LMFDB - Embedded newform 768.2.n.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(97,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, 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("768.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.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:	$6.13251087523$
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			289.4
Character	$\chi$	$=$	768.289
Dual form			768.2.n.b.481.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(2.39923 + 5.79225i) q^{11} +(-0.0173304 - 0.00717850i) q^{13} +3.34804i q^{15} -5.57978i q^{17} +(-1.03052 - 0.426856i) q^{19} +(0.938989 + 2.26692i) q^{21} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(0.923880 - 0.382683i) q^{27} +(0.706079 - 1.70463i) q^{29} -1.38048 q^{31} -6.26948 q^{33} +(3.14377 - 7.58973i) q^{35} +(2.87315 - 1.19010i) q^{37} +(0.0132641 - 0.0132641i) q^{39} +(6.97897 + 6.97897i) q^{41} +(1.67010 + 4.03197i) q^{43} +(-3.09318 - 1.28124i) q^{45} -1.15993i q^{47} +0.979375i q^{49} +(5.15504 + 2.13529i) q^{51} +(-2.56680 - 6.19681i) q^{53} +(14.8425 + 14.8425i) q^{55} +(0.788727 - 0.788727i) q^{57} +(-0.735935 + 0.304834i) q^{59} +(-4.82262 + 11.6428i) q^{61} -2.45370 q^{63} -0.0628036 q^{65} +(-2.05899 + 4.97085i) q^{67} +(2.63753 - 1.09250i) q^{69} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(2.37622 + 5.73670i) q^{75} +(14.2124 + 5.88697i) q^{77} +2.67236i q^{79} +1.00000i q^{81} +(-6.91877 - 2.86585i) q^{83} +(-7.14903 - 17.2593i) q^{85} +(1.30466 + 1.30466i) q^{87} +(6.73869 - 6.73869i) q^{89} +(-0.0425236 + 0.0176139i) q^{91} +(0.528286 - 1.27540i) q^{93} -3.73450 q^{95} -1.75001 q^{97} +(2.39923 - 5.79225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{8}\right)$

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
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		0			0
$5$	3.09318	−	1.28124i	1.38331	−	0.572987i	0.437949	−	0.899000i	$-0.355705\pi$
$5$	3.09318	−	1.28124i	1.38331	−	0.572987i	0.945365	+	0.326013i	$0.105705\pi$
$6$		0			0
$7$	1.73503	−	1.73503i	0.655778	−	0.655778i	−0.298600	−	0.954378i	$-0.596520\pi$
$7$	1.73503	−	1.73503i	0.655778	−	0.655778i	0.954378	+	0.298600i	$0.0965198\pi$
$8$		0			0
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$		0			0
$11$	2.39923	+	5.79225i	0.723394	+	1.74643i	0.663443	+	0.748227i	$0.269095\pi$
$11$	2.39923	+	5.79225i	0.723394	+	1.74643i	0.0599515	+	0.998201i	$0.480905\pi$
$12$		0			0
$13$	−0.0173304	−	0.00717850i	−0.00480660	−	0.00199096i	0.380279	−	0.924872i	$-0.375828\pi$
$13$	−0.0173304	−	0.00717850i	−0.00480660	−	0.00199096i	−0.385085	+	0.922881i	$0.625828\pi$
$14$		0			0
$15$			3.34804i			0.864460i
$16$		0			0
$17$		−	5.57978i		−	1.35329i	−0.736307	−	0.676647i	$-0.763432\pi$
$17$		−	5.57978i		−	1.35329i	0.736307	−	0.676647i	$-0.236568\pi$
$18$		0			0
$19$	−1.03052	−	0.426856i	−0.236418	−	0.0979274i	0.261329	−	0.965250i	$-0.415839\pi$
$19$	−1.03052	−	0.426856i	−0.236418	−	0.0979274i	−0.497747	+	0.867322i	$0.665839\pi$
$20$		0			0
$21$	0.938989	+	2.26692i	0.204904	+	0.494682i
$22$		0			0
$23$	−2.01868	−	2.01868i	−0.420923	−	0.420923i	0.464598	−	0.885522i	$-0.346199\pi$
$23$	−2.01868	−	2.01868i	−0.420923	−	0.420923i	−0.885522	+	0.464598i	$0.846199\pi$
$24$		0			0
$25$	4.39068	−	4.39068i	0.878136	−	0.878136i
$26$		0			0
$27$	0.923880	−	0.382683i	0.177801	−	0.0736475i
$28$		0			0
$29$	0.706079	−	1.70463i	0.131116	−	0.316541i	−0.844664	−	0.535297i	$-0.820200\pi$
$29$	0.706079	−	1.70463i	0.131116	−	0.316541i	0.975780	+	0.218756i	$0.0701998\pi$
$30$		0			0
$31$	−1.38048			−0.247941			−0.123971	−	0.992286i	$-0.539563\pi$
$31$	−1.38048			−0.247941			−0.123971	+	0.992286i	$0.539563\pi$
$32$		0			0
$33$	−6.26948			−1.09138
$34$		0			0
$35$	3.14377	−	7.58973i	0.531394	−	1.28290i
$36$		0			0
$37$	2.87315	−	1.19010i	0.472342	−	0.195651i	−0.133797	−	0.991009i	$-0.542717\pi$
$37$	2.87315	−	1.19010i	0.472342	−	0.195651i	0.606140	+	0.795358i	$0.292717\pi$
$38$		0			0
$39$	0.0132641	−	0.0132641i	0.00212396	−	0.00212396i
$40$		0			0
$41$	6.97897	+	6.97897i	1.08993	+	1.08993i	0.995535	+	0.0943974i	$0.0300924\pi$
$41$	6.97897	+	6.97897i	1.08993	+	1.08993i	0.0943974	+	0.995535i	$0.469908\pi$
$42$		0			0
$43$	1.67010	+	4.03197i	0.254687	+	0.614869i	0.998571	−	0.0534396i	$-0.0170184\pi$
$43$	1.67010	+	4.03197i	0.254687	+	0.614869i	−0.743884	+	0.668309i	$0.767018\pi$
$44$		0			0
$45$	−3.09318	−	1.28124i	−0.461105	−	0.190996i
$46$		0			0
$47$		−	1.15993i		−	0.169193i	−0.996415	−	0.0845966i	$-0.973040\pi$
$47$		−	1.15993i		−	0.169193i	0.996415	−	0.0845966i	$-0.0269601\pi$
$48$		0			0
$49$			0.979375i			0.139911i
$50$		0			0
$51$	5.15504	+	2.13529i	0.721850	+	0.299000i
$52$		0			0
$53$	−2.56680	−	6.19681i	−0.352577	−	0.851197i	−0.996300	−	0.0859383i	$-0.972611\pi$
$53$	−2.56680	−	6.19681i	−0.352577	−	0.851197i	0.643723	−	0.765258i	$-0.277389\pi$
$54$		0			0
$55$	14.8425	+	14.8425i	2.00136	+	2.00136i
$56$		0			0
$57$	0.788727	−	0.788727i	0.104469	−	0.104469i
$58$		0			0
$59$	−0.735935	+	0.304834i	−0.0958106	+	0.0396860i	−0.430074	−	0.902794i	$-0.641513\pi$
$59$	−0.735935	+	0.304834i	−0.0958106	+	0.0396860i	0.334263	+	0.942480i	$0.391513\pi$
$60$		0			0
$61$	−4.82262	+	11.6428i	−0.617473	+	1.49071i	0.237156	+	0.971472i	$0.423785\pi$
$61$	−4.82262	+	11.6428i	−0.617473	+	1.49071i	−0.854629	+	0.519240i	$0.826215\pi$
$62$		0			0
$63$	−2.45370			−0.309137
$64$		0			0
$65$	−0.0628036			−0.00778983
$66$		0			0
$67$	−2.05899	+	4.97085i	−0.251546	+	0.607286i	−0.998329	−	0.0577816i	$-0.981597\pi$
$67$	−2.05899	+	4.97085i	−0.251546	+	0.607286i	0.746783	+	0.665068i	$0.231597\pi$
$68$		0			0
$69$	2.63753	−	1.09250i	0.317521	−	0.131522i
$70$		0			0
$71$	1.78298	−	1.78298i	0.211600	−	0.211600i	−0.593347	−	0.804947i	$-0.702194\pi$
$71$	1.78298	−	1.78298i	0.211600	−	0.211600i	0.804947	+	0.593347i	$0.202194\pi$
$72$		0			0
$73$	1.67500	+	1.67500i	0.196044	+	0.196044i	0.798302	−	0.602258i	$-0.205732\pi$
$73$	1.67500	+	1.67500i	0.196044	+	0.196044i	−0.602258	+	0.798302i	$0.705732\pi$
$74$		0			0
$75$	2.37622	+	5.73670i	0.274382	+	0.662417i
$76$		0			0
$77$	14.2124	+	5.88697i	1.61965	+	0.670883i
$78$		0			0
$79$			2.67236i			0.300664i	0.988636	+	0.150332i	$0.0480343\pi$
$79$			2.67236i			0.300664i	−0.988636	+	0.150332i	$0.951966\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	−6.91877	−	2.86585i	−0.759433	−	0.314568i	−0.0308494	−	0.999524i	$-0.509821\pi$
$83$	−6.91877	−	2.86585i	−0.759433	−	0.314568i	−0.728584	+	0.684956i	$0.759821\pi$
