LMFDB - Embedded newform 896.2.bi.a.143.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(47,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([12, 9, 20]))

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

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

chi := DirichletCharacter("896.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bi (of order $24$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			143.18
Character	$\chi$	$=$	896.143
Dual form			896.2.bi.a.495.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.586792 + 0.0772527i) q^{3} +(3.65404 - 0.481063i) q^{5} +(-0.750581 + 2.53705i) q^{7} +(-2.55942 - 0.685795i) q^{9} +(-0.154965 + 0.118909i) q^{11} +(1.79545 + 4.33461i) q^{13} +2.18132 q^{15} +(-1.63000 + 2.82324i) q^{17} +(5.96708 + 4.57870i) q^{19} +(-0.636429 + 1.43074i) q^{21} +(-0.227620 + 0.849490i) q^{23} +(8.29094 - 2.22155i) q^{25} +(-3.08928 - 1.27962i) q^{27} +(-0.793041 - 1.91457i) q^{29} +(1.85113 - 3.20626i) q^{31} +(-0.100118 + 0.0578032i) q^{33} +(-1.52217 + 9.63156i) q^{35} +(-1.34829 - 10.2413i) q^{37} +(0.718698 + 2.68222i) q^{39} +(3.81582 + 3.81582i) q^{41} +(2.28159 + 0.945065i) q^{43} +(-9.68213 - 1.27468i) q^{45} +(1.58163 - 0.913157i) q^{47} +(-5.87326 - 3.80853i) q^{49} +(-1.17457 + 1.53073i) q^{51} +(-5.48905 - 7.15347i) q^{53} +(-0.509044 + 0.509044i) q^{55} +(3.14772 + 3.14772i) q^{57} +(-6.76333 + 5.18969i) q^{59} +(5.03692 + 3.86496i) q^{61} +(3.66095 - 5.97864i) q^{63} +(8.64588 + 14.9751i) q^{65} +(1.56386 - 11.8787i) q^{67} +(-0.199191 + 0.480890i) q^{69} +(4.95899 - 4.95899i) q^{71} +(7.60300 - 2.03722i) q^{73} +(5.03668 - 0.663091i) q^{75} +(-0.185363 - 0.482404i) q^{77} +(-2.39290 - 4.14462i) q^{79} +(5.17023 + 2.98503i) q^{81} +(-5.02518 + 2.08150i) q^{83} +(-4.59792 + 11.1004i) q^{85} +(-0.317445 - 1.18472i) q^{87} +(0.0968732 + 0.0259571i) q^{89} +(-12.3448 + 1.30168i) q^{91} +(1.33392 - 1.73840i) q^{93} +(24.0066 + 13.8602i) q^{95} +9.39885i q^{97} +(0.478166 - 0.198063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} + 32 q^{15} + 12 q^{19} - 8 q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{29} - 24 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} + 32 q^{43} - 48 q^{45} + 24 q^{47}+ \cdots + 40 q^{99}+O(q^{100}) $ 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

Character values

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

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{8}\right)$

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
$3$	0.586792	+	0.0772527i	0.338785	+	0.0446018i	0.297999	−	0.954566i	$-0.403681\pi$
$3$	0.586792	+	0.0772527i	0.338785	+	0.0446018i	0.0407853	+	0.999168i	$0.487014\pi$
$4$		0			0
$5$	3.65404	−	0.481063i	1.63414	−	0.215138i	0.743135	−	0.669141i	$-0.233338\pi$
$5$	3.65404	−	0.481063i	1.63414	−	0.215138i	0.891000	+	0.454003i	$0.150005\pi$
$6$		0			0
$7$	−0.750581	+	2.53705i	−0.283693	+	0.958915i
$7$	−0.750581	+	2.53705i	−0.283693	+	0.958915i
$8$		0			0
$9$	−2.55942	−	0.685795i	−0.853140	−	0.228598i
$10$		0			0
$11$	−0.154965	+	0.118909i	−0.0467236	+	0.0358523i	−0.631859	−	0.775083i	$-0.717708\pi$
$11$	−0.154965	+	0.118909i	−0.0467236	+	0.0358523i	0.585136	+	0.810935i	$0.301041\pi$
$12$		0			0
$13$	1.79545	+	4.33461i	0.497969	+	1.20220i	0.950575	+	0.310494i	$0.100494\pi$
$13$	1.79545	+	4.33461i	0.497969	+	1.20220i	−0.452606	+	0.891711i	$0.649506\pi$
$14$		0			0
$15$	2.18132			0.563215
$16$		0			0
$17$	−1.63000	+	2.82324i	−0.395333	+	0.684736i	−0.993144	−	0.116901i	$-0.962704\pi$
$17$	−1.63000	+	2.82324i	−0.395333	+	0.684736i	0.597811	+	0.801637i	$0.296037\pi$
$18$		0			0
$19$	5.96708	+	4.57870i	1.36894	+	1.05043i	0.992273	+	0.124077i	$0.0395970\pi$
$19$	5.96708	+	4.57870i	1.36894	+	1.05043i	0.376668	+	0.926348i	$0.377070\pi$
$20$		0			0
$21$	−0.636429	+	1.43074i	−0.138880	+	0.312212i
$22$		0			0
$23$	−0.227620	+	0.849490i	−0.0474621	+	0.177131i	−0.985588	−	0.169163i	$-0.945893\pi$
$23$	−0.227620	+	0.849490i	−0.0474621	+	0.177131i	0.938126	+	0.346294i	$0.112560\pi$
$24$		0			0
$25$	8.29094	−	2.22155i	1.65819	−	0.444310i
$26$		0			0
$27$	−3.08928	−	1.27962i	−0.594532	−	0.246263i
$28$		0			0
$29$	−0.793041	−	1.91457i	−0.147264	−	0.355527i	0.832985	−	0.553296i	$-0.186630\pi$
$29$	−0.793041	−	1.91457i	−0.147264	−	0.355527i	−0.980249	+	0.197769i	$0.936630\pi$
$30$		0			0
$31$	1.85113	−	3.20626i	0.332473	−	0.575861i	−0.650523	−	0.759487i	$-0.725450\pi$
$31$	1.85113	−	3.20626i	0.332473	−	0.575861i	0.982996	+	0.183626i	$0.0587835\pi$
$32$		0			0
$33$	−0.100118	+	0.0578032i	−0.0174283	+	0.0100622i
$34$		0			0
$35$	−1.52217	+	9.63156i	−0.257294	+	1.62803i
$36$		0			0
$37$	−1.34829	−	10.2413i	−0.221657	−	1.68365i	−0.634558	−	0.772876i	$-0.718818\pi$
$37$	−1.34829	−	10.2413i	−0.221657	−	1.68365i	0.412901	−	0.910776i	$-0.364516\pi$
$38$		0			0
$39$	0.718698	+	2.68222i	0.115084	+	0.429499i
$40$		0			0
$41$	3.81582	+	3.81582i	0.595930	+	0.595930i	0.939227	−	0.343297i	$-0.111544\pi$
$41$	3.81582	+	3.81582i	0.595930	+	0.595930i	−0.343297	+	0.939227i	$0.611544\pi$
$42$		0			0
$43$	2.28159	+	0.945065i	0.347939	+	0.144121i	0.549807	−	0.835292i	$-0.314701\pi$
$43$	2.28159	+	0.945065i	0.347939	+	0.144121i	−0.201868	+	0.979413i	$0.564701\pi$
$44$		0			0
$45$	−9.68213	−	1.27468i	−1.44333	−	0.190018i
$46$		0			0
$47$	1.58163	−	0.913157i	0.230705	−	0.133198i	−0.380192	−	0.924907i	$-0.624142\pi$
$47$	1.58163	−	0.913157i	0.230705	−	0.133198i	0.610897	+	0.791710i	$0.290809\pi$
$48$		0			0
$49$	−5.87326	−	3.80853i	−0.839037	−	0.544075i
$50$		0			0
$51$	−1.17457	+	1.53073i	−0.164473	+	0.214346i
$52$		0			0
$53$	−5.48905	−	7.15347i	−0.753979	−	0.982604i	−0.999911	−	0.0133173i	$-0.995761\pi$
$53$	−5.48905	−	7.15347i	−0.753979	−	0.982604i	0.245933	−	0.969287i	$-0.420906\pi$
$54$		0			0
$55$	−0.509044	+	0.509044i	−0.0686395	+	0.0686395i
$56$		0			0
$57$	3.14772	+	3.14772i	0.416925	+	0.416925i
$58$		0			0
$59$	−6.76333	+	5.18969i	−0.880511	+	0.675640i	−0.946682	−	0.322169i	$-0.895588\pi$
$59$	−6.76333	+	5.18969i	−0.880511	+	0.675640i	0.0661717	+	0.997808i	$0.478921\pi$
$60$		0			0
$61$	5.03692	+	3.86496i	0.644911	+	0.494858i	0.878665	−	0.477438i	$-0.158434\pi$
$61$	5.03692	+	3.86496i	0.644911	+	0.494858i	−0.233754	+	0.972296i	$0.575101\pi$
$62$		0			0
$63$	3.66095	−	5.97864i	0.461236	−	0.753237i
$64$		0			0
$65$	8.64588	+	14.9751i	1.07239	+	1.85743i
$66$		0			0
$67$	1.56386	−	11.8787i	0.191056	−	1.45121i	−0.580089	−	0.814553i	$-0.696982\pi$
$67$	1.56386	−	11.8787i	0.191056	−	1.45121i	0.771145	−	0.636660i	$-0.219684\pi$
$68$		0			0
$69$	−0.199191	+	0.480890i	−0.0239798	+	0.0578923i
$70$		0			0
$71$	4.95899	−	4.95899i	0.588524	−	0.588524i	−0.348708	−	0.937231i	$-0.613379\pi$
$71$	4.95899	−	4.95899i	0.588524	−	0.588524i	0.937231	+	0.348708i	$0.113379\pi$
$72$		0			0
$73$	7.60300	−	2.03722i	0.889864	−	0.238438i	0.215206	−	0.976569i	$-0.430958\pi$
$73$	7.60300	−	2.03722i	0.889864	−	0.238438i	0.674658	+	0.738130i	$0.264291\pi$
