201i	$0.674658\pi$
$252$		0			0
$253$	11.2358	−	27.1256i	0.706387	−	1.70537i
$254$		0			0
$255$	−1.27600			−0.0799062
$256$		0			0
$257$	−9.44245			−0.589004			−0.294502	−	0.955651i	$-0.595154\pi$
$257$	−9.44245			−0.589004			−0.294502	+	0.955651i	$0.595154\pi$
$258$		0			0
$259$	12.5122	−	30.2070i	0.777468	−	1.87697i
$260$		0			0
$261$	2.83193	−	1.17302i	0.175292	−	0.0726084i
$262$		0			0
$263$	8.38788	−	8.38788i	0.517219	−	0.517219i	−0.399510	−	0.916729i	$-0.630820\pi$
$263$	8.38788	−	8.38788i	0.517219	−	0.517219i	0.916729	+	0.399510i	$0.130820\pi$
$264$		0			0
$265$	6.14694	+	6.14694i	0.377603	+	0.377603i
$266$		0			0
$267$	−3.32999	−	8.03932i	−0.203792	−	0.491998i
$268$		0			0
$269$	0.0655084	+	0.0271345i	0.00399412	+	0.00165442i	0.384680	−	0.923050i	$-0.374312\pi$
$269$	0.0655084	+	0.0271345i	0.00399412	+	0.00165442i	−0.380685	+	0.924705i	$0.624312\pi$
$270$		0			0
$271$			14.4877i			0.880062i	0.897982	+	0.440031i	$0.145033\pi$
$271$			14.4877i			0.880062i	−0.897982	+	0.440031i	$0.854967\pi$
$272$		0			0
$273$			3.90791i			0.236517i
$274$		0			0
$275$	17.1049	+	7.08507i	1.03146	+	0.427246i
$276$		0			0
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	0.954275	+	0.298931i	$0.0966299\pi$
$277$	8.16981	+	19.7237i	0.490876	+	1.18508i	−0.463398	+	0.886150i	$0.653370\pi$
$278$		0			0
$279$	1.09226	+	1.09226i	0.0653919	+	0.0653919i
$280$		0			0
$281$	2.76272	−	2.76272i	0.164810	−	0.164810i	−0.619884	−	0.784694i	$-0.712820\pi$
$281$	2.76272	−	2.76272i	0.164810	−	0.164810i	0.784694	+	0.619884i	$0.212820\pi$
$282$		0			0
$283$	5.86879	−	2.43093i	0.348864	−	0.144504i	−0.201369	−	0.979515i	$-0.564539\pi$
$283$	5.86879	−	2.43093i	0.348864	−	0.144504i	0.550233	+	0.835011i	$0.314539\pi$
$284$		0			0
$285$	−3.07151	+	7.41527i	−0.181940	+	0.439243i
$286$		0			0
$287$	5.75203			0.339532
$288$		0			0
$289$	16.0415			0.943615
$290$		0			0
$291$	−5.50497	+	13.2902i	−0.322707	+	0.779083i
$292$		0			0
$293$	4.51526	−	1.87028i	0.263784	−	0.109263i	−0.246872	−	0.969048i	$-0.579403\pi$
$293$	4.51526	−	1.87028i	0.263784	−	0.109263i	0.510656	+	0.859785i	$0.329403\pi$
$294$		0			0
$295$	−8.93187	+	8.93187i	−0.520034	+	0.520034i
$296$		0			0
$297$	−3.96543	−	3.96543i	−0.230098	−	0.230098i
$298$		0			0
$299$	−2.13412	−	5.15223i	−0.123420	−	0.297961i
$300$		0			0
$301$	−30.7440	−	12.7346i	−1.77206	−	0.734009i
$302$		0			0
$303$			13.1184i			0.753633i
$304$		0			0
$305$		−	6.83578i		−	0.391416i
$306$		0			0
$307$	−8.44200	−	3.49679i	−0.481810	−	0.199572i	0.128539	−	0.991704i	$-0.458971\pi$
$307$	−8.44200	−	3.49679i	−0.481810	−	0.199572i	−0.610350	+	0.792132i	$0.708971\pi$
$308$		0			0
$309$	5.57742	+	13.4651i	0.317288	+	0.766002i
$310$		0			0
$311$	−20.8439	−	20.8439i	−1.18195	−	1.18195i	−0.979239	−	0.202710i	$-0.935025\pi$
$311$	−20.8439	−	20.8439i	−1.18195	−	1.18195i	−0.202710	−	0.979239i	$-0.564975\pi$
$312$		0			0
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	−0.185517	−	0.982641i	$-0.559396\pi$
$313$	14.1026	−	14.1026i	0.797124	−	0.797124i	0.982641	+	0.185517i	$0.0593959\pi$
$314$		0			0
$315$	−4.41756	+	1.82981i	−0.248901	+	0.103098i
$316$		0			0
$317$	1.07307	−	2.59063i	0.0602698	−	0.145504i	−0.890876	−	0.454247i	$-0.849908\pi$
$317$	1.07307	−	2.59063i	0.0602698	−	0.145504i	0.951145	+	0.308743i	$0.0999083\pi$
$318$		0			0
$319$	17.1899			0.962448
$320$		0			0
$321$	−1.50736			−0.0841325
$322$		0			0
$323$	−2.30735	+	5.57043i	−0.128384	+	0.309947i
$324$		0			0
$325$	3.24890	−	1.34574i	0.180217	−	0.0746482i
$326$		0			0
$327$	8.47554	−	8.47554i	0.468698	−	0.468698i
$328$		0			0
$329$	8.18691	+	8.18691i	0.451359	+	0.451359i
$330$		0			0
$331$	1.37795	+	3.32667i	0.0757390	+	0.182850i	0.957214	−	0.289380i	$-0.0934491\pi$
$331$	1.37795	+	3.32667i	0.0757390	+	0.182850i	−0.881475	+	0.472230i	$0.843449\pi$
$332$		0			0
$333$	8.23352	+	3.41044i	0.451194	+	0.186891i
$334$		0			0
$335$		−	3.89544i		−	0.212830i
$336$		0			0
$337$			0.473748i			0.0258067i	0.999917	+	0.0129034i	$0.00410738\pi$
$337$			0.473748i			0.0258067i	−0.999917	+	0.0129034i	$0.995893\pi$
$338$		0			0
$339$	8.69499	+	3.60158i	0.472247	+	0.195611i
$340$		0			0
$341$	3.31502	+	8.00317i	0.179518	+	0.433396i
$342$		0			0
$343$	−1.40095	−	1.40095i	−0.0756440	−	0.0756440i
$344$		0			0
$345$	4.82489	−	4.82489i	0.259763	−	0.259763i
$346$		0			0
$347$	9.36785	−	3.88029i	0.502893	−	0.208305i	−0.116791	−	0.993156i	$-0.537261\pi$
$347$	9.36785	−	3.88029i	0.502893	−	0.208305i	0.619684	+	0.784852i	$0.287261\pi$
$348$		0			0
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	−0.969068	−	0.246796i	$-0.920622\pi$
$349$	−2.04231	+	4.93057i	−0.109322	+	0.263928i	0.859745	+	0.510723i	$0.170622\pi$