$84$		0			0
$85$	−7.14903	−	17.2593i	−0.775421	−	1.87203i
$86$		0			0
$87$	1.30466	+	1.30466i	0.139875	+	0.139875i
$88$		0			0
$89$	6.73869	−	6.73869i	0.714300	−	0.714300i	−0.253132	−	0.967432i	$-0.581461\pi$
$89$	6.73869	−	6.73869i	0.714300	−	0.714300i	0.967432	+	0.253132i	$0.0814607\pi$
$90$		0			0
$91$	−0.0425236	+	0.0176139i	−0.00445769	+	0.00184643i
$92$		0			0
$93$	0.528286	−	1.27540i	0.0547807	−	0.132252i
$94$		0			0
$95$	−3.73450			−0.383151
$96$		0			0
$97$	−1.75001			−0.177686			−0.0888431	−	0.996046i	$-0.528317\pi$
$97$	−1.75001			−0.177686			−0.0888431	+	0.996046i	$0.528317\pi$
$98$		0			0
$99$	2.39923	−	5.79225i	0.241131	−	0.582143i
$100$		0			0
$101$	7.71200	−	3.19442i	0.767373	−	0.317856i	0.0355651	−	0.999367i	$-0.488677\pi$
$101$	7.71200	−	3.19442i	0.767373	−	0.317856i	0.731808	+	0.681511i	$0.238677\pi$
$102$		0			0
$103$	3.90293	−	3.90293i	0.384567	−	0.384567i	−0.488177	−	0.872744i	$-0.662338\pi$
$103$	3.90293	−	3.90293i	0.384567	−	0.384567i	0.872744	+	0.488177i	$0.162338\pi$
$104$		0			0
$105$	5.80893	+	5.80893i	0.566894	+	0.566894i
$106$		0			0
$107$	−5.55747	−	13.4169i	−0.537261	−	1.29706i	−0.926628	−	0.375981i	$-0.877306\pi$
$107$	−5.55747	−	13.4169i	−0.537261	−	1.29706i	0.389366	−	0.921083i	$-0.372694\pi$
$108$		0			0
$109$	−14.8488	−	6.15056i	−1.42225	−	0.589117i	−0.466828	−	0.884348i	$-0.654603\pi$
$109$	−14.8488	−	6.15056i	−1.42225	−	0.589117i	−0.955426	+	0.295231i	$0.904603\pi$
$110$		0			0
$111$			3.10987i			0.295176i
$112$		0			0
$113$			2.72924i			0.256745i	0.991726	+	0.128373i	$0.0409753\pi$
$113$			2.72924i			0.256745i	−0.991726	+	0.128373i	$0.959025\pi$
$114$		0			0
$115$	−8.83055	−	3.65773i	−0.823453	−	0.341085i
$116$		0			0
$117$	0.00717850	+	0.0173304i	0.000663652	+	0.00160220i
$118$		0			0
$119$	−9.68106	−	9.68106i	−0.887461	−	0.887461i
$120$		0			0
$121$	−20.0157	+	20.0157i	−1.81961	+	1.81961i
$122$		0			0
$123$	−9.11846	+	3.77699i	−0.822184	+	0.340560i
$124$		0			0
$125$	1.54948	−	3.74078i	0.138590	−	0.334585i
$126$		0			0
$127$	−15.3336			−1.36064			−0.680319	−	0.732916i	$-0.738159\pi$
$127$	−15.3336			−1.36064			−0.680319	+	0.732916i	$0.738159\pi$
$128$		0			0
$129$	−4.36417			−0.384244
$130$		0			0
$131$	5.70595	−	13.7754i	0.498531	−	1.20356i	−0.451744	−	0.892148i	$-0.649198\pi$
$131$	5.70595	−	13.7754i	0.498531	−	1.20356i	0.950275	−	0.311412i	$-0.100802\pi$
$132$		0			0
$133$	−2.52859	+	1.04737i	−0.219256	+	0.0908189i
$134$		0			0
$135$	2.36742	−	2.36742i	0.203755	−	0.203755i
$136$		0			0
$137$	−3.06155	−	3.06155i	−0.261566	−	0.261566i	0.564124	−	0.825690i	$-0.309214\pi$
$137$	−3.06155	−	3.06155i	−0.261566	−	0.261566i	−0.825690	+	0.564124i	$0.809214\pi$
$138$		0			0
$139$	0.621401	+	1.50020i	0.0527066	+	0.127245i	0.948040	−	0.318152i	$-0.103062\pi$
$139$	0.621401	+	1.50020i	0.0527066	+	0.127245i	−0.895333	+	0.445397i	$0.853062\pi$
$140$		0			0
$141$	1.07164	+	0.443886i	0.0902480	+	0.0373819i
$142$		0			0
$143$		−	0.117605i		−	0.00983462i
$144$		0			0
$145$		−	6.17738i		−	0.513003i
$146$		0			0
$147$	−0.904825	−	0.374791i	−0.0746287	−	0.0309122i
$148$		0			0
$149$	8.53959	+	20.6164i	0.699591	+	1.68896i	0.724503	+	0.689272i	$0.242070\pi$
$149$	8.53959	+	20.6164i	0.699591	+	1.68896i	−0.0249118	+	0.999690i	$0.507930\pi$
$150$		0			0
$151$	−9.42348	−	9.42348i	−0.766872	−	0.766872i	0.210683	−	0.977555i	$-0.432431\pi$
$151$	−9.42348	−	9.42348i	−0.766872	−	0.766872i	−0.977555	+	0.210683i	$0.932431\pi$
$152$		0			0
$153$	−3.94550	+	3.94550i	−0.318975	+	0.318975i
$154$		0			0
$155$	−4.27007	+	1.76872i	−0.342981	+	0.142067i
$156$		0			0
$157$	−7.53965	+	18.2023i	−0.601729	+	1.45270i	0.270070	+	0.962841i	$0.412953\pi$
$157$	−7.53965	+	18.2023i	−0.601729	+	1.45270i	−0.871800	+	0.489863i	$0.837047\pi$
$158$		0			0
$159$	6.70737			0.531929
$160$		0			0
$161$	−7.00491			−0.552064
$162$		0			0
$163$	−6.01448	+	14.5202i	−0.471090	+	1.13731i	0.492592	+	0.870260i	$0.336050\pi$
$163$	−6.01448	+	14.5202i	−0.471090	+	1.13731i	−0.963682	+	0.267052i	$0.913950\pi$
$164$		0			0
$165$	−19.3927	+	8.03271i	−1.50972	+	0.625345i
$166$		0			0
$167$	11.8392	−	11.8392i	0.916142	−	0.916142i	−0.0806038	−	0.996746i	$-0.525685\pi$
$167$	11.8392	−	11.8392i	0.916142	−	0.916142i	0.996746	+	0.0806038i	$0.0256848\pi$
$168$		0			0
$169$	−9.19214	−	9.19214i	−0.707088	−	0.707088i
$170$		0			0
$171$	0.426856	+	1.03052i	0.0326425	+	0.0788059i
$172$		0			0
$173$	−21.0615	−	8.72397i	−1.60128	−	0.663271i	−0.609683	−	0.792645i	$-0.708703\pi$
$173$	−21.0615	−	8.72397i	−1.60128	−	0.663271i	−0.991596	+	0.129374i	$0.958703\pi$
$174$		0			0
$175$		−	15.2359i		−	1.15172i
$176$		0			0
$177$		−	0.796570i		−	0.0598739i
$178$		0			0
$179$	−4.75826	−	1.97094i	−0.355649	−	0.147315i	0.197703	−	0.980262i	$-0.436652\pi$
$179$	−4.75826	−	1.97094i	−0.355649	−	0.147315i	−0.553353	+	0.832947i	$0.686652\pi$
$180$		0			0
$181$	3.71100	+	8.95914i	0.275836	+	0.665928i	0.999712	−	0.0240027i	$-0.00764102\pi$
$181$	3.71100	+	8.95914i	0.275836	+	0.665928i	−0.723876	+	0.689931i	$0.757641\pi$
$182$		0			0
$183$	−8.91104	−	8.91104i	−0.658723	−	0.658723i
$184$		0			0
$185$	7.36237	−	7.36237i	0.541293	−	0.541293i
$186$		0			0
$187$	32.3195	−	13.3872i	2.36343	−	0.978966i
$188$		0			0
$189$	0.938989	−	2.26692i	0.0683014	−	0.164894i
$190$		0			0
$191$	−11.4844			−0.830980			−0.415490	−	0.909598i	$-0.636390\pi$
$191$	−11.4844			−0.830980			−0.415490	+	0.909598i	$0.636390\pi$
$192$		0			0
$193$	19.2681			1.38695			0.693474	−	0.720482i	$-0.256079\pi$
$193$	19.2681			1.38695			0.693474	+	0.720482i	$0.256079\pi$
$194$		0			0
$195$	0.0240339	−	0.0580229i	0.00172110	−	0.00415511i
$196$		0			0
$197$	−6.48659	+	2.68683i	−0.462151	+	0.191429i	−0.601596	−	0.798801i	$-0.705468\pi$
$197$	−6.48659	+	2.68683i	−0.462151	+	0.191429i	0.139445	+	0.990230i	$0.455468\pi$
$198$		0			0
$199$	−14.6525	+	14.6525i	−1.03868	+	1.03868i	−0.0394638	+	0.999221i	$0.512565\pi$
$199$	−14.6525	+	14.6525i	−1.03868	+	1.03868i	−0.999221	+	0.0394638i	$0.987435\pi$
$200$		0			0
$201$	−3.80452	−	3.80452i	−0.268350	−	0.268350i
$202$		0			0
$203$	−1.73250	−	4.18263i	−0.121598	−	0.293563i
$204$		0			0
$205$	30.5290	+	12.6455i	2.13224	+	0.883201i
$206$		0			0
$207$			2.85484i			0.198425i
$208$		0			0
$209$		−	6.99316i		−	0.483727i
$210$		0			0
$211$	−2.80379	−	1.16137i	−0.193021	−	0.0799519i	0.284079	−	0.958801i	$-0.408312\pi$
$211$	−2.80379	−	1.16137i	−0.193021	−	0.0799519i	−0.477100	+	0.878849i	$0.658312\pi$
$212$		0			0
