LMFDB - Embedded newform 1716.2.z.f.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,2,Mod(157,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8, 0]))

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

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

chi := DirichletCharacter("1716.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1716.z (of order $5$, degree $4$, 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:	$13.7023289869$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 41 x^{18} - 146 x^{17} + 650 x^{16} - 1400 x^{15} + 5756 x^{14} - 2122 x^{13} + \cdots + 4096 $ x^20 - 6x^19 + 41x^18 - 146x^17 + 650x^16 - 1400x^15 + 5756x^14 - 2122x^13 + 27469x^12 + 11286x^11 + 72308x^10 + 48512x^9 + 142448x^8 - 37952x^7 + 295552x^6 + 300160x^5 + 272128x^4 + 194048x^3 + 236544x^2 + 49152*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.5
Root			$-0.687849 - 2.11698i$ of defining polynomial
Character	$\chi$	$=$	1716.157
Dual form			1716.2.z.f.1093.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(3.52109 + 2.55822i) q^{5} +(-1.38105 + 4.25044i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(3.52109 + 2.55822i) q^{5} +(-1.38105 + 4.25044i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-3.14705 + 1.04694i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(1.34494 - 4.13929i) q^{15} +(4.08696 + 2.96935i) q^{17} +(-1.58416 - 4.87554i) q^{19} +4.46917 q^{21} -8.53920 q^{23} +(4.30850 + 13.2602i) q^{25} +(0.809017 + 0.587785i) q^{27} +(0.262102 - 0.806668i) q^{29} +(-0.222884 + 0.161934i) q^{31} +(1.96819 + 2.66950i) q^{33} +(-15.7364 + 11.4331i) q^{35} +(-1.14217 + 3.51523i) q^{37} +(0.809017 + 0.587785i) q^{39} +(-2.82382 - 8.69084i) q^{41} +8.30994 q^{43} -4.35231 q^{45} +(-2.66149 - 8.19121i) q^{47} +(-10.4958 - 7.62565i) q^{49} +(1.56108 - 4.80451i) q^{51} +(-7.31930 + 5.31779i) q^{53} +(-13.7594 - 4.36448i) q^{55} +(-4.14738 + 3.01325i) q^{57} +(-1.35755 + 4.17810i) q^{59} +(-5.80029 - 4.21416i) q^{61} +(-1.38105 - 4.25044i) q^{63} -4.35231 q^{65} -1.93483 q^{67} +(2.63876 + 8.12126i) q^{69} +(12.6379 + 9.18196i) q^{71} +(1.82418 - 5.61424i) q^{73} +(11.2798 - 8.19525i) q^{75} +(-0.103715 - 14.8222i) q^{77} +(-3.73294 + 2.71214i) q^{79} +(0.309017 - 0.951057i) q^{81} +(3.31980 + 2.41197i) q^{83} +(6.79430 + 20.9107i) q^{85} -0.848181 q^{87} +7.68527 q^{89} +(-1.38105 - 4.25044i) q^{91} +(0.222884 + 0.161934i) q^{93} +(6.89474 - 21.2198i) q^{95} +(-6.27491 + 4.55899i) q^{97} +(1.93064 - 2.69678i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	$ 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) $ 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	3.52109	+	2.55822i	1.57468	+	1.14407i	0.922493	+	0.386014i	$0.126148\pi$
$5$	3.52109	+	2.55822i	1.57468	+	1.14407i	0.652187	+	0.758058i	$0.273852\pi$
$6$		0			0
$7$	−1.38105	+	4.25044i	−0.521988	+	1.60651i	0.248208	+	0.968707i	$0.420159\pi$
$7$	−1.38105	+	4.25044i	−0.521988	+	1.60651i	−0.770196	+	0.637808i	$0.779841\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	−3.14705	+	1.04694i	−0.948871	+	0.315664i
$11$	−3.14705	+	1.04694i	−0.948871	+	0.315664i
$12$		0			0
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i
$14$		0			0
$15$	1.34494	−	4.13929i	0.347261	−	1.06876i
$16$		0			0
$17$	4.08696	+	2.96935i	0.991234	+	0.720174i	0.960191	−	0.279344i	$-0.0901171\pi$
$17$	4.08696	+	2.96935i	0.991234	+	0.720174i	0.0310430	+	0.999518i	$0.490117\pi$
$18$		0			0
$19$	−1.58416	−	4.87554i	−0.363431	−	1.11852i	−0.950958	−	0.309320i	$-0.899898\pi$
$19$	−1.58416	−	4.87554i	−0.363431	−	1.11852i	0.587527	−	0.809204i	$-0.300102\pi$
$20$		0			0
$21$	4.46917			0.975254
$22$		0			0
$23$	−8.53920			−1.78055			−0.890273	−	0.455428i	$-0.849486\pi$
$23$	−8.53920			−1.78055			−0.890273	+	0.455428i	$0.849486\pi$
$24$		0			0
$25$	4.30850	+	13.2602i	0.861699	+	2.65204i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	0.262102	−	0.806668i	0.0486712	−	0.149795i	−0.923767	−	0.382955i	$-0.874907\pi$
$29$	0.262102	−	0.806668i	0.0486712	−	0.149795i	0.972438	+	0.233160i	$0.0749066\pi$
$30$		0			0
$31$	−0.222884	+	0.161934i	−0.0400311	+	0.0290843i	−0.607621	−	0.794227i	$-0.707876\pi$
$31$	−0.222884	+	0.161934i	−0.0400311	+	0.0290843i	0.567590	+	0.823311i	$0.307876\pi$
$32$		0			0
$33$	1.96819	+	2.66950i	0.342618	+	0.464700i
$34$		0			0
$35$	−15.7364	+	11.4331i	−2.65993	+	1.93255i
$36$		0			0
$37$	−1.14217	+	3.51523i	−0.187771	+	0.577900i	−0.999985	−	0.00545946i	$-0.998262\pi$
$37$	−1.14217	+	3.51523i	−0.187771	+	0.577900i	0.812214	+	0.583360i	$0.198262\pi$
$38$		0			0
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$		0			0
$41$	−2.82382	−	8.69084i	−0.441007	−	1.35728i	−0.886804	−	0.462146i	$-0.847079\pi$
$41$	−2.82382	−	8.69084i	−0.441007	−	1.35728i	0.445796	−	0.895134i	$-0.352921\pi$
$42$		0			0
$43$	8.30994			1.26725			0.633627	−	0.773639i	$-0.281565\pi$
$43$	8.30994			1.26725			0.633627	+	0.773639i	$0.281565\pi$
$44$		0			0
$45$	−4.35231			−0.648804
$46$		0			0
$47$	−2.66149	−	8.19121i	−0.388218	−	1.19481i	−0.934119	−	0.356962i	$-0.883813\pi$
$47$	−2.66149	−	8.19121i	−0.388218	−	1.19481i	0.545901	−	0.837849i	$-0.316187\pi$
$48$		0			0
$49$	−10.4958	−	7.62565i	−1.49940	−	1.08938i
$50$		0			0
$51$	1.56108	−	4.80451i	0.218595	−	0.672766i
$52$		0			0
$53$	−7.31930	+	5.31779i	−1.00538	+	0.730454i	−0.963236	−	0.268657i	$-0.913420\pi$
$53$	−7.31930	+	5.31779i	−1.00538	+	0.730454i	−0.0421478	+	0.999111i	$0.513420\pi$
$54$		0			0
$55$	−13.7594	−	4.36448i	−1.85531	−	0.588507i
$56$		0			0
$57$	−4.14738	+	3.01325i	−0.549334	+	0.399114i
$58$		0			0
$59$	−1.35755	+	4.17810i	−0.176738	+	0.543942i	−0.999709	−	0.0241410i	$-0.992315\pi$
$59$	−1.35755	+	4.17810i	−0.176738	+	0.543942i	0.822971	+	0.568083i	$0.192315\pi$
$60$		0			0
$61$	−5.80029	−	4.21416i	−0.742651	−	0.539567i	0.150889	−	0.988551i	$-0.451786\pi$
$61$	−5.80029	−	4.21416i	−0.742651	−	0.539567i	−0.893540	+	0.448983i	$0.851786\pi$
$62$		0			0
$63$	−1.38105	−	4.25044i	−0.173996	−	0.535505i
$64$		0			0
$65$	−4.35231			−0.539837
$66$		0			0
$67$	−1.93483			−0.236378			−0.118189	−	0.992991i	$-0.537709\pi$
$67$	−1.93483			−0.236378			−0.118189	+	0.992991i	$0.537709\pi$
$68$		0			0
$69$	2.63876	+	8.12126i	0.317669	+	0.977685i
$70$		0			0
$71$	12.6379	+	9.18196i	1.49984	+	1.08970i	0.970445	+	0.241322i	$0.0775811\pi$
$71$	12.6379	+	9.18196i	1.49984	+	1.08970i	0.529395	+	0.848375i	$0.322419\pi$
$72$		0			0
$73$	1.82418	−	5.61424i	0.213504	−	0.657097i	−0.785753	−	0.618541i	$-0.787724\pi$
$73$	1.82418	−	5.61424i	0.213504	−	0.657097i	0.999256	−	0.0385562i	$-0.0122759\pi$
$74$		0			0
$75$	11.2798	−	8.19525i	1.30248	−	0.946306i
