LMFDB - Embedded newform 1148.2.r.a.737.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(81,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 3]))

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

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

chi := DirichletCharacter("1148.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.r (of order $6$, degree $2$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			737.24
Character	$\chi$	$=$	1148.737
Dual form			1148.2.r.a.81.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.85927 - 1.07345i) q^{3} +(-0.972000 + 1.68355i) q^{5} +(1.16501 + 2.37545i) q^{7} +(0.804601 - 1.39361i) q^{9} +O(q^{10})$	\(q+(1.85927 - 1.07345i) q^{3} +(-0.972000 + 1.68355i) q^{5} +(1.16501 + 2.37545i) q^{7} +(0.804601 - 1.39361i) q^{9} +(-3.48169 + 2.01016i) q^{11} -1.38678i q^{13} +4.17359i q^{15} +(-2.82805 + 1.63278i) q^{17} +(4.09518 + 2.36435i) q^{19} +(4.71600 + 3.16604i) q^{21} +(0.698324 - 1.20953i) q^{23} +(0.610431 + 1.05730i) q^{25} +2.98591i q^{27} +3.17620i q^{29} +(3.80632 + 6.59273i) q^{31} +(-4.31562 + 7.47487i) q^{33} +(-5.13158 - 0.347589i) q^{35} +(1.38004 - 2.39031i) q^{37} +(-1.48864 - 2.57840i) q^{39} +(-0.869811 - 6.34377i) q^{41} +3.50243 q^{43} +(1.56415 + 2.70918i) q^{45} +(-7.73364 - 4.46502i) q^{47} +(-4.28553 + 5.53482i) q^{49} +(-3.50542 + 6.07156i) q^{51} +(3.48036 - 2.00939i) q^{53} -7.81549i q^{55} +10.1521 q^{57} +(2.14618 + 3.71730i) q^{59} +(-0.617288 + 1.06917i) q^{61} +(4.24782 + 0.287727i) q^{63} +(2.33471 + 1.34795i) q^{65} +(-7.30674 + 4.21855i) q^{67} -2.99847i q^{69} -7.37753i q^{71} +(6.61501 + 11.4575i) q^{73} +(2.26992 + 1.31054i) q^{75} +(-8.83122 - 5.92875i) q^{77} +(-2.50173 - 1.44437i) q^{79} +(5.61904 + 9.73246i) q^{81} -6.06065 q^{83} -6.34824i q^{85} +(3.40950 + 5.90542i) q^{87} +(6.56019 + 3.78753i) q^{89} +(3.29422 - 1.61560i) q^{91} +(14.1540 + 8.17180i) q^{93} +(-7.96104 + 4.59631i) q^{95} -16.8727i q^{97} +6.46950i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) $ 56 * q + 4 * q^5 + 32 * q^9	$ 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) $ 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.85927	−	1.07345i	1.07345	−	0.619758i	0.144330	−	0.989530i	$-0.453897\pi$
$3$	1.85927	−	1.07345i	1.07345	−	0.619758i	0.929123	+	0.369771i	$0.120564\pi$
$4$		0			0
$5$	−0.972000	+	1.68355i	−0.434692	+	0.752908i	−0.997270	−	0.0738355i	$-0.976476\pi$
$5$	−0.972000	+	1.68355i	−0.434692	+	0.752908i	0.562579	+	0.826744i	$0.309809\pi$
$6$		0			0
$7$	1.16501	+	2.37545i	0.440331	+	0.897836i
$7$	1.16501	+	2.37545i	0.440331	+	0.897836i
$8$		0			0
$9$	0.804601	−	1.39361i	0.268200	−	0.464537i
$10$		0			0
$11$	−3.48169	+	2.01016i	−1.04977	+	0.606085i	−0.922585	−	0.385794i	$-0.873928\pi$
$11$	−3.48169	+	2.01016i	−1.04977	+	0.606085i	−0.127185	+	0.991879i	$0.540594\pi$
$12$		0			0
$13$		−	1.38678i		−	0.384623i	−0.981334	−	0.192311i	$-0.938402\pi$
$13$		−	1.38678i		−	0.384623i	0.981334	−	0.192311i	$-0.0615983\pi$
$14$		0			0
$15$			4.17359i			1.07762i
$16$		0			0
$17$	−2.82805	+	1.63278i	−0.685904	+	0.396007i	−0.802076	−	0.597222i	$-0.796271\pi$
$17$	−2.82805	+	1.63278i	−0.685904	+	0.396007i	0.116172	+	0.993229i	$0.462938\pi$
$18$		0			0
$19$	4.09518	+	2.36435i	0.939499	+	0.542420i	0.889803	−	0.456344i	$-0.150841\pi$
$19$	4.09518	+	2.36435i	0.939499	+	0.542420i	0.0496959	+	0.998764i	$0.484175\pi$
$20$		0			0
$21$	4.71600	+	3.16604i	1.02912	+	0.690886i
$22$		0			0
$23$	0.698324	−	1.20953i	0.145611	−	0.252205i	−0.783990	−	0.620774i	$-0.786819\pi$
$23$	0.698324	−	1.20953i	0.145611	−	0.252205i	0.929601	+	0.368568i	$0.120152\pi$
$24$		0			0
$25$	0.610431	+	1.05730i	0.122086	+	0.211459i
$26$		0			0
$27$			2.98591i			0.574639i
$28$		0			0
$29$			3.17620i			0.589805i	0.955527	+	0.294903i	$0.0952872\pi$
$29$			3.17620i			0.589805i	−0.955527	+	0.294903i	$0.904713\pi$
$30$		0			0
$31$	3.80632	+	6.59273i	0.683635	+	1.18409i	0.973864	+	0.227133i	$0.0729352\pi$
$31$	3.80632	+	6.59273i	0.683635	+	1.18409i	−0.290229	+	0.956957i	$0.593732\pi$
$32$		0			0
$33$	−4.31562	+	7.47487i	−0.751253	+	1.30121i
$34$		0			0
$35$	−5.13158	−	0.347589i	−0.867396	−	0.0587533i
$36$		0			0
$37$	1.38004	−	2.39031i	0.226878	−	0.392964i	−0.730003	−	0.683444i	$-0.760481\pi$
$37$	1.38004	−	2.39031i	0.226878	−	0.392964i	0.956881	+	0.290479i	$0.0938148\pi$
$38$		0			0
$39$	−1.48864	−	2.57840i	−0.238373	−	0.412874i
$40$		0			0
$41$	−0.869811	−	6.34377i	−0.135842	−	0.990731i
$41$	−0.869811	−	6.34377i	−0.135842	−	0.990731i
$42$		0			0
$43$	3.50243			0.534115			0.267057	−	0.963681i	$-0.413949\pi$
$43$	3.50243			0.534115			0.267057	+	0.963681i	$0.413949\pi$
$44$		0			0
$45$	1.56415	+	2.70918i	0.233169	+	0.403861i
$46$		0			0
$47$	−7.73364	−	4.46502i	−1.12807	−	0.651290i	−0.184620	−	0.982810i	$-0.559105\pi$
$47$	−7.73364	−	4.46502i	−1.12807	−	0.651290i	−0.943448	+	0.331520i	$0.892439\pi$
$48$		0			0
$49$	−4.28553	+	5.53482i	−0.612218	+	0.790689i
$50$		0			0
$51$	−3.50542	+	6.07156i	−0.490857	+	0.850189i
$52$		0			0
$53$	3.48036	−	2.00939i	0.478065	−	0.276011i	−0.241545	−	0.970390i	$-0.577654\pi$
$53$	3.48036	−	2.00939i	0.478065	−	0.276011i	0.719610	+	0.694379i	$0.244321\pi$
$54$		0			0
$55$		−	7.81549i		−	1.05384i
$56$		0			0
$57$	10.1521			1.34468
$58$		0			0
$59$	2.14618	+	3.71730i	0.279409	+	0.483951i	0.971238	−	0.238110i	$-0.0765280\pi$
$59$	2.14618	+	3.71730i	0.279409	+	0.483951i	−0.691829	+	0.722062i	$0.743195\pi$
$60$		0			0
$61$	−0.617288	+	1.06917i	−0.0790356	+	0.136894i	−0.902834	−	0.429989i	$-0.858517\pi$
$61$	−0.617288	+	1.06917i	−0.0790356	+	0.136894i	0.823798	+	0.566883i	$0.191851\pi$
$62$		0			0
$63$	4.24782	+	0.287727i	0.535175	+	0.0362502i
$64$		0			0
$65$	2.33471	+	1.34795i	0.289585	+	0.167192i
$66$		0			0
$67$	−7.30674	+	4.21855i	−0.892661	+	0.515378i	−0.874812	−	0.484463i	$-0.839015\pi$
$67$	−7.30674	+	4.21855i	−0.892661	+	0.515378i	−0.0178490	+	0.999841i	$0.505682\pi$
$68$		0			0
$69$		−	2.99847i		−	0.360974i
$70$		0			0
$71$		−	7.37753i		−	0.875552i	−0.899084	−	0.437776i	$-0.855766\pi$
$71$		−	7.37753i		−	0.875552i	0.899084	−	0.437776i	$-0.144234\pi$
$72$		0			0
$73$	6.61501	+	11.4575i	0.774228	+	1.34100i	0.935227	+	0.354048i	$0.115195\pi$
$73$	6.61501	+	11.4575i	0.774228	+	1.34100i	−0.160999	+	0.986955i	$0.551472\pi$
$74$		0			0
$75$	2.26992	+	1.31054i	0.262107	+	0.151328i
$76$		0			0
$77$	−8.83122	−	5.92875i	−1.00641	−	0.675644i
$78$		0			0