$74$		0			0
$75$	5.03668	−	0.663091i	0.581586	−	0.0765672i
$76$		0			0
$77$	−0.185363	−	0.482404i	−0.0211241	−	0.0549750i
$78$		0			0
$79$	−2.39290	−	4.14462i	−0.269222	−	0.466306i	0.699439	−	0.714692i	$-0.253433\pi$
$79$	−2.39290	−	4.14462i	−0.269222	−	0.466306i	−0.968661	+	0.248386i	$0.920100\pi$
$80$		0			0
$81$	5.17023	+	2.98503i	0.574470	+	0.331670i
$82$		0			0
$83$	−5.02518	+	2.08150i	−0.551585	+	0.228474i	−0.641027	−	0.767518i	$-0.721491\pi$
$83$	−5.02518	+	2.08150i	−0.551585	+	0.228474i	0.0894425	+	0.995992i	$0.471491\pi$
$84$		0			0
$85$	−4.59792	+	11.1004i	−0.498714	+	1.20400i
$86$		0			0
$87$	−0.317445	−	1.18472i	−0.0340336	−	0.127015i
$88$		0			0
$89$	0.0968732	+	0.0259571i	0.0102685	+	0.00275145i	0.263950	−	0.964536i	$-0.414975\pi$
$89$	0.0968732	+	0.0259571i	0.0102685	+	0.00275145i	−0.253681	+	0.967288i	$0.581641\pi$
$90$		0			0
$91$	−12.3448	+	1.30168i	−1.29408	+	0.136453i
$92$		0			0
$93$	1.33392	−	1.73840i	0.138321	−	0.180264i
$94$		0			0
$95$	24.0066	+	13.8602i	2.46302	+	1.42203i
$96$		0			0
$97$			9.39885i			0.954309i	0.878819	+	0.477155i	$0.158332\pi$
$97$			9.39885i			0.954309i	−0.878819	+	0.477155i	$0.841668\pi$
$98$		0			0
$99$	0.478166	−	0.198063i	0.0480575	−	0.0199061i
$100$		0			0
$101$	0.838796	+	1.09314i	0.0834634	+	0.108772i	0.833219	−	0.552944i	$-0.186495\pi$
$101$	0.838796	+	1.09314i	0.0834634	+	0.108772i	−0.749755	+	0.661715i	$0.769829\pi$
$102$		0			0
$103$	2.98824	−	11.1523i	0.294440	−	1.09887i	−0.647221	−	0.762303i	$-0.724069\pi$
$103$	2.98824	−	11.1523i	0.294440	−	1.09887i	0.941661	−	0.336563i	$-0.109265\pi$
$104$		0			0
$105$	−1.63726	+	5.53413i	−0.159780	+	0.540076i
$106$		0			0
$107$	0.839491	+	6.37657i	0.0811566	+	0.616446i	0.982895	+	0.184165i	$0.0589579\pi$
$107$	0.839491	+	6.37657i	0.0811566	+	0.616446i	−0.901739	+	0.432281i	$0.857709\pi$
$108$		0			0
$109$	−0.915766	+	6.95593i	−0.0877144	+	0.666257i	0.889946	+	0.456066i	$0.150742\pi$
$109$	−0.915766	+	6.95593i	−0.0877144	+	0.666257i	−0.977660	+	0.210191i	$0.932591\pi$
$110$		0			0
$111$		−	6.11365i		−	0.580282i
$112$		0			0
$113$		−	1.27034i		−	0.119504i	−0.998213	−	0.0597519i	$-0.980969\pi$
$113$		−	1.27034i		−	0.119504i	0.998213	−	0.0597519i	$-0.0190310\pi$
$114$		0			0
$115$	−0.423074	+	3.21357i	−0.0394519	+	0.299667i
$116$		0			0
$117$	−1.62267	−	12.3254i	−0.150016	−	1.13948i
$118$		0			0
$119$	−5.93926	−	6.25446i	−0.544451	−	0.573345i
$120$		0			0
$121$	−2.83713	+	10.5883i	−0.257921	+	0.962576i
$122$		0			0
$123$	1.94431	+	2.53387i	0.175312	+	0.228472i
$124$		0			0
$125$	12.2016	−	5.05406i	1.09134	−	0.452049i
$126$		0			0
$127$		−	6.29532i		−	0.558619i	−0.960201	−	0.279310i	$-0.909894\pi$
$127$		−	6.29532i		−	0.558619i	0.960201	−	0.279310i	$-0.0901056\pi$
$128$		0			0
$129$	1.26581	+	0.730815i	0.111448	+	0.0643447i
$130$		0			0
$131$	−12.3878	+	16.1441i	−1.08233	+	1.41052i	−0.177820	+	0.984063i	$0.556905\pi$
$131$	−12.3878	+	16.1441i	−1.08233	+	1.41052i	−0.904509	+	0.426455i	$0.859762\pi$
$132$		0			0
$133$	−16.0952	+	11.7021i	−1.39563	+	1.01470i
$134$		0			0
$135$	−11.9039	−	3.18964i	−1.02453	−	0.274521i
$136$		0			0
$137$	−5.66819	−	21.1540i	−0.484266	−	1.80731i	−0.583342	−	0.812226i	$-0.698255\pi$
$137$	−5.66819	−	21.1540i	−0.484266	−	1.80731i	0.0990762	−	0.995080i	$-0.468411\pi$
$138$		0			0
$139$	7.25213	−	17.5082i	0.615118	−	1.48503i	−0.242194	−	0.970228i	$-0.577867\pi$
$139$	7.25213	−	17.5082i	0.615118	−	1.48503i	0.857311	−	0.514798i	$-0.172133\pi$
$140$		0			0
$141$	0.998634	−	0.413648i	0.0841002	−	0.0348354i
$142$		0			0
$143$	−0.793654	−	0.458216i	−0.0663687	−	0.0383180i
$144$		0			0
$145$	−3.81883	−	6.61441i	−0.317137	−	0.549297i
$146$		0			0
$147$	−3.15216	−	2.68854i	−0.259986	−	0.221747i
$148$		0			0
$149$	−7.28989	+	0.959733i	−0.597211	+	0.0786244i	−0.423071	−	0.906096i	$-0.639048\pi$
$149$	−7.28989	+	0.959733i	−0.597211	+	0.0786244i	−0.174140	+	0.984721i	$0.555715\pi$
$150$		0			0
$151$	−20.4835	+	5.48853i	−1.66692	+	0.446650i	−0.964278	−	0.264892i	$-0.914664\pi$
$151$	−20.4835	+	5.48853i	−1.66692	+	0.446650i	−0.702643	+	0.711542i	$0.747997\pi$
$152$		0			0
$153$	6.10801	−	6.10801i	0.493804	−	0.493804i
$154$		0			0
$155$	5.22170	−	12.6063i	0.419417	−	1.01256i
$156$		0			0
$157$	0.482890	−	3.66792i	0.0385389	−	0.292732i	−0.961312	−	0.275462i	$-0.911169\pi$
$157$	0.482890	−	3.66792i	0.0385389	−	0.292732i	0.999851	−	0.0172698i	$-0.00549743\pi$
$158$		0			0
$159$	−2.66831	−	4.62164i	−0.211610	−	0.366520i
$160$		0			0
$161$	−1.98435	−	1.21509i	−0.156389	−	0.0957629i
$162$		0			0
$163$	11.4597	+	8.79335i	0.897595	+	0.688749i	0.950790	−	0.309836i	$-0.100274\pi$
$163$	11.4597	+	8.79335i	0.897595	+	0.688749i	−0.0531956	+	0.998584i	$0.516941\pi$
$164$		0			0
$165$	−0.338028	+	0.259378i	−0.0263154	+	0.0201925i
$166$		0			0
$167$	−8.50231	−	8.50231i	−0.657929	−	0.657929i	0.296961	−	0.954890i	$-0.404027\pi$
$167$	−8.50231	−	8.50231i	−0.657929	−	0.657929i	−0.954890	+	0.296961i	$0.904027\pi$
$168$		0			0
$169$	−6.37280	+	6.37280i	−0.490215	+	0.490215i
$170$		0			0
$171$	−12.1322	−	15.8110i	−0.927773	−	1.20910i
$172$		0			0
$173$	4.42510	−	5.76690i	0.336434	−	0.438449i	−0.594246	−	0.804283i	$-0.702550\pi$
$173$	4.42510	−	5.76690i	0.336434	−	0.438449i	0.930680	+	0.365834i	$0.119216\pi$
$174$		0			0
$175$	−0.586835	+	22.7020i	−0.0443606	+	1.71611i
$176$		0			0
$177$	−4.36959	+	2.52278i	−0.328438	+	0.189624i
$178$		0			0
$179$	−16.6721	−	2.19493i	−1.24613	−	0.164056i	−0.521536	−	0.853229i	$-0.674641\pi$
$179$	−16.6721	−	2.19493i	−1.24613	−	0.164056i	−0.724597	+	0.689173i	$0.757974\pi$
$180$		0			0
$181$	1.48033	+	0.613171i	0.110032	+	0.0455767i	0.437020	−	0.899452i	$-0.356034\pi$
$181$	1.48033	+	0.613171i	0.110032	+	0.0455767i	−0.326988	+	0.945028i	$0.606034\pi$
$182$		0			0
$183$	2.65704	+	2.65704i	0.196414	+	0.196414i
$184$		0			0
$185$	−9.85338	−	36.7733i	−0.724435	−	2.70363i
$186$		0			0
$187$	−0.0831152	−	0.631323i	−0.00607799	−	0.0461669i
$188$		0			0
$189$	5.56522	−	6.87720i	0.404810	−	0.500242i
$190$		0			0
$191$	7.04481	−	4.06732i	0.509745	−	0.294301i	−0.222984	−	0.974822i	$-0.571580\pi$
$191$	7.04481	−	4.06732i	0.509745	−	0.294301i	0.732729	+	0.680521i	$0.238246\pi$
$192$		0			0
$193$	1.59700	−	2.76608i	0.114954	−	0.199107i	−0.802807	−	0.596239i	$-0.796661\pi$
$193$	1.59700	−	2.76608i	0.114954	−	0.199107i	0.917761	+	0.397132i	$0.129995\pi$
$194$		0			0
$195$	3.91647	+	9.45519i	0.280464	+	0.677100i
$196$		0			0
$197$	−22.7704	−	9.43182i	−1.62233	−	0.671989i	−0.627985	−	0.778226i	$-0.716120\pi$
$197$	−22.7704	−	9.43182i	−1.62233	−	0.671989i	−0.994341	+	0.106237i	$0.966120\pi$
$198$		0			0
$199$	13.9754	−	3.74470i	0.990690	−	0.265455i	0.273150	−	0.961972i	$-0.411935\pi$
$199$	13.9754	−	3.74470i	0.990690	−	0.265455i	0.717540	+	0.696517i	$0.245268\pi$
$200$		0			0
$201$	1.83532	−	6.84951i	0.129454	−	0.483127i
$202$		0			0
$203$	5.45261	−	0.574945i	0.382698	−	0.0403533i
$204$		0			0