$76$		0			0
$77$	−0.103715	−	14.8222i	−0.0118194	−	1.68915i
$78$		0			0
$79$	−3.73294	+	2.71214i	−0.419989	+	0.305140i	−0.777633	−	0.628718i	$-0.783580\pi$
$79$	−3.73294	+	2.71214i	−0.419989	+	0.305140i	0.357645	+	0.933858i	$0.383580\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	3.31980	+	2.41197i	0.364395	+	0.264748i	0.754883	−	0.655860i	$-0.227694\pi$
$83$	3.31980	+	2.41197i	0.364395	+	0.264748i	−0.390488	+	0.920608i	$0.627694\pi$
$84$		0			0
$85$	6.79430	+	20.9107i	0.736946	+	2.26809i
$86$		0			0
$87$	−0.848181			−0.0909346
$88$		0			0
$89$	7.68527			0.814637			0.407318	−	0.913286i	$-0.366464\pi$
$89$	7.68527			0.814637			0.407318	+	0.913286i	$0.366464\pi$
$90$		0			0
$91$	−1.38105	−	4.25044i	−0.144773	−	0.445567i
$92$		0			0
$93$	0.222884	+	0.161934i	0.0231119	+	0.0167918i
$94$		0			0
$95$	6.89474	−	21.2198i	0.707386	−	2.17711i
$96$		0			0
$97$	−6.27491	+	4.55899i	−0.637120	+	0.462895i	−0.858860	−	0.512211i	$-0.828827\pi$
$97$	−6.27491	+	4.55899i	−0.637120	+	0.462895i	0.221739	+	0.975106i	$0.428827\pi$
$98$		0			0
$99$	1.93064	−	2.69678i	0.194037	−	0.271037i
$100$		0			0
$101$	6.24651	−	4.53835i	0.621551	−	0.451583i	−0.231912	−	0.972737i	$-0.574498\pi$
$101$	6.24651	−	4.53835i	0.621551	−	0.451583i	0.853463	+	0.521154i	$0.174498\pi$
$102$		0			0
$103$	−1.89223	+	5.82367i	−0.186447	+	0.573824i	−0.999970	−	0.00770817i	$-0.997546\pi$
$103$	−1.89223	+	5.82367i	−0.186447	+	0.573824i	0.813524	+	0.581532i	$0.197546\pi$
$104$		0			0
$105$	15.7364	+	11.4331i	1.53571	+	1.11576i
$106$		0			0
$107$	4.70238	+	14.4724i	0.454596	+	1.39910i	0.871609	+	0.490202i	$0.163077\pi$
$107$	4.70238	+	14.4724i	0.454596	+	1.39910i	−0.417012	+	0.908901i	$0.636923\pi$
$108$		0			0
$109$	0.780058			0.0747161			0.0373580	−	0.999302i	$-0.488106\pi$
$109$	0.780058			0.0747161			0.0373580	+	0.999302i	$0.488106\pi$
$110$		0			0
$111$	3.69613			0.350821
$112$		0			0
$113$	2.93180	+	9.02314i	0.275800	+	0.848826i	0.989007	+	0.147872i	$0.0472422\pi$
$113$	2.93180	+	9.02314i	0.275800	+	0.848826i	−0.713206	+	0.700954i	$0.752758\pi$
$114$		0			0
$115$	−30.0673	−	21.8452i	−2.80379	−	2.03707i
$116$		0			0
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$		0			0
$119$	−18.2653	+	13.2706i	−1.67438	+	1.21651i
$120$		0			0
$121$	8.80784	−	6.58954i	0.800712	−	0.599049i
$122$		0			0
$123$	−7.39287	+	5.37123i	−0.666592	+	0.484308i
$124$		0			0
$125$	−12.0272	+	37.0160i	−1.07575	+	3.31081i
$126$		0			0
$127$	8.64513	+	6.28106i	0.767131	+	0.557354i	0.901089	−	0.433633i	$-0.142769\pi$
$127$	8.64513	+	6.28106i	0.767131	+	0.557354i	−0.133958	+	0.990987i	$0.542769\pi$
$128$		0			0
$129$	−2.56791	−	7.90323i	−0.226092	−	0.695840i
$130$		0			0
$131$	13.5039			1.17984			0.589919	−	0.807462i	$-0.299160\pi$
$131$	13.5039			1.17984			0.589919	+	0.807462i	$0.299160\pi$
$132$		0			0
$133$	22.9110			1.98663
$134$		0			0
$135$	1.34494	+	4.13929i	0.115754	+	0.356253i
$136$		0			0
$137$	3.95403	+	2.87277i	0.337816	+	0.245437i	0.743740	−	0.668469i	$-0.233050\pi$
$137$	3.95403	+	2.87277i	0.337816	+	0.245437i	−0.405924	+	0.913907i	$0.633050\pi$
$138$		0			0
$139$	1.13246	−	3.48534i	0.0960536	−	0.295623i	−0.891473	−	0.453073i	$-0.850328\pi$
$139$	1.13246	−	3.48534i	0.0960536	−	0.295623i	0.987527	+	0.157451i	$0.0503276\pi$
$140$		0			0
$141$	−6.96786	+	5.06245i	−0.586800	+	0.426335i
$142$		0			0
$143$	1.93064	−	2.69678i	0.161448	−	0.225516i
$144$		0			0
$145$	2.98652	−	2.16984i	0.248017	−	0.180195i
$146$		0			0
$147$	−4.00904	+	12.3386i	−0.330660	+	1.01767i
$148$		0			0
$149$	−1.19380	−	0.867344i	−0.0977996	−	0.0710556i	0.537811	−	0.843066i	$-0.319251\pi$
$149$	−1.19380	−	0.867344i	−0.0977996	−	0.0710556i	−0.635610	+	0.772010i	$0.719251\pi$
$150$		0			0
$151$	−1.23238	−	3.79287i	−0.100289	−	0.308659i	0.888307	−	0.459251i	$-0.151882\pi$
$151$	−1.23238	−	3.79287i	−0.100289	−	0.308659i	−0.988596	+	0.150592i	$0.951882\pi$
$152$		0			0
$153$	−5.05176			−0.408411
$154$		0			0
$155$	−1.19906			−0.0963106
$156$		0			0
$157$	5.54085	+	17.0530i	0.442208	+	1.36098i	0.885517	+	0.464608i	$0.153805\pi$
$157$	5.54085	+	17.0530i	0.442208	+	1.36098i	−0.443308	+	0.896369i	$0.646195\pi$
$158$		0			0
$159$	7.31930	+	5.31779i	0.580459	+	0.421728i
$160$		0			0
$161$	11.7931	−	36.2953i	0.929424	−	2.86047i
$162$		0			0
$163$	−7.88161	+	5.72633i	−0.617336	+	0.448521i	−0.851990	−	0.523558i	$-0.824604\pi$
$163$	−7.88161	+	5.72633i	−0.617336	+	0.448521i	0.234654	+	0.972079i	$0.424604\pi$
$164$		0			0
$165$	0.101003	+	14.4346i	0.00786308	+	1.12373i
$166$		0			0
$167$	−8.75223	+	6.35887i	−0.677268	+	0.492064i	−0.872450	−	0.488703i	$-0.837470\pi$
$167$	−8.75223	+	6.35887i	−0.677268	+	0.492064i	0.195182	+	0.980767i	$0.437470\pi$
$168$		0			0
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$		0			0
$171$	4.14738	+	3.01325i	0.317158	+	0.230429i
$172$		0			0
$173$	4.26327	+	13.1210i	0.324130	+	0.997570i	0.971832	+	0.235676i	$0.0757305\pi$
$173$	4.26327	+	13.1210i	0.324130	+	0.997570i	−0.647701	+	0.761894i	$0.724270\pi$
$174$		0			0
$175$	−62.3119			−4.71033
$176$		0			0
$177$	4.39312			0.330207
$178$		0			0
$179$	5.05572	+	15.5599i	0.377882	+	1.16300i	0.941514	+	0.336975i	$0.109404\pi$
$179$	5.05572	+	15.5599i	0.377882	+	1.16300i	−0.563632	+	0.826026i	$0.690596\pi$
$180$		0			0
$181$	12.8501	+	9.33615i	0.955141	+	0.693951i	0.952017	−	0.306044i	$-0.0990056\pi$
$181$	12.8501	+	9.33615i	0.955141	+	0.693951i	0.00312394	+	0.999995i	$0.499006\pi$
$182$		0			0
$183$	−2.21551	+	6.81865i	−0.163775	+	0.504049i
$184$		0			0
$185$	−13.0144	+	9.45553i	−0.956839	+	0.695184i
$186$		0			0
$187$	−15.9706	−	5.06589i	−1.16789	−	0.370455i
$188$		0			0
$189$	−3.61564	+	2.62692i	−0.262999	+	0.191080i
$190$		0			0
$191$	1.79231	−	5.51617i	0.129687	−	0.399136i	−0.865039	−	0.501705i	$-0.832706\pi$
$191$	1.79231	−	5.51617i	0.129687	−	0.399136i	0.994726	+	0.102569i	$0.0327062\pi$
$192$		0			0
$193$	−5.23258	−	3.80170i	−0.376650	−	0.273652i	0.383313	−	0.923618i	$-0.374783\pi$
$193$	−5.23258	−	3.80170i	−0.376650	−	0.273652i	−0.759963	+	0.649966i	$0.774783\pi$
$194$		0			0
$195$	1.34494	+	4.13929i	0.0963130	+	0.296421i
$196$		0			0
$197$	15.9916			1.13936			0.569679	−	0.821868i	$-0.307068\pi$
$197$	15.9916			1.13936			0.569679	+	0.821868i	$0.307068\pi$
$198$		0			0
$199$	−12.4821			−0.884832			−0.442416	−	0.896810i	$-0.645878\pi$
$199$	−12.4821			−0.884832			−0.442416	+	0.896810i	$0.645878\pi$
$200$		0			0
$201$	0.597897	+	1.84014i	0.0421724	+	0.129793i
$202$		0			0
$203$	3.06672	+	2.22810i	0.215241	+	0.156382i
$204$		0			0
$205$	12.2902	−	37.8252i	0.858382	−	2.64183i
$206$		0			0
$207$	6.90835	−	5.01921i	0.480164	−	0.348859i
$208$		0			0
