LMFDB - Embedded newform 352.2.m.a.225.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [352,2,Mod(97,352)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("352.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(352, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$352 = 2^{5} \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	352.m (of order $5$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,-2,0,-6,0,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{3} + x^{2} - x + 1$ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			225.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	352.225
Dual form			352.2.m.a.97.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.363271i) q^{3} +(-0.381966 + 1.17557i) q^{5} +(-3.61803 + 2.62866i) q^{7} +(-0.809017 - 2.48990i) q^{9} +(-2.19098 - 2.48990i) q^{11} +(-1.00000 - 3.07768i) q^{13} +(0.618034 - 0.449028i) q^{15} +(-1.50000 + 4.61653i) q^{17} +(-6.16312 - 4.47777i) q^{19} +2.76393 q^{21} -0.763932 q^{23} +(2.80902 + 2.04087i) q^{25} +(-1.07295 + 3.30220i) q^{27} +(-0.381966 + 0.277515i) q^{29} +(2.61803 + 8.05748i) q^{31} +(0.190983 + 2.04087i) q^{33} +(-1.70820 - 5.25731i) q^{35} +(-3.85410 + 2.80017i) q^{37} +(-0.618034 + 1.90211i) q^{39} +(-6.73607 - 4.89404i) q^{41} +7.09017 q^{43} +3.23607 q^{45} +(-2.00000 - 1.45309i) q^{47} +(4.01722 - 12.3637i) q^{49} +(2.42705 - 1.76336i) q^{51} +(-0.763932 - 2.35114i) q^{53} +(3.76393 - 1.62460i) q^{55} +(1.45492 + 4.47777i) q^{57} +(1.69098 - 1.22857i) q^{59} +(-2.00000 + 6.15537i) q^{61} +(9.47214 + 6.88191i) q^{63} +4.00000 q^{65} +3.61803 q^{67} +(0.381966 + 0.277515i) q^{69} +(3.00000 - 9.23305i) q^{71} +(-5.73607 + 4.16750i) q^{73} +(-0.663119 - 2.04087i) q^{75} +(14.4721 + 3.24920i) q^{77} +(1.85410 + 5.70634i) q^{79} +(-4.61803 + 3.35520i) q^{81} +(1.42705 - 4.39201i) q^{83} +(-4.85410 - 3.52671i) q^{85} +0.291796 q^{87} +8.61803 q^{89} +(11.7082 + 8.50651i) q^{91} +(1.61803 - 4.97980i) q^{93} +(7.61803 - 5.53483i) q^{95} +(1.04508 + 3.21644i) q^{97} +(-4.42705 + 7.46969i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{3} - 6 q^{5} - 10 q^{7} - q^{9} - 11 q^{11} - 4 q^{13} - 2 q^{15} - 6 q^{17} - 9 q^{19} + 20 q^{21} - 12 q^{23} + 9 q^{25} - 11 q^{27} - 6 q^{29} + 6 q^{31} + 3 q^{33} + 20 q^{35} - 2 q^{37}+ \cdots - 11 q^{99}+O(q^{100})$ 4 * q - 2 * q^3 - 6 * q^5 - 10 * q^7 - q^9 - 11 * q^11 - 4 * q^13 - 2 * q^15 - 6 * q^17 - 9 * q^19 + 20 * q^21 - 12 * q^23 + 9 * q^25 - 11 * q^27 - 6 * q^29 + 6 * q^31 + 3 * q^33 + 20 * q^35 - 2 * q^37 + 2 * q^39 - 18 * q^41 + 6 * q^43 + 4 * q^45 - 8 * q^47 - 13 * q^49 + 3 * q^51 - 12 * q^53 + 24 * q^55 + 17 * q^57 + 9 * q^59 - 8 * q^61 + 20 * q^63 + 16 * q^65 + 10 * q^67 + 6 * q^69 + 12 * q^71 - 14 * q^73 + 13 * q^75 + 40 * q^77 - 6 * q^79 - 14 * q^81 - q^83 - 6 * q^85 + 28 * q^87 + 30 * q^89 + 20 * q^91 + 2 * q^93 + 26 * q^95 - 7 * q^97 - 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$ .

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	0.434017	−	0.900905i	$-0.357096\pi$
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	−0.722692	+	0.691170i	$0.757096\pi$
$4$		0			0
$5$	−0.381966	+	1.17557i	−0.170820	+	0.525731i	−0.999418	−	0.0341136i	$-0.989139\pi$
$5$	−0.381966	+	1.17557i	−0.170820	+	0.525731i	0.828598	+	0.559845i	$0.189139\pi$
$6$		0			0
$7$	−3.61803	+	2.62866i	−1.36749	+	0.993538i	−0.369560	+	0.929207i	$0.620491\pi$
$7$	−3.61803	+	2.62866i	−1.36749	+	0.993538i	−0.997929	+	0.0643314i	$0.979509\pi$
$8$		0			0
$9$	−0.809017	−	2.48990i	−0.269672	−	0.829966i
$10$		0			0
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$11$	−2.19098	−	2.48990i	−0.660606	−	0.750733i
$12$		0			0
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	−0.988588	−	0.150644i	$-0.951865\pi$
$13$	−1.00000	−	3.07768i	−0.277350	−	0.853596i	0.711238	−	0.702951i	$-0.248135\pi$
$14$		0			0
$15$	0.618034	−	0.449028i	0.159576	−	0.115939i
$16$		0			0
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	0.586924	+	0.809642i	$0.300339\pi$
$17$	−1.50000	+	4.61653i	−0.363803	+	1.11967i	−0.950727	+	0.310029i	$0.899661\pi$
$18$		0			0
$19$	−6.16312	−	4.47777i	−1.41392	−	1.02727i	−0.992739	−	0.120292i	$-0.961617\pi$
$19$	−6.16312	−	4.47777i	−1.41392	−	1.02727i	−0.421178	−	0.906978i	$-0.638383\pi$
$20$		0			0
$21$	2.76393			0.603139
$22$		0			0
$23$	−0.763932			−0.159291			−0.0796454	−	0.996823i	$-0.525379\pi$
$23$	−0.763932			−0.159291			−0.0796454	+	0.996823i	$0.525379\pi$
$24$		0			0
$25$	2.80902	+	2.04087i	0.561803	+	0.408174i
$26$		0			0
$27$	−1.07295	+	3.30220i	−0.206489	+	0.635508i
$28$		0			0
$29$	−0.381966	+	0.277515i	−0.0709293	+	0.0515332i	−0.622685	−	0.782473i	$-0.713958\pi$
$29$	−0.381966	+	0.277515i	−0.0709293	+	0.0515332i	0.551756	+	0.834006i	$0.313958\pi$
$30$		0			0
$31$	2.61803	+	8.05748i	0.470213	+	1.44717i	0.852307	+	0.523043i	$0.175203\pi$
$31$	2.61803	+	8.05748i	0.470213	+	1.44717i	−0.382094	+	0.924124i	$0.624797\pi$
$32$		0			0
$33$	0.190983	+	2.04087i	0.0332459	+	0.355270i
$34$		0			0
$35$	−1.70820	−	5.25731i	−0.288739	−	0.888648i
$36$		0			0
$37$	−3.85410	+	2.80017i	−0.633610	+	0.460345i	−0.857649	−	0.514235i	$-0.828076\pi$
$37$	−3.85410	+	2.80017i	−0.633610	+	0.460345i	0.224039	+	0.974580i	$0.428076\pi$
$38$		0			0
$39$	−0.618034	+	1.90211i	−0.0989646	+	0.304582i
$40$		0			0
$41$	−6.73607	−	4.89404i	−1.05200	−	0.764321i	−0.0794059	−	0.996842i	$-0.525302\pi$
$41$	−6.73607	−	4.89404i	−1.05200	−	0.764321i	−0.972591	+	0.232522i	$0.925302\pi$
$42$		0			0
$43$	7.09017			1.08124			0.540620	−	0.841267i	$-0.318190\pi$
$43$	7.09017			1.08124			0.540620	+	0.841267i	$0.318190\pi$
$44$		0			0
$45$	3.23607			0.482405
$46$		0			0
$47$	−2.00000	−	1.45309i	−0.291730	−	0.211954i	0.432288	−	0.901736i	$-0.357707\pi$
$47$	−2.00000	−	1.45309i	−0.291730	−	0.211954i	−0.724018	+	0.689782i	$0.757707\pi$
$48$		0			0
$49$	4.01722	−	12.3637i	0.573889	−	1.76625i
$50$		0			0
$51$	2.42705	−	1.76336i	0.339855	−	0.246919i
$52$		0			0
$53$	−0.763932	−	2.35114i	−0.104934	−	0.322954i	0.884781	−	0.466007i	$-0.154308\pi$
$53$	−0.763932	−	2.35114i	−0.104934	−	0.322954i	−0.989715	+	0.143053i	$0.954308\pi$
$54$		0			0
$55$	3.76393	−	1.62460i	0.507528	−	0.219061i
$56$		0			0
$57$	1.45492	+	4.47777i	0.192708	+	0.593095i
$58$		0			0
$59$	1.69098	−	1.22857i	0.220147	−	0.159946i	−0.472246	−	0.881467i	$-0.656556\pi$
$59$	1.69098	−	1.22857i	0.220147	−	0.159946i	0.692393	+	0.721521i	$0.256556\pi$
$60$		0			0
$61$	−2.00000	+	6.15537i	−0.256074	+	0.788114i	0.737542	+	0.675301i	$0.235986\pi$
