LMFDB - Embedded newform 1320.2.bw.f.1081.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,2,Mod(361,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 6]))

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

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

chi := DirichletCharacter("1320.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1320.bw (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:	$10.5402530668$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 7 x^{10} + 15 x^{9} + 51 x^{8} + 175 x^{7} + 1103 x^{6} + 2884 x^{5} + 5561 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 7x^10 + 15x^9 + 51x^8 + 175x^7 + 1103x^6 + 2884x^5 + 5561x^4 + 5670x^3 + 2840x^2 - 125*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.2
Root			$-0.936904 + 0.680700i$ of defining polynomial
Character	$\chi$	$=$	1320.1081
Dual form			1320.2.bw.f.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0488484 + 0.150340i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0488484 + 0.150340i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.31625 + 3.04425i) q^{11} +(-1.94414 + 1.41250i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(0.465340 + 0.338089i) q^{17} +(-0.706985 - 2.17587i) q^{19} +0.158077 q^{21} -1.97162 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.382673 + 1.17775i) q^{29} +(-8.75855 + 6.36346i) q^{31} +(2.48851 - 2.19255i) q^{33} +(0.127887 - 0.0929152i) q^{35} +(-2.56485 + 7.89380i) q^{37} +(1.94414 + 1.41250i) q^{39} +(2.05779 + 6.33322i) q^{41} -0.0121787 q^{43} +1.00000 q^{45} +(-0.258113 - 0.794389i) q^{47} +(5.64290 + 4.09981i) q^{49} +(0.177744 - 0.547040i) q^{51} +(9.93420 - 7.21762i) q^{53} +(0.724500 - 3.23653i) q^{55} +(-1.85091 + 1.34476i) q^{57} +(-0.527464 + 1.62337i) q^{59} +(11.1436 + 8.09631i) q^{61} +(-0.0488484 - 0.150340i) q^{63} +2.40308 q^{65} -0.479663 q^{67} +(0.609265 + 1.87513i) q^{69} +(4.54499 + 3.30213i) q^{71} +(-1.34376 + 4.13567i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-0.521970 + 0.0491779i) q^{77} +(-9.84878 + 7.15556i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.71201 - 1.97039i) q^{83} +(-0.177744 - 0.547040i) q^{85} +1.23835 q^{87} +10.0672 q^{89} +(-0.117387 - 0.361280i) q^{91} +(8.75855 + 6.36346i) q^{93} +(-0.706985 + 2.17587i) q^{95} +(-6.65476 + 4.83497i) q^{97} +(-2.85424 - 1.68918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$1$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−0.0488484	+	0.150340i	−0.0184630	+	0.0568231i	−0.959864	−	0.280468i	$-0.909511\pi$
$7$	−0.0488484	+	0.150340i	−0.0184630	+	0.0568231i	0.941401	+	0.337291i	$0.109511\pi$
$8$		0			0
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	1.31625	+	3.04425i	0.396864	+	0.917877i
$11$	1.31625	+	3.04425i	0.396864	+	0.917877i
$12$		0			0
$13$	−1.94414	+	1.41250i	−0.539206	+	0.391756i	−0.823790	−	0.566895i	$-0.808145\pi$