$209$	10.0898	+	13.6850i	0.697927	+	0.946614i
$210$		0			0
$211$	11.0581	−	8.03419i	0.761272	−	0.553096i	−0.138029	−	0.990428i	$-0.544077\pi$
$211$	11.0581	−	8.03419i	0.761272	−	0.553096i	0.899300	+	0.437332i	$0.144077\pi$
$212$		0			0
$213$	4.82724	−	14.8567i	0.330757	−	1.01797i
$214$		0			0
$215$	29.2601	+	21.2587i	1.99552	+	1.44983i
$216$		0			0
$217$	−0.380478	−	1.17099i	−0.0258286	−	0.0794921i
$218$		0			0
$219$	−5.90316			−0.398899
$220$		0			0
$221$	−5.05176			−0.339818
$222$		0			0
$223$	5.34944	+	16.4639i	0.358225	+	1.10250i	0.954116	+	0.299438i	$0.0967993\pi$
$223$	5.34944	+	16.4639i	0.358225	+	1.10250i	−0.595890	+	0.803066i	$0.703201\pi$
$224$		0			0
$225$	−11.2798	−	8.19525i	−0.751986	−	0.546350i
$226$		0			0
$227$	4.08368	−	12.5683i	0.271043	−	0.834185i	−0.719196	−	0.694807i	$-0.755490\pi$
$227$	4.08368	−	12.5683i	0.271043	−	0.834185i	0.990239	−	0.139378i	$-0.0445102\pi$
$228$		0			0
$229$	−14.7189	+	10.6939i	−0.972655	+	0.706675i	−0.956055	−	0.293187i	$-0.905284\pi$
$229$	−14.7189	+	10.6939i	−0.972655	+	0.706675i	−0.0165996	+	0.999862i	$0.505284\pi$
$230$		0			0
$231$	−14.0647	+	4.67895i	−0.925390	+	0.307853i
$232$		0			0
$233$	13.6581	−	9.92322i	0.894775	−	0.650092i	−0.0423440	−	0.999103i	$-0.513483\pi$
$233$	13.6581	−	9.92322i	0.894775	−	0.650092i	0.937118	+	0.349011i	$0.113483\pi$
$234$		0			0
$235$	11.5836	−	35.6507i	0.755631	−	2.32559i
$236$		0			0
$237$	3.73294	+	2.71214i	0.242480	+	0.176172i
$238$		0			0
$239$	7.40348	+	22.7856i	0.478891	+	1.47388i	0.840637	+	0.541599i	$0.182181\pi$
$239$	7.40348	+	22.7856i	0.478891	+	1.47388i	−0.361745	+	0.932277i	$0.617819\pi$
$240$		0			0
$241$	−20.3865			−1.31321			−0.656606	−	0.754233i	$-0.728009\pi$
$241$	−20.3865			−1.31321			−0.656606	+	0.754233i	$0.728009\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−17.4486	−	53.7012i	−1.11475	−	3.43084i
$246$		0			0
$247$	4.14738	+	3.01325i	0.263891	+	0.191728i
$248$		0			0
$249$	1.26805	−	3.90265i	0.0803593	−	0.247321i
$250$		0			0
$251$	19.1272	−	13.8967i	1.20730	−	0.877152i	0.212313	−	0.977202i	$-0.431900\pi$
$251$	19.1272	−	13.8967i	1.20730	−	0.877152i	0.994982	+	0.100050i	$0.0319003\pi$
$252$		0			0
$253$	26.8733	−	8.94002i	1.68951	−	0.562054i
$254$		0			0
$255$	17.7877	−	12.9235i	1.11391	−	0.809303i
$256$		0			0
$257$	2.55947	−	7.87724i	0.159655	−	0.491369i	−0.838947	−	0.544213i	$-0.816829\pi$
$257$	2.55947	−	7.87724i	0.159655	−	0.491369i	0.998603	+	0.0528437i	$0.0168285\pi$
$258$		0			0
$259$	−13.3639	−	9.70942i	−0.830391	−	0.603314i
$260$		0			0
$261$	0.262102	+	0.806668i	0.0162237	+	0.0499315i
$262$		0			0
$263$	2.05807			0.126906			0.0634529	−	0.997985i	$-0.479789\pi$
$263$	2.05807			0.126906			0.0634529	+	0.997985i	$0.479789\pi$
$264$		0			0
$265$	−39.3760			−2.41885
$266$		0			0
$267$	−2.37488	−	7.30912i	−0.145340	−	0.447311i
$268$		0			0
$269$	11.8286	+	8.59401i	0.721205	+	0.523986i	0.886769	−	0.462213i	$-0.152944\pi$
$269$	11.8286	+	8.59401i	0.721205	+	0.523986i	−0.165564	+	0.986199i	$0.552944\pi$
$270$		0			0
$271$	−3.61738	+	11.1332i	−0.219740	+	0.676291i	0.779043	+	0.626971i	$0.215706\pi$
$271$	−3.61738	+	11.1332i	−0.219740	+	0.676291i	−0.998783	+	0.0493203i	$0.984294\pi$
$272$		0			0
$273$	−3.61564	+	2.62692i	−0.218828	+	0.158988i
$274$		0			0
$275$	−27.4417	−	37.2197i	−1.65479	−	2.24443i
$276$		0			0
$277$	−10.2584	+	7.45317i	−0.616368	+	0.447818i	−0.851651	−	0.524109i	$-0.824398\pi$
$277$	−10.2584	+	7.45317i	−0.616368	+	0.447818i	0.235283	+	0.971927i	$0.424398\pi$
$278$		0			0
$279$	0.0851339	−	0.262015i	0.00509684	−	0.0156864i
$280$		0			0
$281$	0.925685	+	0.672549i	0.0552217	+	0.0401209i	0.615054	−	0.788485i	$-0.289134\pi$
$281$	0.925685	+	0.672549i	0.0552217	+	0.0401209i	−0.559832	+	0.828606i	$0.689134\pi$
$282$		0			0
$283$	−9.63526	−	29.6543i	−0.572757	−	1.76276i	−0.643693	−	0.765284i	$-0.722599\pi$
$283$	−9.63526	−	29.6543i	−0.572757	−	1.76276i	0.0709358	−	0.997481i	$-0.477401\pi$
$284$		0			0
$285$	−22.3119			−1.32164
$286$		0			0
$287$	40.8397			2.41069
$288$		0			0
$289$	2.63292	+	8.10330i	0.154878	+	0.476664i
$290$		0			0
$291$	6.27491	+	4.55899i	0.367842	+	0.267253i
$292$		0			0
$293$	−4.83264	+	14.8733i	−0.282326	+	0.868909i	0.704862	+	0.709345i	$0.251009\pi$
$293$	−4.83264	+	14.8733i	−0.282326	+	0.868909i	−0.987188	+	0.159564i	$0.948991\pi$
$294$		0			0
$295$	−15.4686	+	11.2386i	−0.900615	+	0.654335i
$296$		0			0
$297$	−3.16139	−	1.00280i	−0.183443	−	0.0581882i
$298$		0			0
$299$	6.90835	−	5.01921i	0.399520	−	0.290269i
$300$		0			0
$301$	−11.4765	+	35.3209i	−0.661492	+	2.03586i
$302$		0			0
$303$	−6.24651	−	4.53835i	−0.358853	−	0.260722i
$304$		0			0
$305$	−9.64259	−	29.6769i	−0.552133	−	1.69929i
$306$		0			0
$307$	4.43946			0.253373			0.126687	−	0.991943i	$-0.459566\pi$
$307$	4.43946			0.253373			0.126687	+	0.991943i	$0.459566\pi$
$308$		0			0
$309$	6.12337			0.348346
$310$		0			0
$311$	−1.95019	−	6.00206i	−0.110585	−	0.340346i	0.880416	−	0.474203i	$-0.157264\pi$
$311$	−1.95019	−	6.00206i	−0.110585	−	0.340346i	−0.991001	+	0.133857i	$0.957264\pi$
$312$		0			0
$313$	−12.3584	−	8.97890i	−0.698538	−	0.507518i	0.180918	−	0.983498i	$-0.442093\pi$
$313$	−12.3584	−	8.97890i	−0.698538	−	0.507518i	−0.879456	+	0.475981i	$0.842093\pi$
$314$		0			0
$315$	6.01076	−	18.4992i	0.338668	−	1.04231i
$316$		0			0
$317$	−7.68255	+	5.58170i	−0.431495	+	0.313499i	−0.782246	−	0.622969i	$-0.785926\pi$
$317$	−7.68255	+	5.58170i	−0.431495	+	0.313499i	0.350752	+	0.936469i	$0.385926\pi$
$318$		0			0
$319$	0.0196836	+	2.81303i	0.00110207	+	0.157499i
$320$		0			0
$321$	12.3110	−	8.94446i	0.687132	−	0.499231i
$322$		0			0
$323$	8.00279	−	24.6301i	0.445287	−	1.37045i
$324$		0			0
$325$	−11.2798	−	8.19525i	−0.625690	−	0.454591i
$326$		0			0
$327$	−0.241051	−	0.741880i	−0.0133302	−	0.0410260i
$328$		0			0
$329$	38.4919			2.12213
$330$		0			0
$331$	15.4631			0.849931			0.424965	−	0.905210i	$-0.360286\pi$
$331$	15.4631			0.849931			0.424965	+	0.905210i	$0.360286\pi$
$332$		0			0
$333$	−1.14217	−	3.51523i	−0.0625904	−	0.192633i
$334$		0			0
$335$	−6.81273	−	4.94974i	−0.372219	−	0.270433i
$336$		0			0
$337$	5.97998	−	18.4045i	0.325750	−	1.00256i	−0.645351	−	0.763886i	$-0.723289\pi$
$337$	5.97998	−	18.4045i	0.325750	−	1.00256i	0.971101	−	0.238669i	$-0.0767112\pi$
$338$		0			0
$339$	7.67554	−	5.57661i	0.416878	−	0.302880i
$340$		0			0
$341$	0.531890	−	0.742961i	0.0288035	−	0.0402336i
$342$		0			0
$343$	21.5981	−	15.6919i	1.16619	−	0.847285i
$344$		0			0
$345$	−11.4847	+	35.3462i	−0.618315	+	1.90298i
$346$		0			0
$347$	8.86136	+	6.43815i	0.475703	+	0.345618i	0.799660	−	0.600454i	$-0.205013\pi$
$347$	8.86136	+	6.43815i	0.475703	+	0.345618i	−0.323957	+	0.946072i	$0.605013\pi$