$61$	−2.00000	+	6.15537i	−0.256074	+	0.788114i	−0.993616	+	0.112813i	$0.964014\pi$
$62$		0			0
$63$	9.47214	+	6.88191i	1.19338	+	0.867039i
$64$		0			0
$65$	4.00000			0.496139
$66$		0			0
$67$	3.61803			0.442013			0.221007	−	0.975272i	$-0.429066\pi$
$67$	3.61803			0.442013			0.221007	+	0.975272i	$0.429066\pi$
$68$		0			0
$69$	0.381966	+	0.277515i	0.0459833	+	0.0334088i
$70$		0			0
$71$	3.00000	−	9.23305i	0.356034	−	1.09576i	−0.599373	−	0.800470i	$-0.704583\pi$
$71$	3.00000	−	9.23305i	0.356034	−	1.09576i	0.955407	−	0.295291i	$-0.0954167\pi$
$72$		0			0
$73$	−5.73607	+	4.16750i	−0.671356	+	0.487769i	−0.870479	−	0.492206i	$-0.836191\pi$
$73$	−5.73607	+	4.16750i	−0.671356	+	0.487769i	0.199123	+	0.979975i	$0.436191\pi$
$74$		0			0
$75$	−0.663119	−	2.04087i	−0.0765704	−	0.235659i
$76$		0			0
$77$	14.4721	+	3.24920i	1.64925	+	0.370280i
$78$		0			0
$79$	1.85410	+	5.70634i	0.208603	+	0.642013i	0.999546	+	0.0301240i	$0.00959021\pi$
$79$	1.85410	+	5.70634i	0.208603	+	0.642013i	−0.790943	+	0.611889i	$0.790410\pi$
$80$		0			0
$81$	−4.61803	+	3.35520i	−0.513115	+	0.372800i
$82$		0			0
$83$	1.42705	−	4.39201i	0.156639	−	0.482086i	−0.841684	−	0.539970i	$-0.818435\pi$
$83$	1.42705	−	4.39201i	0.156639	−	0.482086i	0.998323	+	0.0578844i	$0.0184355\pi$
$84$		0			0
$85$	−4.85410	−	3.52671i	−0.526501	−	0.382526i
$86$		0			0
$87$	0.291796			0.0312838
$88$		0			0
$89$	8.61803			0.913510			0.456755	−	0.889593i	$-0.349012\pi$
$89$	8.61803			0.913510			0.456755	+	0.889593i	$0.349012\pi$
$90$		0			0
$91$	11.7082	+	8.50651i	1.22735	+	0.891724i
$92$		0			0
$93$	1.61803	−	4.97980i	0.167782	−	0.516381i
$94$		0			0
$95$	7.61803	−	5.53483i	0.781594	−	0.567861i
$96$		0			0
$97$	1.04508	+	3.21644i	0.106112	+	0.326580i	0.989990	−	0.141138i	$-0.0450762\pi$
$97$	1.04508	+	3.21644i	0.106112	+	0.326580i	−0.883878	+	0.467718i	$0.845076\pi$
$98$		0			0
$99$	−4.42705	+	7.46969i	−0.444935	+	0.750733i
$100$		0			0
$101$	−4.85410	−	14.9394i	−0.483001	−	1.48652i	−0.834855	−	0.550470i	$-0.814449\pi$
$101$	−4.85410	−	14.9394i	−0.483001	−	1.48652i	0.351854	−	0.936055i	$-0.385551\pi$
$102$		0			0
$103$	−10.3262	+	7.50245i	−1.01747	+	0.739238i	−0.965764	−	0.259424i	$-0.916467\pi$
$103$	−10.3262	+	7.50245i	−1.01747	+	0.739238i	−0.0517108	+	0.998662i	$0.516467\pi$
$104$		0			0
$105$	−1.05573	+	3.24920i	−0.103029	+	0.317089i
$106$		0			0
$107$	9.97214	+	7.24518i	0.964043	+	0.700418i	0.954086	−	0.299532i	$-0.0968307\pi$
$107$	9.97214	+	7.24518i	0.964043	+	0.700418i	0.00995663	+	0.999950i	$0.496831\pi$
$108$		0			0
$109$	−14.9443			−1.43140			−0.715701	−	0.698407i	$-0.753893\pi$
$109$	−14.9443			−1.43140			−0.715701	+	0.698407i	$0.753893\pi$
$110$		0			0
$111$	2.94427			0.279458
$112$		0			0
$113$	−6.39919	−	4.64928i	−0.601985	−	0.437368i	0.244598	−	0.969625i	$-0.421344\pi$
$113$	−6.39919	−	4.64928i	−0.601985	−	0.437368i	−0.846583	+	0.532257i	$0.821344\pi$
$114$		0			0
$115$	0.291796	−	0.898056i	0.0272101	−	0.0837441i
$116$		0			0
$117$	−6.85410	+	4.97980i	−0.633662	+	0.460382i
$118$		0			0
$119$	−6.70820	−	20.6457i	−0.614940	−	1.89259i
$120$		0			0
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$		0			0
$123$	1.59017	+	4.89404i	0.143381	+	0.441281i
$124$		0			0
$125$	−8.47214	+	6.15537i	−0.757771	+	0.550553i
$126$		0			0
$127$	3.56231	−	10.9637i	0.316104	−	0.972867i	−0.659194	−	0.751973i	$-0.729103\pi$
$127$	3.56231	−	10.9637i	0.316104	−	0.972867i	0.975298	−	0.220894i	$-0.0708975\pi$
$128$		0			0
$129$	−3.54508	−	2.57565i	−0.312127	−	0.226774i
$130$		0			0
$131$	−10.0902			−0.881582			−0.440791	−	0.897610i	$-0.645302\pi$
$131$	−10.0902			−0.881582			−0.440791	+	0.897610i	$0.645302\pi$
$132$		0			0
$133$	34.0689			2.95415
$134$		0			0
$135$	−3.47214	−	2.52265i	−0.298834	−	0.217116i
$136$		0			0
$137$	4.57295	−	14.0741i	0.390693	−	1.20243i	−0.541572	−	0.840655i	$-0.682171\pi$
$137$	4.57295	−	14.0741i	0.390693	−	1.20243i	0.932265	−	0.361776i	$-0.117829\pi$
$138$		0			0
$139$	−0.763932	+	0.555029i	−0.0647959	+	0.0470770i	−0.619712	−	0.784830i	$-0.712750\pi$
$139$	−0.763932	+	0.555029i	−0.0647959	+	0.0470770i	0.554916	+	0.831907i	$0.312750\pi$
$140$		0			0
$141$	0.472136	+	1.45309i	0.0397610	+	0.122372i
$142$		0			0
$143$	−5.47214	+	9.23305i	−0.457603	+	0.772106i
$144$		0			0
$145$	−0.180340	−	0.555029i	−0.0149764	−	0.0460927i
$146$		0			0
$147$	−6.50000	+	4.72253i	−0.536111	+	0.389507i
$148$		0			0
$149$	−5.47214	+	16.8415i	−0.448295	+	1.37971i	0.430535	+	0.902574i	$0.358325\pi$
$149$	−5.47214	+	16.8415i	−0.448295	+	1.37971i	−0.878830	+	0.477136i	$0.841675\pi$
$150$		0			0
$151$	−4.00000	−	2.90617i	−0.325515	−	0.236501i	0.413010	−	0.910727i	$-0.364477\pi$
$151$	−4.00000	−	2.90617i	−0.325515	−	0.236501i	−0.738525	+	0.674226i	$0.764477\pi$
$152$		0			0
$153$	12.7082			1.02740
$154$		0			0
$155$	−10.4721			−0.841142
$156$		0			0
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	0.701028	−	0.713134i	$-0.252725\pi$
$157$	3.00000	+	2.17963i	0.239426	+	0.173953i	−0.461601	+	0.887087i	$0.652725\pi$
$158$		0			0
$159$	−0.472136	+	1.45309i	−0.0374428	+	0.115237i
$160$		0			0
$161$	2.76393	−	2.00811i	0.217828	−	0.158262i
$162$		0			0
$163$	3.06231	+	9.42481i	0.239858	+	0.738208i	0.996440	+	0.0843084i	$0.0268681\pi$
$163$	3.06231	+	9.42481i	0.239858	+	0.738208i	−0.756581	+	0.653900i	$0.773132\pi$
$164$		0			0
$165$	−2.47214	−	0.555029i	−0.192456	−	0.0432090i
$166$		0			0
$167$	−5.76393	−	17.7396i	−0.446026	−	1.37273i	−0.881354	−	0.472456i	$-0.843367\pi$
$167$	−5.76393	−	17.7396i	−0.446026	−	1.37273i	0.435328	−	0.900272i	$-0.356633\pi$
$168$		0			0
$169$	2.04508	−	1.48584i	0.157314	−	0.114295i
$170$		0			0
$171$	−6.16312	+	18.9681i	−0.471305	+	1.45053i
$172$		0			0
$173$	−7.23607	−	5.25731i	−0.550148	−	0.399706i	0.277692	−	0.960670i	$-0.410431\pi$
$173$	−7.23607	−	5.25731i	−0.550148	−	0.399706i	−0.827840	+	0.560964i	$0.810431\pi$
$174$		0			0
$175$	−15.5279			−1.17380
$176$		0			0
$177$	−1.29180			−0.0970973
$178$		0			0
$179$	−20.4894	−	14.8864i	−1.53145	−	1.11266i	−0.955428	−	0.295224i	$-0.904606\pi$
$179$	−20.4894	−	14.8864i	−1.53145	−	1.11266i	−0.576018	−	0.817437i	$-0.695394\pi$
$180$		0			0
$181$	1.61803	−	4.97980i	0.120268	−	0.370145i	−0.872742	−	0.488182i	$-0.837660\pi$
$181$	1.61803	−	4.97980i	0.120268	−	0.370145i	0.993009	+	0.118037i	$0.0376601\pi$
$182$		0			0
$183$	3.23607	−	2.35114i	0.239217	−	0.173801i
$184$		0			0
$185$	−1.81966	−	5.60034i	−0.133784	−	0.411745i
$186$		0			0
$187$	14.7812	−	6.37988i	1.08090	−	0.466543i
$188$		0			0
$189$	−4.79837	−	14.7679i	−0.349030	−	1.07420i
$190$		0			0