$205$	15.7788	+	12.1075i	1.10204	+	0.845624i
$206$		0			0
$207$	1.16515	−	2.01810i	0.0809836	−	0.140268i
$208$		0			0
$209$	−1.46913			−0.101622
$210$		0			0
$211$	−6.84963	−	16.5365i	−0.471548	−	1.13842i	−0.963479	−	0.267784i	$-0.913709\pi$
$211$	−6.84963	−	16.5365i	−0.471548	−	1.13842i	0.491931	−	0.870634i	$-0.336291\pi$
$212$		0			0
$213$	3.29299	−	2.52680i	0.225632	−	0.173134i
$214$		0			0
$215$	8.79164	+	2.35571i	0.599585	+	0.160658i
$216$		0			0
$217$	6.74501	+	7.10297i	0.457881	+	0.482181i
$218$		0			0
$219$	4.61876	−	0.608071i	0.312107	−	0.0410897i
$220$		0			0
$221$	−15.1642	−	1.99641i	−1.02006	−	0.134293i
$222$		0			0
$223$	−2.20295			−0.147520			−0.0737601	−	0.997276i	$-0.523500\pi$
$223$	−2.20295			−0.147520			−0.0737601	+	0.997276i	$0.523500\pi$
$224$		0			0
$225$	−22.7435			−1.51623
$226$		0			0
$227$	−5.65874	−	0.744988i	−0.375584	−	0.0494466i	−0.0596286	−	0.998221i	$-0.518992\pi$
$227$	−5.65874	−	0.744988i	−0.375584	−	0.0494466i	−0.315955	+	0.948774i	$0.602325\pi$
$228$		0			0
$229$	24.0045	−	3.16025i	1.58626	−	0.208835i	0.714811	−	0.699318i	$-0.246513\pi$
$229$	24.0045	−	3.16025i	1.58626	−	0.208835i	0.871451	+	0.490482i	$0.163179\pi$
$230$		0			0
$231$	−0.0715029	−	0.297390i	−0.00470454	−	0.0195669i
$232$		0			0
$233$	17.1439	+	4.59370i	1.12314	+	0.300944i	0.772152	−	0.635438i	$-0.219180\pi$
$233$	17.1439	+	4.59370i	1.12314	+	0.300944i	0.350984	+	0.936381i	$0.385847\pi$
$234$		0			0
$235$	5.34006	−	4.09757i	0.348347	−	0.267296i
$236$		0			0
$237$	−1.08395	−	2.61689i	−0.0704102	−	0.169985i
$238$		0			0
$239$	−12.6706			−0.819591			−0.409796	−	0.912177i	$-0.634400\pi$
$239$	−12.6706			−0.819591			−0.409796	+	0.912177i	$0.634400\pi$
$240$		0			0
$241$	−4.33725	+	7.51235i	−0.279387	+	0.483913i	−0.971233	−	0.238133i	$-0.923465\pi$
$241$	−4.33725	+	7.51235i	−0.279387	+	0.483913i	0.691845	+	0.722046i	$0.256798\pi$
$242$		0			0
$243$	10.7617	+	8.25776i	0.690365	+	0.529735i
$244$		0			0
$245$	−23.2932	−	11.0911i	−1.48815	−	0.708584i
$246$		0			0
$247$	−9.13326	+	34.0858i	−0.581135	+	2.16883i
$248$		0			0
$249$	−3.10953	+	0.833197i	−0.197059	+	0.0528017i
$250$		0			0
$251$	4.22400	+	1.74964i	0.266617	+	0.110436i	0.511987	−	0.858993i	$-0.328910\pi$
$251$	4.22400	+	1.74964i	0.266617	+	0.110436i	−0.245370	+	0.969429i	$0.578910\pi$
$252$		0			0
$253$	−0.0657385	−	0.158707i	−0.00413294	−	0.00997781i
$254$		0			0
$255$	−3.55555	+	6.15840i	−0.222657	+	0.385654i
$256$		0			0
$257$	−0.0444799	+	0.0256805i	−0.00277458	+	0.00160190i	−0.501387	−	0.865223i	$-0.667177\pi$
$257$	−0.0444799	+	0.0256805i	−0.00277458	+	0.00160190i	0.498612	+	0.866825i	$0.333843\pi$
$258$		0			0
$259$	26.9946	+	4.26622i	1.67736	+	0.265090i
$260$		0			0
$261$	0.716723	+	5.44406i	0.0443641	+	0.336979i
$262$		0			0
$263$	0.444526	+	1.65899i	0.0274106	+	0.102298i	0.978276	−	0.207307i	$-0.0664699\pi$
$263$	0.444526	+	1.65899i	0.0274106	+	0.102298i	−0.950865	+	0.309605i	$0.899803\pi$
$264$		0			0
$265$	−23.4985	−	23.4985i	−1.44350	−	1.44350i
$266$		0			0
$267$	0.0548392	+	0.0227151i	0.00335610	+	0.00139014i
$268$		0			0
$269$	−2.18109	−	0.287147i	−0.132984	−	0.0175076i	0.0637405	−	0.997967i	$-0.479697\pi$
$269$	−2.18109	−	0.287147i	−0.132984	−	0.0175076i	−0.196724	+	0.980459i	$0.563030\pi$
$270$		0			0
$271$	3.98800	−	2.30247i	0.242254	−	0.139865i	−0.373959	−	0.927445i	$-0.622000\pi$
$271$	3.98800	−	2.30247i	0.242254	−	0.139865i	0.616212	+	0.787580i	$0.288666\pi$
$272$		0			0
$273$	−7.34437	−	0.189848i	−0.444501	−	0.0114901i
$274$		0			0
$275$	−1.02064	+	1.33012i	−0.0615469	+	0.0802095i
$276$		0			0
$277$	−3.21758	−	4.19323i	−0.193326	−	0.251947i	0.686625	−	0.727012i	$-0.259091\pi$
$277$	−3.21758	−	4.19323i	−0.193326	−	0.251947i	−0.879951	+	0.475065i	$0.842425\pi$
$278$		0			0
$279$	−6.93666	+	6.93666i	−0.415287	+	0.415287i
$280$		0			0
$281$	6.51561	+	6.51561i	0.388689	+	0.388689i	0.874220	−	0.485531i	$-0.161374\pi$
$281$	6.51561	+	6.51561i	0.388689	+	0.388689i	−0.485531	+	0.874220i	$0.661374\pi$
$282$		0			0
$283$	−9.70876	+	7.44979i	−0.577126	+	0.442844i	−0.855628	−	0.517592i	$-0.826829\pi$
$283$	−9.70876	+	7.44979i	−0.577126	+	0.442844i	0.278502	+	0.960436i	$0.410162\pi$
$284$		0			0
$285$	13.0161	+	9.98762i	0.771009	+	0.591616i
$286$		0			0
$287$	−12.5450	+	6.81684i	−0.740508	+	0.402385i
$288$		0			0
$289$	3.18621	+	5.51868i	0.187424	+	0.324628i
$290$		0			0
$291$	−0.726086	+	5.51517i	−0.0425639	+	0.323305i
$292$		0			0
$293$	9.68853	−	23.3902i	0.566010	−	1.36647i	−0.338883	−	0.940829i	$-0.610049\pi$
$293$	9.68853	−	23.3902i	0.566010	−	1.36647i	0.904892	−	0.425640i	$-0.139951\pi$
$294$		0			0
$295$	−22.2169	+	22.2169i	−1.29352	+	1.29352i
$296$		0			0
$297$	0.630887	−	0.169046i	0.0366078	−	0.00980902i
$298$		0			0
$299$	−4.09089	+	0.538575i	−0.236582	+	0.0311466i
$300$		0			0
$301$	−4.11019	+	5.07916i	−0.236908	+	0.292758i
$302$		0			0
$303$	0.407751	+	0.706246i	0.0234247	+	0.0405728i
$304$		0			0
$305$	20.2644	+	11.6996i	1.16033	+	0.669919i
$306$		0			0
$307$	−1.39053	+	0.575975i	−0.0793616	+	0.0328727i	−0.422011	−	0.906591i	$-0.638676\pi$
$307$	−1.39053	+	0.575975i	−0.0793616	+	0.0328727i	0.342649	+	0.939463i	$0.388676\pi$
$308$		0			0
$309$	2.61502	−	6.31322i	0.148763	−	0.359146i
$310$		0			0
$311$	−7.83483	−	29.2400i	−0.444273	−	1.65805i	−0.717850	−	0.696198i	$-0.754874\pi$
$311$	−7.83483	−	29.2400i	−0.444273	−	1.65805i	0.273577	−	0.961850i	$-0.411793\pi$
$312$		0			0
$313$	2.76399	+	0.740609i	0.156230	+	0.0418617i	0.336086	−	0.941831i	$-0.390897\pi$
$313$	2.76399	+	0.740609i	0.156230	+	0.0418617i	−0.179856	+	0.983693i	$0.557563\pi$
$314$		0			0
$315$	10.5011	−	23.6073i	0.591672	−	1.33012i
$316$		0			0
$317$	−3.24812	+	4.23304i	−0.182433	+	0.237751i	−0.875613	−	0.483013i	$-0.839542\pi$
$317$	−3.24812	+	4.23304i	−0.182433	+	0.237751i	0.693180	+	0.720764i	$0.256209\pi$
$318$		0			0
$319$	0.350552	+	0.202391i	0.0196271	+	0.0113317i
$320$		0			0
$321$			3.80657i			0.212462i
$322$		0			0
$323$	−22.6531	+	9.38321i	−1.26045	+	0.522096i
$324$		0			0
$325$	24.5156	+	31.9493i	1.35988	+	1.77223i
$326$		0			0
$327$	−1.07473	+	4.01094i	−0.0594326	+	0.221805i
$328$		0			0
$329$	1.12958	+	4.69808i	0.0622758	+	0.259014i
$330$		0			0
$331$	2.09490	+	15.9123i	0.115146	+	0.874621i	0.947361	+	0.320168i	$0.103739\pi$
$331$	2.09490	+	15.9123i	0.115146	+	0.874621i	−0.832215	+	0.554453i	$0.812927\pi$
$332$		0			0
$333$	−3.57256	+	27.1363i	−0.195775	+	1.48706i
$334$		0			0
$335$		−	44.1575i		−	2.41258i
$336$		0			0
$337$		−	25.9961i		−	1.41610i	−0.706163	−	0.708049i	$-0.749575\pi$
$337$		−	25.9961i		−	1.41610i	0.706163	−	0.708049i	$-0.250425\pi$
$338$		0			0
$339$	0.0981374	−	0.745428i	0.00533009	−	0.0404861i
$340$		0			0
$341$	0.0943911	+	0.716972i	0.00511157	+	0.0388262i
$342$		0			0
$343$	14.0708	−	12.0421i	0.759751	−	0.650215i
$344$		0			0
$345$	−0.496513	+	1.85301i	−0.0267314	+	0.0997628i
$346$		0			0
$347$	−15.8204	−	20.6175i	−0.849283	−	1.10681i	−0.993108	−	0.117204i	$-0.962607\pi$