$348$		0			0
$349$	−6.89357	−	21.2162i	−0.369004	−	1.13568i	−0.947435	−	0.319947i	$-0.896335\pi$
$349$	−6.89357	−	21.2162i	−0.369004	−	1.13568i	0.578431	−	0.815731i	$-0.303665\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	29.0211			1.54464			0.772318	−	0.635236i	$-0.219097\pi$
$353$	29.0211			1.54464			0.772318	+	0.635236i	$0.219097\pi$
$354$		0			0
$355$	21.0096	+	64.6610i	1.11508	+	3.43185i
$356$		0			0
$357$	18.2653	+	13.2706i	0.966705	+	0.702352i
$358$		0			0
$359$	1.49473	−	4.60031i	0.0788888	−	0.242795i	−0.903832	−	0.427887i	$-0.859258\pi$
$359$	1.49473	−	4.60031i	0.0788888	−	0.242795i	0.982721	+	0.185092i	$0.0592582\pi$
$360$		0			0
$361$	−5.88998	+	4.27932i	−0.309999	+	0.225227i
$362$		0			0
$363$	−8.98879	−	6.34047i	−0.471789	−	0.332788i
$364$		0			0
$365$	20.7856	−	15.1016i	1.08797	−	0.790454i
$366$		0			0
$367$	3.39210	−	10.4398i	0.177066	−	0.544953i	−0.822656	−	0.568540i	$-0.807509\pi$
$367$	3.39210	−	10.4398i	0.177066	−	0.544953i	0.999722	+	0.0235865i	$0.00750852\pi$
$368$		0			0
$369$	7.39287	+	5.37123i	0.384857	+	0.279615i
$370$		0			0
$371$	−12.4946	−	38.4544i	−0.648686	−	1.99645i
$372$		0			0
$373$	5.04148			0.261038			0.130519	−	0.991446i	$-0.458336\pi$
$373$	5.04148			0.261038			0.130519	+	0.991446i	$0.458336\pi$
$374$		0			0
$375$	38.9209			2.00987
$376$		0			0
$377$	0.262102	+	0.806668i	0.0134990	+	0.0415455i
$378$		0			0
$379$	10.5431	+	7.65998i	0.541561	+	0.393467i	0.824664	−	0.565622i	$-0.191364\pi$
$379$	10.5431	+	7.65998i	0.541561	+	0.393467i	−0.283104	+	0.959089i	$0.591364\pi$
$380$		0			0
$381$	3.30215	−	10.1630i	0.169174	−	0.520664i
$382$		0			0
$383$	14.7524	−	10.7183i	0.753813	−	0.547677i	−0.143193	−	0.989695i	$-0.545737\pi$
$383$	14.7524	−	10.7183i	0.753813	−	0.547677i	0.897007	+	0.442017i	$0.145737\pi$
$384$		0			0
$385$	37.5533	−	52.4557i	1.91390	−	2.67339i
$386$		0			0
$387$	−6.72288	+	4.88446i	−0.341743	+	0.248291i
$388$		0			0
$389$	−2.45696	+	7.56174i	−0.124573	+	0.383395i	−0.993823	−	0.110977i	$-0.964602\pi$
$389$	−2.45696	+	7.56174i	−0.124573	+	0.383395i	0.869250	+	0.494372i	$0.164602\pi$
$390$		0			0
$391$	−34.8994	−	25.3559i	−1.76494	−	1.28230i
$392$		0			0
$393$	−4.17293	−	12.8429i	−0.210496	−	0.647841i
$394$		0			0
$395$	−20.0823			−1.01045
$396$		0			0
$397$	−8.43012			−0.423096			−0.211548	−	0.977368i	$-0.567850\pi$
$397$	−8.43012			−0.423096			−0.211548	+	0.977368i	$0.567850\pi$
$398$		0			0
$399$	−7.07988	−	21.7896i	−0.354437	−	1.09085i
$400$		0			0
$401$	−9.24830	−	6.71929i	−0.461838	−	0.335545i	0.332414	−	0.943134i	$-0.392137\pi$
$401$	−9.24830	−	6.71929i	−0.461838	−	0.335545i	−0.794252	+	0.607589i	$0.792137\pi$
$402$		0			0
$403$	0.0851339	−	0.262015i	0.00424082	−	0.0130519i
$404$		0			0
$405$	3.52109	−	2.55822i	0.174964	−	0.127119i
$406$		0			0
$407$	−0.0857753	−	12.2584i	−0.00425172	−	0.607625i
$408$		0			0
$409$	−27.3498	+	19.8708i	−1.35236	+	0.982549i	−0.353473	+	0.935445i	$0.614999\pi$
$409$	−27.3498	+	19.8708i	−1.35236	+	0.982549i	−0.998890	+	0.0471042i	$0.985001\pi$
$410$		0			0
$411$	1.51030	−	4.64824i	0.0744979	−	0.229281i
$412$		0			0
$413$	−15.8839	−	11.5403i	−0.781597	−	0.567863i
$414$		0			0
$415$	5.51894	+	16.9856i	0.270914	+	0.833788i
$416$		0			0
$417$	−3.66470			−0.179461
$418$		0			0
$419$	−36.3155			−1.77413			−0.887064	−	0.461646i	$-0.847259\pi$
$419$	−36.3155			−1.77413			−0.887064	+	0.461646i	$0.847259\pi$
$420$		0			0
$421$	−6.24025	−	19.2055i	−0.304131	−	0.936019i	−0.980000	−	0.198998i	$-0.936231\pi$
$421$	−6.24025	−	19.2055i	−0.304131	−	0.936019i	0.675869	−	0.737022i	$-0.263769\pi$
$422$		0			0
$423$	6.96786	+	5.06245i	0.338789	+	0.246145i
$424$		0			0
$425$	−21.7655	+	66.9873i	−1.05578	+	3.24936i
$426$		0			0
$427$	25.9225	−	18.8338i	1.25448	−	0.911431i
$428$		0			0
$429$	−3.16139	−	1.00280i	−0.152633	−	0.0484155i
$430$		0			0
$431$	−17.9571	+	13.0466i	−0.864964	+	0.628433i	−0.929231	−	0.369500i	$-0.879529\pi$
$431$	−17.9571	+	13.0466i	−0.864964	+	0.628433i	0.0642670	+	0.997933i	$0.479529\pi$
$432$		0			0
$433$	2.93333	−	9.02786i	0.140967	−	0.433851i	−0.855504	−	0.517797i	$-0.826752\pi$
$433$	2.93333	−	9.02786i	0.140967	−	0.433851i	0.996470	+	0.0839458i	$0.0267523\pi$
$434$		0			0
$435$	−2.98652	−	2.16984i	−0.143193	−	0.104036i
$436$		0			0
$437$	13.5274	+	41.6332i	0.647105	+	1.99158i
$438$		0			0
$439$	15.3956			0.734793			0.367396	−	0.930064i	$-0.380249\pi$
$439$	15.3956			0.734793			0.367396	+	0.930064i	$0.380249\pi$
$440$		0			0
$441$	12.9735			0.617787
$442$		0			0
$443$	7.39734	+	22.7667i	0.351458	+	1.08168i	0.958035	+	0.286652i	$0.0925423\pi$
$443$	7.39734	+	22.7667i	0.351458	+	1.08168i	−0.606577	+	0.795025i	$0.707458\pi$
$444$		0			0
$445$	27.0605	+	19.6606i	1.28279	+	0.932003i
$446$		0			0
$447$	−0.455990	+	1.40339i	−0.0215676	+	0.0663781i
$448$		0			0
$449$	11.1795	−	8.12240i	0.527594	−	0.383320i	−0.291863	−	0.956460i	$-0.594275\pi$
$449$	11.1795	−	8.12240i	0.527594	−	0.383320i	0.819457	+	0.573141i	$0.194275\pi$
$450$		0			0
$451$	17.9855	+	24.3941i	0.846904	+	1.14867i
$452$		0			0
$453$	−3.22640	+	2.34412i	−0.151590	+	0.110136i
$454$		0			0
$455$	6.01076	−	18.4992i	0.281789	−	0.867257i
$456$		0			0
$457$	3.29109	+	2.39112i	0.153951	+	0.111852i	0.662094	−	0.749421i	$-0.269668\pi$
$457$	3.29109	+	2.39112i	0.153951	+	0.111852i	−0.508143	+	0.861273i	$0.669668\pi$
$458$		0			0
$459$	1.56108	+	4.80451i	0.0728650	+	0.224255i
$460$		0			0
$461$	−9.41320			−0.438416			−0.219208	−	0.975678i	$-0.570347\pi$
$461$	−9.41320			−0.438416			−0.219208	+	0.975678i	$0.570347\pi$
$462$		0			0
$463$	−20.9935			−0.975650			−0.487825	−	0.872941i	$-0.662210\pi$
$463$	−20.9935			−0.975650			−0.487825	+	0.872941i	$0.662210\pi$
$464$		0			0
$465$	0.370529	+	1.14037i	0.0171829	+	0.0528835i
$466$		0			0
$467$	5.81299	+	4.22338i	0.268993	+	0.195435i	0.714102	−	0.700041i	$-0.246835\pi$
$467$	5.81299	+	4.22338i	0.268993	+	0.195435i	−0.445109	+	0.895476i	$0.646835\pi$
$468$		0			0
$469$	2.67211	−	8.22390i	0.123386	−	0.379744i
$470$		0			0
$471$	14.5061	−	10.5393i	0.668408	−	0.485627i
$472$		0			0
$473$	−26.1518	+	8.70001i	−1.20246	+	0.400027i
$474$		0			0
$475$	57.8252	−	42.0125i	2.65320	−	1.92766i
$476$		0			0
$477$	2.79573	−	8.60436i	0.128007	−	0.393966i
$478$		0			0
$479$	8.18833	+	5.94917i	0.374134	+	0.271825i	0.758923	−	0.651180i	$-0.225726\pi$
$479$	8.18833	+	5.94917i	0.374134	+	0.271825i	−0.384789	+	0.923005i	$0.625726\pi$
$480$		0			0
$481$	−1.14217	−	3.51523i	−0.0520784	−	0.160281i
$482$		0			0
$483$	−38.1632			−1.73648
$484$		0			0
$485$	−33.7574			−1.53285
$486$		0			0
$487$	−1.21333	−	3.73424i	−0.0549811	−	0.169214i	0.919795	−	0.392399i	$-0.128355\pi$