$13$	−1.94414	+	1.41250i	−0.539206	+	0.391756i	0.284584	+	0.958651i	$0.408145\pi$
$14$		0			0
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	0.465340	+	0.338089i	0.112862	+	0.0819987i	0.642784	−	0.766047i	$-0.277779\pi$
$17$	0.465340	+	0.338089i	0.112862	+	0.0819987i	−0.529923	+	0.848046i	$0.677779\pi$
$18$		0			0
$19$	−0.706985	−	2.17587i	−0.162193	−	0.499180i	0.836625	−	0.547776i	$-0.184525\pi$
$19$	−0.706985	−	2.17587i	−0.162193	−	0.499180i	−0.998819	+	0.0485959i	$0.984525\pi$
$20$		0			0
$21$	0.158077			0.0344952
$22$		0			0
$23$	−1.97162			−0.411112			−0.205556	−	0.978645i	$-0.565900\pi$
$23$	−1.97162			−0.411112			−0.205556	+	0.978645i	$0.565900\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$		0			0
$29$	−0.382673	+	1.17775i	−0.0710605	+	0.218702i	−0.980279	−	0.197617i	$-0.936680\pi$
$29$	−0.382673	+	1.17775i	−0.0710605	+	0.218702i	0.909219	+	0.416318i	$0.136680\pi$
$30$		0			0
$31$	−8.75855	+	6.36346i	−1.57308	+	1.14291i	−0.648953	+	0.760828i	$0.724793\pi$
$31$	−8.75855	+	6.36346i	−1.57308	+	1.14291i	−0.924128	+	0.382082i	$0.875207\pi$
$32$		0			0
$33$	2.48851	−	2.19255i	0.433195	−	0.381675i
$34$		0			0
$35$	0.127887	−	0.0929152i	0.0216168	−	0.0157055i
$36$		0			0
$37$	−2.56485	+	7.89380i	−0.421659	+	1.29773i	0.484499	+	0.874792i	$0.339002\pi$
$37$	−2.56485	+	7.89380i	−0.421659	+	1.29773i	−0.906158	+	0.422940i	$0.860998\pi$
$38$		0			0
$39$	1.94414	+	1.41250i	0.311311	+	0.226181i
$40$		0			0
$41$	2.05779	+	6.33322i	0.321373	+	0.989083i	0.973051	+	0.230588i	$0.0740650\pi$
$41$	2.05779	+	6.33322i	0.321373	+	0.989083i	−0.651679	+	0.758495i	$0.725935\pi$
$42$		0			0
$43$	−0.0121787			−0.00185723			−0.000928617	−	1.00000i	$-0.500296\pi$
$43$	−0.0121787			−0.00185723			−0.000928617		1.00000i	$0.500296\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−0.258113	−	0.794389i	−0.0376496	−	0.115874i	0.930465	−	0.366380i	$-0.119403\pi$
$47$	−0.258113	−	0.794389i	−0.0376496	−	0.115874i	−0.968115	+	0.250506i	$0.919403\pi$
$48$		0			0
$49$	5.64290	+	4.09981i	0.806129	+	0.585687i
$50$		0			0
$51$	0.177744	−	0.547040i	0.0248891	−	0.0766009i
$52$		0			0
$53$	9.93420	−	7.21762i	1.36457	−	0.991416i	0.366428	−	0.930447i	$-0.380581\pi$
$53$	9.93420	−	7.21762i	1.36457	−	0.991416i	0.998140	−	0.0609695i	$-0.0194192\pi$
$54$		0			0
$55$	0.724500	−	3.23653i	0.0976915	−	0.436413i
$56$		0			0
$57$	−1.85091	+	1.34476i	−0.245159	+	0.178118i
$58$		0			0
$59$	−0.527464	+	1.62337i	−0.0686700	+	0.211344i	−0.979503	−	0.201431i	$-0.935441\pi$
$59$	−0.527464	+	1.62337i	−0.0686700	+	0.211344i	0.910833	+	0.412776i	$0.135441\pi$
$60$		0			0
$61$	11.1436	+	8.09631i	1.42679	+	1.03663i	0.990603	+	0.136771i	$0.0436726\pi$
$61$	11.1436	+	8.09631i	1.42679	+	1.03663i	0.436190	+	0.899854i	$0.356327\pi$
$62$		0			0
$63$	−0.0488484	−	0.150340i	−0.00615432	−	0.0189410i
$64$		0			0
$65$	2.40308			0.298066
$66$		0			0