$347$	−15.8204	−	20.6175i	−0.849283	−	1.10681i	0.143824	−	0.989603i	$-0.454060\pi$
$348$		0			0
$349$	−9.97430	+	4.13149i	−0.533912	+	0.221154i	−0.633316	−	0.773894i	$-0.718306\pi$
$349$	−9.97430	+	4.13149i	−0.533912	+	0.221154i	0.0994037	+	0.995047i	$0.468306\pi$
$350$		0			0
$351$		−	15.6883i		−	0.837380i
$352$		0			0
$353$	−8.89552	−	5.13583i	−0.473461	−	0.273353i	0.244226	−	0.969718i	$-0.421466\pi$
$353$	−8.89552	−	5.13583i	−0.473461	−	0.273353i	−0.717687	+	0.696365i	$0.754799\pi$
$354$		0			0
$355$	15.7347	−	20.5059i	0.835113	−	1.08834i
$356$		0			0
$357$	−3.00194	−	4.12889i	−0.158879	−	0.218524i
$358$		0			0
$359$	31.7210	+	8.49961i	1.67417	+	0.448592i	0.966230	−	0.257682i	$-0.0829587\pi$
$359$	31.7210	+	8.49961i	1.67417	+	0.448592i	0.707939	+	0.706274i	$0.249625\pi$
$360$		0			0
$361$	9.72395	+	36.2903i	0.511787	+	1.91001i
$362$		0			0
$363$	−2.48279	+	5.99397i	−0.130312	+	0.314602i
$364$		0			0
$365$	26.8016	−	11.1016i	1.40286	−	0.581084i
$366$		0			0
$367$	4.93261	+	2.84784i	0.257480	+	0.148656i	0.623185	−	0.782075i	$-0.285839\pi$
$367$	4.93261	+	2.84784i	0.257480	+	0.148656i	−0.365704	+	0.930731i	$0.619172\pi$
$368$		0			0
$369$	−7.14941	−	12.3831i	−0.372183	−	0.644641i
$370$		0			0
$371$	22.2687	−	8.55674i	1.15613	−	0.444244i
$372$		0			0
$373$	2.53961	−	0.334346i	0.131496	−	0.0173118i	−0.0644909	−	0.997918i	$-0.520542\pi$
$373$	2.53961	−	0.334346i	0.131496	−	0.0173118i	0.195987	+	0.980607i	$0.437209\pi$
$374$		0			0
$375$	7.55024	−	2.02308i	0.389893	−	0.104471i
$376$		0			0
$377$	6.87505	−	6.87505i	0.354083	−	0.354083i
$378$		0			0
$379$	−7.46656	+	18.0259i	−0.383531	+	0.925926i	0.607746	+	0.794132i	$0.292074\pi$
$379$	−7.46656	+	18.0259i	−0.383531	+	0.925926i	−0.991277	+	0.131795i	$0.957926\pi$
$380$		0			0
$381$	0.486330	−	3.69404i	0.0249154	−	0.189252i
$382$		0			0
$383$	9.29771	+	16.1041i	0.475091	+	0.822882i	0.999593	−	0.0285276i	$-0.00908184\pi$
$383$	9.29771	+	16.1041i	0.475091	+	0.822882i	−0.524502	+	0.851409i	$0.675749\pi$
$384$		0			0
$385$	−0.909392	−	1.67355i	−0.0463469	−	0.0852920i
$386$		0			0
$387$	−5.19142	−	3.98352i	−0.263895	−	0.202494i
$388$		0			0
$389$	2.85809	−	2.19309i	0.144911	−	0.111194i	−0.533762	−	0.845635i	$-0.679222\pi$
$389$	2.85809	−	2.19309i	0.144911	−	0.111194i	0.678673	+	0.734441i	$0.262556\pi$
$390$		0			0
$391$	−2.02729	−	2.02729i	−0.102525	−	0.102525i
$392$		0			0
$393$	−8.51625	+	8.51625i	−0.429588	+	0.429588i
$394$		0			0
$395$	−10.7376	−	13.9935i	−0.540266	−	0.704088i
$396$		0			0
$397$	−8.58035	+	11.1821i	−0.430636	+	0.561215i	−0.957388	−	0.288803i	$-0.906743\pi$
$397$	−8.58035	+	11.1821i	−0.430636	+	0.561215i	0.526753	+	0.850018i	$0.323409\pi$
$398$		0			0
$399$	−10.3485	+	5.62330i	−0.518075	+	0.281517i
$400$		0			0
$401$	−9.96747	+	5.75472i	−0.497752	+	0.287377i	−0.727785	−	0.685806i	$-0.759450\pi$
$401$	−9.96747	+	5.75472i	−0.497752	+	0.287377i	0.230033	+	0.973183i	$0.426117\pi$
$402$		0			0
$403$	17.2215	+	2.26725i	0.857864	+	0.112940i
$404$		0			0
$405$	20.3282	+	8.42022i	1.01012	+	0.418404i
$406$		0			0
$407$	1.42671	+	1.42671i	0.0707193	+	0.0707193i
$408$		0			0
$409$	−2.80860	−	10.4818i	−0.138876	−	0.518294i	−0.999952	−	0.00981657i	$-0.996875\pi$
$409$	−2.80860	−	10.4818i	−0.138876	−	0.518294i	0.861075	−	0.508477i	$-0.169791\pi$
$410$		0			0
$411$	−1.69185	−	12.8509i	−0.0834528	−	0.633887i
$412$		0			0
$413$	−8.09007	−	21.0542i	−0.398086	−	1.03601i
$414$		0			0
$415$	−17.3608	+	10.0233i	−0.852211	+	0.492024i
$416$		0			0
$417$	5.60805	−	9.71343i	0.274627	−	0.475669i
$418$		0			0
$419$	−1.14858	−	2.77292i	−0.0561119	−	0.135466i	0.893337	−	0.449387i	$-0.148357\pi$
$419$	−1.14858	−	2.77292i	−0.0561119	−	0.135466i	−0.949449	+	0.313920i	$0.898357\pi$
$420$		0			0
$421$	18.6016	+	7.70504i	0.906587	+	0.375521i	0.786749	−	0.617273i	$-0.211762\pi$
$421$	18.6016	+	7.70504i	0.906587	+	0.375521i	0.119838	+	0.992793i	$0.461762\pi$
$422$		0			0
$423$	−4.67430	+	1.25248i	−0.227272	+	0.0608975i
$424$		0			0
$425$	−7.24225	+	27.0284i	−0.351301	+	1.31107i
$426$		0			0
$427$	−13.5862	+	9.87795i	−0.657483	+	0.478027i
$428$		0			0
$429$	−0.430311	−	0.330190i	−0.0207756	−	0.0159417i
$430$		0			0
$431$	0.410242	−	0.710561i	0.0197607	−	0.0342265i	−0.855976	−	0.517016i	$-0.827043\pi$
$431$	0.410242	−	0.710561i	0.0197607	−	0.0342265i	0.875737	+	0.482789i	$0.160376\pi$
$432$		0			0
$433$	−19.1887			−0.922148			−0.461074	−	0.887362i	$-0.652536\pi$
$433$	−19.1887			−0.922148			−0.461074	+	0.887362i	$0.652536\pi$
$434$		0			0
$435$	−1.72988	−	4.17630i	−0.0829414	−	0.200238i
$436$		0			0
$437$	−5.24778	+	4.02676i	−0.251035	+	0.192626i
$438$		0			0
$439$	29.9726	+	8.03114i	1.43051	+	0.383305i	0.889201	−	0.457516i	$-0.151261\pi$
$439$	29.9726	+	8.03114i	1.43051	+	0.383305i	0.541313	+	0.840821i	$0.317927\pi$
$440$		0			0
$441$	12.4203	+	13.7755i	0.591441	+	0.655974i
$442$		0			0
$443$	6.59091	−	0.867710i	0.313144	−	0.0412261i	0.0276835	−	0.999617i	$-0.491187\pi$
$443$	6.59091	−	0.867710i	0.313144	−	0.0412261i	0.285460	+	0.958391i	$0.407854\pi$
$444$		0			0
$445$	0.366465	+	0.0482461i	0.0173721	+	0.00228708i
$446$		0			0
$447$	−4.35179			−0.205833
$448$		0			0
$449$	−21.8843			−1.03278			−0.516392	−	0.856352i	$-0.672725\pi$
$449$	−21.8843			−1.03278			−0.516392	+	0.856352i	$0.672725\pi$
$450$		0			0
$451$	−1.04505	−	0.137583i	−0.0492095	−	0.00647855i
$452$		0			0
$453$	−12.4435	+	1.63822i	−0.584649	+	0.0769705i
$454$		0			0
$455$	−44.4820	+	10.6950i	−2.08535	+	0.501390i
$456$		0			0
$457$	−18.8375	−	5.04748i	−0.881179	−	0.236111i	−0.210263	−	0.977645i	$-0.567432\pi$
$457$	−18.8375	−	5.04748i	−0.881179	−	0.236111i	−0.670916	+	0.741534i	$0.734099\pi$
$458$		0			0
$459$	8.64819	−	6.63599i	0.403663	−	0.309742i
$460$		0			0
$461$	−5.00740	−	12.0889i	−0.233218	−	0.563038i	0.763335	−	0.646003i	$-0.223561\pi$
$461$	−5.00740	−	12.0889i	−0.233218	−	0.563038i	−0.996552	+	0.0829658i	$0.973561\pi$
$462$		0			0
$463$	37.5037			1.74294			0.871472	−	0.490445i	$-0.163166\pi$
$463$	37.5037			1.74294			0.871472	+	0.490445i	$0.163166\pi$
$464$		0			0
$465$	4.03792	−	6.99388i	0.187254	−	0.324334i
$466$		0			0
$467$	14.9728	+	11.4890i	0.692857	+	0.531648i	0.894086	−	0.447896i	$-0.147827\pi$
$467$	14.9728	+	11.4890i	0.692857	+	0.531648i	−0.201228	+	0.979544i	$0.564493\pi$
$468$		0			0
$469$	28.9630	+	12.8835i	1.33739	+	0.594905i
$470$		0			0
$471$	0.566713	−	2.11500i	0.0261127	−	0.0974541i
$472$		0			0
$473$	−0.465942	+	0.124849i	−0.0214240	+	0.00574055i
$474$		0			0
$475$	59.6445	+	24.7055i	2.73668	+	1.13357i
$476$		0			0
$477$	9.14297	+	22.0731i	0.418628	+	1.01066i
$478$		0			0
$479$	−9.26849	+	16.0535i	−0.423488	+	0.733503i	−0.996278	−	0.0861993i	$-0.972528\pi$
$479$	−9.26849	+	16.0535i	−0.423488	+	0.733503i	0.572790	+	0.819702i	$0.305861\pi$
$480$		0			0
$481$	41.9710	−	24.2320i	1.91372	−	1.10488i
$482$		0			0
$483$	−1.07053	−	0.866304i	−0.0487109	−	0.0394182i
$484$		0			0