$213$	0.964940	+	2.32957i	0.0661166	+	0.159620i
$214$		0			0
$215$	10.3318	+	10.3318i	0.704625	+	0.704625i
$216$		0			0
$217$	−2.39517	+	2.39517i	−0.162594	+	0.162594i
$218$		0			0
$219$	−2.18850	+	0.906505i	−0.147885	+	0.0612559i
$220$		0			0
$221$	−0.0400544	+	0.0966999i	−0.00269435	+	0.00650474i
$222$		0			0
$223$	6.12103			0.409894			0.204947	−	0.978773i	$-0.434298\pi$
$223$	6.12103			0.409894			0.204947	+	0.978773i	$0.434298\pi$
$224$		0			0
$225$	−6.20936			−0.413957
$226$		0			0
$227$	−6.52469	+	15.7520i	−0.433059	+	1.04550i	0.545237	+	0.838282i	$0.316440\pi$
$227$	−6.52469	+	15.7520i	−0.433059	+	1.04550i	−0.978296	+	0.207214i	$0.933560\pi$
$228$		0			0
$229$	8.60895	−	3.56595i	0.568896	−	0.235644i	−0.0796463	−	0.996823i	$-0.525379\pi$
$229$	8.60895	−	3.56595i	0.568896	−	0.235644i	0.648542	+	0.761179i	$0.275379\pi$
$230$		0			0
$231$	−10.8777	+	10.8777i	−0.715701	+	0.715701i
$232$		0			0
$233$	7.99720	+	7.99720i	0.523914	+	0.523914i	0.918751	−	0.394837i	$-0.129199\pi$
$233$	7.99720	+	7.99720i	0.523914	+	0.523914i	−0.394837	+	0.918751i	$0.629199\pi$
$234$		0			0
$235$	−1.48615	−	3.58788i	−0.0969456	−	0.234047i
$236$		0			0
$237$	−2.46894	−	1.02267i	−0.160375	−	0.0664295i
$238$		0			0
$239$		−	6.26707i		−	0.405383i	−0.979243	−	0.202692i	$-0.935031\pi$
$239$		−	6.26707i		−	0.405383i	0.979243	−	0.202692i	$-0.0649689\pi$
$240$		0			0
$241$			15.7602i			1.01520i	0.861592	+	0.507601i	$0.169468\pi$
$241$			15.7602i			1.01520i	−0.861592	+	0.507601i	$0.830532\pi$
$242$		0			0
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$		0			0
$245$	1.25481	+	3.02939i	0.0801671	+	0.193541i
$246$		0			0
$247$	0.0147952	+	0.0147952i	0.000941395	+	0.000941395i
$248$		0			0
$249$	5.29540	−	5.29540i	0.335582	−	0.335582i
$250$		0			0
$251$	−19.0196	+	7.87816i	−1.20050	+	0.497265i	−0.891162	−	0.453686i	$-0.850109\pi$
$251$	−19.0196	+	7.87816i	−1.20050	+	0.497265i	−0.309342	+	0.950951i	$0.600109\pi$
$252$		0			0
$253$	6.84941	−	16.5359i	0.430619	−	1.03961i
$254$		0			0
$255$	18.6813			1.16987
$256$		0			0
$257$	−5.22771			−0.326096			−0.163048	−	0.986618i	$-0.552132\pi$
$257$	−5.22771			−0.326096			−0.163048	+	0.986618i	$0.552132\pi$
$258$		0			0
$259$	2.92013	−	7.04983i	0.181448	−	0.438055i
$260$		0			0
$261$	−1.70463	+	0.706079i	−0.105514	+	0.0437052i
$262$		0			0
$263$	−5.59065	+	5.59065i	−0.344734	+	0.344734i	−0.858144	−	0.513410i	$-0.828382\pi$
$263$	−5.59065	+	5.59065i	−0.344734	+	0.344734i	0.513410	+	0.858144i	$0.328382\pi$
$264$		0			0
$265$	−15.8792	−	15.8792i	−0.975450	−	0.975450i
$266$		0			0
$267$	3.64695	+	8.80452i	0.223190	+	0.538828i
$268$		0			0
$269$	−9.92617	−	4.11155i	−0.605209	−	0.250686i	0.0589693	−	0.998260i	$-0.481219\pi$
$269$	−9.92617	−	4.11155i	−0.605209	−	0.250686i	−0.664179	+	0.747574i	$0.731219\pi$
$270$		0			0
$271$		−	15.4368i		−	0.937717i	−0.883273	−	0.468858i	$-0.844665\pi$
$271$		−	15.4368i		−	0.937717i	0.883273	−	0.468858i	$-0.155335\pi$
$272$		0			0
$273$		−	0.0460272i		−	0.00278569i
$274$		0			0
$275$	35.9662	+	14.8977i	2.16884	+	0.898363i
$276$		0			0
$277$	−1.79136	−	4.32473i	−0.107633	−	0.259848i	0.860882	−	0.508804i	$-0.169912\pi$
$277$	−1.79136	−	4.32473i	−0.107633	−	0.259848i	−0.968515	+	0.248956i	$0.919912\pi$
$278$		0			0
$279$	0.976146	+	0.976146i	0.0584403	+	0.0584403i
$280$		0			0
$281$	−3.70347	+	3.70347i	−0.220931	+	0.220931i	−0.808890	−	0.587960i	$-0.799931\pi$
$281$	−3.70347	+	3.70347i	−0.220931	+	0.220931i	0.587960	+	0.808890i	$0.299931\pi$
$282$		0			0
$283$	−16.1605	+	6.69389i	−0.960641	+	0.397910i	−0.807220	−	0.590250i	$-0.799029\pi$
$283$	−16.1605	+	6.69389i	−0.960641	+	0.397910i	−0.153421	+	0.988161i	$0.549029\pi$
$284$		0			0
$285$	1.42913	−	3.45022i	0.0846543	−	0.204374i
$286$		0			0
$287$	24.2174			1.42951
$288$		0			0
$289$	−14.1339			−0.831407
$290$		0			0
$291$	0.669698	−	1.61679i	0.0392584	−	0.0947782i
$292$		0			0
$293$	−13.5656	+	5.61904i	−0.792509	+	0.328268i	−0.741952	−	0.670453i	$-0.766100\pi$
$293$	−13.5656	+	5.61904i	−0.792509	+	0.328268i	−0.0505573	+	0.998721i	$0.516100\pi$
$294$		0			0
$295$	−1.88582	+	1.88582i	−0.109796	+	0.109796i
$296$		0			0
$297$	4.43319	+	4.43319i	0.257240	+	0.257240i
$298$		0			0
$299$	0.0204935	+	0.0494756i	0.00118517	+	0.00286125i
$300$		0			0
$301$	9.89322	+	4.09791i	0.570236	+	0.236199i
$302$		0			0
$303$			8.34741i			0.479546i
$304$		0			0
$305$			42.1923i			2.41593i
$306$		0			0
$307$	15.6321	+	6.47504i	0.892173	+	0.369550i	0.781206	−	0.624274i	$-0.214605\pi$
$307$	15.6321	+	6.47504i	0.892173	+	0.369550i	0.110968	+	0.993824i	$0.464605\pi$
$308$		0			0
$309$	2.11225	+	5.09942i	0.120162	+	0.290096i
$310$		0			0
$311$	−22.8167	−	22.8167i	−1.29381	−	1.29381i	−0.932408	−	0.361407i	$-0.882297\pi$
$311$	−22.8167	−	22.8167i	−1.29381	−	1.29381i	−0.361407	−	0.932408i	$-0.617703\pi$
$312$		0			0
$313$	7.52178	−	7.52178i	0.425156	−	0.425156i	−0.461819	−	0.886974i	$-0.652803\pi$
$313$	7.52178	−	7.52178i	0.425156	−	0.425156i	0.886974	+	0.461819i	$0.152803\pi$
$314$		0			0
$315$	−7.58973	+	3.14377i	−0.427633	+	0.177131i
$316$		0			0
$317$	9.98241	−	24.0997i	0.560668	−	1.35357i	−0.348565	−	0.937285i	$-0.613331\pi$
$317$	9.98241	−	24.0997i	0.560668	−	1.35357i	0.909233	−	0.416288i	$-0.136669\pi$
$318$		0			0
$319$	11.5677			0.647665
$320$		0			0
$321$	14.5224			0.810560
$322$		0			0
$323$	−2.38176	+	5.75008i	−0.132525	+	0.319943i
$324$		0			0
$325$	−0.107611	+	0.0445739i	−0.00596918	+	0.00247251i
$326$		0			0
$327$	11.3648	−	11.3648i	0.628472	−	0.628472i
$328$		0			0
$329$	−2.01251	−	2.01251i	−0.110953	−	0.110953i
$330$		0			0
$331$	−12.9034	−	31.1516i	−0.709235	−	1.71225i	−0.701903	−	0.712272i	$-0.747666\pi$
$331$	−12.9034	−	31.1516i	−0.709235	−	1.71225i	−0.00733222	−	0.999973i	$-0.502334\pi$
$332$		0			0
$333$	−2.87315	−	1.19010i	−0.157447	−	0.0652169i
$334$		0			0
$335$			18.0138i			0.984200i
$336$		0			0
$337$		−	0.925243i		−	0.0504012i	−0.999682	−	0.0252006i	$-0.991978\pi$
$337$		−	0.925243i		−	0.0504012i	0.999682	−	0.0252006i	$-0.00802245\pi$
$338$		0			0
$339$	−2.52149	−	1.04443i	−0.136948	−	0.0567259i
$340$		0			0
$341$	−3.31208	−	7.99607i	−0.179359	−	0.433012i
$342$		0			0
$343$	13.8444	+	13.8444i	0.747528	+	0.747528i
$344$		0			0
$345$	6.75861	−	6.75861i	0.363871	−	0.363871i
$346$		0			0
$347$	8.68292	−	3.59658i	0.466123	−	0.193075i	−0.137245	−	0.990537i	$-0.543825\pi$
$347$	8.68292	−	3.59658i	0.466123	−	0.193075i	0.603369	+	0.797462i	$0.293825\pi$
$348$		0			0