$67$	−0.479663			−0.0586001			−0.0293001	−	0.999571i	$-0.509328\pi$
$67$	−0.479663			−0.0586001			−0.0293001	+	0.999571i	$0.509328\pi$
$68$		0			0
$69$	0.609265	+	1.87513i	0.0733469	+	0.225739i
$70$		0			0
$71$	4.54499	+	3.30213i	0.539391	+	0.391890i	0.823859	−	0.566795i	$-0.191817\pi$
$71$	4.54499	+	3.30213i	0.539391	+	0.391890i	−0.284468	+	0.958686i	$0.591817\pi$
$72$		0			0
$73$	−1.34376	+	4.13567i	−0.157275	+	0.484043i	−0.998384	−	0.0568221i	$-0.981903\pi$
$73$	−1.34376	+	4.13567i	−0.157275	+	0.484043i	0.841109	+	0.540865i	$0.181903\pi$
$74$		0			0
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$		0			0
$77$	−0.521970	+	0.0491779i	−0.0594840	+	0.00560434i
$78$		0			0
$79$	−9.84878	+	7.15556i	−1.10807	+	0.805063i	−0.982359	−	0.187003i	$-0.940123\pi$
$79$	−9.84878	+	7.15556i	−1.10807	+	0.805063i	−0.125715	+	0.992066i	$0.540123\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	−2.71201	−	1.97039i	−0.297681	−	0.216278i	0.428911	−	0.903347i	$-0.358897\pi$
$83$	−2.71201	−	1.97039i	−0.297681	−	0.216278i	−0.726593	+	0.687068i	$0.758897\pi$
$84$		0			0
$85$	−0.177744	−	0.547040i	−0.0192791	−	0.0593348i
$86$		0			0
$87$	1.23835			0.132766
$88$		0			0
$89$	10.0672			1.06712			0.533561	−	0.845762i	$-0.320854\pi$
$89$	10.0672			1.06712			0.533561	+	0.845762i	$0.320854\pi$
$90$		0			0
$91$	−0.117387	−	0.361280i	−0.0123055	−	0.0378724i
$92$		0			0
$93$	8.75855	+	6.36346i	0.908219	+	0.659860i
$94$		0			0
$95$	−0.706985	+	2.17587i	−0.0725351	+	0.223240i
$96$		0			0
$97$	−6.65476	+	4.83497i	−0.675689	+	0.490917i	−0.871925	−	0.489640i	$-0.837128\pi$
$97$	−6.65476	+	4.83497i	−0.675689	+	0.490917i	0.196236	+	0.980557i	$0.437128\pi$
$98$		0			0
$99$	−2.85424	−	1.68918i	−0.286862	−	0.169769i
$100$		0			0
$101$	2.15546	−	1.56603i	0.214476	−	0.155826i	−0.475361	−	0.879791i	$-0.657682\pi$
$101$	2.15546	−	1.56603i	0.214476	−	0.155826i	0.689837	+	0.723965i	$0.257682\pi$
$102$		0			0
$103$	−0.577285	+	1.77670i	−0.0568815	+	0.175063i	−0.975461	−	0.220174i	$-0.929338\pi$
$103$	−0.577285	+	1.77670i	−0.0568815	+	0.175063i	0.918579	+	0.395237i	$0.129338\pi$
$104$		0			0
$105$	−0.127887	−	0.0929152i	−0.0124805	−	0.00906759i
$106$		0			0
$107$	0.0388088	+	0.119441i	0.00375179	+	0.0115468i	0.952915	−	0.303238i	$-0.0980677\pi$
$107$	0.0388088	+	0.119441i	0.00375179	+	0.0115468i	−0.949163	+	0.314785i	$0.898068\pi$
$108$		0			0
$109$	−11.5011			−1.10161			−0.550805	−	0.834634i	$-0.685679\pi$
$109$	−11.5011			−1.10161			−0.550805	+	0.834634i	$0.685679\pi$
$110$		0			0
$111$	8.30003			0.787804
$112$		0			0
$113$	−0.649173	−	1.99795i	−0.0610691	−	0.187951i	0.915868	−	0.401480i	$-0.131504\pi$
$113$	−0.649173	−	1.99795i	−0.0610691	−	0.187951i	−0.976937	+	0.213529i	$0.931504\pi$
$114$		0			0
$115$	1.59508	+	1.15889i	0.148742	+	0.108067i
$116$		0			0
$117$	0.742594	−	2.28547i	0.0686528	−	0.211292i
$118$		0			0
$119$	−0.0735594	+	0.0534441i	−0.00674318	+	0.00489921i