$79$	−2.50173	−	1.44437i	−0.281466	−	0.162505i	0.352621	−	0.935766i	$-0.385291\pi$
$79$	−2.50173	−	1.44437i	−0.281466	−	0.162505i	−0.634087	+	0.773262i	$0.718624\pi$
$80$		0			0
$81$	5.61904	+	9.73246i	0.624337	+	1.08138i
$82$		0			0
$83$	−6.06065			−0.665243			−0.332621	−	0.943060i	$-0.607933\pi$
$83$	−6.06065			−0.665243			−0.332621	+	0.943060i	$0.607933\pi$
$84$		0			0
$85$		−	6.34824i		−	0.688563i
$86$		0			0
$87$	3.40950	+	5.90542i	0.365537	+	0.633128i
$88$		0			0
$89$	6.56019	+	3.78753i	0.695379	+	0.401477i	0.805624	−	0.592427i	$-0.201830\pi$
$89$	6.56019	+	3.78753i	0.695379	+	0.401477i	−0.110245	+	0.993904i	$0.535164\pi$
$90$		0			0
$91$	3.29422	−	1.61560i	0.345328	−	0.169361i
$92$		0			0
$93$	14.1540	+	8.17180i	1.46770	+	0.847376i
$94$		0			0
$95$	−7.96104	+	4.59631i	−0.816785	+	0.471571i
$96$		0			0
$97$		−	16.8727i		−	1.71316i	−0.516015	−	0.856580i	$-0.672585\pi$
$97$		−	16.8727i		−	1.71316i	0.516015	−	0.856580i	$-0.327415\pi$
$98$		0			0
$99$			6.46950i			0.650209i
$100$		0			0
$101$	7.31156	−	4.22133i	0.727527	−	0.420038i	−0.0899896	−	0.995943i	$-0.528683\pi$
$101$	7.31156	−	4.22133i	0.727527	−	0.420038i	0.817517	+	0.575905i	$0.195350\pi$
$102$		0			0
$103$	9.92627	−	17.1928i	0.978064	−	1.69406i	0.308635	−	0.951180i	$-0.400128\pi$
$103$	9.92627	−	17.1928i	0.978064	−	1.69406i	0.669429	−	0.742876i	$-0.266539\pi$
$104$		0			0
$105$	−9.91414	+	4.86225i	−0.967521	+	0.474507i
$106$		0			0
$107$	6.64411	−	11.5079i	0.642310	−	1.11251i	−0.342606	−	0.939479i	$-0.611309\pi$
$107$	6.64411	−	11.5079i	0.642310	−	1.11251i	0.984916	−	0.173034i	$-0.0553572\pi$
$108$		0			0
$109$	0.359863	−	0.207767i	0.0344686	−	0.0199005i	−0.482667	−	0.875804i	$-0.660332\pi$
$109$	0.359863	−	0.207767i	0.0344686	−	0.0199005i	0.517135	+	0.855904i	$0.326998\pi$
$110$		0			0
$111$		−	5.92565i		−	0.562438i
$112$		0			0
$113$	19.8318			1.86562			0.932810	−	0.360369i	$-0.117349\pi$
$113$	19.8318			1.86562			0.932810	+	0.360369i	$0.117349\pi$
$114$		0			0
$115$	1.35754	+	2.35133i	0.126591	+	0.219263i
$116$		0			0
$117$	−1.93263	−	1.11580i	−0.178671	−	0.103156i
$118$		0			0
$119$	−7.17328	−	4.81571i	−0.657573	−	0.441455i
$120$		0			0
$121$	2.58147	−	4.47123i	0.234679	−	0.406475i
$122$		0			0
$123$	−8.42696	−	10.8611i	−0.759833	−	0.979313i
$124$		0			0
$125$	−12.0934			−1.08166
$126$		0			0
$127$	−0.218837			−0.0194187			−0.00970934	−	0.999953i	$-0.503091\pi$
$127$	−0.218837			−0.0194187			−0.00970934	+	0.999953i	$0.503091\pi$
$128$		0			0
$129$	6.51197	−	3.75969i	0.573347	−	0.331022i
$130$		0			0
$131$	2.72395	−	4.71802i	0.237992	−	0.412215i	−0.722146	−	0.691741i	$-0.756844\pi$
$131$	2.72395	−	4.71802i	0.237992	−	0.412215i	0.960138	+	0.279526i	$0.0901773\pi$
$132$		0			0
$133$	−0.845498	+	12.4824i	−0.0733140	+	1.08236i
$134$		0			0
$135$	−5.02694	−	2.90231i	−0.432650	−	0.249791i
$136$		0			0
$137$	−8.55424	+	4.93879i	−0.730838	+	0.421949i	−0.818729	−	0.574181i	$-0.805321\pi$
$137$	−8.55424	+	4.93879i	−0.730838	+	0.421949i	0.0878908	+	0.996130i	$0.471987\pi$
$138$		0			0
$139$	14.7495			1.25104			0.625520	−	0.780208i	$-0.284887\pi$
$139$	14.7495			1.25104			0.625520	+	0.780208i	$0.284887\pi$
$140$		0			0
$141$	−19.1720			−1.61457
$142$		0			0
$143$	2.78764	+	4.82833i	0.233114	+	0.403765i
$144$		0			0
$145$	−5.34730	−	3.08726i	−0.444069	−	0.256383i
$146$		0			0
$147$	−2.02660	+	14.8911i	−0.167151	+	1.22819i
$148$		0			0
$149$	−6.16314	−	3.55829i	−0.504904	−	0.291506i	0.225833	−	0.974166i	$-0.427490\pi$
$149$	−6.16314	−	3.55829i	−0.504904	−	0.291506i	−0.730736	+	0.682660i	$0.760823\pi$
$150$		0			0
$151$	0.394483	−	0.227755i	0.0321026	−	0.0185344i	−0.483863	−	0.875144i	$-0.660767\pi$
$151$	0.394483	−	0.227755i	0.0321026	−	0.0185344i	0.515965	+	0.856609i	$0.327433\pi$
$152$		0			0
$153$			5.25494i			0.424837i
$154$		0			0
$155$	−14.7990			−1.18868
$156$		0			0
$157$	−20.0418	+	11.5711i	−1.59951	+	0.923475i	−0.607924	+	0.793995i	$0.707998\pi$
$157$	−20.0418	+	11.5711i	−1.59951	+	0.923475i	−0.991582	+	0.129480i	$0.958669\pi$
$158$		0			0
$159$	4.31397	−	7.47201i	0.342120	−	0.592569i
$160$		0			0
$161$	3.68674	+	0.249722i	0.290556	+	0.0196809i
$162$		0			0
$163$	1.70859	−	2.95937i	0.133827	−	0.231796i	−0.791322	−	0.611400i	$-0.790607\pi$
$163$	1.70859	−	2.95937i	0.133827	−	0.231796i	0.925149	+	0.379604i	$0.123940\pi$
$164$		0			0
$165$	−8.38956	−	14.5312i	−0.653127	−	1.13125i
$166$		0			0
$167$		−	2.79306i		−	0.216133i	−0.994144	−	0.108067i	$-0.965534\pi$
$167$		−	2.79306i		−	0.216133i	0.994144	−	0.108067i	$-0.0344660\pi$
$168$		0			0
$169$	11.0769			0.852065
$170$		0			0
$171$	6.58998	−	3.80473i	0.503948	−	0.290955i
$172$		0			0
$173$	1.95912	−	3.39330i	0.148950	−	0.257988i	−0.781890	−	0.623416i	$-0.785744\pi$
$173$	1.95912	−	3.39330i	0.148950	−	0.257988i	0.930839	+	0.365428i	$0.119077\pi$
$174$		0			0
$175$	−1.80040	+	2.68180i	−0.136098	+	0.202725i
$176$		0			0
$177$	7.98069	+	4.60765i	0.599865	+	0.346332i
$178$		0			0
$179$	−1.07193	+	0.618881i	−0.0801201	+	0.0462574i	−0.539525	−	0.841970i	$-0.681396\pi$
$179$	−1.07193	+	0.618881i	−0.0801201	+	0.0462574i	0.459405	+	0.888227i	$0.348063\pi$
$180$		0			0
$181$		−	0.242332i		−	0.0180124i	−0.999959	−	0.00900619i	$-0.997133\pi$
$181$		−	0.242332i		−	0.0180124i	0.999959	−	0.00900619i	$-0.00286680\pi$
$182$		0			0
$183$			2.65052i			0.195932i
$184$		0			0
$185$	2.68281	+	4.64676i	0.197244	+	0.341637i
$186$		0			0
$187$	6.56428	−	11.3697i	0.480028	−	0.831432i
$188$		0			0
$189$	−7.09288	+	3.47860i	−0.515931	+	0.253031i
$190$		0			0
$191$	12.3649	+	7.13886i	0.894690	+	0.516550i	0.875474	−	0.483266i	$-0.160549\pi$
$191$	12.3649	+	7.13886i	0.894690	+	0.516550i	0.0192167	+	0.999815i	$0.493883\pi$
$192$		0			0
$193$	−10.1874	+	5.88169i	−0.733303	+	0.423373i	−0.819629	−	0.572894i	$-0.805821\pi$
$193$	−10.1874	+	5.88169i	−0.733303	+	0.423373i	0.0863260	+	0.996267i	$0.472487\pi$
$194$		0			0
$195$	5.78783			0.414475
$196$		0			0
$197$	−20.9562			−1.49307			−0.746535	−	0.665346i	$-0.768284\pi$
$197$	−20.9562			−1.49307			−0.746535	+	0.665346i	$0.768284\pi$
$198$		0			0
$199$	9.86438	−	5.69520i	0.699268	−	0.403722i	−0.107807	−	0.994172i	$-0.534383\pi$
$199$	9.86438	−	5.69520i	0.699268	−	0.403722i	0.807075	+	0.590450i	$0.201050\pi$
$200$		0			0
$201$	−9.05683	+	15.6869i	−0.638820	+	1.10647i
$202$		0			0
$203$	−7.54490	+	3.70029i	−0.529548	+	0.259709i
$204$		0			0
$205$	11.5255	+	4.70177i	0.804978	+	0.328386i
$206$		0			0
$207$	−1.12375	−	1.94638i	−0.0781057	−	0.135283i