$349$	−0.586633	+	1.41626i	−0.0314017	+	0.0758105i	−0.938802	−	0.344456i	$-0.888063\pi$
$349$	−0.586633	+	1.41626i	−0.0314017	+	0.0758105i	0.907401	+	0.420266i	$0.138063\pi$
$350$		0			0
$351$	−0.0187583			−0.00100125
$352$		0			0
$353$	10.8550			0.577751			0.288876	−	0.957367i	$-0.406719\pi$
$353$	10.8550			0.577751			0.288876	+	0.957367i	$0.406719\pi$
$354$		0			0
$355$	3.23066	−	7.79949i	0.171465	−	0.413954i
$356$		0			0
$357$	12.6489	−	5.23935i	0.669451	−	0.277296i
$358$		0			0
$359$	−21.6767	+	21.6767i	−1.14406	+	1.14406i	−0.156354	+	0.987701i	$0.549974\pi$
$359$	−21.6767	+	21.6767i	−1.14406	+	1.14406i	−0.987701	+	0.156354i	$0.950026\pi$
$360$		0			0
$361$	−12.5553	−	12.5553i	−0.660803	−	0.660803i
$362$		0			0
$363$	−10.8324	−	26.1517i	−0.568553	−	1.37261i
$364$		0			0
$365$	7.32717	+	3.03501i	0.383521	+	0.158860i
$366$		0			0
$367$			0.154514i			0.00806555i	0.999992	+	0.00403277i	$0.00128367\pi$
$367$			0.154514i			0.00806555i	−0.999992	+	0.00403277i	$0.998716\pi$
$368$		0			0
$369$		−	9.86975i		−	0.513799i
$370$		0			0
$371$	−15.2051	−	6.29815i	−0.789408	−	0.326984i
$372$		0			0
$373$	−5.40842	−	13.0571i	−0.280037	−	0.676070i	0.719799	−	0.694183i	$-0.244234\pi$
$373$	−5.40842	−	13.0571i	−0.280037	−	0.676070i	−0.999836	+	0.0181131i	$0.994234\pi$
$374$		0			0
$375$	2.86307	+	2.86307i	0.147848	+	0.147848i
$376$		0			0
$377$	−0.0244733	+	0.0244733i	−0.00126044	+	0.00126044i
$378$		0			0
$379$	17.4888	−	7.24410i	0.898340	−	0.372105i	0.114758	−	0.993393i	$-0.463391\pi$
$379$	17.4888	−	7.24410i	0.898340	−	0.372105i	0.783582	+	0.621289i	$0.213391\pi$
$380$		0			0
$381$	5.86792	−	14.1664i	0.300623	−	0.725767i
$382$		0			0
$383$	30.0898			1.53752			0.768759	−	0.639538i	$-0.220874\pi$
$383$	30.0898			1.53752			0.768759	+	0.639538i	$0.220874\pi$
$384$		0			0
$385$	51.5042			2.62490
$386$		0			0
$387$	1.67010	−	4.03197i	0.0848957	−	0.204956i
$388$		0			0
$389$	−11.7666	+	4.87387i	−0.596589	+	0.247115i	−0.660482	−	0.750842i	$-0.729648\pi$
$389$	−11.7666	+	4.87387i	−0.596589	+	0.247115i	0.0638936	+	0.997957i	$0.479648\pi$
$390$		0			0
$391$	−11.2638	+	11.2638i	−0.569633	+	0.569633i
$392$		0			0
$393$	10.5432	+	10.5432i	0.531835	+	0.531835i
$394$		0			0
$395$	3.42394	+	8.26611i	0.172277	+	0.415913i
$396$		0			0
$397$	−15.2331	−	6.30976i	−0.764527	−	0.316678i	−0.0338739	−	0.999426i	$-0.510784\pi$
$397$	−15.2331	−	6.30976i	−0.764527	−	0.316678i	−0.730653	+	0.682749i	$0.760784\pi$
$398$		0			0
$399$		−	2.73692i		−	0.137017i
$400$		0			0
$401$		−	35.7766i		−	1.78660i	−0.449463	−	0.893299i	$-0.648385\pi$
$401$		−	35.7766i		−	1.78660i	0.449463	−	0.893299i	$-0.351615\pi$
$402$		0			0
$403$	0.0239243	+	0.00990976i	0.00119175	+	0.000493641i
$404$		0			0
$405$	1.28124	+	3.09318i	0.0636653	+	0.153702i
$406$		0			0
$407$	13.7867	+	13.7867i	0.683380	+	0.683380i
$408$		0			0
$409$	−4.31657	+	4.31657i	−0.213440	+	0.213440i	−0.805727	−	0.592287i	$-0.798225\pi$
$409$	−4.31657	+	4.31657i	−0.213440	+	0.213440i	0.592287	+	0.805727i	$0.298225\pi$
$410$		0			0
$411$	4.00011	−	1.65690i	0.197311	−	0.0817289i
$412$		0			0
$413$	−0.747970	+	1.80576i	−0.0368052	+	0.0888557i
$414$		0			0
$415$	−25.0729			−1.23078
$416$		0			0
$417$	−1.62380			−0.0795178
$418$		0			0
$419$	−7.37576	+	17.8067i	−0.360330	+	0.869913i	0.634922	+	0.772576i	$0.281032\pi$
$419$	−7.37576	+	17.8067i	−0.360330	+	0.869913i	−0.995252	+	0.0973364i	$0.968968\pi$
$420$		0			0
$421$	5.03356	−	2.08497i	0.245321	−	0.101615i	−0.256635	−	0.966508i	$-0.582614\pi$
$421$	5.03356	−	2.08497i	0.245321	−	0.101615i	0.501956	+	0.864893i	$0.332614\pi$
$422$		0			0
$423$	−0.820194	+	0.820194i	−0.0398792	+	0.0398792i
$424$		0			0
$425$	−24.4990	−	24.4990i	−1.18838	−	1.18838i
$426$		0			0
$427$	11.8332	+	28.5680i	0.572651	+	1.38250i
$428$		0			0
$429$	0.108653	+	0.0450055i	0.00524581	+	0.00217288i
$430$		0			0
$431$			18.4128i			0.886914i	0.896296	+	0.443457i	$0.146248\pi$
$431$			18.4128i			0.886914i	−0.896296	+	0.443457i	$0.853752\pi$
$432$		0			0
$433$			0.227663i			0.0109408i	0.999985	+	0.00547038i	$0.00174129\pi$
$433$			0.227663i			0.0109408i	−0.999985	+	0.00547038i	$0.998259\pi$
$434$		0			0
$435$	5.70715	+	2.36398i	0.273637	+	0.113344i
$436$		0			0
$437$	1.21860	+	2.94197i	0.0582938	+	0.140734i
$438$		0			0
$439$	19.0619	+	19.0619i	0.909774	+	0.909774i	0.996254	−	0.0864799i	$-0.0275618\pi$
$439$	19.0619	+	19.0619i	0.909774	+	0.909774i	−0.0864799	+	0.996254i	$0.527562\pi$
$440$		0			0
$441$	0.692523	−	0.692523i	0.0329773	−	0.0329773i
$442$		0			0
$443$	28.0493	−	11.6184i	1.33266	−	0.552008i	0.401250	−	0.915968i	$-0.368576\pi$
$443$	28.0493	−	11.6184i	1.33266	−	0.552008i	0.931414	+	0.363961i	$0.118576\pi$
$444$		0			0
$445$	12.2101	−	29.4779i	0.578816	−	1.39739i
$446$		0			0
$447$	−22.3150			−1.05546
$448$		0			0
$449$	33.0005			1.55739			0.778696	−	0.627401i	$-0.215881\pi$
$449$	33.0005			1.55739			0.778696	+	0.627401i	$0.215881\pi$
$450$		0			0
$451$	−23.6798	+	57.1681i	−1.11504	+	2.69194i
$452$		0			0
$453$	12.3124	−	5.09995i	0.578486	−	0.239617i
$454$		0			0
$455$	−0.108966	+	0.108966i	−0.00510839	+	0.00510839i
$456$		0			0
$457$	19.3344	+	19.3344i	0.904423	+	0.904423i	0.995815	−	0.0913920i	$-0.0291316\pi$
$457$	19.3344	+	19.3344i	0.904423	+	0.904423i	−0.0913920	+	0.995815i	$0.529132\pi$
$458$		0			0
$459$	−2.13529	−	5.15504i	−0.0996667	−	0.240617i
$460$		0			0
$461$	19.0532	+	7.89211i	0.887398	+	0.367572i	0.779361	−	0.626575i	$-0.215544\pi$
$461$	19.0532	+	7.89211i	0.887398	+	0.367572i	0.108037	+	0.994147i	$0.465544\pi$
$462$		0			0
$463$			18.6664i			0.867499i	0.901034	+	0.433749i	$0.142810\pi$
$463$			18.6664i			0.867499i	−0.901034	+	0.433749i	$0.857190\pi$
$464$		0			0
$465$		−	4.62190i		−	0.214335i
$466$		0			0
$467$	−1.38748	−	0.574712i	−0.0642048	−	0.0265945i	0.350350	−	0.936619i	$-0.386063\pi$
$467$	−1.38748	−	0.574712i	−0.0642048	−	0.0265945i	−0.414555	+	0.910024i	$0.636063\pi$
$468$		0			0
$469$	5.05214	+	12.1970i	0.233286	+	0.563203i
$470$		0			0
$471$	−13.9315	−	13.9315i	−0.641927	−	0.641927i
$472$		0			0
$473$	−19.3472	+	19.3472i	−0.889586	+	0.889586i
$474$		0			0
$475$	−6.39888	+	2.65050i	−0.293601	+	0.121613i
$476$		0			0
$477$	−2.56680	+	6.19681i	−0.117526	+	0.283732i
$478$		0			0
$479$	20.1621			0.921229			0.460615	−	0.887600i	$-0.347629\pi$
$479$	20.1621			0.921229			0.460615	+	0.887600i	$0.347629\pi$
$480$		0			0
$481$	−0.0583360			−0.00265989
$482$		0			0
$483$	2.68066	−	6.47169i	0.121974	−	0.294472i
$484$		0			0
$485$	−5.41309	+	2.24218i	−0.245796	+	0.101812i