$485$	4.52144	+	34.3438i	0.205308	+	1.55947i
$486$		0			0
$487$	−1.46021	−	5.44957i	−0.0661684	−	0.246944i	0.924918	−	0.380168i	$-0.124134\pi$
$487$	−1.46021	−	5.44957i	−0.0661684	−	0.246944i	−0.991086	+	0.133224i	$0.957467\pi$
$488$		0			0
$489$	6.04516	+	6.04516i	0.273372	+	0.273372i
$490$		0			0
$491$	27.2761	+	11.2981i	1.23095	+	0.509878i	0.900877	−	0.434075i	$-0.142925\pi$
$491$	27.2761	+	11.2981i	1.23095	+	0.509878i	0.330078	+	0.943954i	$0.392925\pi$
$492$		0			0
$493$	6.69795	+	0.881802i	0.301660	+	0.0397143i
$494$		0			0
$495$	1.65196	−	0.953758i	0.0742499	−	0.0428682i
$496$		0			0
$497$	8.85908	+	16.3033i	0.397384	+	0.731304i
$498$		0			0
$499$	−6.88394	+	8.97132i	−0.308167	+	0.401612i	−0.921603	−	0.388133i	$-0.873120\pi$
$499$	−6.88394	+	8.97132i	−0.308167	+	0.401612i	0.613436	+	0.789744i	$0.289787\pi$
$500$		0			0
$501$	−4.33226	−	5.64592i	−0.193551	−	0.252241i
$502$		0			0
$503$	−20.3957	+	20.3957i	−0.909400	+	0.909400i	−0.996224	−	0.0868238i	$-0.972328\pi$
$503$	−20.3957	+	20.3957i	−0.909400	+	0.909400i	0.0868238	+	0.996224i	$0.472328\pi$
$504$		0			0
$505$	3.59086	+	3.59086i	0.159791	+	0.159791i
$506$		0			0
$507$	−4.23182	+	3.24719i	−0.187942	+	0.144213i
$508$		0			0
$509$	20.4675	+	15.7053i	0.907205	+	0.696123i	0.953046	−	0.302826i	$-0.0979300\pi$
$509$	20.4675	+	15.7053i	0.907205	+	0.696123i	−0.0458408	+	0.998949i	$0.514597\pi$
$510$		0			0
$511$	−0.538143	+	20.8183i	−0.0238060	+	0.920947i
$512$		0			0
$513$	−12.5750	−	21.7805i	−0.555198	−	0.961631i
$514$		0			0
$515$	5.55420	−	42.1884i	0.244747	−	1.85904i
$516$		0			0
$517$	−0.136515	+	0.329577i	−0.00600393	+	0.0144948i
$518$		0			0
$519$	3.04212	−	3.04212i	0.133534	−	0.133534i
$520$		0			0
$521$	−1.52994	+	0.409945i	−0.0670277	+	0.0179600i	−0.292177	−	0.956364i	$-0.594380\pi$
$521$	−1.52994	+	0.409945i	−0.0670277	+	0.0179600i	0.225149	+	0.974324i	$0.427713\pi$
$522$		0			0
$523$	−20.2896	+	2.67118i	−0.887203	+	0.116803i	−0.560334	−	0.828267i	$-0.689327\pi$
$523$	−20.2896	+	2.67118i	−0.887203	+	0.116803i	−0.326870	+	0.945069i	$0.605994\pi$
$524$		0			0
$525$	−2.09814	+	13.2760i	−0.0915703	+	0.579413i
$526$		0			0
$527$	6.03469	+	10.4524i	0.262875	+	0.455313i
$528$		0			0
$529$	19.2488	+	11.1133i	0.836903	+	0.483186i
$530$		0			0
$531$	20.8693	−	8.64433i	0.905649	−	0.375132i
$532$		0			0
$533$	−9.68895	+	23.3912i	−0.419675	+	1.01319i
$534$		0			0
$535$	6.13506	+	22.8964i	0.265242	+	0.989896i
$536$		0			0
$537$	−9.61351	−	2.57593i	−0.414853	−	0.111160i
$538$		0			0
$539$	1.36301	−	0.108194i	0.0587091	−	0.00466023i
$540$		0			0
$541$	−20.5201	+	26.7424i	−0.882230	+	1.14974i	0.105632	+	0.994405i	$0.466314\pi$
$541$	−20.5201	+	26.7424i	−0.882230	+	1.14974i	−0.987861	+	0.155339i	$0.950353\pi$
$542$		0			0
$543$	0.821275	+	0.474163i	0.0352443	+	0.0203483i
$544$		0			0
$545$			25.8578i			1.10763i
$546$		0			0
$547$	1.87204	−	0.775425i	0.0800427	−	0.0331548i	−0.342303	−	0.939590i	$-0.611207\pi$
$547$	1.87204	−	0.775425i	0.0800427	−	0.0331548i	0.422346	+	0.906435i	$0.361207\pi$
$548$		0			0
$549$	−10.2410	−	13.3464i	−0.437076	−	0.569608i
$550$		0			0
$551$	4.03410	−	15.0555i	0.171859	−	0.641385i
$552$		0			0
$553$	12.3112	−	2.96003i	0.523525	−	0.125873i
$554$		0			0
$555$	−2.94105	−	22.3395i	−0.124841	−	0.948259i
$556$		0			0
$557$	3.35390	−	25.4754i	0.142109	−	1.07943i	−0.760613	−	0.649205i	$-0.775102\pi$
$557$	3.35390	−	25.4754i	0.142109	−	1.07943i	0.902723	−	0.430223i	$-0.141565\pi$
$558$		0			0
$559$			11.5866i			0.490062i
$560$		0			0
$561$		−	0.376876i		−	0.0159117i
$562$		0			0
$563$	1.66206	−	12.6246i	0.0700475	−	0.532064i	−0.920063	−	0.391771i	$-0.871862\pi$
$563$	1.66206	−	12.6246i	0.0700475	−	0.532064i	0.990110	−	0.140292i	$-0.0448043\pi$
$564$		0			0
$565$	−0.611115	−	4.64188i	−0.0257098	−	0.195285i
$566$		0			0
$567$	−11.4539	+	10.8766i	−0.481017	+	0.456775i
$568$		0			0
$569$	8.01362	−	29.9072i	0.335948	−	1.25378i	−0.566889	−	0.823794i	$-0.691853\pi$
$569$	8.01362	−	29.9072i	0.335948	−	1.25378i	0.902837	−	0.429982i	$-0.141480\pi$
$570$		0			0
$571$	10.0924	+	13.1526i	0.422352	+	0.550419i	0.955265	−	0.295750i	$-0.0955696\pi$
$571$	10.0924	+	13.1526i	0.422352	+	0.550419i	−0.532914	+	0.846170i	$0.678903\pi$
$572$		0			0
$573$	4.44805	−	1.84244i	0.185820	−	0.0769692i
$574$		0			0
$575$			7.54873i			0.314804i
$576$		0			0
$577$	−30.5815	−	17.6562i	−1.27312	−	0.735038i	−0.297549	−	0.954707i	$-0.596169\pi$
$577$	−30.5815	−	17.6562i	−1.27312	−	0.735038i	−0.975575	+	0.219668i	$0.929502\pi$
$578$		0			0
$579$	1.15079	−	1.49974i	0.0478252	−	0.0623271i
$580$		0			0
$581$	−1.50906	−	14.3115i	−0.0626063	−	0.593739i
$582$		0			0
$583$	1.70122	+	0.455840i	0.0704572	+	0.0188789i
$584$		0			0
$585$	−11.8586	−	44.2569i	−0.490292	−	1.82980i
$586$		0			0
$587$	−5.67657	+	13.7044i	−0.234297	+	0.565643i	−0.996674	−	0.0814899i	$-0.974032\pi$
$587$	−5.67657	+	13.7044i	−0.234297	+	0.565643i	0.762377	+	0.647133i	$0.224032\pi$
$588$		0			0
$589$	25.7263	−	10.6562i	1.06003	−	0.439081i
$590$		0			0
$591$	−12.6329	−	7.29359i	−0.519647	−	0.300018i
$592$		0			0
$593$	19.0770	+	33.0424i	0.783400	+	1.35689i	0.929950	+	0.367685i	$0.119850\pi$
$593$	19.0770	+	33.0424i	0.783400	+	1.35689i	−0.146550	+	0.989203i	$0.546817\pi$
$594$		0			0
$595$	−24.7111	−	19.9969i	−1.01305	−	0.819792i
$596$		0			0
$597$	8.48994	−	1.11772i	0.347470	−	0.0457453i
$598$		0			0
$599$	19.9086	−	5.33450i	0.813444	−	0.217962i	0.171966	−	0.985103i	$-0.444988\pi$
$599$	19.9086	−	5.33450i	0.813444	−	0.217962i	0.641478	+	0.767141i	$0.278321\pi$
$600$		0			0
$601$	−11.0600	+	11.0600i	−0.451146	+	0.451146i	−0.895735	−	0.444589i	$-0.853350\pi$
$601$	−11.0600	+	11.0600i	−0.451146	+	0.451146i	0.444589	+	0.895735i	$0.353350\pi$
$602$		0			0
$603$	−12.1489	+	29.3301i	−0.494742	+	1.19441i
$604$		0			0
$605$	−5.27334	+	40.0550i	−0.214392	+	1.62847i
$606$		0			0
$607$	−5.10135	−	8.83580i	−0.207057	−	0.358634i	0.743729	−	0.668481i	$-0.233055\pi$
$607$	−5.10135	−	8.83580i	−0.207057	−	0.358634i	−0.950786	+	0.309847i	$0.899722\pi$
$608$		0			0
$609$	3.24396	+	0.0838548i	0.131452	+	0.00339797i
$610$		0			0
$611$	6.79793	+	5.21623i	0.275015	+	0.211026i
$612$		0			0
$613$	−16.6586	+	12.7826i	−0.672833	+	0.516283i	−0.887736	−	0.460352i	$-0.847723\pi$
$613$	−16.6586	+	12.7826i	−0.672833	+	0.516283i	0.214903	+	0.976635i	$0.431056\pi$
$614$		0			0
$615$	8.32353	+	8.32353i	0.335637	+	0.335637i
$616$		0			0
$617$	24.2795	−	24.2795i	0.977456	−	0.977456i	−0.0222958	−	0.999751i	$-0.507098\pi$
$617$	24.2795	−	24.2795i	0.977456	−	0.977456i	0.999751	+	0.0222958i	$0.00709757\pi$
$618$		0			0
$619$	3.61807	+	4.71516i	0.145423	+	0.189518i	0.860385	−	0.509644i	$-0.170223\pi$
$619$	3.61807	+	4.71516i	0.145423	+	0.189518i	−0.714963	+	0.699163i	$0.753556\pi$
$620$		0			0
$621$	1.79021	−	2.33304i	0.0718385	−	0.0936218i
$622$		0			0
$623$	−0.138566	+	0.226289i	−0.00555152	+	0.00906609i
$624$		0			0
$625$	4.98648	−	2.87894i	0.199459	−	0.115158i
$626$		0			0