$208$		0			0
$209$	−19.0109			−1.31501
$210$		0			0
$211$		−	4.98341i		−	0.343072i	−0.985178	−	0.171536i	$-0.945127\pi$
$211$		−	4.98341i		−	0.343072i	0.985178	−	0.171536i	$-0.0548730\pi$
$212$		0			0
$213$	−7.91943	−	13.7169i	−0.542631	−	0.939864i
$214$		0			0
$215$	−3.40436	+	5.89652i	−0.232175	+	0.402139i
$216$		0			0
$217$	−11.2263	+	16.7223i	−0.762093	+	1.13518i
$218$		0			0
$219$	24.5982	+	14.2018i	1.66220	+	0.959669i
$220$		0			0
$221$	2.26430	+	3.92188i	0.152313	+	0.263814i
$222$		0			0
$223$	−8.07316			−0.540619			−0.270309	−	0.962773i	$-0.587126\pi$
$223$	−8.07316			−0.540619			−0.270309	+	0.962773i	$0.587126\pi$
$224$		0			0
$225$	1.96461			0.130974
$226$		0			0
$227$	−2.35291	+	1.35845i	−0.156168	+	0.0901636i	−0.576047	−	0.817416i	$-0.695406\pi$
$227$	−2.35291	+	1.35845i	−0.156168	+	0.0901636i	0.419880	+	0.907580i	$0.362072\pi$
$228$		0			0
$229$	−17.1060	−	9.87613i	−1.13039	−	0.652633i	−0.186360	−	0.982482i	$-0.559669\pi$
$229$	−17.1060	−	9.87613i	−1.13039	−	0.652633i	−0.944034	+	0.329849i	$0.893002\pi$
$230$		0			0
$231$	−22.7839	−	1.54327i	−1.49907	−	0.101540i
$232$		0			0
$233$	23.9556	+	13.8308i	1.56939	+	0.906086i	0.996240	+	0.0866327i	$0.0276107\pi$
$233$	23.9556	+	13.8308i	1.56939	+	0.906086i	0.573146	+	0.819453i	$0.305723\pi$
$234$		0			0
$235$	15.0342	−	8.68001i	0.980724	−	0.566221i
$236$		0			0
$237$	−6.20187			−0.402854
$238$		0			0
$239$		−	17.3223i		−	1.12049i	−0.828327	−	0.560244i	$-0.810707\pi$
$239$		−	17.3223i		−	1.12049i	0.828327	−	0.560244i	$-0.189293\pi$
$240$		0			0
$241$	−12.2165	−	21.1595i	−0.786931	−	1.36301i	−0.927838	−	0.372982i	$-0.878335\pi$
$241$	−12.2165	−	21.1595i	−0.786931	−	1.36301i	0.140907	−	0.990023i	$-0.454998\pi$
$242$		0			0
$243$	13.1370	+	7.58468i	0.842742	+	0.486557i
$244$		0			0
$245$	−5.15264	−	12.5948i	−0.329190	−	0.804650i
$246$		0			0
$247$	3.27883	−	5.67910i	0.208627	−	0.361353i
$248$		0			0
$249$	−11.2684	+	6.50582i	−0.714106	+	0.412290i
$250$		0			0
$251$	12.2198			0.771305			0.385653	−	0.922644i	$-0.373976\pi$
$251$	12.2198			0.771305			0.385653	+	0.922644i	$0.373976\pi$
$252$		0			0
$253$			5.61497i			0.353010i
$254$		0			0
$255$	−6.81454	−	11.8031i	−0.426743	−	0.739140i
$256$		0			0
$257$	−14.3021	−	8.25729i	−0.892138	−	0.515076i	−0.0174965	−	0.999847i	$-0.505570\pi$
$257$	−14.3021	−	8.25729i	−0.892138	−	0.515076i	−0.874641	+	0.484771i	$0.838903\pi$
$258$		0			0
$259$	7.28582	+	0.493507i	0.452719	+	0.0306650i
$260$		0			0
$261$	4.42638	+	2.55557i	0.273986	+	0.158186i
$262$		0			0
$263$	5.15109	−	2.97399i	0.317630	−	0.183384i	−0.332706	−	0.943031i	$-0.607962\pi$
$263$	5.15109	−	2.97399i	0.317630	−	0.183384i	0.650336	+	0.759647i	$0.274628\pi$
$264$		0			0
$265$			7.81251i			0.479918i
$266$		0			0
$267$	16.2629			0.995275
$268$		0			0
$269$	−0.746310	−	1.29265i	−0.0455033	−	0.0788141i	0.842377	−	0.538889i	$-0.181156\pi$
$269$	−0.746310	−	1.29265i	−0.0455033	−	0.0788141i	−0.887880	+	0.460075i	$0.847822\pi$
$270$		0			0
$271$	9.07756	−	15.7228i	0.551423	−	0.955092i	−0.446749	−	0.894659i	$-0.647418\pi$
$271$	9.07756	−	15.7228i	0.551423	−	0.955092i	0.998172	−	0.0604332i	$-0.0192482\pi$
$272$		0			0
$273$	4.39058	−	6.54003i	0.265730	−	0.395821i
$274$		0			0
$275$	−4.25067	−	2.45412i	−0.256325	−	0.147989i
$276$		0			0
$277$	10.8244	+	18.7484i	0.650374	+	1.12648i	0.983032	+	0.183433i	$0.0587211\pi$
$277$	10.8244	+	18.7484i	0.650374	+	1.12648i	−0.332658	+	0.943047i	$0.607946\pi$
$278$		0			0
$279$	12.2503			0.733405
$280$		0			0
$281$			18.3276i			1.09333i	0.837351	+	0.546666i	$0.184103\pi$
$281$			18.3276i			1.09333i	−0.837351	+	0.546666i	$0.815897\pi$
$282$		0			0
$283$	5.77121	+	9.99603i	0.343063	+	0.594202i	0.985000	−	0.172555i	$-0.0552023\pi$
$283$	5.77121	+	9.99603i	0.343063	+	0.594202i	−0.641937	+	0.766757i	$0.721869\pi$
$284$		0			0
$285$	−9.86783	+	17.0916i	−0.584520	+	1.01242i
$286$		0			0
$287$	14.0560	−	9.45672i	0.829698	−	0.558212i
$288$		0			0
$289$	−3.16808	+	5.48727i	−0.186357	+	0.322780i
$290$		0			0
$291$	−18.1120	−	31.3709i	−1.06174	−	1.83900i
$292$		0			0
$293$		−	3.09973i		−	0.181088i	−0.995892	−	0.0905439i	$-0.971139\pi$
$293$		−	3.09973i		−	0.181088i	0.995892	−	0.0905439i	$-0.0288606\pi$
$294$		0			0
$295$	−8.34437			−0.485828
$296$		0			0
$297$	−6.00215	−	10.3960i	−0.348280	−	0.603239i
$298$		0			0
$299$	−1.67735	−	0.968419i	−0.0970037	−	0.0560051i
$300$		0			0
$301$	4.08034	+	8.31984i	0.235187	+	0.479547i
$302$		0			0
$303$	9.06280	−	15.6972i	0.520644	−	0.901782i
$304$		0			0
$305$	−1.20001	−	2.07848i	−0.0687123	−	0.119013i
$306$		0			0
$307$	−25.9881			−1.48322			−0.741609	−	0.670832i	$-0.765937\pi$
$307$	−25.9881			−1.48322			−0.741609	+	0.670832i	$0.765937\pi$
$308$		0			0
$309$		−	42.6215i		−	2.42465i
$310$		0			0
$311$	12.1826	−	7.03362i	0.690811	−	0.398840i	−0.113105	−	0.993583i	$-0.536080\pi$
$311$	12.1826	−	7.03362i	0.690811	−	0.398840i	0.803916	+	0.594743i	$0.202746\pi$
$312$		0			0
$313$	−4.31232	−	2.48972i	−0.243747	−	0.140727i	0.373151	−	0.927771i	$-0.378277\pi$
$313$	−4.31232	−	2.48972i	−0.243747	−	0.140727i	−0.616898	+	0.787043i	$0.711611\pi$
$314$		0			0
$315$	−4.61328	+	6.87176i	−0.259929	+	0.387180i
$316$		0			0
$317$	−5.16997	−	2.98488i	−0.290375	−	0.167648i	0.347736	−	0.937592i	$-0.386950\pi$
$317$	−5.16997	−	2.98488i	−0.290375	−	0.167648i	−0.638111	+	0.769945i	$0.720284\pi$
$318$		0			0
$319$	−6.38466	−	11.0585i	−0.357472	−	0.619160i
$320$		0			0
$321$		−	28.5285i		−	1.59231i
$322$		0			0
$323$	−15.4419			−0.859208
$324$		0			0
$325$	1.46623	−	0.846531i	0.0813321	−	0.0469571i
$326$		0			0
$327$	0.446056	−	0.772592i	0.0246670	−	0.0427244i
$328$		0			0
$329$	1.59670	−	23.5727i	0.0880290	−	1.29960i
$330$		0			0
$331$	0.322867	+	0.186407i	0.0177463	+	0.0102459i	0.508847	−	0.860857i	$-0.330072\pi$
$331$	0.322867	+	0.186407i	0.0177463	+	0.0102459i	−0.491101	+	0.871103i	$0.663405\pi$
$332$		0			0
$333$	−2.22077	−	3.84649i	−0.121698	−	0.210786i
$334$		0			0
$335$		−	16.4017i		−	0.896122i
$336$		0			0
$337$	26.1947			1.42692			0.713458	−	0.700698i	$-0.247128\pi$
$337$	26.1947			1.42692			0.713458	+	0.700698i	$0.247128\pi$
$338$		0			0
$339$	36.8728	−	21.2885i	2.00265	−	1.15623i
$340$		0			0
$341$	−26.5049	−	15.3026i	−1.43532	−	0.828682i
$342$		0			0
$343$	−18.1404	−	3.73196i	−0.979487	−	0.201507i
$344$		0			0
$345$	5.04809	+	2.91452i	0.271780	+	0.156912i
$346$		0			0
$347$	−11.1645	+	6.44584i	−0.599343	+	0.346031i	−0.768783	−	0.639510i	$-0.779137\pi$