$486$		0			0
$487$	14.3589	−	14.3589i	0.650665	−	0.650665i	−0.302488	−	0.953153i	$-0.597817\pi$
$487$	14.3589	−	14.3589i	0.650665	−	0.650665i	0.953153	+	0.302488i	$0.0978173\pi$
$488$		0			0
$489$	−11.1133	−	11.1133i	−0.502561	−	0.502561i
$490$		0			0
$491$	7.84066	+	18.9290i	0.353844	+	0.854255i	0.996138	+	0.0877968i	$0.0279826\pi$
$491$	7.84066	+	18.9290i	0.353844	+	0.854255i	−0.642294	+	0.766458i	$0.722017\pi$
$492$		0			0
$493$	−9.51144	−	3.93977i	−0.428374	−	0.177438i
$494$		0			0
$495$		−	20.9905i		−	0.943452i
$496$		0			0
$497$		−	6.18702i		−	0.277526i
$498$		0			0
$499$	11.1249	+	4.60809i	0.498020	+	0.206286i	0.617531	−	0.786546i	$-0.288133\pi$
$499$	11.1249	+	4.60809i	0.498020	+	0.206286i	−0.119512	+	0.992833i	$0.538133\pi$
$500$		0			0
$501$	6.40731	+	15.4686i	0.286258	+	0.691087i
$502$		0			0
$503$	10.7388	+	10.7388i	0.478820	+	0.478820i	0.904754	−	0.425934i	$-0.140054\pi$
$503$	10.7388	+	10.7388i	0.478820	+	0.478820i	−0.425934	+	0.904754i	$0.640054\pi$
$504$		0			0
$505$	19.7618	−	19.7618i	0.879390	−	0.879390i
$506$		0			0
$507$	12.0101	−	4.97475i	0.533388	−	0.220936i
$508$		0			0
$509$	7.73386	−	18.6712i	0.342797	−	0.827586i	−0.654633	−	0.755947i	$-0.727177\pi$
$509$	7.73386	−	18.6712i	0.342797	−	0.827586i	0.997431	−	0.0716392i	$-0.0228230\pi$
$510$		0			0
$511$	5.81234			0.257123
$512$		0			0
$513$	−1.11543			−0.0492473
$514$		0			0
$515$	7.07189	−	17.0731i	0.311625	−	0.752329i
$516$		0			0
$517$	6.71860	−	2.78294i	0.295484	−	0.122393i
$518$		0			0
$519$	16.1198	−	16.1198i	0.707581	−	0.707581i
$520$		0			0
$521$	13.6485	+	13.6485i	0.597953	+	0.597953i	0.939767	−	0.341815i	$-0.111042\pi$
$521$	13.6485	+	13.6485i	0.597953	+	0.597953i	−0.341815	+	0.939767i	$0.611042\pi$
$522$		0			0
$523$	−6.91544	−	16.6954i	−0.302391	−	0.730037i	−0.999909	−	0.0134697i	$-0.995712\pi$
$523$	−6.91544	−	16.6954i	−0.302391	−	0.730037i	0.697518	−	0.716567i	$-0.254288\pi$
$524$		0			0
$525$	14.0761	+	5.83052i	0.614332	+	0.254465i
$526$		0			0
$527$			7.70276i			0.335538i
$528$		0			0
$529$		−	14.8499i		−	0.645647i
$530$		0			0
$531$	0.735935	+	0.304834i	0.0319369	+	0.0132287i
$532$		0			0
$533$	−0.0708500	−	0.171047i	−0.00306885	−	0.00740887i
$534$		0			0
$535$	−34.3806	−	34.3806i	−1.48640	−	1.48640i
$536$		0			0
$537$	3.64182	−	3.64182i	0.157156	−	0.157156i
$538$		0			0
$539$	−5.67279	+	2.34974i	−0.244344	+	0.101211i
$540$		0			0
$541$	−9.51555	+	22.9726i	−0.409106	+	0.987668i	0.576268	+	0.817261i	$0.304508\pi$
$541$	−9.51555	+	22.9726i	−0.409106	+	0.987668i	−0.985374	+	0.170407i	$0.945492\pi$
$542$		0			0
$543$	−9.69731			−0.416151
$544$		0			0
$545$	−53.8103			−2.30498
$546$		0			0
$547$	11.3958	−	27.5119i	0.487250	−	1.17633i	−0.468848	−	0.883279i	$-0.655331\pi$
$547$	11.3958	−	27.5119i	0.487250	−	1.17633i	0.956098	−	0.293046i	$-0.0946690\pi$
$548$		0			0
$549$	11.6428	−	4.82262i	0.496904	−	0.205824i
$550$		0			0
$551$	−1.45526	+	1.45526i	−0.0619961	+	0.0619961i
$552$		0			0
$553$	4.63662	+	4.63662i	0.197169	+	0.197169i
$554$		0			0
$555$	3.98449	+	9.61941i	0.169132	+	0.408321i
$556$		0			0
$557$	−1.70939	−	0.708053i	−0.0724292	−	0.0300012i	0.346175	−	0.938170i	$-0.387480\pi$
$557$	−1.70939	−	0.708053i	−0.0724292	−	0.0300012i	−0.418604	+	0.908169i	$0.637480\pi$
$558$		0			0
$559$		−	0.0818645i		−	0.00346250i
$560$		0			0
$561$			34.9823i			1.47695i
$562$		0			0
$563$	19.1605	+	7.93652i	0.807517	+	0.334485i	0.747963	−	0.663741i	$-0.231032\pi$
$563$	19.1605	+	7.93652i	0.807517	+	0.334485i	0.0595542	+	0.998225i	$0.481032\pi$
$564$		0			0
$565$	3.49681	+	8.44204i	0.147112	+	0.355159i
$566$		0			0
$567$	1.73503	+	1.73503i	0.0728642	+	0.0728642i
$568$		0			0
$569$	−15.1289	+	15.1289i	−0.634235	+	0.634235i	−0.949127	−	0.314892i	$-0.898032\pi$
$569$	−15.1289	+	15.1289i	−0.634235	+	0.634235i	0.314892	+	0.949127i	$0.398032\pi$
$570$		0			0
$571$	−12.1094	+	5.01587i	−0.506761	+	0.209907i	−0.621391	−	0.783501i	$-0.713432\pi$
$571$	−12.1094	+	5.01587i	−0.506761	+	0.209907i	0.114629	+	0.993408i	$0.463432\pi$
$572$		0			0
$573$	4.39488	−	10.6102i	0.183599	−	0.443246i
$574$		0			0
$575$	−17.7267			−0.739256
$576$		0			0
$577$	−35.7790			−1.48950			−0.744749	−	0.667344i	$-0.767431\pi$
$577$	−35.7790			−1.48950			−0.744749	+	0.667344i	$0.767431\pi$
$578$		0			0
$579$	−7.37358	+	17.8014i	−0.306435	+	0.739801i
$580$		0			0
$581$	−16.9766	+	7.03192i	−0.704306	+	0.291733i
$582$		0			0
$583$	29.7351	−	29.7351i	1.23150	−	1.23150i
$584$		0			0
$585$	0.0444088	+	0.0444088i	0.00183608	+	0.00183608i
$586$		0			0
$587$	10.9958	+	26.5462i	0.453845	+	1.09568i	0.970848	+	0.239696i	$0.0770477\pi$
$587$	10.9958	+	26.5462i	0.453845	+	1.09568i	−0.517003	+	0.855984i	$0.672952\pi$
$588$		0			0
$589$	1.42261	+	0.589265i	0.0586177	+	0.0242803i
$590$		0			0
$591$		−	7.02104i		−	0.288807i
$592$		0			0
$593$		−	13.4778i		−	0.553469i	−0.960946	−	0.276734i	$-0.910748\pi$
$593$		−	13.4778i		−	0.553469i	0.960946	−	0.276734i	$-0.0892522\pi$
$594$		0			0
$595$	−42.3490	−	17.5415i	−1.73614	−	0.719133i
$596$		0			0
$597$	−7.92985	−	19.1444i	−0.324547	−	0.783526i
$598$		0			0
$599$	11.7247	+	11.7247i	0.479059	+	0.479059i	0.904831	−	0.425771i	$-0.139997\pi$
$599$	11.7247	+	11.7247i	0.479059	+	0.479059i	−0.425771	+	0.904831i	$0.639997\pi$
$600$		0			0
$601$	−14.2752	+	14.2752i	−0.582299	+	0.582299i	−0.935535	−	0.353235i	$-0.885082\pi$
$601$	−14.2752	+	14.2752i	−0.582299	+	0.582299i	0.353235	+	0.935535i	$0.385082\pi$
$602$		0			0
$603$	4.97085	−	2.05899i	0.202429	−	0.0838487i
$604$		0			0
$605$	−36.2673	+	87.5570i	−1.47447	+	3.55970i
$606$		0			0
$607$	30.9234			1.25514			0.627571	−	0.778559i	$-0.284049\pi$
$607$	30.9234			1.25514			0.627571	+	0.778559i	$0.284049\pi$
$608$		0			0
$609$	4.52725			0.183453
$610$		0			0
$611$	−0.00832655	+	0.0201021i	−0.000336856	+	0.000813243i
$612$		0			0
$613$	−34.3535	+	14.2297i	−1.38753	+	0.574732i	−0.946483	−	0.322754i	$-0.895391\pi$
$613$	−34.3535	+	14.2297i	−1.38753	+	0.574732i	−0.441043	+	0.897486i	$0.645391\pi$
$614$		0			0
$615$	−23.3659	+	23.3659i	−0.942202	+	0.942202i
$616$		0			0
$617$	−10.2583	−	10.2583i	−0.412985	−	0.412985i	0.469792	−	0.882777i	$-0.344329\pi$
$617$	−10.2583	−	10.2583i	−0.412985	−	0.412985i	−0.882777	+	0.469792i	$0.844329\pi$
$618$		0			0
$619$	−8.23548	−	19.8822i	−0.331012	−	0.799133i	−0.998512	−	0.0545238i	$-0.982636\pi$
$619$	−8.23548	−	19.8822i	−0.331012	−	0.799133i	0.667501	−	0.744609i	$-0.267364\pi$
$620$		0			0
$621$	−2.63753	−	1.09250i	−0.105840	−	0.0438405i