$350$		0			0
$351$	−1.06518			−0.0568550
$352$		0			0
$353$	34.7185			1.84788			0.923939	−	0.382539i	$-0.124950\pi$
$353$	34.7185			1.84788			0.923939	+	0.382539i	$0.124950\pi$
$354$		0			0
$355$	7.07969	−	17.0919i	0.375751	−	0.907144i
$356$		0			0
$357$	−3.31851	+	1.37457i	−0.175634	+	0.0727502i
$358$		0			0
$359$	4.06394	−	4.06394i	0.214486	−	0.214486i	−0.591684	−	0.806170i	$-0.701537\pi$
$359$	4.06394	−	4.06394i	0.214486	−	0.214486i	0.806170	+	0.591684i	$0.201537\pi$
$360$		0			0
$361$	13.3825	+	13.3825i	0.704343	+	0.704343i
$362$		0			0
$363$	−7.82561	−	18.8927i	−0.410738	−	0.991610i
$364$		0			0
$365$	−13.8118	−	5.72104i	−0.722944	−	0.299453i
$366$		0			0
$367$			30.2747i			1.58033i	0.612896	+	0.790164i	$0.290004\pi$
$367$			30.2747i			1.58033i	−0.612896	+	0.790164i	$0.709996\pi$
$368$		0			0
$369$			1.56783i			0.0816180i
$370$		0			0
$371$	22.6082	+	9.36463i	1.17376	+	0.486188i
$372$		0			0
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	0.976583	+	0.215141i	$0.0690210\pi$
$373$	8.46231	+	20.4298i	0.438162	+	1.05782i	−0.538421	+	0.842676i	$0.680979\pi$
$374$		0			0
$375$	7.65035	+	7.65035i	0.395062	+	0.395062i
$376$		0			0
$377$	2.30874	−	2.30874i	0.118906	−	0.118906i
$378$		0			0
$379$	−21.3128	+	8.82807i	−1.09477	+	0.453467i	−0.855667	−	0.517527i	$-0.826853\pi$
$379$	−21.3128	+	8.82807i	−1.09477	+	0.453467i	−0.239100	+	0.970995i	$0.576853\pi$
$380$		0			0
$381$	6.13130	−	14.8023i	0.314116	−	0.758343i
$382$		0			0
$383$	25.5734			1.30674			0.653370	−	0.757039i	$-0.273355\pi$
$383$	25.5734			1.30674			0.653370	+	0.757039i	$0.273355\pi$
$384$		0			0
$385$	−26.8147			−1.36660
$386$		0			0
$387$	3.47106	−	8.37989i	0.176444	−	0.425974i
$388$		0			0
$389$	−1.19642	+	0.495572i	−0.0606608	+	0.0251265i	−0.412808	−	0.910818i	$-0.635452\pi$
$389$	−1.19642	+	0.495572i	−0.0606608	+	0.0251265i	0.352147	+	0.935945i	$0.385452\pi$
$390$		0			0
$391$	3.62451	−	3.62451i	0.183299	−	0.183299i
$392$		0			0
$393$	−4.03956	−	4.03956i	−0.203769	−	0.203769i
$394$		0			0
$395$	0.0775352	+	0.187187i	0.00390122	+	0.00941838i
$396$		0			0
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	0.515751	−	0.856738i	$-0.327513\pi$
$397$	5.47211	+	2.26662i	0.274637	+	0.113758i	−0.241114	+	0.970497i	$0.577513\pi$
$398$		0			0
$399$			22.5938i			1.13110i
$400$		0			0
$401$			33.2794i			1.66189i	0.556352	+	0.830947i	$0.312201\pi$
$401$			33.2794i			1.66189i	−0.556352	+	0.830947i	$0.687799\pi$
$402$		0			0
$403$	1.52012	+	0.629655i	0.0757227	+	0.0313654i
$404$		0			0
$405$	−0.498752	−	1.20409i	−0.0247832	−	0.0598318i
$406$		0			0
$407$	35.3395	+	35.3395i	1.75172	+	1.75172i
$408$		0			0
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	−0.499909	−	0.866078i	$-0.666633\pi$
$409$	7.40530	−	7.40530i	0.366168	−	0.366168i	0.866078	+	0.499909i	$0.166633\pi$
$410$		0			0
$411$	11.2831	−	4.67363i	0.556556	−	0.230533i
$412$		0			0
$413$	−13.6074	+	32.8511i	−0.669575	+	1.61650i
$414$		0			0
$415$	7.24896			0.355838
$416$		0			0
$417$	−10.5928			−0.518732
$418$		0			0
$419$	6.43037	−	15.5243i	0.314144	−	0.758411i	−0.685399	−	0.728168i	$-0.740372\pi$
$419$	6.43037	−	15.5243i	0.314144	−	0.758411i	0.999543	−	0.0302425i	$-0.00962796\pi$
$420$		0			0
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	−0.241813	−	0.970323i	$-0.577742\pi$
$421$	5.60807	−	2.32294i	0.273321	−	0.113213i	0.515134	+	0.857110i	$0.327742\pi$
$422$		0			0
$423$	−2.23150	+	2.23150i	−0.108499	+	0.108499i
$424$		0			0
$425$	2.28555	+	2.28555i	0.110865	+	0.110865i
$426$		0			0
$427$	−7.36385	−	17.7779i	−0.356362	−	0.860334i
$428$		0			0
$429$	−5.51878	−	2.28595i	−0.266449	−	0.110367i
$430$		0			0
$431$			0.297166i			0.0143140i	0.999974	+	0.00715698i	$0.00227816\pi$
$431$			0.297166i			0.0143140i	−0.999974	+	0.00715698i	$0.997722\pi$
$432$		0			0
$433$			15.4119i			0.740649i	0.928902	+	0.370325i	$0.120754\pi$
$433$			15.4119i			0.740649i	−0.928902	+	0.370325i	$0.879246\pi$
$434$		0			0
$435$	3.69086	+	1.52880i	0.176963	+	0.0733005i
$436$		0			0
$437$	−12.3386	−	29.7879i	−0.590233	−	1.42495i
$438$		0			0
$439$	3.15252	+	3.15252i	0.150462	+	0.150462i	0.778324	−	0.627863i	$-0.216070\pi$
$439$	3.15252	+	3.15252i	0.150462	+	0.150462i	−0.627863	+	0.778324i	$0.716070\pi$
$440$		0			0
$441$	−4.56789	+	4.56789i	−0.217519	+	0.217519i
$442$		0			0
$443$	−2.80647	+	1.16248i	−0.133339	+	0.0552310i	−0.448355	−	0.893855i	$-0.647990\pi$
$443$	−2.80647	+	1.16248i	−0.133339	+	0.0552310i	0.315016	+	0.949086i	$0.397990\pi$
$444$		0			0
$445$	4.33998	−	10.4776i	0.205735	−	0.496688i
$446$		0			0
$447$	−2.88874			−0.136632
$448$		0			0
$449$	−3.57715			−0.168816			−0.0844080	−	0.996431i	$-0.526900\pi$