$487$	−1.21333	−	3.73424i	−0.0549811	−	0.169214i	−0.974776	+	0.223185i	$0.928355\pi$
$488$		0			0
$489$	7.88161	+	5.72633i	0.356419	+	0.258953i
$490$		0			0
$491$	9.21310	−	28.3550i	0.415781	−	1.27964i	−0.495769	−	0.868454i	$-0.665114\pi$
$491$	9.21310	−	28.3550i	0.415781	−	1.27964i	0.911550	−	0.411189i	$-0.134886\pi$
$492$		0			0
$493$	3.46648	−	2.51855i	0.156123	−	0.113430i
$494$		0			0
$495$	13.6969	−	4.55660i	0.615631	−	0.204804i
$496$		0			0
$497$	−56.4809	+	41.0358i	−2.53351	+	1.84071i
$498$		0			0
$499$	−7.41525	+	22.8218i	−0.331952	+	1.02164i	0.636252	+	0.771482i	$0.280484\pi$
$499$	−7.41525	+	22.8218i	−0.331952	+	1.02164i	−0.968204	+	0.250162i	$0.919516\pi$
$500$		0			0
$501$	8.75223	+	6.35887i	0.391021	+	0.284093i
$502$		0			0
$503$	2.07437	+	6.38425i	0.0924915	+	0.284660i	0.986592	−	0.163207i	$-0.0521839\pi$
$503$	2.07437	+	6.38425i	0.0924915	+	0.284660i	−0.894100	+	0.447867i	$0.852184\pi$
$504$		0			0
$505$	33.6047			1.49539
$506$		0			0
$507$	−1.00000			−0.0444116
$508$		0			0
$509$	−10.8952	−	33.5321i	−0.482923	−	1.48629i	−0.834966	−	0.550302i	$-0.814513\pi$
$509$	−10.8952	−	33.5321i	−0.482923	−	1.48629i	0.352043	−	0.935984i	$-0.385487\pi$
$510$		0			0
$511$	21.3437	+	15.5071i	0.944190	+	0.685994i
$512$		0			0
$513$	1.58416	−	4.87554i	0.0699423	−	0.215260i
$514$		0			0
$515$	−21.5610	+	15.6650i	−0.950089	+	0.690280i
$516$		0			0
$517$	16.9515	+	22.9917i	0.745528	+	1.01118i
$518$		0			0
$519$	11.1614	−	8.10922i	0.489930	−	0.355955i
$520$		0			0
$521$	−5.50069	+	16.9294i	−0.240990	+	0.741690i	0.755281	+	0.655402i	$0.227501\pi$
$521$	−5.50069	+	16.9294i	−0.240990	+	0.741690i	−0.996270	+	0.0862882i	$0.972499\pi$
$522$		0			0
$523$	−30.6362	−	22.2585i	−1.33963	−	0.973295i	−0.999458	−	0.0329303i	$-0.989516\pi$
$523$	−30.6362	−	22.2585i	−1.33963	−	0.973295i	−0.340168	−	0.940365i	$-0.610484\pi$
$524$		0			0
$525$	19.2554	+	59.2621i	0.840376	+	2.58641i
$526$		0			0
$527$	−1.39176			−0.0606259
$528$		0			0
$529$	49.9179			2.17034
$530$		0			0
$531$	−1.35755	−	4.17810i	−0.0589125	−	0.181314i
$532$		0			0
$533$	7.39287	+	5.37123i	0.320221	+	0.232654i
$534$		0			0
$535$	−20.4662	+	62.9885i	−0.884831	+	2.72323i
$536$		0			0
$537$	13.2360	−	9.61654i	0.571177	−	0.414985i
$538$		0			0
$539$	41.0144	+	13.0098i	1.76661	+	0.560372i
$540$		0			0
$541$	−5.40294	+	3.92547i	−0.232291	+	0.168769i	−0.697842	−	0.716252i	$-0.745856\pi$
$541$	−5.40294	+	3.92547i	−0.232291	+	0.168769i	0.465551	+	0.885021i	$0.345856\pi$
$542$		0			0
$543$	4.90831	−	15.1062i	0.210636	−	0.648270i
$544$		0			0
$545$	2.74666	+	1.99556i	0.117654	+	0.0854805i
$546$		0			0
$547$	7.58308	+	23.3383i	0.324229	+	0.997875i	0.971787	+	0.235859i	$0.0757903\pi$
$547$	7.58308	+	23.3383i	0.324229	+	0.997875i	−0.647558	+	0.762016i	$0.724210\pi$
$548$		0			0
$549$	7.16955			0.305989
$550$		0			0
$551$	−4.34815			−0.185238
$552$		0			0
$553$	−6.37240	−	19.6122i	−0.270982	−	0.833997i
$554$		0			0
$555$	13.0144	+	9.45553i	0.552431	+	0.401365i
$556$		0			0
$557$	−3.37273	+	10.3802i	−0.142907	+	0.439823i	−0.996736	−	0.0807308i	$-0.974275\pi$
$557$	−3.37273	+	10.3802i	−0.142907	+	0.439823i	0.853829	+	0.520554i	$0.174275\pi$
$558$		0			0
$559$	−6.72288	+	4.88446i	−0.284348	+	0.206591i
$560$		0			0
$561$	0.117235	+	16.7544i	0.00494967	+	0.707371i
$562$		0			0
$563$	−12.5525	+	9.11992i	−0.529024	+	0.384359i	−0.819993	−	0.572374i	$-0.806023\pi$
$563$	−12.5525	+	9.11992i	−0.529024	+	0.384359i	0.290968	+	0.956733i	$0.406023\pi$
$564$		0			0
$565$	−12.7601	+	39.2715i	−0.536821	+	1.65216i
$566$		0			0
$567$	3.61564	+	2.62692i	0.151843	+	0.110320i
$568$		0			0
$569$	1.58020	+	4.86337i	0.0662456	+	0.203883i	0.978700	−	0.205295i	$-0.0658154\pi$
$569$	1.58020	+	4.86337i	0.0662456	+	0.203883i	−0.912454	+	0.409178i	$0.865815\pi$
$570$		0			0
$571$	−36.9239			−1.54522			−0.772608	−	0.634884i	$-0.781048\pi$
$571$	−36.9239			−1.54522			−0.772608	+	0.634884i	$0.781048\pi$
$572$		0			0
$573$	−5.80005			−0.242300
$574$		0			0
$575$	−36.7911	−	113.231i	−1.53429	−	4.72207i
$576$		0			0
$577$	−32.2407	−	23.4242i	−1.34220	−	0.975163i	−0.999360	−	0.0357679i	$-0.988612\pi$
$577$	−32.2407	−	23.4242i	−1.34220	−	0.975163i	−0.342837	−	0.939395i	$-0.611388\pi$
$578$		0			0
$579$	−1.99867	+	6.15127i	−0.0830619	+	0.255638i
$580$		0			0
$581$	−14.8367	+	10.7795i	−0.615532	+	0.447210i
$582$		0			0
$583$	17.4668	−	24.3982i	0.723401	−	1.01047i
$584$		0			0
$585$	3.52109	−	2.55822i	0.145579	−	0.105769i
$586$		0			0
$587$	−0.904745	+	2.78452i	−0.0373428	+	0.114929i	−0.967990	−	0.250988i	$-0.919245\pi$
$587$	−0.904745	+	2.78452i	−0.0373428	+	0.114929i	0.930647	+	0.365917i	$0.119245\pi$
$588$		0			0
$589$	1.14260	+	0.830147i	0.0470800	+	0.0342056i
$590$		0			0
$591$	−4.94169	−	15.2090i	−0.203274	−	0.625613i
$592$		0			0
$593$	−6.39437			−0.262585			−0.131293	−	0.991344i	$-0.541913\pi$
$593$	−6.39437			−0.262585			−0.131293	+	0.991344i	$0.541913\pi$
$594$		0			0
$595$	−98.2630			−4.02839
$596$		0			0
$597$	3.85718	+	11.8712i	0.157864	+	0.485855i
$598$		0			0
$599$	−28.7139	−	20.8619i	−1.17322	−	0.852392i	−0.181827	−	0.983331i	$-0.558201\pi$
$599$	−28.7139	−	20.8619i	−1.17322	−	0.852392i	−0.991391	+	0.130938i	$0.958201\pi$
$600$		0			0
$601$	4.34391	−	13.3692i	0.177192	−	0.545340i	−0.822535	−	0.568714i	$-0.807441\pi$
$601$	4.34391	−	13.3692i	0.177192	−	0.545340i	0.999727	+	0.0233744i	$0.00744098\pi$
$602$		0			0
$603$	1.56531	−	1.13727i	0.0637445	−	0.0463131i
$604$		0			0
$605$	47.8707	−	0.669962i	1.94622	−	0.0272378i
$606$		0			0
$607$	30.3803	−	22.0726i	1.23310	−	0.895898i	0.235979	−	0.971758i	$-0.424170\pi$
$607$	30.3803	−	22.0726i	1.23310	−	0.895898i	0.997118	+	0.0758601i	$0.0241702\pi$
$608$		0			0
$609$	1.17138	−	3.60514i	0.0474668	−	0.146088i
$610$		0			0
$611$	6.96786	+	5.06245i	0.281890	+	0.204805i
$612$		0			0
$613$	1.46403	+	4.50581i	0.0591315	+	0.181988i	0.976259	−	0.216605i	$-0.0694985\pi$
$613$	1.46403	+	4.50581i	0.0591315	+	0.181988i	−0.917128	+	0.398593i	$0.869499\pi$
$614$		0			0
$615$	−39.7718			−1.60375
$616$		0			0
$617$	0.467300			0.0188128			0.00940640	−	0.999956i	$-0.497006\pi$
$617$	0.467300			0.0188128			0.00940640	+	0.999956i	$0.497006\pi$
$618$		0			0
$619$	−3.21764	−	9.90289i	−0.129328	−	0.398031i	0.865337	−	0.501191i	$-0.167105\pi$
$619$	−3.21764	−	9.90289i	−0.129328	−	0.398031i	−0.994665	+	0.103160i	$0.967105\pi$
$620$		0			0
$621$	−6.90835	−	5.01921i	−0.277223	−	0.201414i
$622$		0			0
$623$	−10.6137	+	32.6658i	−0.425231	+	1.30873i
$624$		0			0
$625$	−80.6451	+	58.5921i	−3.22581	+	2.34368i
$626$		0			0
$627$	9.89732	−	13.8249i	0.395261	−	0.552113i
$628$		0			0
$629$	−15.1059	+	10.9751i	−0.602314	+	0.437606i
$630$		0			0