$622$		0			0
$623$		−	23.3836i		−	0.936844i
$624$		0			0
$625$			17.4906i			0.699626i
$626$		0			0
$627$	6.46083	+	2.67617i	0.258021	+	0.106876i
$628$		0			0
$629$	−6.64047	−	16.0315i	−0.264773	−	0.639219i
$630$		0			0
$631$	−10.2772	−	10.2772i	−0.409128	−	0.409128i	0.472307	−	0.881434i	$-0.343421\pi$
$631$	−10.2772	−	10.2772i	−0.409128	−	0.409128i	−0.881434	+	0.472307i	$0.843421\pi$
$632$		0			0
$633$	2.14593	−	2.14593i	0.0852930	−	0.0852930i
$634$		0			0
$635$	−47.4297	+	19.6460i	−1.88219	+	0.779629i
$636$		0			0
$637$	0.00703045	−	0.0169730i	0.000278556	−	0.000672495i
$638$		0			0
$639$	−2.52151			−0.0997494
$640$		0			0
$641$	−14.5702			−0.575489			−0.287745	−	0.957707i	$-0.592905\pi$
$641$	−14.5702			−0.575489			−0.287745	+	0.957707i	$0.592905\pi$
$642$		0			0
$643$	7.72635	−	18.6531i	0.304698	−	0.735605i	−0.695162	−	0.718853i	$-0.744667\pi$
$643$	7.72635	−	18.6531i	0.304698	−	0.735605i	0.999860	−	0.0167519i	$-0.00533255\pi$
$644$		0			0
$645$	−13.4992	+	5.59154i	−0.531530	+	0.220167i
$646$		0			0
$647$	−5.45944	+	5.45944i	−0.214633	+	0.214633i	−0.806232	−	0.591599i	$-0.798497\pi$
$647$	−5.45944	+	5.45944i	−0.214633	+	0.214633i	0.591599	+	0.806232i	$0.298497\pi$
$648$		0			0
$649$	−3.53135	−	3.53135i	−0.138618	−	0.138618i
$650$		0			0
$651$	−1.29625	−	3.12943i	−0.0508042	−	0.122652i
$652$		0			0
$653$	8.05307	+	3.33569i	0.315141	+	0.130536i	0.534647	−	0.845075i	$-0.320445\pi$
$653$	8.05307	+	3.33569i	0.315141	+	0.130536i	−0.219506	+	0.975611i	$0.570445\pi$
$654$		0			0
$655$		−	49.9204i		−	1.95055i
$656$		0			0
$657$		−	2.36881i		−	0.0924161i
$658$		0			0
$659$	11.5755	+	4.79474i	0.450919	+	0.186777i	0.596573	−	0.802559i	$-0.296529\pi$
$659$	11.5755	+	4.79474i	0.450919	+	0.186777i	−0.145654	+	0.989336i	$0.546529\pi$
$660$		0			0
$661$	4.73190	+	11.4238i	0.184049	+	0.444335i	0.988794	−	0.149287i	$-0.0476977\pi$
$661$	4.73190	+	11.4238i	0.184049	+	0.444335i	−0.804745	+	0.593621i	$0.797698\pi$
$662$		0			0
$663$	−0.0740109	−	0.0740109i	−0.00287435	−	0.00287435i
$664$		0			0
$665$	−6.47944	+	6.47944i	−0.251262	+	0.251262i
$666$		0			0
$667$	−4.86643	+	2.01574i	−0.188429	+	0.0780499i
$668$		0			0
$669$	−2.34242	+	5.65509i	−0.0905631	+	0.218639i
$670$		0			0
$671$	−79.0087			−3.05010
$672$		0			0
$673$	11.7838			0.454233			0.227117	−	0.973868i	$-0.427070\pi$
$673$	11.7838			0.454233			0.227117	+	0.973868i	$0.427070\pi$
$674$		0			0
$675$	2.37622	−	5.73670i	0.0914607	−	0.220806i
$676$		0			0
$677$	31.1449	−	12.9006i	1.19700	−	0.495812i	0.306969	−	0.951719i	$-0.400685\pi$
$677$	31.1449	−	12.9006i	1.19700	−	0.495812i	0.890027	+	0.455907i	$0.150685\pi$
$678$		0			0
$679$	−3.03630	+	3.03630i	−0.116523	+	0.116523i
$680$		0			0
$681$	−12.0560	−	12.0560i	−0.461989	−	0.461989i
$682$		0			0
$683$	−2.44866	−	5.91159i	−0.0936954	−	0.226201i	0.870083	−	0.492905i	$-0.164065\pi$
$683$	−2.44866	−	5.91159i	−0.0936954	−	0.226201i	−0.963778	+	0.266705i	$0.914065\pi$
$684$		0			0
$685$	−13.3925	−	5.54737i	−0.511702	−	0.211954i
$686$		0			0
$687$			9.31826i			0.355514i
$688$		0			0
$689$			0.125819i			0.00479333i
$690$		0			0
$691$	6.81893	+	2.82449i	0.259404	+	0.107449i	0.508596	−	0.861005i	$-0.330165\pi$
$691$	6.81893	+	2.82449i	0.259404	+	0.107449i	−0.249191	+	0.968454i	$0.580165\pi$
$692$		0			0
$693$	−5.88697	−	14.2124i	−0.223628	−	0.539885i
$694$		0			0
$695$	3.84422	+	3.84422i	0.145819	+	0.145819i
$696$		0			0
$697$	38.9411	−	38.9411i	1.47500	−	1.47500i
$698$		0			0
$699$	−10.4488	+	4.32805i	−0.395212	+	0.163702i
$700$		0			0
$701$	−2.75369	+	6.64799i	−0.104005	+	0.251091i	−0.967312	−	0.253588i	$-0.918389\pi$
$701$	−2.75369	+	6.64799i	−0.104005	+	0.251091i	0.863307	+	0.504679i	$0.168389\pi$
$702$		0			0
$703$	−3.46884			−0.130830
$704$		0			0
$705$	3.88349			0.146261
$706$		0			0
$707$	7.83813	−	18.9229i	0.294783	−	0.711669i
$708$		0			0
$709$	46.0951	−	19.0932i	1.73114	−	0.717061i	0.731770	−	0.681552i	$-0.238695\pi$
$709$	46.0951	−	19.0932i	1.73114	−	0.717061i	0.999369	−	0.0355098i	$-0.0113055\pi$
$710$		0			0
$711$	1.88965	−	1.88965i	0.0708673	−	0.0708673i
$712$		0			0
$713$	2.78674	+	2.78674i	0.104364	+	0.104364i
$714$		0			0
$715$	−0.150680	−	0.363774i	−0.00563512	−	0.0136044i
$716$		0			0
$717$	5.79002	+	2.39830i	0.216232	+	0.0895663i
$718$		0			0
$719$		−	22.0801i		−	0.823447i	−0.911309	−	0.411724i	$-0.864927\pi$
$719$		−	22.0801i		−	0.823447i	0.911309	−	0.411724i	$-0.135073\pi$
$720$		0			0
$721$		−	13.5434i		−	0.504381i
$722$		0			0
$723$	−14.5605	−	6.03116i	−0.541511	−	0.224301i
$724$		0			0
$725$	−4.38430	−	10.5846i	−0.162829	−	0.393104i
$726$		0			0
$727$	−12.2216	−	12.2216i	−0.453274	−	0.453274i	0.443166	−	0.896440i	$-0.353855\pi$
$727$	−12.2216	−	12.2216i	−0.453274	−	0.453274i	−0.896440	+	0.443166i	$0.853855\pi$
$728$		0			0
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$		0			0
$731$	22.4975	−	9.31876i	0.832100	−	0.344667i
$732$		0			0
$733$	−10.2112	+	24.6520i	−0.377159	+	0.910541i	0.615337	+	0.788264i	$0.289020\pi$
$733$	−10.2112	+	24.6520i	−0.377159	+	0.910541i	−0.992496	+	0.122278i	$0.960980\pi$
$734$		0			0
$735$	−3.27899			−0.120947
$736$		0			0
$737$	−33.7324			−1.24255
$738$		0			0
$739$	12.9929	−	31.3677i	0.477953	−	1.15388i	−0.482614	−	0.875833i	$-0.660313\pi$
$739$	12.9929	−	31.3677i	0.477953	−	1.15388i	0.960567	−	0.278048i	$-0.0896874\pi$
$740$		0			0
$741$	−0.0193308	+	0.00800710i	−0.000710136	+	0.000294148i
$742$		0			0
$743$	14.2568	−	14.2568i	0.523030	−	0.523030i	−0.395455	−	0.918485i	$-0.629413\pi$
$743$	14.2568	−	14.2568i	0.523030	−	0.523030i	0.918485	+	0.395455i	$0.129413\pi$
$744$		0			0
$745$	52.8291	+	52.8291i	1.93551	+	1.93551i
$746$		0			0
$747$	2.86585	+	6.91877i	0.104856	+	0.253144i
$748$		0			0
$749$	−32.9211	−	13.6364i	−1.20291	−	0.498262i
$750$		0			0
$751$			37.4275i			1.36575i	0.730536	+	0.682874i	$0.239270\pi$
$751$			37.4275i			1.36575i	−0.730536	+	0.682874i	$0.760730\pi$
$752$		0			0
$753$		−	20.5866i		−	0.750218i
$754$		0			0
$755$	−41.2223	−	17.0748i	−1.50023	−	0.621417i
$756$		0			0
$757$	−14.2534	−	34.4107i	−0.518048	−	1.25068i	−0.939100	−	0.343643i	$-0.888339\pi$
$757$	−14.2534	−	34.4107i	−0.518048	−	1.25068i	0.421052	−	0.907036i	$-0.361661\pi$
$758$		0			0
$759$	12.6561	+	12.6561i	0.459386	+	0.459386i
$760$		0			0
$761$	4.71958	−	4.71958i	0.171085	−	0.171085i	−0.616371	−	0.787456i	$-0.711398\pi$
$761$	4.71958	−	4.71958i	0.171085	−	0.171085i	0.787456	+	0.616371i	$0.211398\pi$
$762$		0			0