$449$	−3.57715			−0.168816			−0.0844080	+	0.996431i	$0.526900\pi$
$450$		0			0
$451$	−3.36469	+	8.12307i	−0.158437	+	0.382500i
$452$		0			0
$453$	8.36836	−	3.46629i	0.393180	−	0.162860i
$454$		0			0
$455$	−3.60142	+	3.60142i	−0.168837	+	0.168837i
$456$		0			0
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	0.465204	−	0.885204i	$-0.345981\pi$
$457$	−8.97857	−	8.97857i	−0.420000	−	0.420000i	−0.885204	+	0.465204i	$0.845981\pi$
$458$		0			0
$459$	−0.374667	−	0.904527i	−0.0174880	−	0.0422197i
$460$		0			0
$461$	−26.0500	−	10.7903i	−1.21327	−	0.502553i	−0.318006	−	0.948089i	$-0.603013\pi$
$461$	−26.0500	−	10.7903i	−1.21327	−	0.502553i	−0.895264	+	0.445536i	$0.853013\pi$
$462$		0			0
$463$			10.9782i			0.510199i	0.966915	+	0.255100i	$0.0821083\pi$
$463$			10.9782i			0.510199i	−0.966915	+	0.255100i	$0.917892\pi$
$464$		0			0
$465$			2.01319i			0.0933596i
$466$		0			0
$467$	−38.5388	−	15.9633i	−1.78336	−	0.738694i	−0.991829	−	0.127571i	$-0.959282\pi$
$467$	−38.5388	−	15.9633i	−1.78336	−	0.738694i	−0.791535	−	0.611123i	$-0.790718\pi$
$468$		0			0
$469$	−4.19636	−	10.1309i	−0.193770	−	0.467802i
$470$		0			0
$471$	−5.27948	−	5.27948i	−0.243266	−	0.243266i
$472$		0			0
$473$	35.9678	−	35.9678i	1.65380	−	1.65380i
$474$		0			0
$475$	18.7837	−	7.78047i	0.861856	−	0.356992i
$476$		0			0
$477$	−2.55252	+	6.16232i	−0.116872	+	0.282153i
$478$		0			0
$479$	−20.8426			−0.952324			−0.476162	−	0.879357i	$-0.657973\pi$
$479$	−20.8426			−0.952324			−0.476162	+	0.879357i	$0.657973\pi$
$480$		0			0
$481$	9.49276			0.432833
$482$		0			0
$483$	7.35055	−	17.7458i	0.334461	−	0.807461i
$484$		0			0
$485$	−17.3211	+	7.17462i	−0.786510	+	0.325783i
$486$		0			0
$487$	16.3086	−	16.3086i	0.739014	−	0.739014i	−0.233373	−	0.972387i	$-0.574976\pi$
$487$	16.3086	−	16.3086i	0.739014	−	0.739014i	0.972387	+	0.233373i	$0.0749763\pi$
$488$		0			0
$489$	−1.77085	−	1.77085i	−0.0800808	−	0.0800808i
$490$		0			0
$491$	2.22643	+	5.37508i	0.100477	+	0.242574i	0.966122	−	0.258084i	$-0.0830913\pi$
$491$	2.22643	+	5.37508i	0.100477	+	0.242574i	−0.865645	+	0.500658i	$0.833091\pi$
$492$		0			0
$493$	2.77261	+	1.14845i	0.124872	+	0.0517237i
$494$		0			0
$495$		−	7.30887i		−	0.328509i
$496$		0			0
$497$		−	52.0778i		−	2.33601i
$498$		0			0
$499$	−9.39859	−	3.89302i	−0.420739	−	0.174276i	0.162261	−	0.986748i	$-0.448121\pi$
$499$	−9.39859	−	3.89302i	−0.420739	−	0.174276i	−0.583000	+	0.812472i	$0.698121\pi$
$500$		0			0
$501$	−1.95316	−	4.71534i	−0.0872606	−	0.210666i
$502$		0			0
$503$	−21.5760	−	21.5760i	−0.962027	−	0.962027i	0.0372777	−	0.999305i	$-0.488131\pi$
$503$	−21.5760	−	21.5760i	−0.962027	−	0.962027i	−0.999305	+	0.0372777i	$0.988131\pi$
$504$		0			0
$505$	−12.0896	+	12.0896i	−0.537979	+	0.537979i
$506$		0			0
$507$	10.9622	−	4.54069i	0.486848	−	0.201659i
$508$		0			0
$509$	1.30560	−	3.15200i	0.0578697	−	0.139710i	−0.892300	−	0.451443i	$-0.850909\pi$
$509$	1.30560	−	3.15200i	0.0578697	−	0.139710i	0.950170	+	0.311733i	$0.100909\pi$
$510$		0			0
$511$	−42.0836			−1.86167
$512$		0			0
$513$	−6.15839			−0.271899
$514$		0			0
$515$	−7.26906	+	17.5491i	−0.320313	+	0.773304i
$516$		0			0
$517$	−16.3506	+	6.77264i	−0.719099	+	0.297860i
$518$		0			0
$519$	1.66053	−	1.66053i	0.0728892	−	0.0728892i
$520$		0			0
$521$	7.58009	+	7.58009i	0.332090	+	0.332090i	0.853380	−	0.521290i	$-0.174549\pi$
$521$	7.58009	+	7.58009i	0.332090	+	0.332090i	−0.521290	+	0.853380i	$0.674549\pi$
$522$		0			0
$523$	5.67736	+	13.7064i	0.248254	+	0.599337i	0.998056	−	0.0623246i	$-0.0198514\pi$
$523$	5.67736	+	13.7064i	0.248254	+	0.599337i	−0.749802	+	0.661662i	$0.769851\pi$
$524$		0			0
$525$	11.1902	+	4.63512i	0.488379	+	0.202293i
$526$		0			0
$527$			1.51233i			0.0658782i
$528$		0			0
$529$			4.41042i			0.191758i
$530$		0			0
$531$	−8.95423	−	3.70896i	−0.388580	−	0.160955i
$532$		0			0
$533$	0.639089	+	1.54290i	0.0276820	+	0.0668303i
$534$		0			0
$535$	−1.38914	−	1.38914i	−0.0600578	−	0.0600578i
$536$		0			0
$537$	−2.03956	+	2.03956i	−0.0880135	+	0.0880135i
$538$		0			0
$539$	−33.4697	+	13.8636i	−1.44164	+	0.597148i
$540$		0			0
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	0.265247	+	0.964181i	$0.414547\pi$
$541$	−14.0508	+	33.9216i	−0.604090	+	1.45840i	−0.869336	+	0.494221i	$0.835453\pi$
$542$		0			0
$543$	2.89753			0.124345
$544$		0			0
$545$	15.6217			0.669158
$546$		0			0
$547$	−7.85438	+	18.9622i	−0.335829	+	0.810763i	0.662278	+	0.749258i	$0.269590\pi$
$547$	−7.85438	+	18.9622i	−0.335829	+	0.810763i	−0.998107	+	0.0615046i	$0.980410\pi$
$548$		0			0
$549$	4.84573	−	2.00717i	0.206811	−	0.0856637i
$550$		0			0
$551$	13.3481	−	13.3481i	0.568648	−	0.568648i
$552$		0			0