$191$	6.23607	−	4.53077i	0.451226	−	0.327835i	−0.338854	−	0.940839i	$-0.610039\pi$
$191$	6.23607	−	4.53077i	0.451226	−	0.327835i	0.790080	+	0.613004i	$0.210039\pi$
$192$		0			0
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	0.790047	+	0.613046i	$0.210056\pi$
$193$	−2.90983	+	8.95554i	−0.209454	+	0.644634i	−0.999501	+	0.0315871i	$0.989944\pi$
$194$		0			0
$195$	−2.00000	−	1.45309i	−0.143223	−	0.104058i
$196$		0			0
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$		0			0
$199$	−22.3607			−1.58511			−0.792553	−	0.609803i	$-0.791249\pi$
$199$	−22.3607			−1.58511			−0.792553	+	0.609803i	$0.791249\pi$
$200$		0			0
$201$	−1.80902	−	1.31433i	−0.127598	−	0.0927055i
$202$		0			0
$203$	0.652476	−	2.00811i	0.0457948	−	0.140942i
$204$		0			0
$205$	8.32624	−	6.04937i	0.581530	−	0.422506i
$206$		0			0
$207$	0.618034	+	1.90211i	0.0429563	+	0.132206i
$208$		0			0
$209$	2.35410	+	25.1563i	0.162837	+	1.74009i
$210$		0			0
$211$	3.42705	+	10.5474i	0.235928	+	0.726111i	0.996997	+	0.0774406i	$0.0246748\pi$
$211$	3.42705	+	10.5474i	0.235928	+	0.726111i	−0.761069	+	0.648671i	$0.775325\pi$
$212$		0			0
$213$	−4.85410	+	3.52671i	−0.332598	+	0.241646i
$214$		0			0
$215$	−2.70820	+	8.33499i	−0.184698	+	0.568442i
$216$		0			0
$217$	−30.6525	−	22.2703i	−2.08083	−	1.51181i
$218$		0			0
$219$	4.38197			0.296106
$220$		0			0
$221$	15.7082			1.05665
$222$		0			0
$223$	12.7082	+	9.23305i	0.851004	+	0.618291i	0.925423	−	0.378936i	$-0.123710\pi$
$223$	12.7082	+	9.23305i	0.851004	+	0.618291i	−0.0744185	+	0.997227i	$0.523710\pi$
$224$		0			0
$225$	2.80902	−	8.64527i	0.187268	−	0.576351i
$226$		0			0
$227$	−13.8713	+	10.0781i	−0.920672	+	0.668907i	−0.943691	−	0.330828i	$-0.892672\pi$
$227$	−13.8713	+	10.0781i	−0.920672	+	0.668907i	0.0230192	+	0.999735i	$0.492672\pi$
$228$		0			0
$229$	1.90983	+	5.87785i	0.126205	+	0.388419i	0.994119	−	0.108296i	$-0.0345394\pi$
$229$	1.90983	+	5.87785i	0.126205	+	0.388419i	−0.867914	+	0.496715i	$0.834539\pi$
$230$		0			0
$231$	−6.05573	−	6.88191i	−0.398438	−	0.452796i
$232$		0			0
$233$	5.89919	+	18.1558i	0.386469	+	1.18943i	0.935409	+	0.353567i	$0.115031\pi$
$233$	5.89919	+	18.1558i	0.386469	+	1.18943i	−0.548941	+	0.835861i	$0.684969\pi$
$234$		0			0
$235$	2.47214	−	1.79611i	0.161264	−	0.117165i
$236$		0			0
$237$	1.14590	−	3.52671i	0.0744341	−	0.229085i
$238$		0			0
$239$	−22.4164	−	16.2865i	−1.45000	−	1.05348i	−0.985832	−	0.167736i	$-0.946355\pi$
$239$	−22.4164	−	16.2865i	−1.45000	−	1.05348i	−0.464165	−	0.885749i	$-0.653645\pi$
$240$		0			0
$241$	12.6738			0.816389			0.408194	−	0.912895i	$-0.366159\pi$
$241$	12.6738			0.816389			0.408194	+	0.912895i	$0.366159\pi$
$242$		0			0
$243$	13.9443			0.894525
$244$		0			0
$245$	13.0000	+	9.44505i	0.830540	+	0.603422i
$246$		0			0
$247$	−7.61803	+	23.4459i	−0.484724	+	1.49183i
$248$		0			0
$249$	−2.30902	+	1.67760i	−0.146328	+	0.106314i
$250$		0			0
$251$	1.23607	+	3.80423i	0.0780199	+	0.240121i	0.982458	−	0.186485i	$-0.0597094\pi$
$251$	1.23607	+	3.80423i	0.0780199	+	0.240121i	−0.904438	+	0.426605i	$0.859709\pi$
$252$		0			0
$253$	1.67376	+	1.90211i	0.105229	+	0.119585i
$254$		0			0
$255$	1.14590	+	3.52671i	0.0717589	+	0.220851i
$256$		0			0
$257$	−1.26393	+	0.918300i	−0.0788419	+	0.0572820i	−0.626508	−	0.779415i	$-0.715516\pi$
$257$	−1.26393	+	0.918300i	−0.0788419	+	0.0572820i	0.547666	+	0.836697i	$0.315516\pi$
$258$		0			0
$259$	6.58359	−	20.2622i	0.409085	−	1.25903i
$260$		0			0
$261$	1.00000	+	0.726543i	0.0618984	+	0.0449719i
$262$		0			0
$263$	22.1803			1.36770			0.683849	−	0.729623i	$-0.260305\pi$
$263$	22.1803			1.36770			0.683849	+	0.729623i	$0.260305\pi$
$264$		0			0
$265$	3.05573			0.187712
$266$		0			0
$267$	−4.30902	−	3.13068i	−0.263708	−	0.191595i
$268$		0			0
$269$	−2.52786	+	7.77997i	−0.154127	+	0.474353i	−0.998071	−	0.0620772i	$-0.980227\pi$
$269$	−2.52786	+	7.77997i	−0.154127	+	0.474353i	0.843945	+	0.536430i	$0.180227\pi$
$270$		0			0
$271$	−0.381966	+	0.277515i	−0.0232028	+	0.0168578i	−0.599326	−	0.800505i	$-0.704565\pi$
$271$	−0.381966	+	0.277515i	−0.0232028	+	0.0168578i	0.576123	+	0.817363i	$0.304565\pi$
$272$		0			0
$273$	−2.76393	−	8.50651i	−0.167281	−	0.514837i
$274$		0			0
$275$	−1.07295	−	11.4657i	−0.0647013	−	0.691406i
$276$		0			0
$277$	−3.76393	−	11.5842i	−0.226153	−	0.696027i	−0.998173	−	0.0604281i	$-0.980753\pi$
$277$	−3.76393	−	11.5842i	−0.226153	−	0.696027i	0.772020	−	0.635598i	$-0.219247\pi$
$278$		0			0
$279$	17.9443	−	13.0373i	1.07430	−	0.780521i
$280$		0			0
$281$	−2.86475	+	8.81678i	−0.170896	+	0.525965i	−0.999422	−	0.0339857i	$-0.989180\pi$
$281$	−2.86475	+	8.81678i	−0.170896	+	0.525965i	0.828526	+	0.559951i	$0.189180\pi$
$282$		0			0
$283$	−7.23607	−	5.25731i	−0.430140	−	0.312515i	0.351565	−	0.936163i	$-0.385650\pi$
$283$	−7.23607	−	5.25731i	−0.430140	−	0.312515i	−0.781705	+	0.623649i	$0.785650\pi$
$284$		0			0
$285$	−5.81966			−0.344727
$286$		0			0
$287$	37.2361			2.19798
$288$		0			0
$289$	−5.30902	−	3.85723i	−0.312295	−	0.226896i
$290$		0			0
$291$	0.645898	−	1.98787i	0.0378632	−	0.116531i
$292$		0			0
$293$	−18.1803	+	13.2088i	−1.06211	+	0.771666i	−0.974477	−	0.224487i	$-0.927929\pi$
$293$	−18.1803	+	13.2088i	−1.06211	+	0.771666i	−0.0876298	+	0.996153i	$0.527929\pi$
$294$		0			0
$295$	0.798374	+	2.45714i	0.0464831	+	0.143060i
$296$		0			0
$297$	10.5729	−	4.56352i	0.613505	−	0.264803i
$298$		0			0
$299$	0.763932	+	2.35114i	0.0441793	+	0.135970i
$300$		0			0
$301$	−25.6525	+	18.6376i	−1.47858	+	1.07425i
$302$		0			0
$303$	−3.00000	+	9.23305i	−0.172345	+	0.530425i
$304$		0			0
$305$	−6.47214	−	4.70228i	−0.370593	−	0.269252i
$306$		0			0
$307$	−1.85410			−0.105819			−0.0529096	−	0.998599i	$-0.516850\pi$
$307$	−1.85410			−0.105819			−0.0529096	+	0.998599i	$0.516850\pi$
$308$		0			0
$309$	7.88854			0.448764
$310$		0			0
$311$	10.7082	+	7.77997i	0.607207	+	0.441161i	0.848430	−	0.529308i	$-0.177549\pi$
$311$	10.7082	+	7.77997i	0.607207	+	0.441161i	−0.241223	+	0.970470i	$0.577549\pi$
$312$		0			0
$313$	5.44427	−	16.7557i	0.307728	−	0.947091i	−0.670917	−	0.741533i	$-0.734099\pi$
$313$	5.44427	−	16.7557i	0.307728	−	0.947091i	0.978645	−	0.205558i	$-0.0659009\pi$
$314$		0			0
$315$	−11.7082	+	8.50651i	−0.659683	+	0.479287i
$316$		0			0
$317$	−7.47214	−	22.9969i	−0.419677	−	1.29163i	−0.908000	−	0.418970i	$-0.862391\pi$
$317$	−7.47214	−	22.9969i	−0.419677	−	1.29163i	0.488323	−	0.872663i	$-0.337609\pi$
$318$		0			0
$319$	1.52786	+	0.343027i	0.0855440	+	0.0192058i
$320$		0			0
$321$	−2.35410	−	7.24518i	−0.131393	−	0.404387i
$322$		0			0