$631$	7.21692	−	22.2114i	0.287301	−	0.884222i	−0.698398	−	0.715709i	$-0.746104\pi$
$631$	7.21692	−	22.2114i	0.287301	−	0.884222i	0.985699	−	0.168513i	$-0.0538965\pi$
$632$		0			0
$633$	−11.0581	−	8.03419i	−0.439520	−	0.319330i
$634$		0			0
$635$	14.3720	+	44.2323i	0.570334	+	1.75531i
$636$		0			0
$637$	12.9735			0.514030
$638$		0			0
$639$	−15.6213			−0.617968
$640$		0			0
$641$	−10.8169	−	33.2909i	−0.427241	−	1.31491i	−0.900832	−	0.434167i	$-0.857043\pi$
$641$	−10.8169	−	33.2909i	−0.427241	−	1.31491i	0.473591	−	0.880745i	$-0.342957\pi$
$642$		0			0
$643$	22.6387	+	16.4480i	0.892783	+	0.648645i	0.936602	−	0.350395i	$-0.113953\pi$
$643$	22.6387	+	16.4480i	0.892783	+	0.648645i	−0.0438191	+	0.999039i	$0.513953\pi$
$644$		0			0
$645$	11.1764	−	34.3973i	0.440068	−	1.35439i
$646$		0			0
$647$	14.9547	−	10.8653i	0.587931	−	0.427157i	−0.253643	−	0.967298i	$-0.581629\pi$
$647$	14.9547	−	10.8653i	0.587931	−	0.427157i	0.841575	+	0.540141i	$0.181629\pi$
$648$		0			0
$649$	−0.101950	−	14.5700i	−0.00400189	−	0.571921i
$650$		0			0
$651$	−0.996105	+	0.723713i	−0.0390404	+	0.0283645i
$652$		0			0
$653$	7.33365	−	22.5706i	0.286988	−	0.883258i	−0.698808	−	0.715309i	$-0.746286\pi$
$653$	7.33365	−	22.5706i	0.286988	−	0.883258i	0.985796	−	0.167948i	$-0.0537142\pi$
$654$		0			0
$655$	47.5484	+	34.5459i	1.85787	+	1.34982i
$656$		0			0
$657$	1.82418	+	5.61424i	0.0711679	+	0.219032i
$658$		0			0
$659$	−26.2446			−1.02234			−0.511172	−	0.859479i	$-0.670788\pi$
$659$	−26.2446			−1.02234			−0.511172	+	0.859479i	$0.670788\pi$
$660$		0			0
$661$	−6.05152			−0.235377			−0.117688	−	0.993051i	$-0.537548\pi$
$661$	−6.05152			−0.235377			−0.117688	+	0.993051i	$0.537548\pi$
$662$		0			0
$663$	1.56108	+	4.80451i	0.0606273	+	0.186592i
$664$		0			0
$665$	80.6716	+	58.6114i	3.12831	+	2.27285i
$666$		0			0
$667$	−2.23814	+	6.88830i	−0.0866613	+	0.266716i
$668$		0			0
$669$	14.0050	−	10.1752i	0.541466	−	0.393398i
$670$		0			0
$671$	22.6658	+	7.18960i	0.875002	+	0.277552i
$672$		0			0
$673$	34.8533	−	25.3224i	1.34350	−	0.976108i	0.344189	−	0.938900i	$-0.388154\pi$
$673$	34.8533	−	25.3224i	1.34350	−	0.976108i	0.999308	−	0.0372074i	$-0.0118462\pi$
$674$		0			0
$675$	−4.30850	+	13.2602i	−0.165834	+	0.510385i
$676$		0			0
$677$	13.3894	+	9.72794i	0.514595	+	0.373875i	0.814564	−	0.580074i	$-0.196976\pi$
$677$	13.3894	+	9.72794i	0.514595	+	0.373875i	−0.299969	+	0.953949i	$0.596976\pi$
$678$		0			0
$679$	−10.7117	−	32.9673i	−0.411078	−	1.26517i
$680$		0			0
$681$	−13.2151			−0.506402
$682$		0			0
$683$	−3.00936			−0.115150			−0.0575749	−	0.998341i	$-0.518337\pi$
$683$	−3.00936			−0.115150			−0.0575749	+	0.998341i	$0.518337\pi$
$684$		0			0
$685$	6.57331	+	20.2306i	0.251153	+	0.772971i
$686$		0			0
$687$	14.7189	+	10.6939i	0.561562	+	0.407999i
$688$		0			0
$689$	2.79573	−	8.60436i	0.106509	−	0.327800i
$690$		0			0
$691$	−8.65196	+	6.28602i	−0.329136	+	0.239131i	−0.740064	−	0.672537i	$-0.765205\pi$
$691$	−8.65196	+	6.28602i	−0.329136	+	0.239131i	0.410928	+	0.911668i	$0.365205\pi$
$692$		0			0
$693$	8.79619	+	11.9305i	0.334139	+	0.453201i
$694$		0			0
$695$	12.9038	−	9.37513i	0.489467	−	0.355619i
$696$		0			0
$697$	14.2653	−	43.9041i	0.540336	−	1.66298i
$698$		0			0
$699$	−13.6581	−	9.92322i	−0.516598	−	0.375331i
$700$		0			0
$701$	2.61421	+	8.04572i	0.0987374	+	0.303883i	0.988210	−	0.153107i	$-0.0489278\pi$
$701$	2.61421	+	8.04572i	0.0987374	+	0.303883i	−0.889472	+	0.456989i	$0.848928\pi$
$702$		0			0
$703$	18.9480			0.714638
$704$		0			0
$705$	−37.4854			−1.41178
$706$		0			0
$707$	10.6632	+	32.8181i	0.401033	+	1.23425i
$708$		0			0
$709$	0.516557	+	0.375301i	0.0193997	+	0.0140947i	0.597443	−	0.801911i	$-0.296183\pi$
$709$	0.516557	+	0.375301i	0.0193997	+	0.0140947i	−0.578043	+	0.816006i	$0.696183\pi$
$710$		0			0
$711$	1.42586	−	4.38833i	0.0534738	−	0.164575i
$712$		0			0
$713$	1.90325	−	1.38279i	0.0712771	−	0.0517859i
$714$		0			0
$715$	13.6969	−	4.55660i	0.512236	−	0.170407i
$716$		0			0
$717$	19.3826	−	14.0823i	0.723855	−	0.525912i
$718$		0			0
$719$	0.223639	−	0.688289i	0.00834032	−	0.0256689i	−0.946800	−	0.321823i	$-0.895704\pi$
$719$	0.223639	−	0.688289i	0.00834032	−	0.0256689i	0.955140	+	0.296154i	$0.0957043\pi$
$720$		0			0
$721$	−22.1399	−	16.0856i	−0.824533	−	0.599058i
$722$		0			0
$723$	6.29979	+	19.3888i	0.234292	+	0.721076i
$724$		0			0
$725$	11.8258			0.439201
$726$		0			0
$727$	31.6952			1.17551			0.587754	−	0.809040i	$-0.300012\pi$
$727$	31.6952			1.17551			0.587754	+	0.809040i	$0.300012\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	33.9624	+	24.6751i	1.25615	+	0.912643i
$732$		0			0
$733$	10.6872	−	32.8917i	0.394740	−	1.21488i	−0.534424	−	0.845216i	$-0.679472\pi$
$733$	10.6872	−	32.8917i	0.394740	−	1.21488i	0.929164	−	0.369667i	$-0.120528\pi$
$734$		0			0
$735$	−45.6810	+	33.1892i	−1.68497	+	1.22420i
$736$		0			0
$737$	6.08902	−	2.02565i	0.224292	−	0.0746160i
$738$		0			0
$739$	−14.1006	+	10.2447i	−0.518701	+	0.376858i	−0.816114	−	0.577891i	$-0.803876\pi$
$739$	−14.1006	+	10.2447i	−0.518701	+	0.376858i	0.297413	+	0.954749i	$0.403876\pi$
$740$		0			0
$741$	1.58416	−	4.87554i	0.0581955	−	0.179107i
$742$		0			0
$743$	24.7502	+	17.9821i	0.907998	+	0.659699i	0.940508	−	0.339772i	$-0.110350\pi$
$743$	24.7502	+	17.9821i	0.907998	+	0.659699i	−0.0325099	+	0.999471i	$0.510350\pi$
$744$		0			0
$745$	−1.98461	−	6.10799i	−0.0727104	−	0.223780i
$746$		0			0
$747$	−4.10349			−0.150139
$748$		0			0
$749$	−68.0084			−2.48497
$750$		0			0
$751$	4.76538	+	14.6663i	0.173891	+	0.535182i	0.999581	−	0.0289421i	$-0.00921385\pi$
$751$	4.76538	+	14.6663i	0.173891	+	0.535182i	−0.825690	+	0.564124i	$0.809214\pi$
$752$		0			0
$753$	−19.1272	−	13.8967i	−0.697032	−	0.506424i
$754$		0			0
$755$	5.36368	−	16.5077i	0.195204	−	0.600778i
$756$		0			0
$757$	19.2644	−	13.9964i	0.700175	−	0.508707i	−0.179814	−	0.983701i	$-0.557550\pi$
$757$	19.2644	−	13.9964i	0.700175	−	0.508707i	0.879989	+	0.474993i	$0.157550\pi$
$758$		0			0
$759$	−16.8068	−	22.7954i	−0.610047	−	0.827420i
$760$		0			0
$761$	19.5559	−	14.2082i	0.708900	−	0.515046i	−0.173918	−	0.984760i	$-0.555643\pi$
$761$	19.5559	−	14.2082i	0.708900	−	0.515046i	0.882819	+	0.469714i	$0.155643\pi$
$762$		0			0
$763$	−1.07730	+	3.31559i	−0.0390009	+	0.120032i
$764$		0			0
$765$	−17.7877	−	12.9235i	−0.643116	−	0.467251i
$766$		0			0
$767$	−1.35755	−	4.17810i	−0.0490182	−	0.150862i
$768$		0			0
$769$	31.0175			1.11852			0.559260	−	0.828992i	$-0.311085\pi$
$769$	31.0175			1.11852			0.559260	+	0.828992i	$0.311085\pi$
$770$		0			0
$771$	−8.28262			−0.298291
$772$		0			0
$773$	−7.37341	−	22.6930i	−0.265203	−	0.816211i	−0.991647	−	0.128985i	$-0.958828\pi$