$553$	0.403294	+	0.403294i	0.0171498	+	0.0171498i
$554$		0			0
$555$	4.44482	+	10.7308i	0.188672	+	0.455495i
$556$		0			0
$557$	−20.1683	−	8.35400i	−0.854560	−	0.353970i	−0.0879825	−	0.996122i	$-0.528042\pi$
$557$	−20.1683	−	8.35400i	−0.854560	−	0.353970i	−0.766578	+	0.642152i	$0.778042\pi$
$558$		0			0
$559$		−	9.66152i		−	0.408639i
$560$		0			0
$561$		−	5.49050i		−	0.231809i
$562$		0			0
$563$	21.3521	+	8.84433i	0.899884	+	0.372744i	0.784175	−	0.620539i	$-0.213086\pi$
$563$	21.3521	+	8.84433i	0.899884	+	0.372744i	0.115708	+	0.993283i	$0.463086\pi$
$564$		0			0
$565$	4.69395	+	11.3322i	0.197476	+	0.476749i
$566$		0			0
$567$	−2.59422	−	2.59422i	−0.108947	−	0.108947i
$568$		0			0
$569$	−7.60582	+	7.60582i	−0.318853	+	0.318853i	−0.848326	−	0.529474i	$-0.822389\pi$
$569$	−7.60582	+	7.60582i	−0.318853	+	0.318853i	0.529474	+	0.848326i	$0.322389\pi$
$570$		0			0
$571$	−0.616329	+	0.255292i	−0.0257926	+	0.0106836i	−0.395542	−	0.918448i	$-0.629443\pi$
$571$	−0.616329	+	0.255292i	−0.0257926	+	0.0106836i	0.369750	+	0.929131i	$0.379443\pi$
$572$		0			0
$573$	3.19656	−	7.71717i	0.133538	−	0.322389i
$574$		0			0
$575$	−17.2845			−0.720814
$576$		0			0
$577$	−8.78481			−0.365716			−0.182858	−	0.983139i	$-0.558535\pi$
$577$	−8.78481			−0.365716			−0.182858	+	0.983139i	$0.558535\pi$
$578$		0			0
$579$	4.72041	−	11.3961i	0.196173	−	0.473605i
$580$		0			0
$581$	18.8525	−	7.80896i	0.782133	−	0.323970i
$582$		0			0
$583$	−26.4496	+	26.4496i	−1.09543	+	1.09543i
$584$		0			0
$585$	−0.981639	−	0.981639i	−0.0405858	−	0.0405858i
$586$		0			0
$587$	10.5345	+	25.4324i	0.434803	+	1.04971i	0.977718	+	0.209921i	$0.0673206\pi$
$587$	10.5345	+	25.4324i	0.434803	+	1.04971i	−0.542915	+	0.839788i	$0.682679\pi$
$588$		0			0
$589$	8.78867	+	3.64039i	0.362131	+	0.150000i
$590$		0			0
$591$		−	23.2881i		−	0.957944i
$592$		0			0
$593$		−	12.6478i		−	0.519384i	−0.965691	−	0.259692i	$-0.916379\pi$
$593$		−	12.6478i		−	0.519384i	0.965691	−	0.259692i	$-0.0836211\pi$
$594$		0			0
$595$	−4.32502	−	1.79148i	−0.177309	−	0.0734436i
$596$		0			0
$597$	9.21839	+	22.2552i	0.377283	+	0.910843i
$598$		0			0
$599$	−10.2749	−	10.2749i	−0.419820	−	0.419820i	0.465322	−	0.885142i	$-0.345939\pi$
$599$	−10.2749	−	10.2749i	−0.419820	−	0.419820i	−0.885142	+	0.465322i	$0.845939\pi$
$600$		0			0
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.624552	+	0.780983i	$0.714719\pi$
$601$	−34.4571	+	34.4571i	−1.40554	+	1.40554i	−0.780983	+	0.624552i	$0.785281\pi$
$602$		0			0
$603$	2.76138	−	1.14380i	0.112452	−	0.0465792i
$604$		0			0
$605$	10.1991	−	24.6229i	0.414653	−	1.00106i
$606$		0			0
$607$	−5.97427			−0.242488			−0.121244	−	0.992623i	$-0.538688\pi$
$607$	−5.97427			−0.242488			−0.121244	+	0.992623i	$0.538688\pi$
$608$		0			0
$609$	11.2458			0.455702
$610$		0			0
$611$	−1.28640	+	3.10563i	−0.0520420	+	0.125641i
$612$		0			0
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	−0.354666	−	0.934993i	$-0.615405\pi$
$613$	1.37874	−	0.571093i	0.0556868	−	0.0230662i	0.410353	+	0.911927i	$0.365405\pi$
$614$		0			0
$615$	−1.44487	+	1.44487i	−0.0582628	+	0.0582628i
$616$		0			0
$617$	20.4851	+	20.4851i	0.824698	+	0.824698i	0.986778	−	0.162080i	$-0.0518203\pi$
$617$	20.4851	+	20.4851i	0.824698	+	0.824698i	−0.162080	+	0.986778i	$0.551820\pi$
$618$		0			0
$619$	−13.2969	−	32.1015i	−0.534447	−	1.29027i	−0.928552	−	0.371203i	$-0.878945\pi$
$619$	−13.2969	−	32.1015i	−0.534447	−	1.29027i	0.394105	−	0.919065i	$-0.371055\pi$
$620$		0			0
$621$	4.83697	+	2.00354i	0.194101	+	0.0803992i
$622$		0			0
$623$		−	31.9246i		−	1.27903i
$624$		0			0
$625$		−	2.40633i		−	0.0962532i
$626$		0			0
$627$	−31.9071	−	13.2164i	−1.27425	−	0.527811i
$628$		0			0
$629$	3.33900	+	8.06106i	0.133135	+	0.321415i
$630$		0			0
$631$	−2.04327	−	2.04327i	−0.0813412	−	0.0813412i	0.665266	−	0.746607i	$-0.268318\pi$
$631$	−2.04327	−	2.04327i	−0.0813412	−	0.0813412i	−0.746607	+	0.665266i	$0.768318\pi$
$632$		0			0
$633$	−6.78535	+	6.78535i	−0.269694	+	0.269694i
$634$		0			0
$635$	19.2918	−	7.99093i	0.765572	−	0.317110i
$636$		0			0
$637$	−2.63325	+	6.35724i	−0.104333	+	0.251883i
$638$		0			0
$639$	14.1948			0.561539
$640$		0			0
$641$	−20.3790			−0.804922			−0.402461	−	0.915437i	$-0.631845\pi$
$641$	−20.3790			−0.804922			−0.402461	+	0.915437i	$0.631845\pi$
$642$		0			0
$643$	−4.75816	+	11.4872i	−0.187644	+	0.453012i	−0.989505	−	0.144498i	$-0.953843\pi$
$643$	−4.75816	+	11.4872i	−0.187644	+	0.453012i	0.801861	+	0.597510i	$0.203843\pi$
$644$		0			0
$645$	10.9215	−	4.52384i	0.430034	−	0.178126i
$646$		0			0
$647$	−8.97597	+	8.97597i	−0.352882	+	0.352882i	−0.861181	−	0.508299i	$-0.830274\pi$
$647$	−8.97597	+	8.97597i	−0.352882	+	0.352882i	0.508299	+	0.861181i	$0.330274\pi$