$347$	−11.1645	+	6.44584i	−0.599343	+	0.346031i	0.169440	+	0.985540i	$0.445804\pi$
$348$		0			0
$349$	16.5220			0.884403			0.442202	−	0.896916i	$-0.354198\pi$
$349$	16.5220			0.884403			0.442202	+	0.896916i	$0.354198\pi$
$350$		0			0
$351$	4.14079			0.221019
$352$		0			0
$353$	3.75477	+	6.50346i	0.199846	+	0.346144i	0.948479	−	0.316841i	$-0.102622\pi$
$353$	3.75477	+	6.50346i	0.199846	+	0.346144i	−0.748632	+	0.662986i	$0.769289\pi$
$354$		0			0
$355$	12.4205	+	7.17096i	0.659210	+	0.380595i
$356$		0			0
$357$	−18.5065	−	1.25355i	−0.979469	−	0.0663447i
$358$		0			0
$359$	−3.17549	+	5.50011i	−0.167596	+	0.290285i	−0.937574	−	0.347786i	$-0.886934\pi$
$359$	−3.17549	+	5.50011i	−0.167596	+	0.290285i	0.769978	+	0.638070i	$0.220267\pi$
$360$		0			0
$361$	1.68034	+	2.91044i	0.0884391	+	0.153181i
$362$		0			0
$363$		−	11.0843i		−	0.581776i
$364$		0			0
$365$	−25.7192			−1.34620
$366$		0			0
$367$	−8.18681	−	14.1800i	−0.427348	−	0.740188i	0.569289	−	0.822138i	$-0.307219\pi$
$367$	−8.18681	−	14.1800i	−0.427348	−	0.740188i	−0.996636	+	0.0819496i	$0.973885\pi$
$368$		0			0
$369$	−9.54060	−	3.89203i	−0.496664	−	0.202611i
$370$		0			0
$371$	8.82784	+	5.92648i	0.458319	+	0.307688i
$372$		0			0
$373$	−4.61289	+	7.98977i	−0.238847	+	0.413694i	−0.960384	−	0.278681i	$-0.910103\pi$
$373$	−4.61289	+	7.98977i	−0.238847	+	0.413694i	0.721537	+	0.692376i	$0.243436\pi$
$374$		0			0
$375$	−22.4849	+	12.9816i	−1.16111	+	0.670369i
$376$		0			0
$377$	4.40468			0.226852
$378$		0			0
$379$	35.6769			1.83260			0.916299	−	0.400495i	$-0.131162\pi$
$379$	35.6769			1.83260			0.916299	+	0.400495i	$0.131162\pi$
$380$		0			0
$381$	−0.406879	+	0.234912i	−0.0208450	+	0.0120349i
$382$		0			0
$383$	−11.3121	−	6.53104i	−0.578021	−	0.333721i	0.182325	−	0.983238i	$-0.441638\pi$
$383$	−11.3121	−	6.53104i	−0.578021	−	0.333721i	−0.760347	+	0.649518i	$0.774971\pi$
$384$		0			0
$385$	18.5653	−	9.10509i	0.946176	−	0.464038i
$386$		0			0
$387$	2.81806	−	4.88102i	0.143250	−	0.248116i
$388$		0			0
$389$	0.680975	+	1.17948i	0.0345268	+	0.0598022i	0.882772	−	0.469801i	$-0.155674\pi$
$389$	0.680975	+	1.17948i	0.0345268	+	0.0598022i	−0.848246	+	0.529603i	$0.822341\pi$
$390$		0			0
$391$			4.56083i			0.230651i
$392$		0			0
$393$		−	11.6961i		−	0.589991i
$394$		0			0
$395$	4.86336	−	2.80786i	0.244702	−	0.141279i
$396$		0			0
$397$	22.5030	+	12.9921i	1.12939	+	0.652056i	0.943783	−	0.330567i	$-0.107240\pi$
$397$	22.5030	+	12.9921i	1.12939	+	0.652056i	0.185612	+	0.982623i	$0.440573\pi$
$398$		0			0
$399$	11.8272	+	24.1158i	0.592102	+	1.20730i
$400$		0			0
$401$	−9.59516	+	16.6193i	−0.479160	+	0.829929i	−0.999714	−	0.0238994i	$-0.992392\pi$
$401$	−9.59516	+	16.6193i	−0.479160	+	0.829929i	0.520555	+	0.853828i	$0.325725\pi$
$402$		0			0
$403$	9.14265	−	5.27851i	0.455428	−	0.262941i
$404$		0			0
$405$	−21.8468			−1.08558
$406$		0			0
$407$			11.0964i			0.550030i
$408$		0			0
$409$	2.65341	+	4.59585i	0.131203	+	0.227250i	0.924141	−	0.382053i	$-0.124783\pi$
$409$	2.65341	+	4.59585i	0.131203	+	0.227250i	−0.792938	+	0.609303i	$0.791449\pi$
$410$		0			0
$411$	−10.6031	+	18.3651i	−0.523013	+	0.905885i
$412$		0			0
$413$	−6.32995	+	9.42883i	−0.311476	+	0.463962i
$414$		0			0
$415$	5.89095	−	10.2034i	0.289175	−	0.500867i
$416$		0			0
$417$	27.4235	−	15.8329i	1.34293	−	0.775342i
$418$		0			0
$419$	−15.8813			−0.775854			−0.387927	−	0.921690i	$-0.626809\pi$
$419$	−15.8813			−0.775854			−0.387927	+	0.921690i	$0.626809\pi$
$420$		0			0
$421$		−	0.960498i		−	0.0468118i	−0.999726	−	0.0234059i	$-0.992549\pi$
$421$		−	0.960498i		−	0.0468118i	0.999726	−	0.0234059i	$-0.00745101\pi$
$422$		0			0
$423$	−12.4450	+	7.18513i	−0.605097	+	0.349353i
$424$		0			0
$425$	−3.45266	−	1.99340i	−0.167479	−	0.0966939i
$426$		0			0
$427$	−3.25891	−	0.220744i	−0.157710	−	0.0106825i
$428$		0			0
$429$	10.3660	+	5.98480i	0.500474	+	0.288949i
$430$		0			0
$431$	9.22972	+	15.9863i	0.444580	+	0.770035i	0.998023	−	0.0628521i	$-0.0200196\pi$
$431$	9.22972	+	15.9863i	0.444580	+	0.770035i	−0.553443	+	0.832887i	$0.686686\pi$
$432$		0			0
$433$	21.4665			1.03162			0.515808	−	0.856705i	$-0.327492\pi$
$433$	21.4665			1.03162			0.515808	+	0.856705i	$0.327492\pi$
$434$		0			0
$435$	−13.2561			−0.635583
$436$		0			0
$437$	5.71953	−	3.30217i	0.273602	−	0.157964i
$438$		0			0
$439$	−13.6558	−	7.88418i	−0.651755	−	0.376291i	0.137373	−	0.990519i	$-0.456134\pi$
$439$	−13.6558	−	7.88418i	−0.651755	−	0.376291i	−0.789128	+	0.614228i	$0.789467\pi$
$440$		0			0
$441$	4.26525	+	10.4257i	0.203107	+	0.496461i
$442$		0			0
$443$	−8.88460	+	15.3886i	−0.422120	+	0.731134i	−0.996147	−	0.0877030i	$-0.972047\pi$
$443$	−8.88460	+	15.3886i	−0.422120	+	0.731134i	0.574026	+	0.818837i	$0.305381\pi$
$444$		0			0
$445$	−12.7530	+	7.36295i	−0.604551	+	0.349038i
$446$		0			0
$447$	−15.2786			−0.722654
$448$		0			0
$449$	17.6809			0.834412			0.417206	−	0.908812i	$-0.363009\pi$
$449$	17.6809			0.834412			0.417206	+	0.908812i	$0.363009\pi$
$450$		0			0
$451$	15.7804	+	20.3386i	0.743070	+	0.957708i
$452$		0			0
$453$	0.488968	−	0.846917i	0.0229737	−	0.0397917i
$454$		0			0
$455$	−0.482029	+	7.11636i	−0.0225979	+	0.333620i
$456$		0			0
$457$	2.60040	+	1.50134i	0.121642	+	0.0702298i	0.559586	−	0.828772i	$-0.310960\pi$
$457$	2.60040	+	1.50134i	0.121642	+	0.0702298i	−0.437945	+	0.899002i	$0.644293\pi$
$458$		0			0
$459$	−4.87533	−	8.44431i	−0.227561	−	0.394147i
$460$		0			0
$461$	29.1015			1.35539			0.677696	−	0.735342i	$-0.262978\pi$
$461$	29.1015			1.35539			0.677696	+	0.735342i	$0.262978\pi$
$462$		0			0
$463$			1.58251i			0.0735454i	0.999324	+	0.0367727i	$0.0117078\pi$
$463$			1.58251i			0.0735454i	−0.999324	+	0.0367727i	$0.988292\pi$
$464$		0			0
$465$	−27.5153	+	15.8860i	−1.27599	+	0.736695i
$466$		0			0
$467$	10.5928	−	18.3473i	0.490178	−	0.849013i	−0.509758	−	0.860318i	$-0.670265\pi$
$467$	10.5928	−	18.3473i	0.490178	−	0.849013i	0.999936	+	0.0113050i	$0.00359858\pi$
$468$		0			0
$469$	−18.5334	−	12.4422i	−0.855791	−	0.574526i
$470$		0			0
$471$	−24.8421	+	43.0278i	−1.14466	+	1.98261i
$472$		0			0
$473$	−12.1944	+	7.04043i	−0.560698	+	0.323719i
$474$		0			0
$475$			5.77310i			0.264888i
$476$		0			0
$477$		−	6.46703i		−	0.296105i
$478$		0			0
$479$	36.6350	−	21.1512i	1.67389	−	0.966423i	0.708469	−	0.705742i	$-0.249386\pi$
$479$	36.6350	−	21.1512i	1.67389	−	0.966423i	0.965425	−	0.260681i	$-0.0839472\pi$
$480$		0			0
$481$	−3.31482	−	1.91381i	−0.151143	−	0.0872624i
$482$		0			0