$120$		0			0
$121$	−7.53497	+	8.01400i	−0.684998	+	0.728545i
$122$		0			0
$123$	5.38736	−	3.91415i	0.485762	−	0.352927i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−10.2889	−	7.47532i	−0.912992	−	0.663327i	0.0287779	−	0.999586i	$-0.490838\pi$
$127$	−10.2889	−	7.47532i	−0.912992	−	0.663327i	−0.941770	+	0.336258i	$0.890838\pi$
$128$		0			0
$129$	0.00376342	+	0.0115826i	0.000331351	+	0.00101979i
$130$		0			0
$131$	−11.2197			−0.980272			−0.490136	−	0.871646i	$-0.663053\pi$
$131$	−11.2197			−0.980272			−0.490136	+	0.871646i	$0.663053\pi$
$132$		0			0
$133$	0.361656			0.0313595
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	9.28500	+	6.74595i	0.793271	+	0.576345i	0.908932	−	0.416944i	$-0.136899\pi$
$137$	9.28500	+	6.74595i	0.793271	+	0.576345i	−0.115661	+	0.993289i	$0.536899\pi$
$138$		0			0
$139$	5.08631	−	15.6540i	0.431415	−	1.32776i	−0.465301	−	0.885152i	$-0.654054\pi$
$139$	5.08631	−	15.6540i	0.431415	−	1.32776i	0.896716	−	0.442606i	$-0.145946\pi$
$140$		0			0
$141$	−0.675747	+	0.490959i	−0.0569082	+	0.0413462i
$142$		0			0
$143$	−6.85897	−	4.05925i	−0.573576	−	0.339451i
$144$		0			0
$145$	1.00185	−	0.727887i	0.0831991	−	0.0604477i
$146$		0			0
$147$	2.15540	−	6.63363i	0.177774	−	0.547133i
$148$		0			0
$149$	10.9154	+	7.93052i	0.894226	+	0.649693i	0.936976	−	0.349393i	$-0.113612\pi$
$149$	10.9154	+	7.93052i	0.894226	+	0.649693i	−0.0427505	+	0.999086i	$0.513612\pi$
$150$		0			0
$151$	3.51705	+	10.8244i	0.286213	+	0.880874i	0.986032	+	0.166554i	$0.0532640\pi$
$151$	3.51705	+	10.8244i	0.286213	+	0.880874i	−0.699819	+	0.714320i	$0.746736\pi$
$152$		0			0
$153$	−0.575192			−0.0465015
$154$		0			0
$155$	10.8262			0.869578
$156$		0			0
$157$	0.840171	+	2.58578i	0.0670529	+	0.206368i	0.978969	−	0.204009i	$-0.0653972\pi$
$157$	0.840171	+	2.58578i	0.0670529	+	0.206368i	−0.911916	+	0.410377i	$0.865397\pi$
$158$		0			0
$159$	−9.93420	−	7.21762i	−0.787833	−	0.572394i
$160$		0			0
$161$	0.0963106	−	0.296414i	0.00759034	−	0.0233607i
$162$		0			0
$163$	10.8583	−	7.88900i	0.850486	−	0.617914i	−0.0747942	−	0.997199i	$-0.523830\pi$
$163$	10.8583	−	7.88900i	0.850486	−	0.617914i	0.925280	+	0.379285i	$0.123830\pi$
$164$		0			0
$165$	−3.30200	+	0.311101i	−0.257060	+	0.0242192i
$166$		0			0
$167$	−9.85918	+	7.16312i	−0.762926	+	0.554299i	−0.899807	−	0.436289i	$-0.856292\pi$
$167$	−9.85918	+	7.16312i	−0.762926	+	0.554299i	0.136880	+	0.990588i	$0.456292\pi$
$168$		0			0
$169$	−2.23270	+	6.87156i	−0.171747	+	0.528581i
$170$		0			0
$171$	1.85091	+	1.34476i	0.141543	+	0.102837i
$172$		0			0
$173$	−6.49745	−	19.9971i	−0.493992	−	1.52035i	−0.818522	−	0.574475i	$-0.805206\pi$
$173$	−6.49745	−	19.9971i	−0.493992	−	1.52035i	0.324530	−	0.945875i	$-0.394794\pi$
$174$		0			0
$175$	−0.158077			−0.0119495
$176$		0			0
$177$	1.70691			0.128299
$178$		0			0
$179$	0.224409	+	0.690660i	0.0167731	+	0.0516224i	0.959093	−	0.283092i	$-0.0913602\pi$