$648$		0			0
$649$	−38.4329	−	38.4329i	−1.50862	−	1.50862i
$650$		0			0
$651$	2.16872	+	5.23574i	0.0849987	+	0.205205i
$652$		0			0
$653$	42.2027	+	17.4809i	1.65152	+	0.684082i	0.997383	−	0.0722952i	$-0.0230324\pi$
$653$	42.2027	+	17.4809i	1.65152	+	0.684082i	0.654136	+	0.756377i	$0.273032\pi$
$654$		0			0
$655$		−	7.44549i		−	0.290919i
$656$		0			0
$657$		−	11.4707i		−	0.447516i
$658$		0			0
$659$	−5.50356	−	2.27965i	−0.214388	−	0.0888025i	0.272905	−	0.962041i	$-0.412016\pi$
$659$	−5.50356	−	2.27965i	−0.214388	−	0.0888025i	−0.487293	+	0.873239i	$0.662016\pi$
$660$		0			0
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	−0.758557	−	0.651606i	$-0.774095\pi$
$661$	−17.5581	−	42.3890i	−0.682931	−	1.64874i	0.0756260	−	0.997136i	$-0.475905\pi$
$662$		0			0
$663$	−0.737417	−	0.737417i	−0.0286389	−	0.0286389i
$664$		0			0
$665$	−20.8218	+	20.8218i	−0.807436	+	0.807436i
$666$		0			0
$667$	−14.8266	+	6.14136i	−0.574087	+	0.237795i
$668$		0			0
$669$	2.64425	−	6.38378i	0.102233	−	0.246811i
$670$		0			0
$671$	29.4137			1.13550
$672$		0			0
$673$	−14.4979			−0.558853			−0.279427	−	0.960167i	$-0.590144\pi$
$673$	−14.4979			−0.558853			−0.279427	+	0.960167i	$0.590144\pi$
$674$		0			0
$675$	−1.26339	+	3.05010i	−0.0486281	+	0.117399i
$676$		0			0
$677$	−11.0022	+	4.55726i	−0.422849	+	0.175150i	−0.583953	−	0.811788i	$-0.698495\pi$
$677$	−11.0022	+	4.55726i	−0.422849	+	0.175150i	0.161104	+	0.986937i	$0.448495\pi$
$678$		0			0
$679$	−37.3183	+	37.3183i	−1.43215	+	1.43215i
$680$		0			0
$681$	−3.05088	−	3.05088i	−0.116910	−	0.116910i
$682$		0			0
$683$	3.03396	+	7.32464i	0.116091	+	0.280269i	0.971236	−	0.238121i	$-0.0765314\pi$
$683$	3.03396	+	7.32464i	0.116091	+	0.280269i	−0.855144	+	0.518390i	$0.826531\pi$
$684$		0			0
$685$	14.7053	+	6.09114i	0.561861	+	0.232730i
$686$		0			0
$687$			7.67495i			0.292818i
$688$		0			0
$689$			7.10479i			0.270671i
$690$		0			0
$691$	21.8871	+	9.06592i	0.832623	+	0.344884i	0.757941	−	0.652324i	$-0.226206\pi$
$691$	21.8871	+	9.06592i	0.832623	+	0.344884i	0.0746825	+	0.997207i	$0.476206\pi$
$692$		0			0
$693$	−7.87349	−	19.0083i	−0.299089	−	0.722065i
$694$		0			0
$695$	−9.76203	−	9.76203i	−0.370295	−	0.370295i
$696$		0			0
$697$	−1.08540	+	1.08540i	−0.0411125	+	0.0411125i
$698$		0			0
$699$	1.95216	−	0.808612i	0.0738376	−	0.0305845i
$700$		0			0
$701$	18.8146	−	45.4224i	0.710617	−	1.71558i	0.0121647	−	0.999926i	$-0.496128\pi$
$701$	18.8146	−	45.4224i	0.710617	−	1.71558i	0.698453	−	0.715656i	$-0.253872\pi$
$702$		0			0
$703$	54.8829			2.06995
$704$		0			0
$705$	−4.11299			−0.154904
$706$		0			0
$707$	−18.4180	+	44.4650i	−0.692681	+	1.67228i
$708$		0			0
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.763445	−	0.645873i	$-0.776494\pi$
$709$	−22.5420	+	9.33718i	−0.846581	+	0.350665i	−0.0831359	+	0.996538i	$0.526494\pi$
$710$		0			0
$711$	−0.109926	+	0.109926i	−0.00412254	+	0.00412254i
$712$		0			0
$713$	−5.71852	−	5.71852i	−0.214160	−	0.214160i
$714$		0			0
$715$	−2.97928	−	7.19263i	−0.111419	−	0.268989i
$716$		0			0
$717$	−5.00015	−	2.07113i	−0.186734	−	0.0773478i
$718$		0			0
$719$		−	38.2799i		−	1.42760i	−0.700350	−	0.713800i	$-0.746973\pi$
$719$		−	38.2799i		−	1.42760i	0.700350	−	0.713800i	$-0.253027\pi$
$720$		0			0
$721$			53.4707i			1.99135i
$722$		0			0
$723$	18.1712	+	7.52676i	0.675795	+	0.279923i
$724$		0			0
$725$	−3.87263	−	9.34936i	−0.143826	−	0.347226i
$726$		0			0
$727$	2.75063	+	2.75063i	0.102015	+	0.102015i	0.756272	−	0.654257i	$-0.227019\pi$
$727$	2.75063	+	2.75063i	0.102015	+	0.102015i	−0.654257	+	0.756272i	$0.727019\pi$
$728$		0			0
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$		0			0
$731$	8.20436	−	3.39836i	0.303449	−	0.125693i
$732$		0			0
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	−0.998155	−	0.0607106i	$-0.980663\pi$
$733$	−6.75290	+	16.3029i	−0.249424	+	0.602163i	0.748731	+	0.662874i	$0.230663\pi$
$734$		0			0
$735$	−8.41929			−0.310550
$736$		0			0
$737$	16.7617			0.617424
$738$		0			0
$739$	−9.62421	+	23.2349i	−0.354032	+	0.854709i	0.642082	+	0.766636i	$0.278071\pi$
$739$	−9.62421	+	23.2349i	−0.354032	+	0.854709i	−0.996114	+	0.0880732i	$0.971929\pi$
$740$		0			0
$741$	−6.06045	+	2.51032i	−0.222636	+	0.0922189i
$742$		0			0
$743$	32.2711	−	32.2711i	1.18391	−	1.18391i	0.205192	−	0.978722i	$-0.434218\pi$
$743$	32.2711	−	32.2711i	1.18391	−	1.18391i	0.978722	−	0.205192i	$-0.0657817\pi$
$744$		0			0
$745$	−2.66218	−	2.66218i	−0.0975347	−	0.0975347i
$746$		0			0
$747$	2.12849	+	5.13862i	0.0778773	+	0.188012i
$748$		0			0
$749$	−5.10921	−	2.11630i	−0.186687	−	0.0773281i
$750$		0			0
$751$		−	2.67256i		−	0.0975231i	−0.998810	−	0.0487616i	$-0.984473\pi$