$483$	7.12272	−	3.49323i	0.324095	−	0.158948i
$484$		0			0
$485$	28.4060	+	16.4002i	1.28985	+	0.744696i
$486$		0			0
$487$	2.67577	+	4.63457i	0.121251	+	0.210012i	0.920261	−	0.391305i	$-0.127976\pi$
$487$	2.67577	+	4.63457i	0.121251	+	0.210012i	−0.799010	+	0.601317i	$0.794643\pi$
$488$		0			0
$489$		−	7.33637i		−	0.331762i
$490$		0			0
$491$	−32.7571			−1.47831			−0.739155	−	0.673536i	$-0.764775\pi$
$491$	−32.7571			−1.47831			−0.739155	+	0.673536i	$0.764775\pi$
$492$		0			0
$493$	−5.18602	−	8.98246i	−0.233567	−	0.404549i
$494$		0			0
$495$	−10.8918	−	6.28836i	−0.489548	−	0.282641i
$496$		0			0
$497$	17.5250	−	8.59486i	0.786102	−	0.385532i
$498$		0			0
$499$	19.2834	+	11.1333i	0.863246	+	0.498395i	0.865098	−	0.501603i	$-0.167256\pi$
$499$	19.2834	+	11.1333i	0.863246	+	0.498395i	−0.00185220	+	0.999998i	$0.500590\pi$
$500$		0			0
$501$	−2.99821	−	5.19306i	−0.133950	−	0.232009i
$502$		0			0
$503$		−	7.44473i		−	0.331944i	−0.986130	−	0.165972i	$-0.946924\pi$
$503$		−	7.44473i		−	0.331944i	0.986130	−	0.165972i	$-0.0530762\pi$
$504$		0			0
$505$			16.4125i			0.730348i
$506$		0			0
$507$	20.5949	−	11.8905i	0.914652	−	0.528075i
$508$		0			0
$509$	−1.75049	−	1.01065i	−0.0775893	−	0.0447962i	0.460703	−	0.887554i	$-0.347597\pi$
$509$	−1.75049	−	1.01065i	−0.0775893	−	0.0447962i	−0.538293	+	0.842758i	$0.680931\pi$
$510$		0			0
$511$	−19.5103	+	29.0617i	−0.863084	+	1.28561i
$512$		0			0
$513$	−7.05975	+	12.2278i	−0.311696	+	0.539873i
$514$		0			0
$515$	19.2967	+	33.4228i	0.850313	+	1.47278i
$516$		0			0
$517$	35.9016			1.57895
$518$		0			0
$519$		−	8.41211i		−	0.369251i
$520$		0			0
$521$	−16.7917	+	9.69470i	−0.735658	+	0.424733i	−0.820489	−	0.571663i	$-0.806299\pi$
$521$	−16.7917	+	9.69470i	−0.735658	+	0.424733i	0.0848302	+	0.996395i	$0.472965\pi$
$522$		0			0
$523$	13.2360	−	22.9253i	0.578768	−	1.00246i	−0.416853	−	0.908974i	$-0.636867\pi$
$523$	13.2360	−	22.9253i	0.578768	−	1.00246i	0.995621	−	0.0934814i	$-0.0297996\pi$
$524$		0			0
$525$	−0.468651	+	6.91886i	−0.0204536	+	0.301964i
$526$		0			0
$527$	−21.5289	−	12.4297i	−0.937815	−	0.541448i
$528$		0			0
$529$	10.5247	+	18.2293i	0.457595	+	0.792578i
$530$		0			0
$531$	6.90729			0.299751
$532$		0			0
$533$	−8.79739	+	1.20623i	−0.381057	+	0.0522478i
$534$		0			0
$535$	12.9161	+	22.3714i	0.558414	+	0.967201i
$536$		0			0
$537$	−1.32868	+	2.30134i	−0.0573368	+	0.0993102i
$538$		0			0
$539$	3.79503	−	27.8851i	0.163464	−	1.20110i
$540$		0			0
$541$	−12.6246	+	21.8664i	−0.542774	+	0.940112i	0.455970	+	0.889995i	$0.349293\pi$
$541$	−12.6246	+	21.8664i	−0.542774	+	0.940112i	−0.998743	+	0.0501165i	$0.984041\pi$
$542$		0			0
$543$	−0.260132	−	0.450562i	−0.0111633	−	0.0193354i
$544$		0			0
$545$			0.807798i			0.0346023i
$546$		0			0
$547$			21.9017i			0.936450i	0.883609	+	0.468225i	$0.155106\pi$
$547$			21.9017i			0.936450i	−0.883609	+	0.468225i	$0.844894\pi$
$548$		0			0
$549$	0.993342	+	1.72052i	0.0423948	+	0.0734299i
$550$		0			0
$551$	−7.50966	+	13.0071i	−0.319922	+	0.554121i
$552$		0			0
$553$	0.516511	−	7.62543i	0.0219643	−	0.324266i
$554$		0			0
$555$	9.97615	+	5.75974i	0.423464	+	0.244487i
$556$		0			0
$557$	−10.3670	+	5.98541i	−0.439265	+	0.253610i	−0.703286	−	0.710907i	$-0.748285\pi$
$557$	−10.3670	+	5.98541i	−0.439265	+	0.253610i	0.264021	+	0.964517i	$0.414951\pi$
$558$		0			0
$559$		−	4.85708i		−	0.205433i
$560$		0			0
$561$		−	28.1858i		−	1.19000i
$562$		0			0
$563$	16.3174	−	9.42086i	0.687697	−	0.397042i	−0.115052	−	0.993359i	$-0.536703\pi$
$563$	16.3174	−	9.42086i	0.687697	−	0.397042i	0.802749	+	0.596318i	$0.203370\pi$
$564$		0			0
$565$	−19.2765	+	33.3879i	−0.810969	+	1.40464i
$566$		0			0
$567$	−16.5728	+	24.6861i	−0.695991	+	1.03672i
$568$		0			0
$569$	−15.9195	+	27.5733i	−0.667379	+	1.15593i	0.311255	+	0.950326i	$0.399251\pi$
$569$	−15.9195	+	27.5733i	−0.667379	+	1.15593i	−0.978634	+	0.205608i	$0.934083\pi$
$570$		0			0
$571$	29.9787	−	17.3082i	1.25457	−	0.724326i	0.282555	−	0.959251i	$-0.408818\pi$
$571$	29.9787	−	17.3082i	1.25457	−	0.724326i	0.972013	+	0.234925i	$0.0754846\pi$
$572$		0			0
$573$	30.6529			1.28054
$574$		0			0
$575$	1.70511			0.0711082
$576$		0			0
$577$	3.23982	−	1.87051i	0.134876	−	0.0778704i	−0.431044	−	0.902331i	$-0.641855\pi$
$577$	3.23982	−	1.87051i	0.134876	−	0.0778704i	0.565920	+	0.824460i	$0.308521\pi$
$578$		0			0
$579$	−12.6274	+	21.8713i	−0.524778	+	0.908942i
$580$		0			0
$581$	−7.06069	−	14.3968i	−0.292927	−	0.597279i
$582$		0			0
$583$	−8.07838	+	13.9922i	−0.334572	+	0.579496i
$584$		0			0
$585$	3.75703	−	2.16912i	0.155334	−	0.0896821i
$586$		0			0
$587$			23.8101i			0.982746i	0.870949	+	0.491373i	$0.163505\pi$
$587$			23.8101i			0.982746i	−0.870949	+	0.491373i	$0.836495\pi$
$588$		0			0
$589$			35.9979i			1.48327i
$590$		0			0
$591$	−38.9634	+	22.4955i	−1.60274	+	0.925343i
$592$		0			0
$593$	40.1531	+	23.1824i	1.64889	+	0.951986i	0.977515	+	0.210867i	$0.0676288\pi$
$593$	40.1531	+	23.1824i	1.64889	+	0.951986i	0.671374	+	0.741119i	$0.265705\pi$
$594$		0			0
$595$	15.0799	−	7.39573i	0.618217	−	0.303195i
$596$		0			0
$597$	12.2271	−	21.1779i	0.500420	−	0.866754i
$598$		0			0
$599$	−0.685637	−	1.18756i	−0.0280144	−	0.0485223i	0.851678	−	0.524065i	$-0.175585\pi$
$599$	−0.685637	−	1.18756i	−0.0280144	−	0.0485223i	−0.879693	+	0.475543i	$0.842252\pi$
$600$		0			0
$601$			31.7734i			1.29606i	0.761614	+	0.648031i	$0.224407\pi$
$601$			31.7734i			1.29606i	−0.761614	+	0.648031i	$0.775593\pi$
$602$		0			0
$603$			13.5770i			0.552899i
$604$		0			0
$605$	5.01837	+	8.69207i	0.204026	+	0.353383i
$606$		0			0
$607$	8.88952	−	15.3971i	0.360815	−	0.624949i	−0.627280	−	0.778793i	$-0.715832\pi$
$607$	8.88952	−	15.3971i	0.360815	−	0.624949i	0.988095	+	0.153844i	$0.0491654\pi$
$608$		0			0
$609$	−10.0560	+	14.9789i	−0.407488	+	0.606977i
$610$		0			0
$611$	−6.19199	+	10.7248i	−0.250501	+	0.433880i
$612$		0			0
$613$	−1.10479	−	1.91356i	−0.0446221	−	0.0772878i	0.842852	−	0.538146i	$-0.180875\pi$
$613$	−1.10479	−	1.91356i	−0.0446221	−	0.0772878i	−0.887474	+	0.460858i	$0.847542\pi$
$614$		0			0
$615$	26.4763	−	3.63023i	1.06763	−	0.146385i
$616$		0			0
$617$	30.4171			1.22455			0.612273	−	0.790647i	$-0.290255\pi$
$617$	30.4171			1.22455			0.612273	+	0.790647i	$0.290255\pi$
$618$		0			0
$619$	−23.5949	−	40.8675i	−0.948358	−	1.64260i	−0.748884	−	0.662701i	$-0.769410\pi$
$619$	−23.5949	−	40.8675i	−0.948358	−	1.64260i	−0.199474	−	0.979903i	$-0.563923\pi$
$620$		0			0
$621$	3.61156	+	2.08513i	0.144927	+	0.0836735i