$179$	0.224409	+	0.690660i	0.0167731	+	0.0516224i	−0.942320	+	0.334714i	$0.891360\pi$
$180$		0			0
$181$	−13.1407	−	9.54729i	−0.976742	−	0.709645i	−0.0197638	−	0.999805i	$-0.506291\pi$
$181$	−13.1407	−	9.54729i	−0.976742	−	0.709645i	−0.956978	+	0.290160i	$0.906291\pi$
$182$		0			0
$183$	4.25648	−	13.1001i	0.314648	−	0.968387i
$184$		0			0
$185$	6.71486	−	4.87863i	0.493687	−	0.358684i
$186$		0			0
$187$	−0.416726	+	1.86162i	−0.0304740	+	0.136135i
$188$		0			0
$189$	−0.127887	+	0.0929152i	−0.00930239	+	0.00675858i
$190$		0			0
$191$	−4.27760	+	13.1651i	−0.309516	+	0.952593i	0.668437	+	0.743769i	$0.266964\pi$
$191$	−4.27760	+	13.1651i	−0.309516	+	0.952593i	−0.977953	+	0.208824i	$0.933036\pi$
$192$		0			0
$193$	14.3406	+	10.4190i	1.03226	+	0.749978i	0.968759	−	0.248004i	$-0.0797746\pi$
$193$	14.3406	+	10.4190i	1.03226	+	0.749978i	0.0634971	+	0.997982i	$0.479775\pi$
$194$		0			0
$195$	−0.742594	−	2.28547i	−0.0531783	−	0.163666i
$196$		0			0
$197$	−12.7046			−0.905167			−0.452583	−	0.891722i	$-0.649498\pi$
$197$	−12.7046			−0.905167			−0.452583	+	0.891722i	$0.649498\pi$
$198$		0			0
$199$	−17.5728			−1.24570			−0.622851	−	0.782340i	$-0.714026\pi$
$199$	−17.5728			−1.24570			−0.622851	+	0.782340i	$0.714026\pi$
$200$		0			0
$201$	0.148224	+	0.456186i	0.0104549	+	0.0321769i
$202$		0			0
$203$	−0.158369	−	0.115062i	−0.0111153	−	0.00807576i
$204$		0			0
$205$	2.05779	−	6.33322i	0.143722	−	0.442331i
$206$		0			0
$207$	1.59508	−	1.15889i	0.110865	−	0.0805485i
$208$		0			0
$209$	5.69335	−	5.01624i	0.393817	−	0.346980i
$210$		0			0
$211$	−15.0004	+	10.8984i	−1.03267	+	0.750279i	−0.968842	−	0.247681i	$-0.920331\pi$
$211$	−15.0004	+	10.8984i	−1.03267	+	0.750279i	−0.0638295	+	0.997961i	$0.520331\pi$
$212$		0			0
$213$	1.73603	−	5.34295i	0.118951	−	0.366093i
$214$		0			0
$215$	0.00985277	+	0.00715846i	0.000671953	+	0.000488203i
$216$		0			0
$217$	−0.528841	−	1.62760i	−0.0359000	−	0.110489i
$218$		0			0
$219$	4.34850			0.293844
$220$		0			0
$221$	−1.38223			−0.0929792
$222$		0			0
$223$	−7.75292	−	23.8610i	−0.519174	−	1.59785i	−0.775557	−	0.631277i	$-0.782531\pi$
$223$	−7.75292	−	23.8610i	−0.519174	−	1.59785i	0.256384	−	0.966575i	$-0.417469\pi$
$224$		0			0
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	6.83907	−	21.0485i	0.453925	−	1.39704i	−0.418467	−	0.908232i	$-0.637433\pi$
$227$	6.83907	−	21.0485i	0.453925	−	1.39704i	0.872393	−	0.488806i	$-0.162567\pi$
$228$		0			0
$229$	−5.46467	+	3.97032i	−0.361116	+	0.262366i	−0.753517	−	0.657428i	$-0.771644\pi$
$229$	−5.46467	+	3.97032i	−0.361116	+	0.262366i	0.392402	+	0.919794i	$0.371644\pi$
$230$		0			0
$231$	0.208068	+	0.481226i	0.0136899	+	0.0316623i
$232$		0			0
$233$	−3.65449	+	2.65515i	−0.239414	+	0.173944i	−0.701022	−	0.713140i	$-0.747273\pi$
$233$	−3.65449	+	2.65515i	−0.239414	+	0.173944i	0.461608	+	0.887084i	$0.347273\pi$
$234$		0			0