$751$		−	2.67256i		−	0.0975231i	0.998810	−	0.0487616i	$-0.0155274\pi$
$752$		0			0
$753$		−	25.6145i		−	0.933443i
$754$		0			0
$755$	10.9065	+	4.51762i	0.396928	+	0.164413i
$756$		0			0
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	−0.997604	−	0.0691822i	$-0.977961\pi$
$757$	−9.38519	−	22.6579i	−0.341111	−	0.823514i	0.656493	−	0.754332i	$-0.272039\pi$
$758$		0			0
$759$	20.7610	+	20.7610i	0.753577	+	0.753577i
$760$		0			0
$761$	−12.8473	+	12.8473i	−0.465714	+	0.465714i	−0.900523	−	0.434809i	$-0.856816\pi$
$761$	−12.8473	+	12.8473i	−0.465714	+	0.465714i	0.434809	+	0.900523i	$0.356816\pi$
$762$		0			0
$763$	40.6275	−	16.8285i	1.47081	−	0.609231i
$764$		0			0
$765$	0.488304	−	1.17887i	0.0176547	−	0.0426222i
$766$		0			0
$767$	−10.3237			−0.372767
$768$		0			0
$769$	15.9481			0.575102			0.287551	−	0.957765i	$-0.407159\pi$
$769$	15.9481			0.575102			0.287551	+	0.957765i	$0.407159\pi$
$770$		0			0
$771$	3.61347	−	8.72369i	0.130136	−	0.314176i
$772$		0			0
$773$	4.77420	−	1.97754i	0.171716	−	0.0711271i	−0.295169	−	0.955445i	$-0.595376\pi$
$773$	4.77420	−	1.97754i	0.171716	−	0.0711271i	0.466885	+	0.884318i	$0.345376\pi$
$774$		0			0
$775$	3.60599	−	3.60599i	0.129531	−	0.129531i
$776$		0			0
$777$	23.1194	+	23.1194i	0.829406	+	0.829406i
$778$		0			0
$779$	3.69493	+	8.92034i	0.132385	+	0.319604i
$780$		0			0
$781$	73.5447	+	30.4632i	2.63164	+	1.09006i
$782$		0			0
$783$			3.06526i			0.109543i
$784$		0			0
$785$		−	9.73086i		−	0.347309i
$786$		0			0
$787$	14.1033	+	5.84179i	0.502730	+	0.208237i	0.619612	−	0.784908i	$-0.287290\pi$
$787$	14.1033	+	5.84179i	0.502730	+	0.208237i	−0.116882	+	0.993146i	$0.537290\pi$
$788$		0			0
$789$	4.53949	+	10.9593i	0.161610	+	0.390161i
$790$		0			0
$791$	24.4152	+	24.4152i	0.868106	+	0.868106i
$792$		0			0
$793$	3.95049	−	3.95049i	0.140286	−	0.140286i
$794$		0			0
$795$	−8.03136	+	3.32670i	−0.284843	+	0.117986i
$796$		0			0
$797$	−15.7714	+	38.0755i	−0.558652	+	1.34870i	0.352182	+	0.935931i	$0.385440\pi$
$797$	−15.7714	+	38.0755i	−0.558652	+	1.34870i	−0.910834	+	0.412773i	$0.864560\pi$
$798$		0			0
$799$	−3.08972			−0.109306
$800$		0			0
$801$	8.70170			0.307459
$802$		0			0
$803$	24.6171	−	59.4308i	0.868717	−	2.09727i
$804$		0			0
$805$	23.1281	−	9.57997i	0.815158	−	0.337650i
$806$		0			0
$807$	−0.0501380	+	0.0501380i	−0.00176494	+	0.00176494i
$808$		0			0
$809$	−22.3087	−	22.3087i	−0.784333	−	0.784333i	0.196226	−	0.980559i	$-0.437131\pi$
$809$	−22.3087	−	22.3087i	−0.784333	−	0.784333i	−0.980559	+	0.196226i	$0.937131\pi$
$810$		0			0
$811$	17.0179	+	41.0848i	0.597579	+	1.44268i	0.876041	+	0.482236i	$0.160175\pi$
$811$	17.0179	+	41.0848i	0.597579	+	1.44268i	−0.278462	+	0.960447i	$0.589825\pi$
$812$		0			0
$813$	−13.3848	−	5.54419i	−0.469427	−	0.194443i
$814$		0			0
$815$		−	3.26394i		−	0.114331i
$816$		0			0
$817$		−	55.8586i		−	1.95425i
$818$		0			0
$819$	−3.61044	−	1.49549i	−0.126159	−	0.0522567i
$820$		0			0
$821$	4.17316	+	10.0749i	0.145644	+	0.351616i	0.979820	−	0.199883i	$-0.0640561\pi$
$821$	4.17316	+	10.0749i	0.145644	+	0.351616i	−0.834176	+	0.551499i	$0.814056\pi$
$822$		0			0
$823$	21.0647	+	21.0647i	0.734269	+	0.734269i	0.971462	−	0.237194i	$-0.0762276\pi$
$823$	21.0647	+	21.0647i	0.734269	+	0.734269i	−0.237194	+	0.971462i	$0.576228\pi$
$824$		0			0
$825$	−13.0915	+	13.0915i	−0.455788	+	0.455788i
$826$		0			0
$827$	51.5584	−	21.3562i	1.79286	−	0.742627i	0.803840	−	0.594845i	$-0.202787\pi$
$827$	51.5584	−	21.3562i	1.79286	−	0.742627i	0.989020	−	0.147782i	$-0.0472134\pi$
$828$		0			0
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	−0.560000	−	0.828493i	$-0.689199\pi$
$829$	12.1450	−	29.3206i	0.421813	−	1.01835i	0.981812	−	0.189853i	$-0.0608013\pi$
$830$		0			0
$831$	−21.3487			−0.740580
$832$		0			0
$833$	−6.32466			−0.219136
$834$		0			0
$835$	2.54555	−	6.14550i	0.0880924	−	0.212674i
$836$		0			0
$837$	−1.42711	+	0.591127i	−0.0493280	+	0.0204323i
$838$		0			0
$839$	−21.1653	+	21.1653i	−0.730706	+	0.730706i	−0.970760	−	0.240054i	$-0.922835\pi$
$839$	−21.1653	+	21.1653i	−0.730706	+	0.730706i	0.240054	+	0.970760i	$0.422835\pi$
$840$		0			0
$841$	13.8623	+	13.8623i	0.478009	+	0.478009i
$842$		0			0
$843$	1.49517	+	3.60966i	0.0514964	+	0.124323i
$844$		0			0
$845$	14.2870	+	5.91788i	0.491489	+	0.203581i
$846$		0			0
$847$		−	75.0241i		−	2.57786i
$848$		0			0
$849$			6.35234i			0.218012i
$850$		0			0
$851$	−43.1066	−	17.8553i	−1.47767	−	0.612073i
$852$		0			0
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	0.996701	−	0.0811601i	$-0.0258625\pi$
$853$	6.84996	+	16.5373i	0.234538	+	0.566225i	−0.762163	+	0.647385i	$0.775863\pi$
$854$		0			0