$622$		0			0
$623$	−1.35443	+	19.9959i	−0.0542640	+	0.801118i
$624$		0			0
$625$	8.70259	−	15.0733i	0.348104	−	0.602933i
$626$		0			0
$627$	−35.3465	+	20.4073i	−1.41160	+	0.814989i
$628$		0			0
$629$			9.01323i			0.359381i
$630$		0			0
$631$	−2.70804			−0.107805			−0.0539027	−	0.998546i	$-0.517166\pi$
$631$	−2.70804			−0.107805			−0.0539027	+	0.998546i	$0.517166\pi$
$632$		0			0
$633$	−5.34946	−	9.26553i	−0.212622	−	0.368272i
$634$		0			0
$635$	0.212710	−	0.368425i	0.00844114	−	0.0146205i
$636$		0			0
$637$	7.67556	+	5.94307i	0.304117	+	0.235473i
$638$		0			0
$639$	−10.2814	−	5.93597i	−0.406726	−	0.234823i
$640$		0			0
$641$	−39.6974	+	22.9193i	−1.56795	+	0.905259i	−0.571547	+	0.820569i	$0.693657\pi$
$641$	−39.6974	+	22.9193i	−1.56795	+	0.905259i	−0.996407	+	0.0846898i	$0.973010\pi$
$642$		0			0
$643$		−	32.6876i		−	1.28907i	−0.764574	−	0.644536i	$-0.777050\pi$
$643$		−	32.6876i		−	1.28907i	0.764574	−	0.644536i	$-0.222950\pi$
$644$		0			0
$645$			14.6177i			0.575570i
$646$		0			0
$647$	−20.1439	−	34.8903i	−0.791938	−	1.37168i	−0.924765	−	0.380538i	$-0.875739\pi$
$647$	−20.1439	−	34.8903i	−0.791938	−	1.37168i	0.132827	−	0.991139i	$-0.457595\pi$
$648$		0			0
$649$	−14.9447	−	8.62834i	−0.586631	−	0.338692i
$650$		0			0
$651$	−2.92225	+	43.1423i	−0.114532	+	1.69088i
$652$		0			0
$653$	30.8188	+	17.7933i	1.20603	+	0.696304i	0.961890	−	0.273435i	$-0.0881599\pi$
$653$	30.8188	+	17.7933i	1.20603	+	0.696304i	0.244144	+	0.969739i	$0.421493\pi$
$654$		0			0
$655$	5.29536	+	9.17182i	0.206907	+	0.358373i
$656$		0			0
$657$	21.2898			0.830594
$658$		0			0
$659$			15.0924i			0.587916i	0.955818	+	0.293958i	$0.0949726\pi$
$659$			15.0924i			0.587916i	−0.955818	+	0.293958i	$0.905027\pi$
$660$		0			0
$661$	12.0821	+	20.9268i	0.469938	+	0.813956i	0.999409	−	0.0343715i	$-0.0109429\pi$
$661$	12.0821	+	20.9268i	0.469938	+	0.813956i	−0.529471	+	0.848328i	$0.677610\pi$
$662$		0			0
$663$	8.41990	+	4.86123i	0.327002	+	0.188795i
$664$		0			0
$665$	−20.1929	−	13.5563i	−0.783049	−	0.525692i
$666$		0			0
$667$	3.84172	+	2.21802i	0.148752	+	0.0858819i
$668$		0			0
$669$	−15.0102	+	8.66616i	−0.580329	+	0.335053i
$670$		0			0
$671$		−	4.96338i		−	0.191609i
$672$		0			0
$673$		−	25.5780i		−	0.985959i	−0.870041	−	0.492979i	$-0.835908\pi$
$673$		−	25.5780i		−	0.985959i	0.870041	−	0.492979i	$-0.164092\pi$
$674$		0			0
$675$	−3.15699	+	1.82269i	−0.121513	+	0.0701554i
$676$		0			0
$677$	−19.6174	+	33.9784i	−0.753960	+	1.30590i	0.191930	+	0.981409i	$0.438525\pi$
$677$	−19.6174	+	33.9784i	−0.753960	+	1.30590i	−0.945890	+	0.324488i	$0.894808\pi$
$678$		0			0
$679$	40.0802	−	19.6567i	1.53814	−	0.754356i
$680$		0			0
$681$	−2.91647	+	5.05147i	−0.111759	+	0.193573i
$682$		0			0
$683$	−32.4703	+	18.7467i	−1.24244	+	0.717324i	−0.969591	−	0.244733i	$-0.921300\pi$
$683$	−32.4703	+	18.7467i	−1.24244	+	0.717324i	−0.272850	+	0.962056i	$0.587966\pi$
$684$		0			0
$685$		−	19.2020i		−	0.733672i
$686$		0			0
$687$	−42.4062			−1.61790
$688$		0			0
$689$	−2.78657	−	4.82649i	−0.106160	−	0.183874i
$690$		0			0
$691$	−29.3717	−	16.9578i	−1.11735	−	0.645104i	−0.176629	−	0.984277i	$-0.556519\pi$
$691$	−29.3717	−	16.9578i	−1.11735	−	0.645104i	−0.940724	+	0.339173i	$0.889853\pi$
$692$		0			0
$693$	−15.3680	+	7.53700i	−0.583781	+	0.286307i
$694$		0			0
$695$	−14.3366	+	24.8317i	−0.543817	+	0.941918i
$696$		0			0
$697$	12.8178	+	16.5203i	0.485510	+	0.625752i
$698$		0			0
$699$	59.3868			2.24622
$700$		0			0
$701$	−21.0469			−0.794929			−0.397464	−	0.917618i	$-0.630110\pi$
$701$	−21.0469			−0.794929			−0.397464	+	0.917618i	$0.630110\pi$
$702$		0			0
$703$	11.3031	−	6.52583i	0.426303	−	0.246126i
$704$		0			0
$705$	18.6352	−	32.2770i	0.701840	−	1.21562i
$706$		0			0
$707$	18.5456	+	12.4504i	0.697478	+	0.468244i
$708$		0			0
$709$	−4.47078	−	2.58121i	−0.167904	−	0.0969393i	0.413693	−	0.910416i	$-0.364239\pi$
$709$	−4.47078	−	2.58121i	−0.167904	−	0.0969393i	−0.581597	+	0.813477i	$0.697572\pi$
$710$		0			0
$711$	−4.02579	+	2.32429i	−0.150979	+	0.0871677i
$712$		0			0
$713$	10.6322			0.398178
$714$		0			0
$715$	−10.8383			−0.405331
$716$		0			0
$717$	−18.5947	−	32.2070i	−0.694432	−	1.20279i
$718$		0			0
$719$	27.5680	+	15.9164i	1.02811	+	0.593581i	0.916443	−	0.400164i	$-0.131047\pi$
$719$	27.5680	+	15.9164i	1.02811	+	0.593581i	0.111669	+	0.993745i	$0.464380\pi$
$720$		0			0
$721$	52.4048	+	3.54965i	1.95166	+	0.132196i
$722$		0			0
$723$	−45.4275	−	26.2276i	−1.68947	−	0.975414i
$724$		0			0
$725$	−3.35818	+	1.93885i	−0.124720	+	0.0720070i
$726$		0			0
$727$		−	49.3165i		−	1.82905i	−0.404530	−	0.914525i	$-0.632565\pi$
$727$		−	49.3165i		−	1.82905i	0.404530	−	0.914525i	$-0.367435\pi$
$728$		0			0
$729$	−1.14706			−0.0424836
$730$		0			0
$731$	−9.90505	+	5.71868i	−0.366351	+	0.211513i
$732$		0			0
$733$	2.30072	−	3.98496i	0.0849789	−	0.147188i	−0.820403	−	0.571785i	$-0.806251\pi$
$733$	2.30072	−	3.98496i	0.0849789	−	0.147188i	0.905382	+	0.424597i	$0.139584\pi$
$734$		0			0
$735$	−23.1001	−	17.8860i	−0.852058	−	0.659735i
$736$		0			0
$737$	16.9599	−	29.3754i	0.624726	−	1.08206i
$738$		0			0
$739$	19.1777	+	33.2168i	0.705464	+	1.22190i	0.966524	+	0.256576i	$0.0825945\pi$
$739$	19.1777	+	33.2168i	0.705464	+	1.22190i	−0.261060	+	0.965323i	$0.584072\pi$
$740$		0			0
$741$		−	14.0787i		−	0.517193i
$742$		0			0
$743$	7.34417			0.269432			0.134716	−	0.990884i	$-0.456988\pi$
$743$	7.34417			0.269432			0.134716	+	0.990884i	$0.456988\pi$
$744$		0			0
$745$	11.9811	−	6.91731i	0.438955	−	0.253431i
$746$		0			0
$747$	−4.87641	+	8.44618i	−0.178418	+	0.309030i
$748$		0			0
$749$	35.0769	+	2.37595i	1.28168	+	0.0868152i
$750$		0			0
$751$	10.3682	+	5.98606i	0.378340	+	0.218435i	0.677096	−	0.735895i	$-0.263238\pi$
$751$	10.3682	+	5.98606i	0.378340	+	0.218435i	−0.298756	+	0.954330i	$0.596572\pi$
$752$		0			0
$753$	22.7199	−	13.1174i	0.827960	−	0.478023i
$754$		0			0
$755$			0.885511i			0.0322270i
$756$		0			0
$757$		−	49.8091i		−	1.81034i	−0.425045	−	0.905172i	$-0.639742\pi$
$757$		−	49.8091i		−	1.81034i	0.425045	−	0.905172i	$-0.360258\pi$
$758$		0			0
$759$	6.02740	+	10.4398i	0.218781	+	0.378939i
$760$		0			0
$761$	21.6643	−	37.5237i	0.785331	−	1.36023i	−0.143469	−	0.989655i	$-0.545826\pi$
$761$	21.6643	−	37.5237i	0.785331	−	1.36023i	0.928801	−	0.370579i	$-0.120841\pi$
$762$		0			0
$763$	0.912782	+	0.612787i	0.0330449	+	0.0221844i
$764$		0			0
$765$	−8.84698	−	5.10780i	−0.319863	−	0.184673i
$766$		0			0