$235$	−0.258113	+	0.794389i	−0.0168374	+	0.0518202i
$236$		0			0
$237$	9.84878	+	7.15556i	0.639747	+	0.464803i
$238$		0			0
$239$	−2.03711	−	6.26958i	−0.131770	−	0.405546i	0.863304	−	0.504685i	$-0.168391\pi$
$239$	−2.03711	−	6.26958i	−0.131770	−	0.405546i	−0.995074	+	0.0991389i	$0.968391\pi$
$240$		0			0
$241$	−6.82419			−0.439585			−0.219792	−	0.975547i	$-0.570538\pi$
$241$	−6.82419			−0.439585			−0.219792	+	0.975547i	$0.570538\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	−2.15540	−	6.63363i	−0.137703	−	0.423807i
$246$		0			0
$247$	4.44789	+	3.23158i	0.283013	+	0.205621i
$248$		0			0
$249$	−1.03589	+	3.18815i	−0.0656471	+	0.202041i
$250$		0			0
$251$	6.52317	−	4.73936i	0.411739	−	0.299146i	−0.362566	−	0.931958i	$-0.618099\pi$
$251$	6.52317	−	4.73936i	0.411739	−	0.299146i	0.774306	+	0.632812i	$0.218099\pi$
$252$		0			0
$253$	−2.59515	−	6.00212i	−0.163156	−	0.377350i
$254$		0			0
$255$	−0.465340	+	0.338089i	−0.0291407	+	0.0211720i
$256$		0			0
$257$	−2.56044	+	7.88022i	−0.159716	+	0.491555i	−0.998608	−	0.0527426i	$-0.983204\pi$
$257$	−2.56044	+	7.88022i	−0.159716	+	0.491555i	0.838892	+	0.544298i	$0.183204\pi$
$258$		0			0
$259$	−1.06146	−	0.771199i	−0.0659562	−	0.0479199i
$260$		0			0
$261$	−0.382673	−	1.17775i	−0.0236868	−	0.0729006i
$262$		0			0
$263$	6.40150			0.394733			0.197367	−	0.980330i	$-0.436761\pi$
$263$	6.40150			0.394733			0.197367	+	0.980330i	$0.436761\pi$
$264$		0			0
$265$	−12.2793			−0.754314
$266$		0			0
$267$	−3.11094	−	9.57448i	−0.190386	−	0.585948i
$268$		0			0
$269$	6.30462	+	4.58057i	0.384399	+	0.279282i	0.763157	−	0.646214i	$-0.223648\pi$
$269$	6.30462	+	4.58057i	0.384399	+	0.279282i	−0.378757	+	0.925496i	$0.623648\pi$
$270$		0			0
$271$	−4.86832	+	14.9832i	−0.295729	+	0.910162i	0.687246	+	0.726425i	$0.258819\pi$
$271$	−4.86832	+	14.9832i	−0.295729	+	0.910162i	−0.982975	+	0.183737i	$0.941181\pi$
$272$		0			0
$273$	−0.307323	+	0.223283i	−0.0186000	+	0.0135137i
$274$		0			0
$275$	−2.48851	+	2.19255i	−0.150063	+	0.132216i
$276$		0			0
$277$	−12.2302	+	8.88578i	−0.734843	+	0.533895i	−0.891092	−	0.453823i	$-0.850060\pi$
$277$	−12.2302	+	8.88578i	−0.734843	+	0.533895i	0.156249	+	0.987718i	$0.450060\pi$
$278$		0			0
$279$	3.34547	−	10.2963i	0.200288	−	0.616423i
$280$		0			0
$281$	−4.11896	−	2.99260i	−0.245716	−	0.178523i	0.458110	−	0.888896i	$-0.348527\pi$
$281$	−4.11896	−	2.99260i	−0.245716	−	0.178523i	−0.703826	+	0.710372i	$0.748527\pi$
$282$		0			0
$283$	−7.55875	−	23.2634i	−0.449321	−	1.38287i	−0.877675	−	0.479257i	$-0.840906\pi$
$283$	−7.55875	−	23.2634i	−0.449321	−	1.38287i	0.428354	−	0.903611i	$-0.359094\pi$
$284$		0			0
$285$	2.28785			0.135521
$286$		0			0
$287$	−1.05266			−0.0621363
$288$		0			0
$289$	−5.15105	−	15.8533i	−0.303003	−	0.932548i
$290$		0			0
$291$	6.65476	+	4.83497i	0.390109	+	0.283431i
$292$		0			0
$293$	9.01644	−	27.7497i	0.526746	−	1.62116i	−0.234092	−	0.972215i	$-0.575212\pi$