$323$	29.9164	−	21.7355i	1.66459	−	1.20940i
$324$		0			0
$325$	3.47214	−	10.6861i	0.192599	−	0.592760i
$326$		0			0
$327$	7.47214	+	5.42882i	0.413210	+	0.300215i
$328$		0			0
$329$	11.0557			0.609522
$330$		0			0
$331$	5.20163			0.285907			0.142954	−	0.989729i	$-0.454340\pi$
$331$	5.20163			0.285907			0.142954	+	0.989729i	$0.454340\pi$
$332$		0			0
$333$	10.0902	+	7.33094i	0.552938	+	0.401733i
$334$		0			0
$335$	−1.38197	+	4.25325i	−0.0755049	+	0.232380i
$336$		0			0
$337$	12.2533	−	8.90254i	0.667479	−	0.484952i	−0.201701	−	0.979447i	$-0.564647\pi$
$337$	12.2533	−	8.90254i	0.667479	−	0.484952i	0.869180	+	0.494495i	$0.164647\pi$
$338$		0			0
$339$	1.51064	+	4.64928i	0.0820469	+	0.252514i
$340$		0			0
$341$	14.3262	−	24.1724i	0.775809	−	1.30901i
$342$		0			0
$343$	8.29180	+	25.5195i	0.447715	+	1.37792i
$344$		0			0
$345$	−0.472136	+	0.343027i	−0.0254189	+	0.0184679i
$346$		0			0
$347$	−0.409830	+	1.26133i	−0.0220008	+	0.0677116i	−0.961454	−	0.274965i	$-0.911334\pi$
$347$	−0.409830	+	1.26133i	−0.0220008	+	0.0677116i	0.939453	+	0.342677i	$0.111334\pi$
$348$		0			0
$349$	20.4164	+	14.8334i	1.09287	+	0.794013i	0.979881	−	0.199584i	$-0.0639590\pi$
$349$	20.4164	+	14.8334i	1.09287	+	0.794013i	0.112984	+	0.993597i	$0.463959\pi$
$350$		0			0
$351$	11.2361			0.599737
$352$		0			0
$353$	−11.5066			−0.612433			−0.306217	−	0.951962i	$-0.599063\pi$
$353$	−11.5066			−0.612433			−0.306217	+	0.951962i	$0.599063\pi$
$354$		0			0
$355$	9.70820	+	7.05342i	0.515258	+	0.374357i
$356$		0			0
$357$	−4.14590	+	12.7598i	−0.219424	+	0.675318i
$358$		0			0
$359$	−6.23607	+	4.53077i	−0.329127	+	0.239125i	−0.740060	−	0.672541i	$-0.765203\pi$
$359$	−6.23607	+	4.53077i	−0.329127	+	0.239125i	0.410933	+	0.911666i	$0.365203\pi$
$360$		0			0
$361$	12.0623	+	37.1240i	0.634858	+	1.95389i
$362$		0			0
$363$	4.66312	−	4.94704i	0.244750	−	0.259652i
$364$		0			0
$365$	−2.70820	−	8.33499i	−0.141754	−	0.436274i
$366$		0			0
$367$	−8.61803	+	6.26137i	−0.449858	+	0.326841i	−0.789540	−	0.613700i	$-0.789681\pi$
$367$	−8.61803	+	6.26137i	−0.449858	+	0.326841i	0.339682	+	0.940540i	$0.389681\pi$
$368$		0			0
$369$	−6.73607	+	20.7315i	−0.350666	+	1.07924i
$370$		0			0
$371$	8.94427	+	6.49839i	0.464363	+	0.337380i
$372$		0			0
$373$	−14.6525			−0.758676			−0.379338	−	0.925258i	$-0.623848\pi$
$373$	−14.6525			−0.758676			−0.379338	+	0.925258i	$0.623848\pi$
$374$		0			0
$375$	6.47214			0.334220
$376$		0			0
$377$	1.23607	+	0.898056i	0.0636607	+	0.0462522i
$378$		0			0
$379$	8.66312	−	26.6623i	0.444995	−	1.36955i	−0.437495	−	0.899221i	$-0.644134\pi$
$379$	8.66312	−	26.6623i	0.444995	−	1.36955i	0.882490	−	0.470332i	$-0.155866\pi$
$380$		0			0
$381$	−5.76393	+	4.18774i	−0.295295	+	0.214545i
$382$		0			0
$383$	6.00000	+	18.4661i	0.306586	+	0.943574i	0.979081	+	0.203472i	$0.0652226\pi$
$383$	6.00000	+	18.4661i	0.306586	+	0.943574i	−0.672495	+	0.740102i	$0.734777\pi$
$384$		0			0
$385$	−9.34752	+	15.7719i	−0.476394	+	0.803812i
$386$		0			0
$387$	−5.73607	−	17.6538i	−0.291581	−	0.897393i
$388$		0			0
$389$	21.1803	−	15.3884i	1.07389	−	0.780224i	0.0972792	−	0.995257i	$-0.468986\pi$
$389$	21.1803	−	15.3884i	1.07389	−	0.780224i	0.976607	+	0.215033i	$0.0689860\pi$
$390$		0			0
$391$	1.14590	−	3.52671i	0.0579506	−	0.178353i
$392$		0			0
$393$	5.04508	+	3.66547i	0.254491	+	0.184898i
$394$		0			0
$395$	−7.41641			−0.373160
$396$		0			0
$397$	13.2361			0.664299			0.332150	−	0.943227i	$-0.392226\pi$
$397$	13.2361			0.664299			0.332150	+	0.943227i	$0.392226\pi$
$398$		0			0
$399$	−17.0344	−	12.3762i	−0.852789	−	0.619587i
$400$		0			0
$401$	8.75329	−	26.9399i	0.437118	−	1.34531i	−0.453782	−	0.891113i	$-0.649925\pi$
$401$	8.75329	−	26.9399i	0.437118	−	1.34531i	0.890900	−	0.454199i	$-0.150075\pi$
$402$		0			0
$403$	22.1803	−	16.1150i	1.10488	−	0.802743i
$404$		0			0
$405$	−2.18034	−	6.71040i	−0.108342	−	0.333442i
$406$		0			0
$407$	15.4164	+	3.46120i	0.764163	+	0.171565i
$408$		0			0
$409$	1.09017	+	3.35520i	0.0539054	+	0.165904i	0.974385	−	0.224887i	$-0.0722014\pi$
$409$	1.09017	+	3.35520i	0.0539054	+	0.165904i	−0.920479	+	0.390791i	$0.872201\pi$
$410$		0			0
$411$	−7.39919	+	5.37582i	−0.364975	+	0.265170i
$412$		0			0
$413$	−2.88854	+	8.89002i	−0.142136	+	0.437449i
$414$		0			0
$415$	4.61803	+	3.35520i	0.226690	+	0.164700i
$416$		0			0
$417$	0.583592			0.0285786
$418$		0			0
$419$	−28.6180			−1.39808			−0.699041	−	0.715081i	$-0.746390\pi$
$419$	−28.6180			−1.39808			−0.699041	+	0.715081i	$0.746390\pi$
$420$		0			0
$421$	−24.6525	−	17.9111i	−1.20149	−	0.872932i	−0.207058	−	0.978329i	$-0.566389\pi$
$421$	−24.6525	−	17.9111i	−1.20149	−	0.872932i	−0.994430	+	0.105396i	$0.966389\pi$
$422$		0			0
$423$	−2.00000	+	6.15537i	−0.0972433	+	0.299284i
$424$		0			0
$425$	−13.6353	+	9.90659i	−0.661407	+	0.480540i
$426$		0			0
$427$	−8.94427	−	27.5276i	−0.432844	−	1.33216i
$428$		0			0
$429$	6.09017	−	2.62866i	0.294036	−	0.126913i
$430$		0			0
$431$	−1.81966	−	5.60034i	−0.0876499	−	0.269759i	0.897619	−	0.440773i	$-0.145296\pi$
$431$	−1.81966	−	5.60034i	−0.0876499	−	0.269759i	−0.985269	+	0.171014i	$0.945296\pi$
$432$		0			0
$433$	9.16312	−	6.65740i	0.440351	−	0.319934i	−0.345423	−	0.938447i	$-0.612265\pi$
$433$	9.16312	−	6.65740i	0.440351	−	0.319934i	0.785775	+	0.618513i	$0.212265\pi$
$434$		0			0
$435$	−0.111456	+	0.343027i	−0.00534391	+	0.0164469i
$436$		0			0
$437$	4.70820	+	3.42071i	0.225224	+	0.163635i
$438$		0			0
$439$	−6.00000			−0.286364			−0.143182	−	0.989696i	$-0.545733\pi$
$439$	−6.00000			−0.286364			−0.143182	+	0.989696i	$0.545733\pi$
$440$		0			0
$441$	−34.0344			−1.62069
$442$		0			0
$443$	6.26393	+	4.55101i	0.297608	+	0.216225i	0.726561	−	0.687102i	$-0.241117\pi$
$443$	6.26393	+	4.55101i	0.297608	+	0.216225i	−0.428953	+	0.903327i	$0.641117\pi$
$444$		0			0
$445$	−3.29180	+	10.1311i	−0.156046	+	0.480261i
$446$		0			0
$447$	8.85410	−	6.43288i	0.418785	−	0.304265i
$448$		0			0
$449$	−9.50000	−	29.2380i	−0.448333	−	1.37983i	−0.878787	−	0.477214i	$-0.841647\pi$
$449$	−9.50000	−	29.2380i	−0.448333	−	1.37983i	0.430454	−	0.902612i	$-0.358353\pi$
$450$		0			0
$451$	2.57295	+	27.4949i	0.121155	+	1.29468i
$452$		0			0
$453$	0.944272	+	2.90617i	0.0443658	+	0.136544i
$454$		0			0
$455$	−14.4721	+	10.5146i	−0.678464	+	0.492933i
$456$		0			0
$457$	2.28115	−	7.02067i	0.106708	−	0.328413i	−0.883420	−	0.468583i	$-0.844765\pi$
$457$	2.28115	−	7.02067i	0.106708	−	0.328413i	0.990127	+	0.140170i	$0.0447648\pi$
$458$		0			0
$459$	−13.6353	−	9.90659i	−0.636439	−	0.462400i
$460$		0			0
$461$	0.652476			0.0303888			0.0151944	−	0.999885i	$-0.495163\pi$