$767$	5.15506	−	2.97628i	0.186139	−	0.107467i
$768$		0			0
$769$	17.1080			0.616929			0.308465	−	0.951236i	$-0.400185\pi$
$769$	17.1080			0.616929			0.308465	+	0.951236i	$0.400185\pi$
$770$		0			0
$771$	−35.4553			−1.27689
$772$		0			0
$773$	14.4229	−	8.32707i	0.518756	−	0.299504i	−0.217670	−	0.976023i	$-0.569846\pi$
$773$	14.4229	−	8.32707i	0.518756	−	0.299504i	0.736425	+	0.676519i	$0.236512\pi$
$774$		0			0
$775$	−4.64699	+	8.04882i	−0.166925	+	0.289122i
$776$		0			0
$777$	14.0761	−	6.90341i	0.504977	−	0.247659i
$778$		0			0
$779$	11.4369	−	28.0354i	0.409769	−	1.00447i
$780$		0			0
$781$	14.8300	+	25.6863i	0.530659	+	0.919129i
$782$		0			0
$783$	−9.48384			−0.338925
$784$		0			0
$785$		−	44.9885i		−	1.60571i
$786$		0			0
$787$	−8.77813	−	15.2042i	−0.312906	−	0.541970i	0.666084	−	0.745877i	$-0.267969\pi$
$787$	−8.77813	−	15.2042i	−0.312906	−	0.541970i	−0.978990	+	0.203907i	$0.934636\pi$
$788$		0			0
$789$	6.38487	−	11.0589i	0.227307	−	0.393708i
$790$		0			0
$791$	23.1042	+	47.1095i	0.821489	+	1.67502i
$792$		0			0
$793$	1.48271	+	0.856040i	0.0526524	+	0.0303989i
$794$		0			0
$795$	8.38636	+	14.5256i	0.297433	+	0.515170i
$796$		0			0
$797$	−33.1564			−1.17446			−0.587230	−	0.809420i	$-0.699782\pi$
$797$	−33.1564			−1.17446			−0.587230	+	0.809420i	$0.699782\pi$
$798$		0			0
$799$	29.1615			1.03166
$800$		0			0
$801$	10.5567	−	6.09490i	0.373002	−	0.215353i
$802$		0			0
$803$	−46.0629	−	26.5944i	−1.62552	−	0.938497i
$804$		0			0
$805$	−4.00393	+	5.96409i	−0.141120	+	0.210207i
$806$		0			0
$807$	−2.77519	−	1.60226i	−0.0976913	−	0.0564021i
$808$		0			0
$809$	36.1642	−	20.8794i	1.27147	−	0.734082i	0.296203	−	0.955125i	$-0.404279\pi$
$809$	36.1642	−	20.8794i	1.27147	−	0.734082i	0.975264	+	0.221043i	$0.0709462\pi$
$810$		0			0
$811$	−23.5147			−0.825713			−0.412857	−	0.910796i	$-0.635469\pi$
$811$	−23.5147			−0.825713			−0.412857	+	0.910796i	$0.635469\pi$
$812$		0			0
$813$		−	38.9773i		−	1.36700i
$814$		0			0
$815$	3.32151	+	5.75302i	0.116347	+	0.201519i
$816$		0			0
$817$	14.3431	+	8.28097i	0.501800	+	0.289715i
$818$		0			0
$819$	0.399013	−	5.89077i	0.0139427	−	0.205840i
$820$		0			0
$821$	−0.0546197	+	0.0946040i	−0.00190624	+	0.00330170i	−0.866977	−	0.498348i	$-0.833940\pi$
$821$	−0.0546197	+	0.0946040i	−0.00190624	+	0.00330170i	0.865071	+	0.501650i	$0.167273\pi$
$822$		0			0
$823$	11.7656	−	6.79288i	0.410124	−	0.236785i	−0.280719	−	0.959790i	$-0.590573\pi$
$823$	11.7656	−	6.79288i	0.410124	−	0.236785i	0.690843	+	0.723005i	$0.257240\pi$
$824$		0			0
$825$	−10.5375			−0.366870
$826$		0			0
$827$			41.3847i			1.43909i	0.694447	+	0.719544i	$0.255649\pi$
$827$			41.3847i			1.43909i	−0.694447	+	0.719544i	$0.744351\pi$
$828$		0			0
$829$	−2.55590	−	4.42695i	−0.0887701	−	0.153754i	0.818221	−	0.574903i	$-0.194960\pi$
$829$	−2.55590	−	4.42695i	−0.0887701	−	0.153754i	−0.906992	+	0.421149i	$0.861627\pi$
$830$		0			0
$831$	40.2510	+	23.2389i	1.39629	+	0.806149i
$832$		0			0
$833$	3.08256	−	22.6501i	0.106805	−	0.784779i
$834$		0			0
$835$	4.70226	+	2.71485i	0.162729	+	0.0939513i
$836$		0			0
$837$	−19.6853	+	11.3653i	−0.680424	+	0.392843i
$838$		0			0
$839$		−	2.33514i		−	0.0806181i	−0.999187	−	0.0403090i	$-0.987166\pi$
$839$		−	2.33514i		−	0.0806181i	0.999187	−	0.0403090i	$-0.0128342\pi$
$840$		0			0
$841$	18.9118			0.652130
$842$		0			0
$843$	19.6738	+	34.0760i	0.677601	+	1.17364i
$844$		0			0
$845$	−10.7667	+	18.6485i	−0.370386	+	0.641527i
$846$		0			0
$847$	13.6286	+	0.923138i	0.468284	+	0.0317194i
$848$		0			0
$849$	21.4605	+	12.3902i	0.736524	+	0.425232i
$850$		0			0
$851$	−1.92744	−	3.33842i	−0.0660717	−	0.114440i
$852$		0			0
$853$	−28.4105			−0.972759			−0.486379	−	0.873748i	$-0.661683\pi$
$853$	−28.4105			−0.972759			−0.486379	+	0.873748i	$0.661683\pi$
$854$		0			0
$855$			14.7928i			0.505902i
$856$		0			0
$857$	−19.8352	−	34.3555i	−0.677556	−	1.17356i	−0.975715	−	0.219046i	$-0.929706\pi$
$857$	−19.8352	−	34.3555i	−0.677556	−	1.17356i	0.298158	−	0.954516i	$-0.403628\pi$
$858$		0			0
$859$	−5.03381	+	8.71882i	−0.171751	+	0.297482i	−0.939032	−	0.343829i	$-0.888276\pi$
$859$	−5.03381	+	8.71882i	−0.171751	+	0.297482i	0.767281	+	0.641311i	$0.221609\pi$
$860$		0			0
$861$	15.9826	−	32.6711i	0.544685	−	1.11343i
$862$		0			0
$863$	−5.54847	+	9.61023i	−0.188872	+	0.327136i	−0.944874	−	0.327433i	$-0.893816\pi$
$863$	−5.54847	+	9.61023i	−0.188872	+	0.327136i	0.756002	+	0.654569i	$0.227150\pi$
$864$		0			0
$865$	3.80854	+	6.59659i	0.129494	+	0.224291i
$866$		0			0
$867$			13.6031i			0.461986i
$868$		0			0
$869$	11.6137			0.393967
$870$		0			0
$871$	5.85019	+	10.1328i	0.198226	+	0.343338i
$872$		0			0
$873$	−23.5139	−	13.5758i	−0.795826	−	0.459470i
$874$		0			0
$875$	−14.0888	−	28.7272i	−0.476289	−	0.971156i
$876$		0			0
$877$	−10.1657	+	17.6075i	−0.343271	+	0.594563i	−0.985038	−	0.172336i	$-0.944868\pi$
$877$	−10.1657	+	17.6075i	−0.343271	+	0.594563i	0.641767	+	0.766900i	$0.278202\pi$
$878$		0			0
$879$	−3.32741	−	5.76324i	−0.112231	−	0.194389i
$880$		0			0
$881$	−49.3696			−1.66330			−0.831652	−	0.555298i	$-0.812604\pi$
$881$	−49.3696			−1.66330			−0.831652	+	0.555298i	$0.812604\pi$
$882$		0			0
$883$		−	28.5048i		−	0.959264i	−0.877470	−	0.479632i	$-0.840770\pi$
$883$		−	28.5048i		−	0.959264i	0.877470	−	0.479632i	$-0.159230\pi$
$884$		0			0
$885$	−15.5145	+	8.95728i	−0.521513	+	0.301096i
$886$		0			0
$887$	30.4447	+	17.5773i	1.02223	+	0.590187i	0.914750	−	0.404019i	$-0.132387\pi$
$887$	30.4447	+	17.5773i	1.02223	+	0.590187i	0.107484	+	0.994207i	$0.465721\pi$
$888$		0			0
$889$	−0.254947	−	0.519838i	−0.00855064	−	0.0174348i
$890$		0			0
$891$	−39.1275	−	22.5903i	−1.31082	−	0.756803i
$892$		0			0
$893$	−21.1138	−	36.5702i	−0.706546	−	1.22377i
$894$		0			0
$895$		−	2.40621i		−	0.0804308i
$896$		0			0
$897$	−4.15821			−0.138839
$898$		0			0
$899$	−20.9398	+	12.0896i	−0.698382	+	0.403211i
$900$		0			0
$901$	−6.56177	+	11.3653i	−0.218604	+	0.378634i
$902$		0			0
$903$	16.5174	+	11.0888i	0.549666	+	0.369012i
$904$		0			0
$905$	0.407979	+	0.235547i	0.0135617	+	0.00782984i
$906$		0			0
$907$	−14.1941	−	24.5849i	−0.471308	−	0.816329i	0.528153	−	0.849149i	$-0.322885\pi$
$907$	−14.1941	−	24.5849i	−0.471308	−	0.816329i	−0.999461	+	0.0328196i	$0.989551\pi$
$908$		0			0
$909$		−	13.5860i		−	0.450618i
$910$		0			0
$911$	−20.9580			−0.694368			−0.347184	−	0.937797i	$-0.612862\pi$
$911$	−20.9580			−0.694368			−0.347184	+	0.937797i	$0.612862\pi$
$912$		0			0