$627$	−0.862075	−	0.113494i	−0.0344280	−	0.00453253i
$628$		0			0
$629$	31.1112	+	12.8867i	1.24049	+	0.513826i
$630$		0			0
$631$	2.39818	+	2.39818i	0.0954700	+	0.0954700i	0.753229	−	0.657759i	$-0.228495\pi$
$631$	2.39818	+	2.39818i	0.0954700	+	0.0954700i	−0.657759	+	0.753229i	$0.728495\pi$
$632$		0			0
$633$	−2.74182	−	10.2326i	−0.108978	−	0.406711i
$634$		0			0
$635$	−3.02845	−	23.0033i	−0.120180	−	0.912859i
$636$		0			0
$637$	5.96331	−	32.2963i	0.236275	−	1.27963i
$638$		0			0
$639$	−16.0930	+	9.29129i	−0.636629	+	0.367558i
$640$		0			0
$641$	5.60572	−	9.70939i	0.221413	−	0.383498i	−0.733825	−	0.679339i	$-0.762267\pi$
$641$	5.60572	−	9.70939i	0.221413	−	0.383498i	0.955237	+	0.295841i	$0.0955999\pi$
$642$		0			0
$643$	1.05264	+	2.54130i	0.0415121	+	0.100219i	0.943276	−	0.332011i	$-0.107727\pi$
$643$	1.05264	+	2.54130i	0.0415121	+	0.100219i	−0.901764	+	0.432230i	$0.857727\pi$
$644$		0			0
$645$	4.97688	+	2.06149i	0.195965	+	0.0811712i
$646$		0			0
$647$	28.9642	−	7.76092i	1.13870	−	0.305113i	0.360271	−	0.932848i	$-0.382684\pi$
$647$	28.9642	−	7.76092i	1.13870	−	0.305113i	0.778428	+	0.627734i	$0.216018\pi$
$648$		0			0
$649$	0.430979	−	1.60844i	0.0169174	−	0.0631366i
$650$		0			0
$651$	3.40920	+	4.68904i	0.133617	+	0.183778i
$652$		0			0
$653$	−7.67521	−	5.88940i	−0.300354	−	0.230470i	0.447578	−	0.894245i	$-0.352287\pi$
$653$	−7.67521	−	5.88940i	−0.300354	−	0.230470i	−0.747932	+	0.663775i	$0.768953\pi$
$654$		0			0
$655$	−37.4992	+	64.9505i	−1.46522	+	2.53783i
$656$		0			0
$657$	−20.8564			−0.813685
$658$		0			0
$659$	−8.00070	−	19.3154i	−0.311663	−	0.752421i	−0.999644	−	0.0266921i	$-0.991503\pi$
$659$	−8.00070	−	19.3154i	−0.311663	−	0.752421i	0.687981	−	0.725729i	$-0.258497\pi$
$660$		0			0
$661$	10.9122	−	8.37320i	0.424434	−	0.325680i	−0.374361	−	0.927283i	$-0.622138\pi$
$661$	10.9122	−	8.37320i	0.424434	−	0.325680i	0.798795	+	0.601603i	$0.205471\pi$
$662$		0			0
$663$	−8.74402	−	2.34295i	−0.339590	−	0.0909928i
$664$		0			0
$665$	−53.1829	+	50.5027i	−2.06234	+	1.95841i
$666$		0			0
$667$	1.80692	−	0.237886i	0.0699642	−	0.00921096i
$668$		0			0
$669$	−1.29267	−	0.170184i	−0.0499776	−	0.00657968i
$670$		0			0
$671$	−1.24012			−0.0478743
$672$		0			0
$673$	28.1723			1.08596			0.542982	−	0.839744i	$-0.317295\pi$
$673$	28.1723			1.08596			0.542982	+	0.839744i	$0.317295\pi$
$674$		0			0
$675$	−28.4558	−	3.74627i	−1.09526	−	0.144194i
$676$		0			0
$677$	−8.24681	+	1.08571i	−0.316951	+	0.0417274i	−0.287323	−	0.957834i	$-0.592765\pi$
$677$	−8.24681	+	1.08571i	−0.316951	+	0.0417274i	−0.0296274	+	0.999561i	$0.509432\pi$
$678$		0			0
$679$	−23.8454	−	7.05460i	−0.915101	−	0.270731i
$680$		0			0
$681$	−3.26295	−	0.874306i	−0.125037	−	0.0335035i
$682$		0			0
$683$	−12.2945	+	9.43387i	−0.470434	+	0.360977i	−0.816607	−	0.577194i	$-0.804148\pi$
$683$	−12.2945	+	9.43387i	−0.470434	+	0.360977i	0.346173	+	0.938171i	$0.387481\pi$
$684$		0			0
$685$	−30.8882	−	74.5707i	−1.18018	−	2.84920i
$686$		0			0
$687$	14.3298			0.546716
$688$		0			0
$689$	21.1522	−	36.6366i	0.805833	−	1.39574i
$690$		0			0
$691$	−9.68571	−	7.43211i	−0.368462	−	0.282731i	0.407889	−	0.913031i	$-0.366265\pi$
$691$	−9.68571	−	7.43211i	−0.368462	−	0.282731i	−0.776351	+	0.630301i	$0.782932\pi$
$692$		0			0
$693$	0.143593	+	1.36179i	0.00545466	+	0.0517303i
$694$		0			0
$695$	18.0770	−	67.4643i	0.685700	−	2.55907i
$696$		0			0
$697$	−16.9927	+	4.55319i	−0.643646	+	0.172464i
$698$		0			0
$699$	9.70505	+	4.01996i	0.367079	+	0.152049i
$700$		0			0
$701$	−10.0224	−	24.1963i	−0.378542	−	0.913881i	−0.992240	−	0.124340i	$-0.960319\pi$
$701$	−10.0224	−	24.1963i	−0.378542	−	0.913881i	0.613698	−	0.789541i	$-0.289681\pi$
$702$		0			0
$703$	38.8463	−	67.2837i	1.46512	−	2.53765i
$704$		0			0
$705$	3.45006	−	1.99189i	0.129937	−	0.0750189i
$706$		0			0
$707$	−3.40294	+	1.30758i	−0.127981	+	0.0491766i
$708$		0			0
$709$	−4.37598	−	33.2389i	−0.164343	−	1.24831i	−0.852491	−	0.522742i	$-0.824909\pi$
$709$	−4.37598	−	33.2389i	−0.164343	−	1.24831i	0.688148	−	0.725571i	$-0.258424\pi$
$710$		0			0
$711$	3.28207	+	12.2489i	0.123087	+	0.459368i
$712$		0			0
$713$	2.30233	+	2.30233i	0.0862228	+	0.0862228i
$714$		0			0
$715$	−3.12047	−	1.29254i	−0.116699	−	0.0483383i
$716$		0			0
$717$	−7.43499	−	0.978836i	−0.277665	−	0.0365553i
$718$		0			0
$719$	−22.7929	+	13.1595i	−0.850031	+	0.490766i	−0.860661	−	0.509178i	$-0.829950\pi$
$719$	−22.7929	+	13.1595i	−0.850031	+	0.490766i	0.0106300	+	0.999943i	$0.496616\pi$
$720$		0			0
$721$	26.0510	+	15.9520i	0.970189	+	0.594084i
$722$		0			0
$723$	−3.12542	+	4.07312i	−0.116235	+	0.151481i
$724$		0			0
$725$	−10.8284	−	14.1118i	−0.402156	−	0.524099i
$726$		0			0
$727$	32.3640	−	32.3640i	1.20031	−	1.20031i	0.226244	−	0.974071i	$-0.427355\pi$
$727$	32.3640	−	32.3640i	1.20031	−	1.20031i	0.974071	−	0.226244i	$-0.0726447\pi$
$728$		0			0
$729$	−6.98747	−	6.98747i	−0.258795	−	0.258795i
$730$		0			0
$731$	−6.38713	+	4.90102i	−0.236237	+	0.181271i
$732$		0			0
$733$	−34.7704	−	26.6803i	−1.28428	−	0.985459i	−0.999640	−	0.0268237i	$-0.991461\pi$
$733$	−34.7704	−	26.6803i	−1.28428	−	0.985459i	−0.284636	−	0.958636i	$-0.591873\pi$
$734$		0			0
$735$	−12.8115	−	8.30763i	−0.472558	−	0.306431i
$736$		0			0
$737$	1.17013	+	2.02673i	0.0431025	+	0.0746557i
$738$		0			0
$739$	−2.55495	+	19.4067i	−0.0939852	+	0.713889i	0.877969	+	0.478718i	$0.158898\pi$
$739$	−2.55495	+	19.4067i	−0.0939852	+	0.713889i	−0.971954	+	0.235171i	$0.924435\pi$
$740$		0			0
$741$	−7.99254	+	19.2957i	−0.293613	+	0.708845i
$742$		0			0
$743$	−6.32677	+	6.32677i	−0.232107	+	0.232107i	−0.813572	−	0.581465i	$-0.802480\pi$
$743$	−6.32677	+	6.32677i	−0.232107	+	0.232107i	0.581465	+	0.813572i	$0.302480\pi$
$744$		0			0
$745$	−26.1759	+	7.01380i	−0.959009	+	0.256966i
$746$		0			0
$747$	14.2890	−	1.88118i	0.522808	−	0.0688289i
$748$		0			0
$749$	−16.8078	−	2.65630i	−0.614143	−	0.0970590i
$750$		0			0
$751$	−20.1360	−	34.8765i	−0.734772	−	1.27266i	−0.954823	−	0.297174i	$-0.903956\pi$
$751$	−20.1360	−	34.8765i	−0.734772	−	1.27266i	0.220051	−	0.975488i	$-0.429377\pi$
$752$		0			0
$753$	2.34345	+	1.35299i	0.0853999	+	0.0493057i
$754$		0			0
$755$	−72.2070	+	29.9091i	−2.62788	+	1.08850i
$756$		0			0
$757$	−12.9976	+	31.3791i	−0.472408	+	1.14049i	0.490688	+	0.871335i	$0.336745\pi$
$757$	−12.9976	+	31.3791i	−0.472408	+	1.14049i	−0.963096	+	0.269158i	$0.913255\pi$
$758$		0			0
$759$	−0.0263143	−	0.0982064i	−0.000955149	−	0.00356466i
$760$		0			0
$761$	−4.50078	−	1.20598i	−0.163153	−	0.0437167i	0.176318	−	0.984333i	$-0.443581\pi$
$761$	−4.50078	−	1.20598i	−0.163153	−	0.0437167i	−0.339471	+	0.940617i	$0.610248\pi$
$762$		0			0
$763$	−16.9602	−	7.54433i	−0.614000	−	0.273123i
$764$		0			0
$765$	19.3806	−	25.2572i	0.700706	−	0.913178i
$766$		0			0
$767$	−34.6385	−	19.9986i	−1.25072	−	0.722106i
$768$		0			0
$769$			17.4876i			0.630619i	0.948989	+	0.315310i	$0.102108\pi$
$769$			17.4876i			0.630619i	−0.948989	+	0.315310i	$0.897892\pi$