$773$	−7.37341	−	22.6930i	−0.265203	−	0.816211i	0.726444	−	0.687226i	$-0.241172\pi$
$774$		0			0
$775$	−3.10757	−	2.25778i	−0.111627	−	0.0811020i
$776$		0			0
$777$	−5.10455	+	15.7102i	−0.183125	+	0.563599i
$778$		0			0
$779$	−37.8991	+	27.5353i	−1.35788	+	0.986555i
$780$		0			0
$781$	−49.3850	−	15.6650i	−1.76713	−	0.560537i
$782$		0			0
$783$	0.686193	−	0.498548i	0.0245225	−	0.0178167i
$784$		0			0
$785$	−24.1155	+	74.2199i	−0.860719	+	2.64902i
$786$		0			0
$787$	−35.3068	−	25.6519i	−1.25855	−	0.914391i	−0.259866	−	0.965645i	$-0.583678\pi$
$787$	−35.3068	−	25.6519i	−1.25855	−	0.914391i	−0.998686	+	0.0512536i	$0.983678\pi$
$788$		0			0
$789$	−0.635977	−	1.95734i	−0.0226414	−	0.0696830i
$790$		0			0
$791$	−42.4013			−1.50762
$792$		0			0
$793$	7.16955			0.254598
$794$		0			0
$795$	12.1679	+	37.4488i	0.431549	+	1.32817i
$796$		0			0
$797$	−6.05400	−	4.39849i	−0.214444	−	0.155802i	0.475378	−	0.879781i	$-0.342311\pi$
$797$	−6.05400	−	4.39849i	−0.214444	−	0.155802i	−0.689822	+	0.723979i	$0.742311\pi$
$798$		0			0
$799$	13.4452	−	41.3801i	0.475657	−	1.46392i
$800$		0			0
$801$	−6.21751	+	4.51729i	−0.219685	+	0.159610i
$802$		0			0
$803$	0.136993	+	19.5781i	0.00483439	+	0.690896i
$804$		0			0
$805$	134.376	−	97.6299i	4.73613	−	3.44100i
$806$		0			0
$807$	4.51814	−	13.9054i	0.159046	−	0.489493i
$808$		0			0
$809$	42.5100	+	30.8853i	1.49457	+	1.08587i	0.972481	+	0.232982i	$0.0748482\pi$
$809$	42.5100	+	30.8853i	1.49457	+	1.08587i	0.522092	+	0.852889i	$0.325152\pi$
$810$		0			0
$811$	3.88791	+	11.9657i	0.136523	+	0.420174i	0.995824	−	0.0912961i	$-0.0291010\pi$
$811$	3.88791	+	11.9657i	0.136523	+	0.420174i	−0.859301	+	0.511470i	$0.829101\pi$
$812$		0			0
$813$	11.7061			0.410551
$814$		0			0
$815$	−42.4011			−1.48525
$816$		0			0
$817$	−13.1643	−	40.5154i	−0.460559	−	1.41746i
$818$		0			0
$819$	3.61564	+	2.62692i	0.126341	+	0.0917918i
$820$		0			0
$821$	2.16924	−	6.67624i	0.0757070	−	0.233002i	−0.906041	−	0.423191i	$-0.860910\pi$
$821$	2.16924	−	6.67624i	0.0757070	−	0.233002i	0.981748	+	0.190189i	$0.0609100\pi$
$822$		0			0
$823$	5.83569	−	4.23988i	0.203419	−	0.147793i	−0.481412	−	0.876494i	$-0.659876\pi$
$823$	5.83569	−	4.23988i	0.203419	−	0.147793i	0.684831	+	0.728702i	$0.259876\pi$
$824$		0			0
$825$	−26.9181	+	37.6001i	−0.937169	+	1.30907i
$826$		0			0
$827$	−9.33176	+	6.77992i	−0.324497	+	0.235761i	−0.738092	−	0.674700i	$-0.764273\pi$
$827$	−9.33176	+	6.77992i	−0.324497	+	0.235761i	0.413595	+	0.910461i	$0.364273\pi$
$828$		0			0
$829$	−14.9212	+	45.9227i	−0.518234	+	1.59496i	0.259085	+	0.965854i	$0.416579\pi$
$829$	−14.9212	+	45.9227i	−0.518234	+	1.59496i	−0.777319	+	0.629106i	$0.783421\pi$
$830$		0			0
$831$	10.2584	+	7.45317i	0.355860	+	0.258548i
$832$		0			0
$833$	−20.2527	−	62.3315i	−0.701715	−	2.15966i
$834$		0			0
$835$	−47.0848			−1.62944
$836$		0			0
$837$	−0.275499			−0.00952264
$838$		0			0
$839$	−15.3059	−	47.1066i	−0.528417	−	1.62630i	−0.757459	−	0.652883i	$-0.773559\pi$
$839$	−15.3059	−	47.1066i	−0.528417	−	1.62630i	0.229042	−	0.973417i	$-0.426441\pi$
$840$		0			0
$841$	22.8795	+	16.6229i	0.788947	+	0.573204i
$842$		0			0
$843$	0.353580	−	1.08821i	0.0121779	−	0.0374799i
$844$		0			0
$845$	3.52109	−	2.55822i	0.121129	−	0.0880055i
$846$		0			0
$847$	15.8444	+	46.5376i	0.544418	+	1.59905i
$848$		0			0
$849$	−25.2254	+	18.3274i	−0.865735	+	0.628993i
$850$		0			0
$851$	9.75319	−	30.0172i	0.334335	−	1.02898i
$852$		0			0
$853$	2.48398	+	1.80472i	0.0850499	+	0.0617924i	0.629498	−	0.777002i	$-0.283261\pi$
$853$	2.48398	+	1.80472i	0.0850499	+	0.0617924i	−0.544448	+	0.838795i	$0.683261\pi$
$854$		0			0
$855$	6.89474	+	21.2198i	0.235795	+	0.725703i
$856$		0			0
$857$	23.5746			0.805294			0.402647	−	0.915355i	$-0.368090\pi$
$857$	23.5746			0.805294			0.402647	+	0.915355i	$0.368090\pi$
$858$		0			0
$859$	−33.6876			−1.14940			−0.574702	−	0.818363i	$-0.694882\pi$
$859$	−33.6876			−1.14940			−0.574702	+	0.818363i	$0.694882\pi$
$860$		0			0
$861$	−12.6202	−	38.8409i	−0.430094	−	1.32369i
$862$		0			0
$863$	22.1988	+	16.1284i	0.755657	+	0.549017i	0.897575	−	0.440862i	$-0.145327\pi$
$863$	22.1988	+	16.1284i	0.755657	+	0.549017i	−0.141918	+	0.989878i	$0.545327\pi$
$864$		0			0
$865$	−18.5551	+	57.1066i	−0.630891	+	1.94168i
$866$		0			0
$867$	6.89308	−	5.00811i	0.234101	−	0.170084i
$868$		0			0
$869$	8.90830	−	12.4434i	0.302193	−	0.422113i
$870$		0			0
$871$	1.56531	−	1.13727i	0.0530387	−	0.0385348i
$872$		0			0
$873$	2.39680	−	7.37660i	0.0811194	−	0.249660i
$874$		0			0
$875$	−140.724	−	102.242i	−4.75734	−	3.45641i
$876$		0			0
$877$	0.429912	+	1.32313i	0.0145171	+	0.0446791i	0.958053	−	0.286592i	$-0.0925225\pi$
$877$	0.429912	+	1.32313i	0.0145171	+	0.0446791i	−0.943536	+	0.331271i	$0.892522\pi$
$878$		0			0
$879$	15.6387			0.527482
$880$		0			0
$881$	12.4462			0.419324			0.209662	−	0.977774i	$-0.432764\pi$
$881$	12.4462			0.419324			0.209662	+	0.977774i	$0.432764\pi$
$882$		0			0
$883$	−13.0694	−	40.2234i	−0.439819	−	1.35362i	−0.888067	−	0.459715i	$-0.847952\pi$
$883$	−13.0694	−	40.2234i	−0.439819	−	1.35362i	0.448248	−	0.893909i	$-0.352048\pi$
$884$		0			0
$885$	15.4686	+	11.2386i	0.519970	+	0.377780i
$886$		0			0
$887$	9.55065	−	29.3939i	0.320679	−	0.986949i	−0.652674	−	0.757639i	$-0.726353\pi$
$887$	9.55065	−	29.3939i	0.320679	−	0.986949i	0.973353	−	0.229311i	$-0.0736471\pi$
$888$		0			0
$889$	−38.6366	+	28.0711i	−1.29583	+	0.941476i
$890$		0			0
$891$	0.0232068	+	3.31654i	0.000777457	+	0.111108i
$892$		0			0
$893$	−35.7203	+	25.9524i	−1.19534	+	0.868462i
$894$		0			0
$895$	−22.0040	+	67.7215i	−0.735514	+	2.26368i
$896$		0			0
$897$	−6.90835	−	5.01921i	−0.230663	−	0.167587i
$898$		0			0
$899$	0.0722090	+	0.222236i	0.00240831	+	0.00741200i
$900$		0			0
$901$	−45.7041			−1.52262
$902$		0			0
$903$	37.1386			1.23589
$904$		0			0
$905$	21.3625	+	65.7469i	0.710112	+	2.18550i
$906$		0			0
$907$	45.9575	+	33.3901i	1.52600	+	1.10870i	0.958414	+	0.285383i	$0.0921208\pi$
$907$	45.9575	+	33.3901i	1.52600	+	1.10870i	0.567582	+	0.823317i	$0.307879\pi$
$908$		0			0
$909$	−2.38595	+	7.34321i	−0.0791371	+	0.243559i
$910$		0			0
$911$	30.2923	−	22.0086i	1.00363	−	0.729178i	0.0407642	−	0.999169i	$-0.487021\pi$
$911$	30.2923	−	22.0086i	1.00363	−	0.729178i	0.962863	+	0.269991i	$0.0870207\pi$
$912$		0			0
$913$	−12.9727	−	4.11497i	−0.429335	−	0.136186i
$914$		0			0
$915$	−25.2446	+	18.3413i	−0.834562	+	0.606345i
$916$		0			0
$917$	−18.6495	+	57.3974i	−0.615862	+	1.89543i
$918$		0			0
$919$	−14.0111	−	10.1797i	−0.462185	−	0.335797i	0.332203	−	0.943208i	$-0.392208\pi$
$919$	−14.0111	−	10.1797i	−0.462185	−	0.335797i	−0.794388	+	0.607411i	$0.792208\pi$
$920$		0			0