$763$	−36.4344	+	15.0916i	−1.31901	+	0.546353i
$764$		0			0
$765$	−7.14903	+	17.2593i	−0.258474	+	0.624011i
$766$		0			0
$767$	0.0149423			0.000539536
$768$		0			0
$769$	−0.848264			−0.0305892			−0.0152946	−	0.999883i	$-0.504869\pi$
$769$	−0.848264			−0.0305892			−0.0152946	+	0.999883i	$0.504869\pi$
$770$		0			0
$771$	2.00056	−	4.82977i	0.0720483	−	0.173940i
$772$		0			0
$773$	7.34212	−	3.04121i	0.264078	−	0.109385i	−0.246716	−	0.969088i	$-0.579352\pi$
$773$	7.34212	−	3.04121i	0.264078	−	0.109385i	0.510794	+	0.859703i	$0.329352\pi$
$774$		0			0
$775$	−6.06124	+	6.06124i	−0.217726	+	0.217726i
$776$		0			0
$777$	5.39571	+	5.39571i	0.193570	+	0.193570i
$778$		0			0
$779$	−4.21296	−	10.1710i	−0.150945	−	0.364413i
$780$		0			0
$781$	14.6052	+	6.04967i	0.522615	+	0.216474i
$782$		0			0
$783$		−	1.84507i		−	0.0659376i
$784$		0			0
$785$			65.9632i			2.35433i
$786$		0			0
$787$	−19.1514	−	7.93278i	−0.682674	−	0.282773i	0.0142701	−	0.999898i	$-0.495458\pi$
$787$	−19.1514	−	7.93278i	−0.682674	−	0.282773i	−0.696944	+	0.717125i	$0.745458\pi$
$788$		0			0
$789$	−3.02564	−	7.30453i	−0.107716	−	0.260048i
$790$		0			0
$791$	4.73530	+	4.73530i	0.168368	+	0.168368i
$792$		0			0
$793$	0.167156	−	0.167156i	0.00593589	−	0.00593589i
$794$		0			0
$795$	20.7471	−	8.59375i	0.735825	−	0.304789i
$796$		0			0
$797$	8.34929	−	20.1570i	0.295747	−	0.713997i	−0.704245	−	0.709957i	$-0.748714\pi$
$797$	8.34929	−	20.1570i	0.295747	−	0.713997i	0.999992	−	0.00403944i	$-0.00128580\pi$
$798$		0			0
$799$	−6.47215			−0.228968
$800$		0			0
$801$	−9.52995			−0.336724
$802$		0			0
$803$	−5.68331	+	13.7207i	−0.200560	+	0.484194i
$804$		0			0
$805$	−21.6675	+	8.97496i	−0.763678	+	0.316326i
$806$		0			0
$807$	7.59716	−	7.59716i	0.267433	−	0.267433i
$808$		0			0
$809$	2.49506	+	2.49506i	0.0877217	+	0.0877217i	0.749606	−	0.661884i	$-0.230243\pi$
$809$	2.49506	+	2.49506i	0.0877217	+	0.0877217i	−0.661884	+	0.749606i	$0.730243\pi$
$810$		0			0
$811$	11.3640	+	27.4351i	0.399044	+	0.963378i	0.987893	+	0.155135i	$0.0495812\pi$
$811$	11.3640	+	27.4351i	0.399044	+	0.963378i	−0.588849	+	0.808243i	$0.700419\pi$
$812$		0			0
$813$	14.2617	+	5.90740i	0.500180	+	0.207181i
$814$		0			0
$815$			52.6197i			1.84319i
$816$		0			0
$817$		−	4.86792i		−	0.170307i
$818$		0			0
$819$	0.0425236	+	0.0176139i	0.00148590	+	0.000615478i
$820$		0			0
$821$	11.7466	+	28.3588i	0.409959	+	0.989728i	0.985148	+	0.171708i	$0.0549285\pi$
$821$	11.7466	+	28.3588i	0.409959	+	0.989728i	−0.575189	+	0.818020i	$0.695072\pi$
$822$		0			0
$823$	13.6697	+	13.6697i	0.476496	+	0.476496i	0.904009	−	0.427513i	$-0.140610\pi$
$823$	13.6697	+	13.6697i	0.476496	+	0.476496i	−0.427513	+	0.904009i	$0.640610\pi$
$824$		0			0
$825$	−27.5273	+	27.5273i	−0.958378	+	0.958378i
$826$		0			0
$827$	35.2612	−	14.6057i	1.22615	−	0.507889i	0.326792	−	0.945096i	$-0.394032\pi$
$827$	35.2612	−	14.6057i	1.22615	−	0.507889i	0.899361	+	0.437207i	$0.144032\pi$
$828$		0			0
$829$	16.0030	−	38.6346i	0.555806	−	1.34184i	−0.357253	−	0.934008i	$-0.616286\pi$
$829$	16.0030	−	38.6346i	0.555806	−	1.34184i	0.913059	−	0.407828i	$-0.133714\pi$
$830$		0			0
$831$	4.68106			0.162384
$832$		0			0
$833$	5.46470			0.189341
$834$		0			0
$835$	21.4519	−	51.7895i	0.742375	−	1.79225i
$836$		0			0
$837$	−1.27540	+	0.528286i	−0.0440841	+	0.0182602i
$838$		0			0
$839$	−14.1294	+	14.1294i	−0.487800	+	0.487800i	−0.907611	−	0.419811i	$-0.862096\pi$
$839$	−14.1294	+	14.1294i	−0.487800	+	0.487800i	0.419811	+	0.907611i	$0.362096\pi$
$840$		0			0
$841$	18.0989	+	18.0989i	0.624100	+	0.624100i
$842$		0			0
$843$	−2.00430	−	4.83882i	−0.0690319	−	0.166658i
$844$		0			0
$845$	−40.2103	−	16.6557i	−1.38328	−	0.572972i
$846$		0			0
$847$			69.4554i			2.38651i
$848$		0			0
$849$		−	17.4920i		−	0.600323i
$850$		0			0
$851$	−8.20237	−	3.39753i	−0.281174	−	0.116466i
$852$		0			0
$853$	19.9078	+	48.0618i	0.681631	+	1.64560i	0.760995	+	0.648758i	$0.224711\pi$
$853$	19.9078	+	48.0618i	0.681631	+	1.64560i	−0.0793634	+	0.996846i	$0.525289\pi$
$854$		0			0
$855$	2.64069	+	2.64069i	0.0903096	+	0.0903096i
$856$		0			0
$857$	34.0981	−	34.0981i	1.16477	−	1.16477i	0.181349	−	0.983419i	$-0.441954\pi$
$857$	34.0981	−	34.0981i	1.16477	−	1.16477i	0.983419	−	0.181349i	$-0.0580463\pi$
$858$		0			0
$859$	3.10766	−	1.28723i	0.106032	−	0.0439199i	−0.329037	−	0.944317i	$-0.606724\pi$
$859$	3.10766	−	1.28723i	0.106032	−	0.0439199i	0.435069	+	0.900397i	$0.356724\pi$
$860$		0			0
$861$	−9.26759	+	22.3739i	−0.315839	+	0.762502i
$862$		0			0
$863$	10.0110			0.340777			0.170389	−	0.985377i	$-0.445498\pi$
$863$	10.0110			0.340777			0.170389	+	0.985377i	$0.445498\pi$
$864$		0			0
$865$	−76.3247			−2.59512
$866$		0			0
$867$	5.40882	−	13.0580i	0.183693	−	0.443474i
$868$		0			0
$869$	−15.4790	+	6.41161i	−0.525089	+	0.217499i
$870$		0			0
$871$	0.0713665	−	0.0713665i	0.00241816	−	0.00241816i
$872$		0			0
$873$	1.23744	+	1.23744i	0.0418810	+	0.0418810i
$874$		0			0
$875$	−3.80195	−	9.17873i	−0.128529	−	0.310298i
$876$		0			0
$877$	−22.1720	−	9.18393i	−0.748694	−	0.310119i	−0.0244855	−	0.999700i	$-0.507795\pi$
$877$	−22.1720	−	9.18393i	−0.748694	−	0.310119i	−0.724209	+	0.689581i	$0.757795\pi$
$878$		0			0
$879$		−	14.6833i		−	0.495254i
$880$		0			0
$881$			16.0746i			0.541568i	0.962640	+	0.270784i	$0.0872829\pi$
$881$			16.0746i			0.541568i	−0.962640	+	0.270784i	$0.912717\pi$
$882$		0			0
$883$	−12.8293	−	5.31406i	−0.431740	−	0.178832i	0.156221	−	0.987722i	$-0.450069\pi$
$883$	−12.8293	−	5.31406i	−0.431740	−	0.178832i	−0.587960	+	0.808890i	$0.700069\pi$
$884$		0			0
$885$	−1.02060	−	2.46394i	−0.0343070	−	0.0828244i
$886$		0			0
$887$	−29.2489	−	29.2489i	−0.982081	−	0.982081i	0.0177612	−	0.999842i	$-0.494346\pi$
$887$	−29.2489	−	29.2489i	−0.982081	−	0.982081i	−0.999842	+	0.0177612i	$0.994346\pi$
$888$		0			0
$889$	−26.6042	+	26.6042i	−0.892276	+	0.892276i
$890$		0			0
$891$	−5.79225	+	2.39923i	−0.194048	+	0.0803771i
$892$		0			0
$893$	−0.495123	+	1.19533i	−0.0165687	+	0.0400003i
$894$		0			0
$895$	−17.2434			−0.576384
$896$		0			0
$897$	−0.0535520			−0.00178805
$898$		0			0
$899$	−0.974727	+	2.35320i	−0.0325090	+	0.0784836i
$900$		0			0
$901$	−34.5768	+	14.3222i	−1.15192	+	0.477141i
$902$		0			0
$903$	−7.57195	+	7.57195i	−0.251979	+	0.251979i
$904$		0			0
$905$	22.9576	+	22.9576i	0.763137	+	0.763137i
$906$		0			0
$907$	21.8942	+	52.8573i	0.726986	+	1.75510i	0.652387	+	0.757886i	$0.273768\pi$
$907$	21.8942	+	52.8573i	0.726986	+	1.75510i	0.0745987	+	0.997214i	$0.476232\pi$