$770$		0			0
$771$	−0.0280843	+	0.0116329i	−0.00101143	+	0.000418949i
$772$		0			0
$773$	−17.5375	−	22.8553i	−0.630779	−	0.822047i	0.363189	−	0.931715i	$-0.381688\pi$
$773$	−17.5375	−	22.8553i	−0.630779	−	0.822047i	−0.993968	+	0.109668i	$0.965021\pi$
$774$		0			0
$775$	8.22477	−	30.6953i	0.295442	−	1.10261i
$776$		0			0
$777$	15.5106	+	4.58879i	0.556441	+	0.164622i
$778$		0			0
$779$	5.29779	+	40.2407i	0.189813	+	1.44177i
$780$		0			0
$781$	−0.178802	+	1.35813i	−0.00639803	+	0.0485978i
$782$		0			0
$783$			6.92943i			0.247638i
$784$		0			0
$785$		−	13.6350i		−	0.486654i
$786$		0			0
$787$	−5.28263	+	40.1255i	−0.188305	+	1.43032i	0.592512	+	0.805561i	$0.298136\pi$
$787$	−5.28263	+	40.1255i	−0.188305	+	1.43032i	−0.780818	+	0.624759i	$0.785197\pi$
$788$		0			0
$789$	0.132683	+	1.00782i	0.00472363	+	0.0358795i
$790$		0			0
$791$	3.22293	+	0.953496i	0.114594	+	0.0339024i
$792$		0			0
$793$	−7.70955	+	28.7724i	−0.273774	+	1.02174i
$794$		0			0
$795$	−11.9734	−	15.6040i	−0.424652	−	0.553418i
$796$		0			0
$797$	−30.2358	+	12.5241i	−1.07101	+	0.443625i	−0.847345	−	0.531042i	$-0.821801\pi$
$797$	−30.2358	+	12.5241i	−1.07101	+	0.443625i	−0.223660	+	0.974667i	$0.571801\pi$
$798$		0			0
$799$			5.95378i			0.210629i
$800$		0			0
$801$	−0.230138	−	0.132870i	−0.00813153	−	0.00469474i
$802$		0			0
$803$	−0.935953	+	1.21976i	−0.0330291	+	0.0430443i
$804$		0			0
$805$	−7.83543	−	3.48540i	−0.276163	−	0.122844i
$806$		0			0
$807$	−1.25767	−	0.336991i	−0.0442720	−	0.0118626i
$808$		0			0
$809$	5.81756	+	21.7114i	0.204535	+	0.763333i	0.989591	+	0.143909i	$0.0459673\pi$
$809$	5.81756	+	21.7114i	0.204535	+	0.763333i	−0.785056	+	0.619424i	$0.787366\pi$
$810$		0			0
$811$	0.866622	−	2.09221i	0.0304312	−	0.0734675i	−0.907933	−	0.419115i	$-0.862341\pi$
$811$	0.866622	−	2.09221i	0.0304312	−	0.0734675i	0.938365	+	0.345647i	$0.112341\pi$
$812$		0			0
$813$	2.51800	−	1.04299i	0.0883100	−	0.0365792i
$814$		0			0
$815$	46.1044	+	26.6184i	1.61497	+	0.932402i
$816$		0			0
$817$	9.28724	+	16.0860i	0.324919	+	0.562777i
$818$		0			0
$819$	32.4881	+	5.13442i	1.13523	+	0.179411i
$820$		0			0
$821$	43.4115	−	5.71523i	1.51507	−	0.199463i	0.673329	−	0.739343i	$-0.264864\pi$
$821$	43.4115	−	5.71523i	1.51507	−	0.199463i	0.841742	+	0.539880i	$0.181530\pi$
$822$		0			0
$823$	34.8906	−	9.34890i	1.21621	−	0.325882i	0.407014	−	0.913422i	$-0.366570\pi$
$823$	34.8906	−	9.34890i	1.21621	−	0.325882i	0.809195	+	0.587540i	$0.199903\pi$
$824$		0			0
$825$	−0.701660	+	0.701660i	−0.0244287	+	0.0244287i
$826$		0			0
$827$	−8.76859	+	21.1692i	−0.304914	+	0.736127i	0.694941	+	0.719067i	$0.255431\pi$
$827$	−8.76859	+	21.1692i	−0.304914	+	0.736127i	−0.999854	+	0.0170597i	$0.994569\pi$
$828$		0			0
$829$	−5.71739	+	43.4279i	−0.198573	+	1.50831i	0.544305	+	0.838887i	$0.316793\pi$
$829$	−5.71739	+	43.4279i	−0.198573	+	1.50831i	−0.742878	+	0.669426i	$0.766540\pi$
$830$		0			0
$831$	−1.56411	−	2.70912i	−0.0542585	−	0.0939785i
$832$		0			0
$833$	20.3258	−	10.3737i	0.704246	−	0.359428i
$834$		0			0
$835$	−35.1579	−	26.9776i	−1.21669	−	0.933599i
$836$		0			0
$837$	−9.82146	+	7.53627i	−0.339479	+	0.260492i
$838$		0			0
$839$	37.8886	+	37.8886i	1.30806	+	1.30806i	0.922813	+	0.385248i	$0.125884\pi$
$839$	37.8886	+	37.8886i	1.30806	+	1.30806i	0.385248	+	0.922813i	$0.374116\pi$
$840$		0			0
$841$	17.4694	−	17.4694i	0.602394	−	0.602394i
$842$		0			0
$843$	3.31996	+	4.32666i	0.114346	+	0.149018i
$844$		0			0
$845$	−20.2207	+	26.3521i	−0.695614	+	0.906541i
$846$		0			0
$847$	−24.7336	−	15.1454i	−0.849858	−	0.520401i
$848$		0			0
$849$	−6.27254	+	3.62145i	−0.215273	+	0.124288i
$850$		0			0
$851$	9.00673	+	1.18576i	0.308747	+	0.0406473i
$852$		0			0
$853$	18.0841	+	7.49066i	0.619186	+	0.256475i	0.670151	−	0.742225i	$-0.266230\pi$
$853$	18.0841	+	7.49066i	0.619186	+	0.256475i	−0.0509644	+	0.998700i	$0.516230\pi$
$854$		0			0
$855$	−51.9376	−	51.9376i	−1.77623	−	1.77623i
$856$		0			0
$857$	5.95862	+	22.2379i	0.203543	+	0.759631i	0.989889	+	0.141845i	$0.0453036\pi$
$857$	5.95862	+	22.2379i	0.203543	+	0.759631i	−0.786346	+	0.617786i	$0.788030\pi$
$858$		0			0
$859$	0.117615	+	0.893376i	0.00401298	+	0.0304816i	0.993334	−	0.115270i	$-0.0367733\pi$
$859$	0.117615	+	0.893376i	0.00401298	+	0.0304816i	−0.989321	+	0.145752i	$0.953440\pi$
$860$		0			0
$861$	−7.88793	+	3.03093i	−0.268820	+	0.103294i
$862$		0			0
$863$	26.9099	−	15.5365i	0.916024	−	0.528867i	0.0336599	−	0.999433i	$-0.489284\pi$
$863$	26.9099	−	15.5365i	0.916024	−	0.528867i	0.882365	+	0.470566i	$0.155950\pi$
$864$		0			0
$865$	13.3952	−	23.2012i	0.455451	−	0.788865i
$866$		0			0
$867$	1.44331	+	3.48446i	0.0490174	+	0.118339i
$868$		0			0
$869$	0.863646	+	0.357734i	0.0292972	+	0.0121353i
$870$		0			0
$871$	54.2973	−	14.5489i	1.83979	−	0.492972i
$872$		0			0
$873$	6.44568	−	24.0556i	0.218153	−	0.814159i
$874$		0			0
$875$	3.66414	+	34.7495i	0.123870	+	1.17475i
$876$		0			0
$877$	−27.2095	−	20.8786i	−0.918801	−	0.705021i	0.0369128	−	0.999318i	$-0.488248\pi$
$877$	−27.2095	−	20.8786i	−0.918801	−	0.705021i	−0.955714	+	0.294298i	$0.904914\pi$
$878$		0			0
$879$	7.49211	−	12.9767i	0.252702	−	0.437694i
$880$		0			0
$881$	8.67844			0.292384			0.146192	−	0.989256i	$-0.453298\pi$
$881$	8.67844			0.292384			0.146192	+	0.989256i	$0.453298\pi$
$882$		0			0
$883$	3.72606	+	8.99549i	0.125392	+	0.302722i	0.974092	−	0.226151i	$-0.0726144\pi$
$883$	3.72606	+	8.99549i	0.125392	+	0.302722i	−0.848700	+	0.528874i	$0.822614\pi$
$884$		0			0
$885$	−14.7530	+	11.3204i	−0.495917	+	0.380531i
$886$		0			0
$887$	−19.8501	−	5.31881i	−0.666501	−	0.178588i	−0.0903226	−	0.995913i	$-0.528790\pi$
$887$	−19.8501	−	5.31881i	−0.666501	−	0.178588i	−0.576178	+	0.817324i	$0.695456\pi$
$888$		0			0
$889$	15.9715	+	4.72515i	0.535668	+	0.158476i
$890$		0			0
$891$	−1.15615	+	0.152210i	−0.0387324	+	0.00509922i
$892$		0			0
$893$	13.6188	+	1.79295i	0.455736	+	0.0599987i
$894$		0			0
$895$	−61.9765			−2.07164
$896$		0			0
$897$	−2.44211			−0.0815396
$898$		0			0
$899$	−7.60663	−	1.00143i	−0.253695	−	0.0333996i
$900$		0			0
$901$	29.1431	−	3.83676i	0.970897	−	0.127821i
$902$		0			0
$903$	−2.80421	+	2.66289i	−0.0933182	+	0.0886153i
$904$		0			0
$905$	5.70414	+	1.52842i	0.189612	+	0.0508064i
$906$		0			0
$907$	−11.1069	+	8.52263i	−0.368799	+	0.282989i	−0.776489	−	0.630131i	$-0.783001\pi$
$907$	−11.1069	+	8.52263i	−0.368799	+	0.282989i	0.407690	+	0.913120i	$0.366334\pi$
$908$		0			0
$909$	−1.39716	−	3.37305i	−0.0463410	−	0.111877i
$910$		0			0
$911$	29.8181			0.987917			0.493958	−	0.869486i	$-0.335550\pi$
$911$	29.8181			0.987917			0.493958	+	0.869486i	$0.335550\pi$
$912$		0			0
$913$	0.531217	−	0.920094i	0.0175807	−	0.0304507i
$914$		0			0
$915$	10.9871	+	8.43073i	0.363224	+	0.278711i
$916$		0			0
$917$	−31.6604	−	43.5460i	−1.04552	−	1.43802i
$918$		0			0
$919$	−4.70223	+	17.5490i	−0.155112	+	0.578887i	0.843983	+	0.536369i	$0.180205\pi$
$919$	−4.70223	+	17.5490i	−0.155112	+	0.578887i	−0.999096	+	0.0425176i	$0.986462\pi$