$461$	0.652476			0.0303888			0.0151944	+	0.999885i	$0.495163\pi$
$462$		0			0
$463$	−34.4721			−1.60206			−0.801028	−	0.598627i	$-0.795713\pi$
$463$	−34.4721			−1.60206			−0.801028	+	0.598627i	$0.795713\pi$
$464$		0			0
$465$	5.23607	+	3.80423i	0.242817	+	0.176417i
$466$		0			0
$467$	−10.6525	+	32.7849i	−0.492938	+	1.51711i	0.327208	+	0.944952i	$0.393892\pi$
$467$	−10.6525	+	32.7849i	−0.492938	+	1.51711i	−0.820146	+	0.572154i	$0.806108\pi$
$468$		0			0
$469$	−13.0902	+	9.51057i	−0.604448	+	0.439157i
$470$		0			0
$471$	−0.708204	−	2.17963i	−0.0326323	−	0.100432i
$472$		0			0
$473$	−15.5344	−	17.6538i	−0.714274	−	0.811723i
$474$		0			0
$475$	−8.17376	−	25.1563i	−0.375038	−	1.15425i
$476$		0			0
$477$	−5.23607	+	3.80423i	−0.239743	+	0.174184i
$478$		0			0
$479$	−3.88854	+	11.9677i	−0.177672	+	0.546819i	−0.999745	−	0.0225631i	$-0.992817\pi$
$479$	−3.88854	+	11.9677i	−0.177672	+	0.546819i	0.822073	+	0.569382i	$0.192817\pi$
$480$		0			0
$481$	12.4721	+	9.06154i	0.568680	+	0.413171i
$482$		0			0
$483$	−2.11146			−0.0960746
$484$		0			0
$485$	−4.18034			−0.189819
$486$		0			0
$487$	−5.76393	−	4.18774i	−0.261189	−	0.189765i	0.449482	−	0.893289i	$-0.351609\pi$
$487$	−5.76393	−	4.18774i	−0.261189	−	0.189765i	−0.710671	+	0.703525i	$0.751609\pi$
$488$		0			0
$489$	1.89261	−	5.82485i	0.0855867	−	0.263409i
$490$		0			0
$491$	20.4443	−	14.8536i	0.922637	−	0.670335i	−0.0215419	−	0.999768i	$-0.506858\pi$
$491$	20.4443	−	14.8536i	0.922637	−	0.670335i	0.944179	+	0.329433i	$0.106858\pi$
$492$		0			0
$493$	−0.708204	−	2.17963i	−0.0318959	−	0.0981655i
$494$		0			0
$495$	−7.09017	−	8.05748i	−0.318679	−	0.362157i
$496$		0			0
$497$	13.4164	+	41.2915i	0.601808	+	1.85218i
$498$		0			0
$499$	−31.8607	+	23.1481i	−1.42628	+	1.03625i	−0.435586	+	0.900147i	$0.643459\pi$
$499$	−31.8607	+	23.1481i	−1.42628	+	1.03625i	−0.990694	+	0.136106i	$0.956541\pi$
$500$		0			0
$501$	−3.56231	+	10.9637i	−0.159152	+	0.489820i
$502$		0			0
$503$	19.1803	+	13.9353i	0.855209	+	0.621346i	0.926577	−	0.376104i	$-0.122737\pi$
$503$	19.1803	+	13.9353i	0.855209	+	0.621346i	−0.0713683	+	0.997450i	$0.522737\pi$
$504$		0			0
$505$	19.4164			0.864019
$506$		0			0
$507$	−1.56231			−0.0693844
$508$		0			0
$509$	7.09017	+	5.15131i	0.314266	+	0.228328i	0.733725	−	0.679447i	$-0.237780\pi$
$509$	7.09017	+	5.15131i	0.314266	+	0.228328i	−0.419459	+	0.907774i	$0.637780\pi$
$510$		0			0
$511$	9.79837	−	30.1563i	0.433455	−	1.33404i
$512$		0			0
$513$	21.3992	−	15.5474i	0.944797	−	0.686435i
$514$		0			0
$515$	−4.87539	−	15.0049i	−0.214835	−	0.661195i
$516$		0			0
$517$	0.763932	+	8.16348i	0.0335977	+	0.359029i
$518$		0			0
$519$	1.70820	+	5.25731i	0.0749818	+	0.230770i
$520$		0			0
$521$	13.6353	−	9.90659i	0.597371	−	0.434016i	−0.247574	−	0.968869i	$-0.579633\pi$
$521$	13.6353	−	9.90659i	0.597371	−	0.434016i	0.844945	+	0.534853i	$0.179633\pi$
$522$		0			0
$523$	0.0623059	−	0.191758i	0.00272445	−	0.00838498i	−0.949685	−	0.313206i	$-0.898597\pi$
$523$	0.0623059	−	0.191758i	0.00272445	−	0.00838498i	0.952409	+	0.304821i	$0.0985968\pi$
$524$		0			0
$525$	7.76393	+	5.64083i	0.338846	+	0.246186i
$526$		0			0
$527$	−41.1246			−1.79142
$528$		0			0
$529$	−22.4164			−0.974626
$530$		0			0
$531$	−4.42705	−	3.21644i	−0.192118	−	0.139582i
$532$		0			0
$533$	−8.32624	+	25.6255i	−0.360649	+	1.10996i
$534$		0			0
$535$	−12.3262	+	8.95554i	−0.532910	+	0.387182i
$536$		0			0
$537$	4.83688	+	14.8864i	0.208727	+	0.642395i
$538$		0			0
$539$	−39.5861	+	17.0863i	−1.70509	+	0.735957i
$540$		0			0
$541$	−2.05573	−	6.32688i	−0.0883827	−	0.272014i	0.897090	−	0.441848i	$-0.145677\pi$
$541$	−2.05573	−	6.32688i	−0.0883827	−	0.272014i	−0.985473	+	0.169834i	$0.945677\pi$
$542$		0			0
$543$	−2.61803	+	1.90211i	−0.112351	+	0.0816275i
$544$		0			0
$545$	5.70820	−	17.5680i	0.244513	−	0.752532i
$546$		0			0
$547$	14.1631	+	10.2901i	0.605571	+	0.439973i	0.847852	−	0.530233i	$-0.177896\pi$
$547$	14.1631	+	10.2901i	0.605571	+	0.439973i	−0.242281	+	0.970206i	$0.577896\pi$
$548$		0			0
$549$	16.9443			0.723164
$550$		0			0
$551$	3.59675			0.153227
$552$		0			0
$553$	−21.7082	−	15.7719i	−0.923127	−	0.670691i
$554$		0			0
$555$	−1.12461	+	3.46120i	−0.0477371	+	0.146920i
$556$		0			0
$557$	17.9443	−	13.0373i	0.760323	−	0.552407i	−0.138686	−	0.990336i	$-0.544288\pi$
$557$	17.9443	−	13.0373i	0.760323	−	0.552407i	0.899009	+	0.437929i	$0.144288\pi$
$558$		0			0
$559$	−7.09017	−	21.8213i	−0.299882	−	0.922943i
$560$		0			0
$561$	−9.70820	−	2.17963i	−0.409881	−	0.0920239i
$562$		0			0
$563$	11.6074	+	35.7239i	0.489193	+	1.50558i	0.825815	+	0.563942i	$0.190716\pi$
$563$	11.6074	+	35.7239i	0.489193	+	1.50558i	−0.336621	+	0.941640i	$0.609284\pi$
$564$		0			0
$565$	7.90983	−	5.74683i	0.332769	−	0.241771i
$566$		0			0
$567$	7.88854	−	24.2784i	0.331288	−	1.01960i
$568$		0			0
$569$	−5.30902	−	3.85723i	−0.222566	−	0.161703i	0.470915	−	0.882178i	$-0.343924\pi$
$569$	−5.30902	−	3.85723i	−0.222566	−	0.161703i	−0.693481	+	0.720475i	$0.743924\pi$
$570$		0			0
$571$	−13.5279			−0.566123			−0.283062	−	0.959102i	$-0.591350\pi$
$571$	−13.5279			−0.566123			−0.283062	+	0.959102i	$0.591350\pi$
$572$		0			0
$573$	−4.76393			−0.199016
$574$		0			0
$575$	−2.14590	−	1.55909i	−0.0894901	−	0.0650184i
$576$		0			0
$577$	−9.55573	+	29.4095i	−0.397810	+	1.22433i	0.528941	+	0.848658i	$0.322589\pi$
$577$	−9.55573	+	29.4095i	−0.397810	+	1.22433i	−0.926751	+	0.375675i	$0.877411\pi$
$578$		0			0
$579$	4.70820	−	3.42071i	0.195666	−	0.142160i
$580$		0			0
$581$	6.38197	+	19.6417i	0.264769	+	0.814874i
$582$		0			0
$583$	−4.18034	+	7.05342i	−0.173132	+	0.292123i
$584$		0			0
$585$	−3.23607	−	9.95959i	−0.133795	−	0.411778i
$586$		0			0
$587$	−25.1074	+	18.2416i	−1.03629	+	0.752911i	−0.969558	−	0.244860i	$-0.921258\pi$
$587$	−25.1074	+	18.2416i	−1.03629	+	0.752911i	−0.0667345	+	0.997771i	$0.521258\pi$
$588$		0			0
$589$	19.9443	−	61.3822i	0.821789	−	2.52921i
$590$		0			0
$591$	4.00000	+	2.90617i	0.164538	+	0.119544i
$592$		0			0
$593$	−10.2016			−0.418931			−0.209465	−	0.977816i	$-0.567172\pi$
$593$	−10.2016			−0.418931			−0.209465	+	0.977816i	$0.567172\pi$
$594$		0			0
$595$	26.8328			1.10004
$596$		0			0
$597$	11.1803	+	8.12299i	0.457581	+	0.332452i
$598$		0			0
$599$	12.6180	−	38.8343i	0.515559	−	1.58673i	−0.266704	−	0.963779i	$-0.585935\pi$
$599$	12.6180	−	38.8343i	0.515559	−	1.58673i	0.782263	−	0.622949i	$-0.214065\pi$
$600$		0			0
$601$	9.97214	−	7.24518i	0.406772	−	0.295537i	−0.365522	−	0.930803i	$-0.619109\pi$