$913$	21.1013	−	12.1829i	0.698352	−	0.403194i
$914$		0			0
$915$	−4.46229	−	2.57630i	−0.147519	−	0.0851700i
$916$		0			0
$917$	14.3808	+	0.974090i	0.474897	+	0.0321673i
$918$		0			0
$919$	−8.68126	−	5.01213i	−0.286368	−	0.165335i	0.349935	−	0.936774i	$-0.386204\pi$
$919$	−8.68126	−	5.01213i	−0.286368	−	0.165335i	−0.636303	+	0.771439i	$0.719537\pi$
$920$		0			0
$921$	−48.3190	+	27.8970i	−1.59216	+	0.919237i
$922$		0			0
$923$	−10.2310			−0.336757
$924$		0			0
$925$	3.36969			0.110795
$926$		0			0
$927$	−15.9734	−	27.6667i	−0.524634	−	0.908694i
$928$		0			0
$929$	−9.83520	−	5.67836i	−0.322682	−	0.186301i	0.329905	−	0.944014i	$-0.392983\pi$
$929$	−9.83520	−	5.67836i	−0.322682	−	0.186301i	−0.652588	+	0.757713i	$0.726317\pi$
$930$		0			0
$931$	−30.6363	+	12.5336i	−1.00406	+	0.410772i
$932$		0			0
$933$	15.1005	−	26.1549i	0.494369	−	0.856272i
$934$		0			0
$935$	12.7610	+	22.1026i	0.417328	+	0.722833i
$936$		0			0
$937$			16.5498i			0.540659i	0.962768	+	0.270329i	$0.0871326\pi$
$937$			16.5498i			0.540659i	−0.962768	+	0.270329i	$0.912867\pi$
$938$		0			0
$939$	−10.6904			−0.348868
$940$		0			0
$941$	−1.93041	−	3.34357i	−0.0629297	−	0.108997i	0.832844	−	0.553508i	$-0.186711\pi$
$941$	−1.93041	−	3.34357i	−0.0629297	−	0.108997i	−0.895774	+	0.444510i	$0.853378\pi$
$942$		0			0
$943$	−8.28041	−	3.37794i	−0.269647	−	0.110001i
$944$		0			0
$945$	1.03787	−	15.3224i	0.0337619	−	0.498439i
$946$		0			0
$947$	−5.50282	+	9.53116i	−0.178818	+	0.309721i	−0.941476	−	0.337081i	$-0.890561\pi$
$947$	−5.50282	+	9.53116i	−0.178818	+	0.309721i	0.762658	+	0.646802i	$0.223894\pi$
$948$		0			0
$949$	15.8890	−	9.17354i	0.515780	−	0.297786i
$950$		0			0
$951$	−12.8165			−0.415604
$952$		0			0
$953$	48.9101			1.58435			0.792177	−	0.610292i	$-0.208948\pi$
$953$	48.9101			1.58435			0.792177	+	0.610292i	$0.208948\pi$
$954$		0			0
$955$	−24.0373	+	13.8779i	−0.777829	+	0.449080i
$956$		0			0
$957$	−23.7417	−	13.7073i	−0.767459	−	0.443093i
$958$		0			0
$959$	−21.6976	−	14.5664i	−0.700651	−	0.470375i
$960$		0			0
$961$	−13.4761	+	23.3413i	−0.434713	+	0.752945i
$962$		0			0
$963$	−10.6917	−	18.5186i	−0.344536	−	0.596753i
$964$		0			0
$965$		−	22.8680i		−	0.736147i
$966$		0			0
$967$			51.5603i			1.65807i	0.559198	+	0.829034i	$0.311109\pi$
$967$			51.5603i			1.65807i	−0.559198	+	0.829034i	$0.688891\pi$
$968$		0			0
$969$	−28.7107	+	16.5761i	−0.922319	+	0.532501i
$970$		0			0
$971$	13.4836	+	7.78475i	0.432709	+	0.249825i	0.700500	−	0.713652i	$-0.252960\pi$
$971$	13.4836	+	7.78475i	0.432709	+	0.249825i	−0.267791	+	0.963477i	$0.586294\pi$
$972$		0			0
$973$	17.1833	+	35.0368i	0.550871	+	1.12323i
$974$		0			0
$975$	1.81742	−	3.14787i	0.0582041	−	0.100812i
$976$		0			0
$977$	−7.18614	+	4.14892i	−0.229905	+	0.132736i	−0.610528	−	0.791994i	$-0.709043\pi$
$977$	−7.18614	+	4.14892i	−0.229905	+	0.132736i	0.380623	+	0.924730i	$0.375709\pi$
$978$		0			0
$979$	−30.4541			−0.973317
$980$		0			0
$981$		−	0.668679i		−	0.0213493i
$982$		0			0
$983$	16.2480	+	28.1423i	0.518229	+	0.897600i	0.999776	+	0.0211790i	$0.00674197\pi$
$983$	16.2480	+	28.1423i	0.518229	+	0.897600i	−0.481546	+	0.876421i	$0.659925\pi$
$984$		0			0
$985$	20.3695	−	35.2810i	0.649025	−	1.12414i
$986$		0			0
$987$	−22.3354	−	45.5420i	−0.710945	−	1.44962i
$988$		0			0
$989$	2.44583	−	4.23630i	0.0777728	−	0.134706i
$990$		0			0
$991$	40.7529	−	23.5287i	1.29456	−	0.747414i	0.315100	−	0.949058i	$-0.397962\pi$
$991$	40.7529	−	23.5287i	1.29456	−	0.747414i	0.979459	+	0.201645i	$0.0646286\pi$
$992$		0			0
$993$	0.800397			0.0253998
$994$		0			0
$995$			22.1430i			0.701979i
$996$		0			0
$997$	−19.9681	+	11.5286i	−0.632396	+	0.365114i	−0.781679	−	0.623680i	$-0.785637\pi$
$997$	−19.9681	+	11.5286i	−0.632396	+	0.365114i	0.149283	+	0.988794i	$0.452303\pi$
$998$		0			0
$999$	7.13724	+	4.12069i	0.225812	+	0.130373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.r.a.737.24	yes	56
7.4	even	3	inner	1148.2.r.a.81.5	✓	56
41.40	even	2	inner	1148.2.r.a.737.5	yes	56
287.81	even	6	inner	1148.2.r.a.81.24	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.r.a.81.5	✓	56	7.4	even	3	inner
1148.2.r.a.81.24	yes	56	287.81	even	6	inner
1148.2.r.a.737.5	yes	56	41.40	even	2	inner
1148.2.r.a.737.24	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.85927 - 1.07345i) q^{3} +(-0.972000 + 1.68355i) q^{5} +(1.16501 + 2.37545i) q^{7} +(0.804601 - 1.39361i) q^{9} +O(q^{10})\)	\(q+(1.85927 - 1.07345i) q^{3} +(-0.972000 + 1.68355i) q^{5} +(1.16501 + 2.37545i) q^{7} +(0.804601 - 1.39361i) q^{9} +(-3.48169 + 2.01016i) q^{11} -1.38678i q^{13} +4.17359i q^{15} +(-2.82805 + 1.63278i) q^{17} +(4.09518 + 2.36435i) q^{19} +(4.71600 + 3.16604i) q^{21} +(0.698324 - 1.20953i) q^{23} +(0.610431 + 1.05730i) q^{25} +2.98591i q^{27} +3.17620i q^{29} +(3.80632 + 6.59273i) q^{31} +(-4.31562 + 7.47487i) q^{33} +(-5.13158 - 0.347589i) q^{35} +(1.38004 - 2.39031i) q^{37} +(-1.48864 - 2.57840i) q^{39} +(-0.869811 - 6.34377i) q^{41} +3.50243 q^{43} +(1.56415 + 2.70918i) q^{45} +(-7.73364 - 4.46502i) q^{47} +(-4.28553 + 5.53482i) q^{49} +(-3.50542 + 6.07156i) q^{51} +(3.48036 - 2.00939i) q^{53} -7.81549i q^{55} +10.1521 q^{57} +(2.14618 + 3.71730i) q^{59} +(-0.617288 + 1.06917i) q^{61} +(4.24782 + 0.287727i) q^{63} +(2.33471 + 1.34795i) q^{65} +(-7.30674 + 4.21855i) q^{67} -2.99847i q^{69} -7.37753i q^{71} +(6.61501 + 11.4575i) q^{73} +(2.26992 + 1.31054i) q^{75} +(-8.83122 - 5.92875i) q^{77} +(-2.50173 - 1.44437i) q^{79} +(5.61904 + 9.73246i) q^{81} -6.06065 q^{83} -6.34824i q^{85} +(3.40950 + 5.90542i) q^{87} +(6.56019 + 3.78753i) q^{89} +(3.29422 - 1.61560i) q^{91} +(14.1540 + 8.17180i) q^{93} +(-7.96104 + 4.59631i) q^{95} -16.8727i q^{97} +6.46950i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{5} + 32 q^{9}+O(q^{10}) \) 56 * q + 4 * q^5 + 32 * q^9	\( 56 q + 4 q^{5} + 32 q^{9} - 6 q^{21} + 2 q^{23} - 24 q^{25} - 4 q^{31} + 10 q^{33} + 10 q^{37} + 10 q^{39} + 20 q^{41} + 8 q^{43} - 22 q^{45} - 4 q^{49} + 18 q^{51} + 28 q^{57} - 16 q^{59} + 16 q^{61} + 2 q^{73} + 34 q^{77} - 28 q^{81} - 48 q^{83} - 2 q^{87} - 42 q^{91}+O(q^{100}) \) 56 * q + 4 * q^5 + 32 * q^9 - 6 * q^21 + 2 * q^23 - 24 * q^25 - 4 * q^31 + 10 * q^33 + 10 * q^37 + 10 * q^39 + 20 * q^41 + 8 * q^43 - 22 * q^45 - 4 * q^49 + 18 * q^51 + 28 * q^57 - 16 * q^59 + 16 * q^61 + 2 * q^73 + 34 * q^77 - 28 * q^81 - 48 * q^83 - 2 * q^87 - 42 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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