$921$	−1.37187	−	4.22217i	−0.0452046	−	0.139125i
$922$		0			0
$923$	−15.6213			−0.514181
$924$		0			0
$925$	−51.5336			−1.69442
$926$		0			0
$927$	−1.89223	−	5.82367i	−0.0621489	−	0.191275i
$928$		0			0
$929$	−0.417823	−	0.303566i	−0.0137083	−	0.00995967i	0.580910	−	0.813968i	$-0.302697\pi$
$929$	−0.417823	−	0.303566i	−0.0137083	−	0.00995967i	−0.594618	+	0.804008i	$0.702697\pi$
$930$		0			0
$931$	−20.5521	+	63.2529i	−0.673568	+	2.07303i
$932$		0			0
$933$	−5.10566	+	3.70948i	−0.167152	+	0.121443i
$934$		0			0
$935$	−43.2743	−	58.6938i	−1.41522	−	1.91949i
$936$		0			0
$937$	41.5591	−	30.1945i	1.35768	−	0.986410i	0.359088	−	0.933304i	$-0.383088\pi$
$937$	41.5591	−	30.1945i	1.35768	−	0.986410i	0.998589	−	0.0531063i	$-0.0169122\pi$
$938$		0			0
$939$	−4.72049	+	14.5282i	−0.154047	+	0.474109i
$940$		0			0
$941$	28.1856	+	20.4781i	0.918825	+	0.667566i	0.943231	−	0.332136i	$-0.107769\pi$
$941$	28.1856	+	20.4781i	0.918825	+	0.667566i	−0.0244060	+	0.999702i	$0.507769\pi$
$942$		0			0
$943$	24.1132	+	74.2128i	0.785233	+	2.41670i
$944$		0			0
$945$	−19.4512			−0.632748
$946$		0			0
$947$	1.77512			0.0576838			0.0288419	−	0.999584i	$-0.490818\pi$
$947$	1.77512			0.0576838			0.0288419	+	0.999584i	$0.490818\pi$
$948$		0			0
$949$	1.82418	+	5.61424i	0.0592153	+	0.182246i
$950$		0			0
$951$	7.68255	+	5.58170i	0.249124	+	0.180999i
$952$		0			0
$953$	0.878030	−	2.70230i	0.0284422	−	0.0875360i	−0.935828	−	0.352458i	$-0.885346\pi$
$953$	0.878030	−	2.70230i	0.0284422	−	0.0875360i	0.964270	+	0.264922i	$0.0853461\pi$
$954$		0			0
$955$	20.4225	−	14.8378i	0.660857	−	0.480140i
$956$		0			0
$957$	2.66927	−	0.887994i	0.0862852	−	0.0287048i
$958$		0			0
$959$	−17.6713	+	12.8389i	−0.570634	+	0.414590i
$960$		0			0
$961$	−9.55607	+	29.4106i	−0.308260	+	0.948728i
$962$		0			0
$963$	−12.3110	−	8.94446i	−0.396716	−	0.288231i
$964$		0			0
$965$	−8.69883	−	26.7722i	−0.280025	−	0.861829i
$966$		0			0
$967$	0.665147			0.0213897			0.0106948	−	0.999943i	$-0.496596\pi$
$967$	0.665147			0.0213897			0.0106948	+	0.999943i	$0.496596\pi$
$968$		0			0
$969$	−25.8976			−0.831950
$970$		0			0
$971$	17.0569	+	52.4956i	0.547381	+	1.68466i	0.715261	+	0.698858i	$0.246308\pi$
$971$	17.0569	+	52.4956i	0.547381	+	1.68466i	−0.167880	+	0.985807i	$0.553692\pi$
$972$		0			0
$973$	13.2502	+	9.62686i	0.424783	+	0.308623i
$974$		0			0
$975$	−4.30850	+	13.2602i	−0.137982	+	0.424666i
$976$		0			0
$977$	21.4701	−	15.5990i	0.686890	−	0.499055i	−0.188746	−	0.982026i	$-0.560442\pi$
$977$	21.4701	−	15.5990i	0.686890	−	0.499055i	0.875636	+	0.482971i	$0.160442\pi$
$978$		0			0
$979$	−24.1859	+	8.04601i	−0.772985	+	0.257152i
$980$		0			0
$981$	−0.631081	+	0.458507i	−0.0201489	+	0.0146390i
$982$		0			0
$983$	2.84809	−	8.76553i	0.0908401	−	0.279577i	−0.895307	−	0.445449i	$-0.853044\pi$
$983$	2.84809	−	8.76553i	0.0908401	−	0.279577i	0.986147	+	0.165872i	$0.0530439\pi$
$984$		0			0
$985$	56.3080	+	40.9102i	1.79412	+	1.30351i
$986$		0			0
$987$	−11.8946	−	36.6080i	−0.378611	−	1.16524i
$988$		0			0
$989$	−70.9602			−2.25640
$990$		0			0
$991$	12.3137			0.391159			0.195579	−	0.980688i	$-0.437341\pi$
$991$	12.3137			0.391159			0.195579	+	0.980688i	$0.437341\pi$
$992$		0			0
$993$	−4.77837	−	14.7063i	−0.151637	−	0.466691i
$994$		0			0
$995$	−43.9506	−	31.9320i	−1.39333	−	1.01231i
$996$		0			0
$997$	4.03538	−	12.4196i	0.127802	−	0.393334i	−0.866599	−	0.499005i	$-0.833699\pi$
$997$	4.03538	−	12.4196i	0.127802	−	0.393334i	0.994401	+	0.105671i	$0.0336990\pi$
$998$		0			0
$999$	−2.99023	+	2.17253i	−0.0946068	+	0.0687359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.2.z.f.157.5	✓	20
11.4	even	5	inner	1716.2.z.f.1093.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.2.z.f.157.5	✓	20	1.1	even	1	trivial
1716.2.z.f.1093.5	yes	20	11.4	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1716.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(3.52109 + 2.55822i) q^{5} +(-1.38105 + 4.25044i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(3.52109 + 2.55822i) q^{5} +(-1.38105 + 4.25044i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-3.14705 + 1.04694i) q^{11} +(-0.809017 + 0.587785i) q^{13} +(1.34494 - 4.13929i) q^{15} +(4.08696 + 2.96935i) q^{17} +(-1.58416 - 4.87554i) q^{19} +4.46917 q^{21} -8.53920 q^{23} +(4.30850 + 13.2602i) q^{25} +(0.809017 + 0.587785i) q^{27} +(0.262102 - 0.806668i) q^{29} +(-0.222884 + 0.161934i) q^{31} +(1.96819 + 2.66950i) q^{33} +(-15.7364 + 11.4331i) q^{35} +(-1.14217 + 3.51523i) q^{37} +(0.809017 + 0.587785i) q^{39} +(-2.82382 - 8.69084i) q^{41} +8.30994 q^{43} -4.35231 q^{45} +(-2.66149 - 8.19121i) q^{47} +(-10.4958 - 7.62565i) q^{49} +(1.56108 - 4.80451i) q^{51} +(-7.31930 + 5.31779i) q^{53} +(-13.7594 - 4.36448i) q^{55} +(-4.14738 + 3.01325i) q^{57} +(-1.35755 + 4.17810i) q^{59} +(-5.80029 - 4.21416i) q^{61} +(-1.38105 - 4.25044i) q^{63} -4.35231 q^{65} -1.93483 q^{67} +(2.63876 + 8.12126i) q^{69} +(12.6379 + 9.18196i) q^{71} +(1.82418 - 5.61424i) q^{73} +(11.2798 - 8.19525i) q^{75} +(-0.103715 - 14.8222i) q^{77} +(-3.73294 + 2.71214i) q^{79} +(0.309017 - 0.951057i) q^{81} +(3.31980 + 2.41197i) q^{83} +(6.79430 + 20.9107i) q^{85} -0.848181 q^{87} +7.68527 q^{89} +(-1.38105 - 4.25044i) q^{91} +(0.222884 + 0.161934i) q^{93} +(6.89474 - 21.2198i) q^{95} +(-6.27491 + 4.55899i) q^{97} +(1.93064 - 2.69678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9}+O(q^{10}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9	\( 20 q + 5 q^{3} + 4 q^{5} - q^{7} - 5 q^{9} - 24 q^{11} - 5 q^{13} - 4 q^{15} - 6 q^{17} - 16 q^{19} + 6 q^{21} - 34 q^{23} + 13 q^{25} + 5 q^{27} + 4 q^{29} - 12 q^{31} - 11 q^{33} - 20 q^{37} + 5 q^{39} + 24 q^{41} - 32 q^{43} - 16 q^{45} - 6 q^{47} + 6 q^{49} - 9 q^{51} + 3 q^{53} - 20 q^{55} - 14 q^{57} - 61 q^{59} + 18 q^{61} - q^{63} - 16 q^{65} - 32 q^{67} - 6 q^{69} + 16 q^{71} + 17 q^{73} + 37 q^{75} + 22 q^{77} - 41 q^{79} - 5 q^{81} + 58 q^{83} + 42 q^{85} - 4 q^{87} - 6 q^{89} - q^{91} + 12 q^{93} + 55 q^{95} - 62 q^{97} + 6 q^{99}+O(q^{100}) \) 20 * q + 5 * q^3 + 4 * q^5 - q^7 - 5 * q^9 - 24 * q^11 - 5 * q^13 - 4 * q^15 - 6 * q^17 - 16 * q^19 + 6 * q^21 - 34 * q^23 + 13 * q^25 + 5 * q^27 + 4 * q^29 - 12 * q^31 - 11 * q^33 - 20 * q^37 + 5 * q^39 + 24 * q^41 - 32 * q^43 - 16 * q^45 - 6 * q^47 + 6 * q^49 - 9 * q^51 + 3 * q^53 - 20 * q^55 - 14 * q^57 - 61 * q^59 + 18 * q^61 - q^63 - 16 * q^65 - 32 * q^67 - 6 * q^69 + 16 * q^71 + 17 * q^73 + 37 * q^75 + 22 * q^77 - 41 * q^79 - 5 * q^81 + 58 * q^83 + 42 * q^85 - 4 * q^87 - 6 * q^89 - q^91 + 12 * q^93 + 55 * q^95 - 62 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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