$601$	9.97214	−	7.24518i	0.406772	−	0.295537i	0.772294	+	0.635266i	$0.219109\pi$
$602$		0			0
$603$	−2.92705	−	9.00854i	−0.119199	−	0.366856i
$604$		0			0
$605$	−12.2918	−	5.81234i	−0.499733	−	0.236305i
$606$		0			0
$607$	−10.4164	−	32.0584i	−0.422789	−	1.30121i	−0.905096	−	0.425208i	$-0.860201\pi$
$607$	−10.4164	−	32.0584i	−0.422789	−	1.30121i	0.482307	−	0.876002i	$-0.339799\pi$
$608$		0			0
$609$	−1.05573	+	0.767031i	−0.0427803	+	0.0310817i
$610$		0			0
$611$	−2.47214	+	7.60845i	−0.100012	+	0.307805i
$612$		0			0
$613$	−9.09017	−	6.60440i	−0.367149	−	0.266749i	0.388879	−	0.921289i	$-0.372862\pi$
$613$	−9.09017	−	6.60440i	−0.367149	−	0.266749i	−0.756028	+	0.654540i	$0.772862\pi$
$614$		0			0
$615$	−6.36068			−0.256487
$616$		0			0
$617$	−16.0902			−0.647766			−0.323883	−	0.946097i	$-0.604988\pi$
$617$	−16.0902			−0.647766			−0.323883	+	0.946097i	$0.604988\pi$
$618$		0			0
$619$	−7.39919	−	5.37582i	−0.297398	−	0.216073i	0.429072	−	0.903270i	$-0.358841\pi$
$619$	−7.39919	−	5.37582i	−0.297398	−	0.216073i	−0.726471	+	0.687198i	$0.758841\pi$
$620$		0			0
$621$	0.819660	−	2.52265i	0.0328918	−	0.101231i
$622$		0			0
$623$	−31.1803	+	22.6538i	−1.24921	+	0.907607i
$624$		0			0
$625$	1.36475	+	4.20025i	0.0545898	+	0.168010i
$626$		0			0
$627$	7.96149	−	13.4333i	0.317951	−	0.536474i
$628$		0			0
$629$	−7.14590	−	21.9928i	−0.284926	−	0.876911i
$630$		0			0
$631$	13.0902	−	9.51057i	0.521111	−	0.378610i	−0.295911	−	0.955216i	$-0.595623\pi$
$631$	13.0902	−	9.51057i	0.521111	−	0.378610i	0.817022	+	0.576606i	$0.195623\pi$
$632$		0			0
$633$	2.11803	−	6.51864i	0.0841843	−	0.259093i
$634$		0			0
$635$	11.5279	+	8.37548i	0.457469	+	0.332371i
$636$		0			0
$637$	−42.0689			−1.66683
$638$		0			0
$639$	−25.4164			−1.00546
$640$		0			0
$641$	21.1525	+	15.3682i	0.835473	+	0.607006i	0.921102	−	0.389321i	$-0.127290\pi$
$641$	21.1525	+	15.3682i	0.835473	+	0.607006i	−0.0856297	+	0.996327i	$0.527290\pi$
$642$		0			0
$643$	−0.774575	+	2.38390i	−0.0305463	+	0.0940117i	−0.965167	−	0.261633i	$-0.915739\pi$
$643$	−0.774575	+	2.38390i	−0.0305463	+	0.0940117i	0.934621	+	0.355645i	$0.115739\pi$
$644$		0			0
$645$	4.38197	−	3.18368i	0.172540	−	0.125357i
$646$		0			0
$647$	10.0344	+	30.8828i	0.394495	+	1.21413i	0.929354	+	0.369189i	$0.120364\pi$
$647$	10.0344	+	30.8828i	0.394495	+	1.21413i	−0.534860	+	0.844941i	$0.679636\pi$
$648$		0			0
$649$	−6.76393	−	1.51860i	−0.265508	−	0.0596102i
$650$		0			0
$651$	7.23607	+	22.2703i	0.283604	+	0.872843i
$652$		0			0
$653$	−25.0902	+	18.2291i	−0.981854	+	0.713359i	−0.958122	−	0.286360i	$-0.907555\pi$
$653$	−25.0902	+	18.2291i	−0.981854	+	0.713359i	−0.0237320	+	0.999718i	$0.507555\pi$
$654$		0			0
$655$	3.85410	−	11.8617i	0.150592	−	0.463475i
$656$		0			0
$657$	15.0172	+	10.9106i	0.585878	+	0.425665i
$658$		0			0
$659$	49.5066			1.92850			0.964251	−	0.264990i	$-0.0853686\pi$
$659$	49.5066			1.92850			0.964251	+	0.264990i	$0.0853686\pi$
$660$		0			0
$661$	5.41641			0.210674			0.105337	−	0.994437i	$-0.466408\pi$
$661$	5.41641			0.210674			0.105337	+	0.994437i	$0.466408\pi$
$662$		0			0
$663$	−7.85410	−	5.70634i	−0.305028	−	0.221616i
$664$		0			0
$665$	−13.0132	+	40.0504i	−0.504629	+	1.55309i
$666$		0			0
$667$	0.291796	−	0.212002i	0.0112984	−	0.00820876i
$668$		0			0
$669$	−3.00000	−	9.23305i	−0.115987	−	0.356970i
$670$		0			0
$671$	19.7082	−	8.50651i	0.760827	−	0.328390i
$672$		0			0
$673$	9.08359	+	27.9564i	0.350147	+	1.07764i	0.958770	+	0.284182i	$0.0917219\pi$
$673$	9.08359	+	27.9564i	0.350147	+	1.07764i	−0.608624	+	0.793459i	$0.708278\pi$
$674$		0			0
$675$	−9.75329	+	7.08618i	−0.375404	+	0.272747i
$676$		0			0
$677$	−1.09017	+	3.35520i	−0.0418986	+	0.128951i	−0.969818	−	0.243831i	$-0.921596\pi$
$677$	−1.09017	+	3.35520i	−0.0418986	+	0.128951i	0.927919	+	0.372781i	$0.121596\pi$
$678$		0			0
$679$	−12.2361	−	8.89002i	−0.469577	−	0.341168i
$680$		0			0
$681$	10.5967			0.406068
$682$		0			0
$683$	−0.583592			−0.0223305			−0.0111653	−	0.999938i	$-0.503554\pi$
$683$	−0.583592			−0.0223305			−0.0111653	+	0.999938i	$0.503554\pi$
$684$		0			0
$685$	14.7984	+	10.7516i	0.565417	+	0.410799i
$686$		0			0
$687$	1.18034	−	3.63271i	0.0450328	−	0.138597i
$688$		0			0
$689$	−6.47214	+	4.70228i	−0.246569	+	0.179143i
$690$		0			0
$691$	2.46556	+	7.58821i	0.0937943	+	0.288669i	0.986938	−	0.161103i	$-0.0515052\pi$
$691$	2.46556	+	7.58821i	0.0937943	+	0.288669i	−0.893143	+	0.449772i	$0.851505\pi$
$692$		0			0
$693$	−3.61803	−	38.6628i	−0.137438	−	1.46868i
$694$		0			0
$695$	−0.360680	−	1.11006i	−0.0136814	−	0.0421069i
$696$		0			0
$697$	32.6976	−	23.7562i	1.23851	−	0.899829i
$698$		0			0
$699$	3.64590	−	11.2209i	0.137901	−	0.424414i
$700$		0			0
$701$	37.8885	+	27.5276i	1.43103	+	1.03970i	0.989824	+	0.142299i	$0.0454495\pi$
$701$	37.8885	+	27.5276i	1.43103	+	1.03970i	0.441207	+	0.897405i	$0.354551\pi$
$702$		0			0
$703$	36.2918			1.36877
$704$		0			0
$705$	−1.88854			−0.0711267
$706$		0			0
$707$	56.8328	+	41.2915i	2.13742	+	1.55293i
$708$		0			0
$709$	−13.4508	+	41.3975i	−0.505157	+	1.55471i	0.295349	+	0.955390i	$0.404564\pi$
$709$	−13.4508	+	41.3975i	−0.505157	+	1.55471i	−0.800506	+	0.599325i	$0.795436\pi$
$710$		0			0
$711$	12.7082	−	9.23305i	0.476595	−	0.346266i
$712$		0			0
$713$	−2.00000	−	6.15537i	−0.0749006	−	0.230520i
$714$		0			0
$715$	−8.76393	−	9.95959i	−0.327752	−	0.372468i
$716$		0			0
$717$	5.29180	+	16.2865i	0.197626	+	0.608230i
$718$		0			0
$719$	9.70820	−	7.05342i	0.362055	−	0.263048i	−0.391854	−	0.920028i	$-0.628166\pi$
$719$	9.70820	−	7.05342i	0.362055	−	0.263048i	0.753909	+	0.656979i	$0.228166\pi$
$720$		0			0
$721$	17.6393	−	54.2882i	0.656923	−	2.02180i
$722$		0			0
$723$	−6.33688	−	4.60401i	−0.235671	−	0.171225i
$724$		0			0
$725$	−1.63932			−0.0608828
$726$		0			0
$727$	47.1246			1.74776			0.873878	−	0.486146i	$-0.161598\pi$
$727$	47.1246			1.74776			0.873878	+	0.486146i	$0.161598\pi$
$728$		0			0
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$		0			0
$731$	−10.6353	+	32.7319i	−0.393359	+	1.21063i
$732$		0			0
$733$	27.7984	−	20.1967i	1.02676	−	0.745982i	0.0590995	−	0.998252i	$-0.481177\pi$
$733$	27.7984	−	20.1967i	1.02676	−	0.745982i	0.967657	+	0.252270i	$0.0811771\pi$
$734$		0			0
$735$	−3.06888	−	9.44505i	−0.113197	−	0.348386i
$736$		0			0
$737$	−7.92705	−	9.00854i	−0.291997	−	0.331834i
$738$		0			0
$739$	−8.53444	−	26.2663i	−0.313945	−	0.966222i	−0.976187	−	0.216932i	$-0.930395\pi$
$739$	−8.53444	−	26.2663i	−0.313945	−	0.966222i	0.662242	−	0.749290i	$-0.269605\pi$
$740$		0			0
$741$	12.3262	−	8.95554i	0.452816	−	0.328990i
$742$		0			0