$855$	−5.67540	−	5.67540i	−0.194095	−	0.194095i
$856$		0			0
$857$	−33.6370	+	33.6370i	−1.14902	+	1.14902i	−0.162272	+	0.986746i	$0.551882\pi$
$857$	−33.6370	+	33.6370i	−1.14902	+	1.14902i	−0.986746	+	0.162272i	$0.948118\pi$
$858$		0			0
$859$	−35.7350	+	14.8019i	−1.21926	+	0.505035i	−0.897175	−	0.441674i	$-0.854385\pi$
$859$	−35.7350	+	14.8019i	−1.21926	+	0.505035i	−0.322088	+	0.946710i	$0.604385\pi$
$860$		0			0
$861$	−2.20121	+	5.31418i	−0.0750169	+	0.181107i
$862$		0			0
$863$	−44.4296			−1.51240			−0.756201	−	0.654340i	$-0.772947\pi$
$863$	−44.4296			−1.51240			−0.756201	+	0.654340i	$0.772947\pi$
$864$		0			0
$865$	3.06060			0.104064
$866$		0			0
$867$	−6.13880	+	14.8204i	−0.208485	+	0.503326i
$868$		0			0
$869$	−0.805445	+	0.333626i	−0.0273228	+	0.0113175i
$870$		0			0
$871$	2.25122	−	2.25122i	0.0762798	−	0.0762798i
$872$		0			0
$873$	−10.1718	−	10.1718i	−0.344265	−	0.344265i
$874$		0			0
$875$	15.1900	+	36.6719i	0.513516	+	1.23974i
$876$		0			0
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.847543	−	0.530727i	$-0.178081\pi$
$877$	31.7336	+	13.1445i	1.07157	+	0.443857i	0.224023	+	0.974584i	$0.428081\pi$
$878$		0			0
$879$			4.88728i			0.164844i
$880$		0			0
$881$			42.6814i			1.43797i	0.695023	+	0.718987i	$0.255394\pi$
$881$			42.6814i			1.43797i	−0.695023	+	0.718987i	$0.744606\pi$
$882$		0			0
$883$	−22.4520	−	9.29994i	−0.755571	−	0.312968i	−0.0285587	−	0.999592i	$-0.509092\pi$
$883$	−22.4520	−	9.29994i	−0.755571	−	0.312968i	−0.727012	+	0.686624i	$0.759092\pi$
$884$		0			0
$885$	−4.83389	−	11.6700i	−0.162490	−	0.392284i
$886$		0			0
$887$	25.1413	+	25.1413i	0.844161	+	0.844161i	0.989397	−	0.145236i	$-0.0463941\pi$
$887$	25.1413	+	25.1413i	0.844161	+	0.844161i	−0.145236	+	0.989397i	$0.546394\pi$
$888$		0			0
$889$	41.5643	−	41.5643i	1.39402	−	1.39402i
$890$		0			0
$891$	5.18109	−	2.14608i	0.173573	−	0.0718963i
$892$		0			0
$893$	−7.43737	+	17.9554i	−0.248882	+	0.600855i
$894$		0			0
$895$	−3.75920			−0.125656
$896$		0			0
$897$	5.57674			0.186202
$898$		0			0
$899$	1.81196	−	4.37445i	0.0604321	−	0.145896i
$900$		0			0
$901$	−6.03324	+	2.49905i	−0.200996	+	0.0832554i
$902$		0			0
$903$	23.5304	−	23.5304i	0.783044	−	0.783044i
$904$		0			0
$905$	2.67028	+	2.67028i	0.0887632	+	0.0887632i
$906$		0			0
$907$	−14.9664	−	36.1321i	−0.496951	−	1.19975i	−0.951118	−	0.308829i	$-0.900063\pi$
$907$	−14.9664	−	36.1321i	−0.496951	−	1.19975i	0.454167	−	0.890917i	$-0.349937\pi$
$908$		0			0
$909$	−12.1198	−	5.02020i	−0.401989	−	0.166509i
$910$		0			0
$911$			23.3974i			0.775190i	0.921830	+	0.387595i	$0.126694\pi$
$911$			23.3974i			0.775190i	−0.921830	+	0.387595i	$0.873306\pi$
$912$		0			0
$913$			31.1915i			1.03229i
$914$		0			0
$915$	6.31544	+	2.61594i	0.208782	+	0.0864803i
$916$		0			0
$917$	−8.02067	−	19.3636i	−0.264866	−	0.639442i
$918$		0			0
$919$	−20.8473	−	20.8473i	−0.687689	−	0.687689i	0.274032	−	0.961721i	$-0.411643\pi$
$919$	−20.8473	−	20.8473i	−0.687689	−	0.687689i	−0.961721	+	0.274032i	$0.911643\pi$
$920$		0			0
$921$	6.46123	−	6.46123i	0.212905	−	0.212905i
$922$		0			0
$923$	13.9691	−	5.78618i	0.459798	−	0.190455i
$924$		0			0
$925$	11.2592	−	27.1822i	0.370202	−	0.893746i
$926$		0			0
$927$	−14.5745			−0.478690
$928$		0			0
$929$	55.9215			1.83472			0.917362	−	0.398055i	$-0.130315\pi$
$929$	55.9215			1.83472			0.917362	+	0.398055i	$0.130315\pi$
$930$		0			0
$931$	−15.2243	+	36.7547i	−0.498956	+	1.20459i
$932$		0			0
$933$	27.2339	−	11.2806i	0.891596	−	0.369311i
$934$		0			0
$935$	5.05989	−	5.05989i	0.165476	−	0.165476i
$936$		0			0
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.999440	+	0.0334692i	$0.0106556\pi$
$937$	31.6178	+	31.6178i	1.03291	+	1.03291i	0.0334692	+	0.999440i	$0.489344\pi$
$938$		0			0
$939$	7.63226	+	18.4259i	0.249069	+	0.601306i
$940$		0			0
$941$	23.4212	+	9.70137i	0.763509	+	0.316256i	0.730240	−	0.683191i	$-0.239408\pi$
$941$	23.4212	+	9.70137i	0.763509	+	0.316256i	0.0332688	+	0.999446i	$0.489408\pi$
$942$		0			0
$943$		−	8.20837i		−	0.267301i
$944$		0			0
$945$		−	4.78153i		−	0.155543i
$946$		0			0
$947$	−30.2016	−	12.5099i	−0.981419	−	0.406517i	−0.166468	−	0.986047i	$-0.553236\pi$
$947$	−30.2016	−	12.5099i	−0.981419	−	0.406517i	−0.814951	+	0.579530i	$0.803236\pi$
$948$		0			0
$949$	−4.67577	−	11.2883i	−0.151782	−	0.366434i
$950$		0			0
$951$	1.98278	+	1.98278i	0.0642961	+	0.0642961i
$952$		0			0
$953$	−17.7752	+	17.7752i	−0.575795	+	0.575795i	−0.933742	−	0.357947i	$-0.883477\pi$
$953$	−17.7752	+	17.7752i	−0.575795	+	0.575795i	0.357947	+	0.933742i	$0.383477\pi$
$954$		0			0
$955$	10.0578	−	4.16607i	0.325462	−	0.134811i
$956$		0			0
$957$	−6.57828	+	15.8814i	−0.212646	+	0.513372i