$920$		0			0
$921$	−0.860446	+	0.230556i	−0.0283527	+	0.00759708i
$922$		0			0
$923$	30.3989	+	12.5916i	1.00059	+	0.414459i
$924$		0			0
$925$	−33.9300	−	81.9143i	−1.11561	−	2.69333i
$926$		0			0
$927$	−15.2963	+	26.4940i	−0.502398	+	0.870178i
$928$		0			0
$929$	−44.1260	+	25.4762i	−1.44773	+	0.835846i	−0.998346	−	0.0574938i	$-0.981689\pi$
$929$	−44.1260	+	25.4762i	−1.44773	+	0.835846i	−0.449382	+	0.893340i	$0.648356\pi$
$930$		0			0
$931$	−17.6081	−	49.6176i	−0.577081	−	1.62615i
$932$		0			0
$933$	−2.33855	−	17.7631i	−0.0765607	−	0.581537i
$934$		0			0
$935$	−0.607412	−	2.26689i	−0.0198645	−	0.0741354i
$936$		0			0
$937$	21.8870	+	21.8870i	0.715016	+	0.715016i	0.967580	−	0.252564i	$-0.0812739\pi$
$937$	21.8870	+	21.8870i	0.715016	+	0.715016i	−0.252564	+	0.967580i	$0.581274\pi$
$938$		0			0
$939$	1.56467	+	0.648109i	0.0510612	+	0.0211503i
$940$		0			0
$941$	−25.3000	−	3.33081i	−0.824756	−	0.108581i	−0.293678	−	0.955904i	$-0.594879\pi$
$941$	−25.3000	−	3.33081i	−0.824756	−	0.108581i	−0.531078	+	0.847323i	$0.678213\pi$
$942$		0			0
$943$	−4.11005	+	2.37294i	−0.133842	+	0.0772735i
$944$		0			0
$945$	17.0271	−	27.8068i	0.553893	−	0.904554i
$946$		0			0
$947$	9.54325	−	12.4370i	0.310114	−	0.404148i	−0.612130	−	0.790757i	$-0.709687\pi$
$947$	9.54325	−	12.4370i	0.310114	−	0.404148i	0.922244	+	0.386609i	$0.126354\pi$
$948$		0			0
$949$	22.4814	+	29.2983i	0.729776	+	0.951063i
$950$		0			0
$951$	−2.23299	+	2.23299i	−0.0724095	+	0.0724095i
$952$		0			0
$953$	35.1047	+	35.1047i	1.13715	+	1.13715i	0.988958	+	0.148196i	$0.0473467\pi$
$953$	35.1047	+	35.1047i	1.13715	+	1.13715i	0.148196	+	0.988958i	$0.452653\pi$
$954$		0			0
$955$	23.7854	−	18.2512i	0.769676	−	0.590593i
$956$		0			0
$957$	0.190066	+	0.145843i	0.00614396	+	0.00471443i
$958$		0			0
$959$	57.9232	+	1.49729i	1.87044	+	0.0483499i
$960$		0			0
$961$	8.64661	+	14.9764i	0.278923	+	0.483109i
$962$		0			0
$963$	2.22440	−	16.8960i	0.0716804	−	0.544467i
$964$		0			0
$965$	4.50482	−	10.8756i	0.145015	−	0.350098i
$966$		0			0
$967$	−4.13197	+	4.13197i	−0.132875	+	0.132875i	−0.770416	−	0.637541i	$-0.779952\pi$
$967$	−4.13197	+	4.13197i	−0.132875	+	0.132875i	0.637541	+	0.770416i	$0.279952\pi$
$968$		0			0
$969$	−14.0175	+	3.75599i	−0.450308	+	0.120660i
$970$		0			0
$971$	−38.8209	+	5.11086i	−1.24582	+	0.164015i	−0.724458	−	0.689319i	$-0.757910\pi$
$971$	−38.8209	+	5.11086i	−1.24582	+	0.164015i	−0.521363	+	0.853335i	$0.674576\pi$
$972$		0			0
$973$	38.9759	+	31.5404i	1.24951	+	1.01114i
$974$		0			0
$975$	11.9174	+	20.6415i	0.381661	+	0.661057i
$976$		0			0
$977$	−26.3775	−	15.2291i	−0.843892	−	0.487221i	0.0146935	−	0.999892i	$-0.495323\pi$
$977$	−26.3775	−	15.2291i	−0.843892	−	0.487221i	−0.858585	+	0.512671i	$0.828656\pi$
$978$		0			0
$979$	−0.0180984	+	0.00749662i	−0.000578429	+	0.000239593i
$980$		0			0
$981$	7.11417	−	17.1751i	0.227138	−	0.548359i
$982$		0			0
$983$	8.63630	+	32.2311i	0.275455	+	1.02801i	0.955536	+	0.294875i	$0.0952782\pi$
$983$	8.63630	+	32.2311i	0.275455	+	1.02801i	−0.680080	+	0.733138i	$0.738055\pi$
$984$		0			0
$985$	−87.7413	−	23.5102i	−2.79567	−	0.749097i
$986$		0			0
$987$	0.299890	+	2.84406i	0.00954559	+	0.0905275i
$988$		0			0
$989$	−1.32216	+	1.72307i	−0.0420422	+	0.0547904i
$990$		0			0
$991$	−14.8667	−	8.58331i	−0.472257	−	0.272658i	0.244927	−	0.969542i	$-0.421236\pi$
$991$	−14.8667	−	8.58331i	−0.472257	−	0.272658i	−0.717184	+	0.696884i	$0.754569\pi$
$992$		0			0
$993$			9.49907i			0.301444i
$994$		0			0
$995$	49.2652	−	20.4063i	1.56181	−	0.646924i
$996$		0			0
$997$	7.34440	+	9.57141i	0.232599	+	0.303129i	0.895041	−	0.445984i	$-0.147146\pi$
$997$	7.34440	+	9.57141i	0.232599	+	0.303129i	−0.662441	+	0.749114i	$0.730480\pi$
$998$		0			0
$999$	−8.93969	+	33.3634i	−0.282839	+	1.05557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bi.a.143.18		240
4.3	odd	2		224.2.be.a.59.24	yes	240
7.5	odd	6	inner	896.2.bi.a.271.18		240
28.19	even	6		224.2.be.a.187.17	yes	240
32.13	even	8		224.2.be.a.115.17	yes	240
32.19	odd	8	inner	896.2.bi.a.367.18		240
224.19	even	24	inner	896.2.bi.a.495.18		240
224.173	odd	24		224.2.be.a.19.24	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.19.24	✓	240	224.173	odd	24
224.2.be.a.59.24	yes	240	4.3	odd	2
224.2.be.a.115.17	yes	240	32.13	even	8
224.2.be.a.187.17	yes	240	28.19	even	6
896.2.bi.a.143.18		240	1.1	even	1	trivial
896.2.bi.a.271.18		240	7.5	odd	6	inner
896.2.bi.a.367.18		240	32.19	odd	8	inner
896.2.bi.a.495.18		240	224.19	even	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bi (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.586792 + 0.0772527i) q^{3} +(3.65404 - 0.481063i) q^{5} +(-0.750581 + 2.53705i) q^{7} +(-2.55942 - 0.685795i) q^{9} +(-0.154965 + 0.118909i) q^{11} +(1.79545 + 4.33461i) q^{13} +2.18132 q^{15} +(-1.63000 + 2.82324i) q^{17} +(5.96708 + 4.57870i) q^{19} +(-0.636429 + 1.43074i) q^{21} +(-0.227620 + 0.849490i) q^{23} +(8.29094 - 2.22155i) q^{25} +(-3.08928 - 1.27962i) q^{27} +(-0.793041 - 1.91457i) q^{29} +(1.85113 - 3.20626i) q^{31} +(-0.100118 + 0.0578032i) q^{33} +(-1.52217 + 9.63156i) q^{35} +(-1.34829 - 10.2413i) q^{37} +(0.718698 + 2.68222i) q^{39} +(3.81582 + 3.81582i) q^{41} +(2.28159 + 0.945065i) q^{43} +(-9.68213 - 1.27468i) q^{45} +(1.58163 - 0.913157i) q^{47} +(-5.87326 - 3.80853i) q^{49} +(-1.17457 + 1.53073i) q^{51} +(-5.48905 - 7.15347i) q^{53} +(-0.509044 + 0.509044i) q^{55} +(3.14772 + 3.14772i) q^{57} +(-6.76333 + 5.18969i) q^{59} +(5.03692 + 3.86496i) q^{61} +(3.66095 - 5.97864i) q^{63} +(8.64588 + 14.9751i) q^{65} +(1.56386 - 11.8787i) q^{67} +(-0.199191 + 0.480890i) q^{69} +(4.95899 - 4.95899i) q^{71} +(7.60300 - 2.03722i) q^{73} +(5.03668 - 0.663091i) q^{75} +(-0.185363 - 0.482404i) q^{77} +(-2.39290 - 4.14462i) q^{79} +(5.17023 + 2.98503i) q^{81} +(-5.02518 + 2.08150i) q^{83} +(-4.59792 + 11.1004i) q^{85} +(-0.317445 - 1.18472i) q^{87} +(0.0968732 + 0.0259571i) q^{89} +(-12.3448 + 1.30168i) q^{91} +(1.33392 - 1.73840i) q^{93} +(24.0066 + 13.8602i) q^{95} +9.39885i q^{97} +(0.478166 - 0.198063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{3} - 12 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} + 32 q^{15} + 12 q^{19} - 8 q^{21} - 4 q^{23} - 4 q^{25} - 16 q^{29} - 24 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} + 32 q^{43} - 48 q^{45} + 24 q^{47}+ \cdots + 40 q^{99}+O(q^{100}) \) 240 * q + 12 * q^3 - 12 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 + 32 * q^15 + 12 * q^19 - 8 * q^21 - 4 * q^23 - 4 * q^25 - 16 * q^29 - 24 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 + 32 * q^43 - 48 * q^45 + 24 * q^47 - 20 * q^51 - 20 * q^53 - 16 * q^57 - 84 * q^59 - 12 * q^61 - 8 * q^65 - 36 * q^67 + 80 * q^71 - 12 * q^73 + 72 * q^75 - 8 * q^77 + 8 * q^79 + 24 * q^85 + 12 * q^87 - 12 * q^89 - 40 * q^91 + 20 * q^93 + 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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