$743$	−0.381966	+	1.17557i	−0.0140130	+	0.0431275i	−0.957819	−	0.287374i	$-0.907218\pi$
$743$	−0.381966	+	1.17557i	−0.0140130	+	0.0431275i	0.943806	+	0.330501i	$0.107218\pi$
$744$		0			0
$745$	−17.7082	−	12.8658i	−0.648778	−	0.471365i
$746$		0			0
$747$	−12.0902			−0.442356
$748$		0			0
$749$	−55.1246			−2.01421
$750$		0			0
$751$	−8.38197	−	6.08985i	−0.305862	−	0.222222i	0.424257	−	0.905542i	$-0.360535\pi$
$751$	−8.38197	−	6.08985i	−0.305862	−	0.222222i	−0.730119	+	0.683320i	$0.760535\pi$
$752$		0			0
$753$	0.763932	−	2.35114i	0.0278392	−	0.0856803i
$754$		0			0
$755$	4.94427	−	3.59222i	0.179940	−	0.130734i
$756$		0			0
$757$	14.7426	+	45.3732i	0.535831	+	1.64912i	0.741848	+	0.670569i	$0.233950\pi$
$757$	14.7426	+	45.3732i	0.535831	+	1.64912i	−0.206017	+	0.978548i	$0.566050\pi$
$758$		0			0
$759$	−0.145898	−	1.55909i	−0.00529576	−	0.0565912i
$760$		0			0
$761$	4.38854	+	13.5065i	0.159085	+	0.489612i	0.998552	−	0.0537983i	$-0.0171328\pi$
$761$	4.38854	+	13.5065i	0.159085	+	0.489612i	−0.839467	+	0.543410i	$0.817133\pi$
$762$		0			0
$763$	54.0689	−	39.2833i	1.95743	−	1.42215i
$764$		0			0
$765$	−4.85410	+	14.9394i	−0.175500	+	0.540135i
$766$		0			0
$767$	−5.47214	−	3.97574i	−0.197587	−	0.143556i
$768$		0			0
$769$	−45.4164			−1.63776			−0.818879	−	0.573967i	$-0.805404\pi$
$769$	−45.4164			−1.63776			−0.818879	+	0.573967i	$0.805404\pi$
$770$		0			0
$771$	0.965558			0.0347737
$772$		0			0
$773$	−23.3262	−	16.9475i	−0.838986	−	0.609559i	0.0831009	−	0.996541i	$-0.473518\pi$
$773$	−23.3262	−	16.9475i	−0.838986	−	0.609559i	−0.922087	+	0.386982i	$0.873518\pi$
$774$		0			0
$775$	−9.09017	+	27.9767i	−0.326529	+	1.00495i
$776$		0			0
$777$	−10.6525	+	7.73948i	−0.382155	+	0.277652i
$778$		0			0
$779$	19.6008	+	60.3251i	0.702272	+	2.16137i
$780$		0			0
$781$	−29.5623	+	12.7598i	−1.05782	+	0.456580i
$782$		0			0
$783$	−0.506578	−	1.55909i	−0.0181036	−	0.0557172i
$784$		0			0
$785$	−3.70820	+	2.69417i	−0.132351	+	0.0961590i
$786$		0			0
$787$	−16.8262	+	51.7858i	−0.599791	+	1.84597i	−0.0705240	+	0.997510i	$0.522467\pi$
$787$	−16.8262	+	51.7858i	−0.599791	+	1.84597i	−0.529267	+	0.848456i	$0.677533\pi$
$788$		0			0
$789$	−11.0902	−	8.05748i	−0.394821	−	0.286854i
$790$		0			0
$791$	35.3738			1.25775
$792$		0			0
$793$	20.9443			0.743753
$794$		0			0
$795$	−1.52786	−	1.11006i	−0.0541878	−	0.0393697i
$796$		0			0
$797$	1.43769	−	4.42477i	0.0509257	−	0.156733i	−0.922359	−	0.386333i	$-0.873742\pi$
$797$	1.43769	−	4.42477i	0.0509257	−	0.156733i	0.973285	+	0.229599i	$0.0737416\pi$
$798$		0			0
$799$	9.70820	−	7.05342i	0.343452	−	0.249532i
$800$		0			0
$801$	−6.97214	−	21.4580i	−0.246348	−	0.758182i
$802$		0			0
$803$	22.9443	+	5.15131i	0.809686	+	0.181786i
$804$		0			0
$805$	1.30495	+	4.01623i	0.0459935	+	0.141553i
$806$		0			0
$807$	4.09017	−	2.97168i	0.143981	−	0.104608i
$808$		0			0
$809$	4.68034	−	14.4046i	0.164552	−	0.506439i	−0.834451	−	0.551082i	$-0.814215\pi$
$809$	4.68034	−	14.4046i	0.164552	−	0.506439i	0.999003	+	0.0446432i	$0.0142151\pi$
$810$		0			0
$811$	−11.4443	−	8.31475i	−0.401863	−	0.291970i	0.368437	−	0.929653i	$-0.379893\pi$
$811$	−11.4443	−	8.31475i	−0.401863	−	0.291970i	−0.770299	+	0.637683i	$0.779893\pi$
$812$		0			0
$813$	0.291796			0.0102337
$814$		0			0
$815$	−12.2492			−0.429072
$816$		0			0
$817$	−43.6976	−	31.7481i	−1.52878	−	1.11073i
$818$		0			0
$819$	11.7082	−	36.0341i	0.409118	−	1.25913i
$820$		0			0
$821$	29.5623	−	21.4783i	1.03173	−	0.749597i	0.0630771	−	0.998009i	$-0.479909\pi$
$821$	29.5623	−	21.4783i	1.03173	−	0.749597i	0.968655	+	0.248412i	$0.0799086\pi$
$822$		0			0
$823$	13.3262	+	41.0139i	0.464523	+	1.42966i	0.859581	+	0.511000i	$0.170725\pi$
$823$	13.3262	+	41.0139i	0.464523	+	1.42966i	−0.395057	+	0.918656i	$0.629275\pi$
$824$		0			0
$825$	−3.62868	+	6.12261i	−0.126334	+	0.213162i
$826$		0			0
$827$	−6.53444	−	20.1109i	−0.227225	−	0.699326i	−0.998058	−	0.0622892i	$-0.980160\pi$
$827$	−6.53444	−	20.1109i	−0.227225	−	0.699326i	0.770833	−	0.637037i	$-0.219840\pi$
$828$		0			0
$829$	41.1246	−	29.8788i	1.42832	−	1.03773i	0.437990	−	0.898980i	$-0.355691\pi$
$829$	41.1246	−	29.8788i	1.42832	−	1.03773i	0.990327	−	0.138753i	$-0.0443094\pi$
$830$		0			0
$831$	−2.32624	+	7.15942i	−0.0806963	+	0.248358i
$832$		0			0
$833$	51.0517	+	37.0912i	1.76884	+	1.28513i
$834$		0			0
$835$	23.0557			0.797876
$836$		0			0
$837$	−29.4164			−1.01678
$838$		0			0
$839$	−1.14590	−	0.832544i	−0.0395608	−	0.0287426i	0.567829	−	0.823146i	$-0.307783\pi$
$839$	−1.14590	−	0.832544i	−0.0395608	−	0.0287426i	−0.607390	+	0.794404i	$0.707783\pi$
$840$		0			0
$841$	−8.89261	+	27.3686i	−0.306642	+	0.943746i
$842$		0			0
$843$	4.63525	−	3.36771i	0.159647	−	0.115990i
$844$		0			0
$845$	0.965558	+	2.97168i	0.0332162	+	0.102229i
$846$		0			0
$847$	−23.6180	−	43.1531i	−0.811525	−	1.48276i
$848$		0			0
$849$	1.70820	+	5.25731i	0.0586254	+	0.180430i
$850$		0			0
$851$	2.94427	−	2.13914i	0.100928	−	0.0733287i
$852$		0			0
$853$	8.76393	−	26.9726i	0.300071	−	0.923525i	−0.681399	−	0.731912i	$-0.738628\pi$
$853$	8.76393	−	26.9726i	0.300071	−	0.923525i	0.981471	−	0.191613i	$-0.0613717\pi$
$854$		0			0
$855$	−19.9443	−	14.4904i	−0.682080	−	0.495560i
$856$		0			0
$857$	31.7426			1.08431			0.542154	−	0.840279i	$-0.317609\pi$
$857$	31.7426			1.08431			0.542154	+	0.840279i	$0.317609\pi$
$858$		0			0
$859$	−6.49342			−0.221553			−0.110776	−	0.993845i	$-0.535334\pi$
$859$	−6.49342			−0.221553			−0.110776	+	0.993845i	$0.535334\pi$
$860$		0			0
$861$	−18.6180	−	13.5268i	−0.634501	−	0.460992i
$862$		0			0
$863$	−6.23607	+	19.1926i	−0.212278	+	0.653325i	0.787057	+	0.616880i	$0.211604\pi$
$863$	−6.23607	+	19.1926i	−0.212278	+	0.653325i	−0.999336	+	0.0364454i	$0.988396\pi$
$864$		0			0
$865$	8.94427	−	6.49839i	0.304114	−	0.220952i
$866$		0			0
$867$	1.25329	+	3.85723i	0.0425639	+	0.130998i
$868$		0			0
$869$	10.1459	−	17.1190i	0.344176	−	0.580723i
$870$		0			0
$871$	−3.61803	−	11.1352i	−0.122592	−	0.377301i
$872$		0			0
$873$	7.16312	−	5.20431i	0.242435	−	0.176139i
$874$		0			0
$875$	14.4721	−	44.5407i	0.489247	−	1.50575i
$876$		0			0
$877$	44.1246	+	32.0584i	1.48998	+	1.08254i	0.974165	+	0.225837i	$0.0725116\pi$
$877$	44.1246	+	32.0584i	1.48998	+	1.08254i	0.515817	+	0.856699i	$0.327488\pi$
$878$		0			0
$879$	13.8885			0.468449
$880$		0			0
$881$	−27.3820			−0.922522			−0.461261	−	0.887265i	$-0.652603\pi$
$881$	−27.3820			−0.922522			−0.461261	+	0.887265i	$0.652603\pi$
$882$		0			0
$883$	−37.8607	−	27.5074i	−1.27411	−	0.925698i	−0.274755	−	0.961514i	$-0.588597\pi$