$958$		0			0
$959$	44.8060			1.44686
$960$		0			0
$961$	−28.6139			−0.923030
$962$		0			0
$963$	0.576841	−	1.39262i	0.0185884	−	0.0448765i
$964$		0			0
$965$	14.8525	−	6.15211i	0.478119	−	0.198043i
$966$		0			0
$967$	−5.23073	+	5.23073i	−0.168209	+	0.168209i	−0.786192	−	0.617983i	$-0.787950\pi$
$967$	−5.23073	+	5.23073i	−0.168209	+	0.168209i	0.617983	+	0.786192i	$0.287950\pi$
$968$		0			0
$969$	−4.26342	−	4.26342i	−0.136961	−	0.136961i
$970$		0			0
$971$	−6.01158	−	14.5132i	−0.192921	−	0.465752i	0.797588	−	0.603203i	$-0.206109\pi$
$971$	−6.01158	−	14.5132i	−0.192921	−	0.465752i	−0.990509	+	0.137451i	$0.956109\pi$
$972$		0			0
$973$	−35.9044	−	14.8721i	−1.15104	−	0.476778i
$974$		0			0
$975$			3.51659i			0.112621i
$976$		0			0
$977$		−	48.6725i		−	1.55717i	−0.627539	−	0.778585i	$-0.715938\pi$
$977$		−	48.6725i		−	1.55717i	0.627539	−	0.778585i	$-0.284062\pi$
$978$		0			0
$979$	45.0842	+	18.6745i	1.44090	+	0.596840i
$980$		0			0
$981$	4.58693	+	11.0738i	0.146449	+	0.353560i
$982$		0			0
$983$	−7.17484	−	7.17484i	−0.228842	−	0.228842i	0.583367	−	0.812209i	$-0.301735\pi$
$983$	−7.17484	−	7.17484i	−0.228842	−	0.228842i	−0.812209	+	0.583367i	$0.801735\pi$
$984$		0			0
$985$	21.4617	−	21.4617i	0.683826	−	0.683826i
$986$		0			0
$987$	−10.6967	+	4.43072i	−0.340480	+	0.141031i
$988$		0			0
$989$	−18.1727	+	43.8729i	−0.577860	+	1.39508i
$990$		0			0
$991$	20.8957			0.663774			0.331887	−	0.943319i	$-0.392315\pi$
$991$	20.8957			0.663774			0.331887	+	0.943319i	$0.392315\pi$
$992$		0			0
$993$	−3.60076			−0.114267
$994$		0			0
$995$	−12.0143	+	29.0051i	−0.380880	+	0.919525i
$996$		0			0
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.979787	−	0.200042i	$-0.935892\pi$
$997$	−48.3465	+	20.0258i	−1.53115	+	0.634223i	−0.551363	+	0.834266i	$0.685892\pi$
$998$		0			0
$999$	−6.30167	+	6.30167i	−0.199376	+	0.199376i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.n.a.145.2		32
3.2	odd	2		1152.2.v.c.145.5		32
4.3	odd	2		96.2.n.a.13.4	✓	32
8.3	odd	2		768.2.n.a.289.3		32
8.5	even	2		768.2.n.b.289.7		32
12.11	even	2		288.2.v.d.109.5		32
32.5	even	8	inner	384.2.n.a.241.2		32
32.11	odd	8		768.2.n.a.481.3		32
32.21	even	8		768.2.n.b.481.7		32
32.27	odd	8		96.2.n.a.37.4	yes	32
96.5	odd	8		1152.2.v.c.1009.5		32
96.59	even	8		288.2.v.d.37.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.4	✓	32	4.3	odd	2
96.2.n.a.37.4	yes	32	32.27	odd	8
288.2.v.d.37.5		32	96.59	even	8
288.2.v.d.109.5		32	12.11	even	2
384.2.n.a.145.2		32	1.1	even	1	trivial
384.2.n.a.241.2		32	32.5	even	8	inner
768.2.n.a.289.3		32	8.3	odd	2
768.2.n.a.481.3		32	32.11	odd	8
768.2.n.b.289.7		32	8.5	even	2
768.2.n.b.481.7		32	32.21	even	8
1152.2.v.c.145.5		32	3.2	odd	2
1152.2.v.c.1009.5		32	96.5	odd	8

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 + 0.923880i) q^{3} +(-1.20409 + 0.498752i) q^{5} +(-2.59422 + 2.59422i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-2.14608 - 5.18109i) q^{11} +(-0.984096 - 0.407626i) q^{13} -1.30330i q^{15} -0.979053i q^{17} +(-5.68961 - 2.35671i) q^{19} +(-1.40398 - 3.38951i) q^{21} +(3.70206 + 3.70206i) q^{23} +(-2.33445 + 2.33445i) q^{25} +(0.923880 - 0.382683i) q^{27} +(-1.17302 + 2.83193i) q^{29} -1.54469 q^{31} +5.60797 q^{33} +(1.82981 - 4.41756i) q^{35} +(-8.23352 + 3.41044i) q^{37} +(0.753195 - 0.753195i) q^{39} +(-1.10862 - 1.10862i) q^{41} +(3.47106 + 8.37989i) q^{43} +(1.20409 + 0.498752i) q^{45} -3.15582i q^{47} -6.45997i q^{49} +(0.904527 + 0.374667i) q^{51} +(-2.55252 - 6.16232i) q^{53} +(5.16815 + 5.16815i) q^{55} +(4.35464 - 4.35464i) q^{57} +(8.95423 - 3.70896i) q^{59} +(-2.00717 + 4.84573i) q^{61} +3.66878 q^{63} +1.38825 q^{65} +(-1.14380 + 2.76138i) q^{67} +(-4.83697 + 2.00354i) q^{69} +(-10.0373 + 10.0373i) q^{71} +(8.11103 + 8.11103i) q^{73} +(-1.26339 - 3.05010i) q^{75} +(19.0083 + 7.87349i) q^{77} -0.155459i q^{79} +1.00000i q^{81} +(-5.13862 - 2.12849i) q^{83} +(0.488304 + 1.17887i) q^{85} +(-2.16747 - 2.16747i) q^{87} +(-6.15303 + 6.15303i) q^{89} +(3.61044 - 1.49549i) q^{91} +(0.591127 - 1.42711i) q^{93} +8.02623 q^{95} +14.3852 q^{97} +(-2.14608 + 5.18109i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 16 q^{23} + 48 q^{31} + 48 q^{35} + 16 q^{43} - 16 q^{51} - 32 q^{53} - 32 q^{55} - 64 q^{59} - 32 q^{61} - 16 q^{63} - 16 q^{67} - 32 q^{69} - 64 q^{71} - 32 q^{75} - 32 q^{77} + 48 q^{91}+O(q^{100}) \) 32 * q + 16 * q^23 + 48 * q^31 + 48 * q^35 + 16 * q^43 - 16 * q^51 - 32 * q^53 - 32 * q^55 - 64 * q^59 - 32 * q^61 - 16 * q^63 - 16 * q^67 - 32 * q^69 - 64 * q^71 - 32 * q^75 - 32 * q^77 + 48 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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