$908$		0			0
$909$	−7.71200	−	3.19442i	−0.255791	−	0.105952i
$910$		0			0
$911$		−	59.8222i		−	1.98200i	−0.133873	−	0.990999i	$-0.542741\pi$
$911$		−	59.8222i		−	1.98200i	0.133873	−	0.990999i	$-0.457259\pi$
$912$		0			0
$913$		−	46.9510i		−	1.55385i
$914$		0			0
$915$	−38.9806	−	16.1463i	−1.28866	−	0.533781i
$916$		0			0
$917$	−14.0007	−	33.8006i	−0.462342	−	1.11619i
$918$		0			0
$919$	−17.5355	−	17.5355i	−0.578444	−	0.578444i	0.356030	−	0.934474i	$-0.384130\pi$
$919$	−17.5355	−	17.5355i	−0.578444	−	0.578444i	−0.934474	+	0.356030i	$0.884130\pi$
$920$		0			0
$921$	−11.9643	+	11.9643i	−0.394238	+	0.394238i
$922$		0			0
$923$	−0.0436988	+	0.0181006i	−0.00143836	+	0.000595790i
$924$		0			0
$925$	7.38974	−	17.8404i	0.242973	−	0.586589i
$926$		0			0
$927$	−5.51957			−0.181287
$928$		0			0
$929$	47.3964			1.55502			0.777512	−	0.628868i	$-0.216481\pi$
$929$	47.3964			1.55502			0.777512	+	0.628868i	$0.216481\pi$
$930$		0			0
$931$	0.418052	−	1.00927i	0.0137011	−	0.0330774i
$932$		0			0
$933$	29.8114	−	12.3483i	0.975982	−	0.404265i
$934$		0			0
$935$	82.8179	−	82.8179i	2.70843	−	2.70843i
$936$		0			0
$937$	−3.12631	−	3.12631i	−0.102132	−	0.102132i	0.654194	−	0.756326i	$-0.273008\pi$
$937$	−3.12631	−	3.12631i	−0.102132	−	0.102132i	−0.756326	+	0.654194i	$0.773008\pi$
$938$		0			0
$939$	4.07076	+	9.82767i	0.132844	+	0.320714i
$940$		0			0
$941$	−6.78357	−	2.80985i	−0.221138	−	0.0915984i	0.269364	−	0.963038i	$-0.413187\pi$
$941$	−6.78357	−	2.80985i	−0.221138	−	0.0915984i	−0.490502	+	0.871440i	$0.663187\pi$
$942$		0			0
$943$		−	28.1766i		−	0.917555i
$944$		0			0
$945$		−	8.21507i		−	0.267236i
$946$		0			0
$947$	−48.2859	−	20.0007i	−1.56908	−	0.649935i	−0.582444	−	0.812871i	$-0.697904\pi$
$947$	−48.2859	−	20.0007i	−1.56908	−	0.649935i	−0.986637	+	0.162936i	$0.947904\pi$
$948$		0			0
$949$	−0.0170045	−	0.0410525i	−0.000551990	−	0.00133262i
$950$		0			0
$951$	18.4451	+	18.4451i	0.598123	+	0.598123i
$952$		0			0
$953$	−12.2493	+	12.2493i	−0.396794	+	0.396794i	−0.877101	−	0.480307i	$-0.840525\pi$
$953$	−12.2493	+	12.2493i	−0.396794	+	0.396794i	0.480307	+	0.877101i	$0.340525\pi$
$954$		0			0
$955$	−35.5233	+	14.7142i	−1.14951	+	0.476141i
$956$		0			0
$957$	−4.42675	+	10.6871i	−0.143097	+	0.345466i
$958$		0			0
$959$	−10.6237			−0.343059
$960$		0			0
$961$	−29.0943			−0.938525
$962$		0			0
$963$	−5.55747	+	13.4169i	−0.179087	+	0.432355i
$964$		0			0
$965$	59.5997	−	24.6870i	1.91858	−	0.794703i
$966$		0			0
$967$	11.6821	−	11.6821i	0.375671	−	0.375671i	−0.493867	−	0.869538i	$-0.664417\pi$
$967$	11.6821	−	11.6821i	0.375671	−	0.375671i	0.869538	+	0.493867i	$0.164417\pi$
$968$		0			0
$969$	−4.40092	−	4.40092i	−0.141378	−	0.141378i
$970$		0			0
$971$	−12.0421	−	29.0723i	−0.386451	−	0.932975i	−0.990686	−	0.136168i	$-0.956521\pi$
$971$	−12.0421	−	29.0723i	−0.386451	−	0.932975i	0.604235	−	0.796806i	$-0.293479\pi$
$972$		0			0
$973$	3.68102	+	1.52473i	0.118008	+	0.0488806i
$974$		0			0
$975$		−	0.116477i		−	0.00373026i
$976$		0			0
$977$		−	46.2289i		−	1.47899i	−0.673159	−	0.739497i	$-0.735063\pi$
$977$		−	46.2289i		−	1.47899i	0.673159	−	0.739497i	$-0.264937\pi$
$978$		0			0
$979$	55.1998	+	22.8645i	1.76419	+	0.730753i
$980$		0			0
$981$	6.15056	+	14.8488i	0.196372	+	0.474085i
$982$		0			0
$983$	36.8328	+	36.8328i	1.17478	+	1.17478i	0.981055	+	0.193729i	$0.0620583\pi$
$983$	36.8328	+	36.8328i	1.17478	+	1.17478i	0.193729	+	0.981055i	$0.437942\pi$
$984$		0			0
$985$	−16.6217	+	16.6217i	−0.529613	+	0.529613i
$986$		0			0
$987$	2.62947	−	1.08916i	0.0836969	−	0.0346684i
$988$		0			0
$989$	4.76786	−	11.5106i	0.151609	−	0.366016i
$990$		0			0
$991$	0.0778010			0.00247143			0.00123571	−	0.999999i	$-0.499607\pi$
$991$	0.0778010			0.00247143			0.00123571	+	0.999999i	$0.499607\pi$
$992$		0			0
$993$	33.7182			1.07002
$994$		0			0
$995$	−26.5494	+	64.0960i	−0.841674	+	2.03198i
$996$		0			0
$997$	14.8961	−	6.17018i	0.471765	−	0.195412i	−0.134118	−	0.990965i	$-0.542820\pi$
$997$	14.8961	−	6.17018i	0.471765	−	0.195412i	0.605883	+	0.795554i	$0.292820\pi$
$998$		0			0
$999$	2.19901	−	2.19901i	0.0695736	−	0.0695736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.n.b.289.4		32
4.3	odd	2		768.2.n.a.289.8		32
8.3	odd	2		96.2.n.a.13.2	✓	32
8.5	even	2		384.2.n.a.145.5		32
24.5	odd	2		1152.2.v.c.145.8		32
24.11	even	2		288.2.v.d.109.7		32
32.5	even	8	inner	768.2.n.b.481.4		32
32.11	odd	8		96.2.n.a.37.2	yes	32
32.21	even	8		384.2.n.a.241.5		32
32.27	odd	8		768.2.n.a.481.8		32
96.11	even	8		288.2.v.d.37.7		32
96.53	odd	8		1152.2.v.c.1009.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.2.n.a.13.2	✓	32	8.3	odd	2
96.2.n.a.37.2	yes	32	32.11	odd	8
288.2.v.d.37.7		32	96.11	even	8
288.2.v.d.109.7		32	24.11	even	2
384.2.n.a.145.5		32	8.5	even	2
384.2.n.a.241.5		32	32.21	even	8
768.2.n.a.289.8		32	4.3	odd	2
768.2.n.a.481.8		32	32.27	odd	8
768.2.n.b.289.4		32	1.1	even	1	trivial
768.2.n.b.481.4		32	32.5	even	8	inner
1152.2.v.c.145.8		32	24.5	odd	2
1152.2.v.c.1009.8		32	96.53	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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.382683 + 0.923880i) q^{3} +(3.09318 - 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(2.39923 + 5.79225i) q^{11} +(-0.0173304 - 0.00717850i) q^{13} +3.34804i q^{15} -5.57978i q^{17} +(-1.03052 - 0.426856i) q^{19} +(0.938989 + 2.26692i) q^{21} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(0.923880 - 0.382683i) q^{27} +(0.706079 - 1.70463i) q^{29} -1.38048 q^{31} -6.26948 q^{33} +(3.14377 - 7.58973i) q^{35} +(2.87315 - 1.19010i) q^{37} +(0.0132641 - 0.0132641i) q^{39} +(6.97897 + 6.97897i) q^{41} +(1.67010 + 4.03197i) q^{43} +(-3.09318 - 1.28124i) q^{45} -1.15993i q^{47} +0.979375i q^{49} +(5.15504 + 2.13529i) q^{51} +(-2.56680 - 6.19681i) q^{53} +(14.8425 + 14.8425i) q^{55} +(0.788727 - 0.788727i) q^{57} +(-0.735935 + 0.304834i) q^{59} +(-4.82262 + 11.6428i) q^{61} -2.45370 q^{63} -0.0628036 q^{65} +(-2.05899 + 4.97085i) q^{67} +(2.63753 - 1.09250i) q^{69} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(2.37622 + 5.73670i) q^{75} +(14.2124 + 5.88697i) q^{77} +2.67236i q^{79} +1.00000i q^{81} +(-6.91877 - 2.86585i) q^{83} +(-7.14903 - 17.2593i) q^{85} +(1.30466 + 1.30466i) q^{87} +(6.73869 - 6.73869i) q^{89} +(-0.0425236 + 0.0176139i) q^{91} +(0.528286 - 1.27540i) q^{93} -3.73450 q^{95} -1.75001 q^{97} +(2.39923 - 5.79225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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