$883$	−37.8607	−	27.5074i	−1.27411	−	0.925698i	−0.999358	+	0.0358168i	$0.988597\pi$
$884$		0			0
$885$	0.493422	−	1.51860i	0.0165862	−	0.0510471i
$886$		0			0
$887$	0.381966	−	0.277515i	0.0128252	−	0.00931803i	−0.581354	−	0.813651i	$-0.697477\pi$
$887$	0.381966	−	0.277515i	0.0128252	−	0.00931803i	0.594179	+	0.804333i	$0.297477\pi$
$888$		0			0
$889$	15.9311	+	49.0309i	0.534312	+	1.64444i
$890$		0			0
$891$	18.4721	+	4.14725i	0.618840	+	0.138938i
$892$		0			0
$893$	5.81966	+	17.9111i	0.194748	+	0.599371i
$894$		0			0
$895$	25.3262	−	18.4006i	0.846563	−	0.615064i
$896$		0			0
$897$	0.472136	−	1.45309i	0.0157642	−	0.0485171i
$898$		0			0
$899$	−3.23607	−	2.35114i	−0.107929	−	0.0784149i
$900$		0			0
$901$	12.0000			0.399778
$902$		0			0
$903$	19.5967			0.652139
$904$		0			0
$905$	5.23607	+	3.80423i	0.174053	+	0.126457i
$906$		0			0
$907$	0.881966	−	2.71441i	0.0292852	−	0.0901306i	−0.935346	−	0.353735i	$-0.884911\pi$
$907$	0.881966	−	2.71441i	0.0292852	−	0.0901306i	0.964631	+	0.263605i	$0.0849114\pi$
$908$		0			0
$909$	−33.2705	+	24.1724i	−1.10351	+	0.801749i
$910$		0			0
$911$	−6.05573	−	18.6376i	−0.200635	−	0.617492i	−0.999864	−	0.0164654i	$-0.994759\pi$
$911$	−6.05573	−	18.6376i	−0.200635	−	0.617492i	0.799229	−	0.601026i	$-0.205241\pi$
$912$		0			0
$913$	−14.0623	+	6.06961i	−0.465394	+	0.200875i
$914$		0			0
$915$	1.52786	+	4.70228i	0.0505096	+	0.155453i
$916$		0			0
$917$	36.5066	−	26.5236i	1.20555	−	0.875886i
$918$		0			0
$919$	−5.12461	+	15.7719i	−0.169045	+	0.520268i	−0.999312	−	0.0370989i	$-0.988188\pi$
$919$	−5.12461	+	15.7719i	−0.169045	+	0.520268i	0.830266	+	0.557367i	$0.188188\pi$
$920$		0			0
$921$	0.927051	+	0.673542i	0.0305474	+	0.0221940i
$922$		0			0
$923$	−31.4164			−1.03408
$924$		0			0
$925$	−16.5410			−0.543865
$926$		0			0
$927$	27.0344	+	19.6417i	0.887928	+	0.645117i
$928$		0			0
$929$	8.79180	−	27.0584i	0.288449	−	0.887756i	−0.696894	−	0.717174i	$-0.745435\pi$
$929$	8.79180	−	27.0584i	0.288449	−	0.887756i	0.985343	−	0.170582i	$-0.0545648\pi$
$930$		0			0
$931$	−80.1205	+	58.2110i	−2.62584	+	1.90779i
$932$		0			0
$933$	−2.52786	−	7.77997i	−0.0827586	−	0.254705i
$934$		0			0
$935$	1.85410	+	19.8132i	0.0606356	+	0.647960i
$936$		0			0
$937$	−3.84752	−	11.8415i	−0.125693	−	0.386844i	0.868334	−	0.495981i	$-0.165191\pi$
$937$	−3.84752	−	11.8415i	−0.125693	−	0.386844i	−0.994027	+	0.109137i	$0.965191\pi$
$938$		0			0
$939$	−8.80902	+	6.40013i	−0.287471	+	0.208860i
$940$		0			0
$941$	0.201626	−	0.620541i	0.00657282	−	0.0202291i	−0.947716	−	0.319114i	$-0.896615\pi$
$941$	0.201626	−	0.620541i	0.00657282	−	0.0202291i	0.954289	+	0.298885i	$0.0966147\pi$
$942$		0			0
$943$	5.14590	+	3.73871i	0.167573	+	0.121749i
$944$		0			0
$945$	19.1935			0.624364
$946$		0			0
$947$	0.201626			0.00655197			0.00327598	−	0.999995i	$-0.498957\pi$
$947$	0.201626			0.00655197			0.00327598	+	0.999995i	$0.498957\pi$
$948$		0			0
$949$	18.5623	+	13.4863i	0.602558	+	0.437784i
$950$		0			0
$951$	−4.61803	+	14.2128i	−0.149750	+	0.460883i
$952$		0			0
$953$	−16.4443	+	11.9475i	−0.532682	+	0.387016i	−0.821360	−	0.570410i	$-0.806784\pi$
$953$	−16.4443	+	11.9475i	−0.532682	+	0.387016i	0.288678	+	0.957426i	$0.406784\pi$
$954$		0			0
$955$	2.94427	+	9.06154i	0.0952744	+	0.293224i
$956$		0			0
$957$	−0.639320	−	0.726543i	−0.0206663	−	0.0234858i
$958$		0			0
$959$	20.4508	+	62.9412i	0.660392	+	2.03248i
$960$		0			0
$961$	−32.9894	+	23.9682i	−1.06417	+	0.773167i
$962$		0			0
$963$	9.97214	−	30.6911i	0.321348	−	0.989006i
$964$		0			0
$965$	−9.41641	−	6.84142i	−0.303125	−	0.220233i
$966$		0			0
$967$	−34.3607			−1.10496			−0.552482	−	0.833525i	$-0.686319\pi$
$967$	−34.3607			−1.10496			−0.552482	+	0.833525i	$0.686319\pi$
$968$		0			0
$969$	−22.8541			−0.734180
$970$		0			0
$971$	−28.9443	−	21.0292i	−0.928866	−	0.674861i	0.0168490	−	0.999858i	$-0.494637\pi$
$971$	−28.9443	−	21.0292i	−0.928866	−	0.674861i	−0.945715	+	0.324997i	$0.894637\pi$
$972$		0			0
$973$	1.30495	−	4.01623i	0.0418348	−	0.128754i
$974$		0			0
$975$	−5.61803	+	4.08174i	−0.179921	+	0.130720i
$976$		0			0
$977$	−10.0344	−	30.8828i	−0.321030	−	0.988029i	−0.973201	−	0.229957i	$-0.926141\pi$
$977$	−10.0344	−	30.8828i	−0.321030	−	0.988029i	0.652171	−	0.758072i	$-0.273859\pi$
$978$		0			0
$979$	−18.8820	−	21.4580i	−0.603470	−	0.685802i
$980$		0			0
$981$	12.0902	+	37.2097i	0.386009	+	1.18801i
$982$		0			0
$983$	−43.2148	+	31.3974i	−1.37834	+	1.00142i	−0.381304	+	0.924450i	$0.624525\pi$
$983$	−43.2148	+	31.3974i	−1.37834	+	1.00142i	−0.997033	+	0.0769712i	$0.975475\pi$
$984$		0			0
$985$	3.05573	−	9.40456i	0.0973636	−	0.299654i
$986$		0			0
$987$	−5.52786	−	4.01623i	−0.175954	−	0.127838i
$988$		0			0
$989$	−5.41641			−0.172232
$990$		0			0
$991$	1.70820			0.0542629			0.0271314	−	0.999632i	$-0.491363\pi$
$991$	1.70820			0.0542629			0.0271314	+	0.999632i	$0.491363\pi$
$992$		0			0
$993$	−2.60081	−	1.88960i	−0.0825343	−	0.0599647i
$994$		0			0
$995$	8.54102	−	26.2866i	0.270769	−	0.833340i
$996$		0			0
$997$	−10.6180	+	7.71445i	−0.336277	+	0.244319i	−0.743089	−	0.669192i	$-0.766640\pi$
$997$	−10.6180	+	7.71445i	−0.336277	+	0.244319i	0.406813	+	0.913512i	$0.366640\pi$
$998$		0			0
$999$	−5.11146	−	15.7314i	−0.161719	−	0.497721i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.a.225.1	yes	4
4.3	odd	2		352.2.m.b.225.1	yes	4
8.3	odd	2		704.2.m.c.577.1		4
8.5	even	2		704.2.m.f.577.1		4
11.3	even	5		3872.2.a.n.1.2		2
11.8	odd	10		3872.2.a.o.1.2		2
11.9	even	5	inner	352.2.m.a.97.1	✓	4
44.3	odd	10		3872.2.a.y.1.1		2
44.19	even	10		3872.2.a.z.1.1		2
44.31	odd	10		352.2.m.b.97.1	yes	4
88.3	odd	10		7744.2.a.ca.1.2		2
88.19	even	10		7744.2.a.bz.1.2		2
88.53	even	10		704.2.m.f.449.1		4
88.69	even	10		7744.2.a.cp.1.1		2
88.75	odd	10		704.2.m.c.449.1		4
88.85	odd	10		7744.2.a.co.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.a.97.1	✓	4	11.9	even	5	inner
352.2.m.a.225.1	yes	4	1.1	even	1	trivial
352.2.m.b.97.1	yes	4	44.31	odd	10
352.2.m.b.225.1	yes	4	4.3	odd	2
704.2.m.c.449.1		4	88.75	odd	10
704.2.m.c.577.1		4	8.3	odd	2
704.2.m.f.449.1		4	88.53	even	10
704.2.m.f.577.1		4	8.5	even	2
3872.2.a.n.1.2		2	11.3	even	5
3872.2.a.o.1.2		2	11.8	odd	10
3872.2.a.y.1.1		2	44.3	odd	10
3872.2.a.z.1.1		2	44.19	even	10
7744.2.a.bz.1.2		2	88.19	even	10
7744.2.a.ca.1.2		2	88.3	odd	10
7744.2.a.co.1.1		2	88.85	odd	10
7744.2.a.cp.1.1		2	88.69	even	10

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	352.2.m.a.225.1

Level	$352$
Weight	$2$
Character	352.225
Analytic conductor	$2.811$
Analytic rank	$1$
Dimension	$4$
Inner twists	$2$