$293$	9.01644	−	27.7497i	0.526746	−	1.62116i	0.760837	−	0.648942i	$-0.224788\pi$
$294$		0			0
$295$	1.38092	−	1.00330i	0.0804002	−	0.0584142i
$296$		0			0
$297$	−0.724500	+	3.23653i	−0.0420397	+	0.187802i
$298$		0			0
$299$	3.83310	−	2.78491i	0.221674	−	0.161056i
$300$		0			0
$301$	0.000594910	−	0.00183094i	3.42900e−5	−	0.000105534i
$302$		0			0
$303$	−2.15546	−	1.56603i	−0.123828	−	0.0899661i
$304$		0			0
$305$	−4.25648	−	13.1001i	−0.243725	−	0.750109i
$306$		0			0
$307$	−1.25901			−0.0718556			−0.0359278	−	0.999354i	$-0.511439\pi$
$307$	−1.25901			−0.0718556			−0.0359278	+	0.999354i	$0.511439\pi$
$308$		0			0
$309$	1.86813			0.106274
$310$		0			0
$311$	2.61635	+	8.05230i	0.148360	+	0.456604i	0.997428	−	0.0716795i	$-0.0228359\pi$
$311$	2.61635	+	8.05230i	0.148360	+	0.456604i	−0.849068	+	0.528283i	$0.822836\pi$
$312$		0			0
$313$	−11.5384	−	8.38315i	−0.652190	−	0.473844i	0.211826	−	0.977307i	$-0.432059\pi$
$313$	−11.5384	−	8.38315i	−0.652190	−	0.473844i	−0.864017	+	0.503463i	$0.832059\pi$
$314$		0			0
$315$	−0.0488484	+	0.150340i	−0.00275230	+	0.00847069i
$316$		0			0
$317$	12.8819	−	9.35924i	0.723519	−	0.525667i	−0.163988	−	0.986462i	$-0.552436\pi$
$317$	12.8819	−	9.35924i	0.723519	−	0.525667i	0.887506	+	0.460795i	$0.152436\pi$
$318$		0			0
$319$	−4.08905	+	0.385254i	−0.228943	+	0.0215701i
$320$		0			0
$321$	0.101603	−	0.0738187i	0.00567091	−	0.00412016i
$322$		0			0
$323$	0.406652	−	1.25155i	0.0226267	−	0.0696379i
$324$		0			0
$325$	−1.94414	−	1.41250i	−0.107841	−	0.0783513i
$326$		0			0
$327$	3.55405	+	10.9382i	0.196539	+	0.604886i
$328$		0			0
$329$	0.132037			0.00727942
$330$		0			0
$331$	23.6300			1.29882			0.649412	−	0.760437i	$-0.275015\pi$
$331$	23.6300			1.29882			0.649412	+	0.760437i	$0.275015\pi$
$332$		0			0
$333$	−2.56485	−	7.89380i	−0.140553	−	0.432577i
$334$		0			0
$335$	0.388055	+	0.281939i	0.0212017	+	0.0154040i
$336$		0			0
$337$	−2.23562	+	6.88052i	−0.121782	+	0.374806i	−0.993301	−	0.115556i	$-0.963135\pi$
$337$	−2.23562	+	6.88052i	−0.121782	+	0.374806i	0.871519	+	0.490361i	$0.163135\pi$
$338$		0			0
$339$	−1.69956	+	1.23480i	−0.0923073	+	0.0670652i
$340$		0			0
$341$	−30.9004	−	18.2874i	−1.67335	−	0.990316i
$342$		0			0
$343$	−1.78722	+	1.29849i	−0.0965008	+	0.0701119i
$344$		0			0
$345$	0.609265	−	1.87513i	0.0328017	−	0.100953i
$346$		0			0
$347$	−0.798106	−	0.579858i	−0.0428446	−	0.0311284i	0.566157	−	0.824298i	$-0.308430\pi$
$347$	−0.798106	−	0.579858i	−0.0428446	−	0.0311284i	−0.609001	+	0.793169i	$0.708430\pi$
$348$		0			0
$349$	7.26082	+	22.3465i	0.388663	+	1.19618i	0.933788	+	0.357827i	$0.116482\pi$
$349$	7.26082	+	22.3465i	0.388663	+	1.19618i	−0.545125	+	0.838355i	$0.683518\pi$
$350$		0			0
$351$	−2.40308			−0.128267
$352$		0			0
$353$	6.11068			0.325239			0.162619	−	0.986689i	$-0.448006\pi$
$353$	6.11068			0.325239			0.162619	+	0.986689i	$0.448006\pi$
$354$		0			0
$355$	−1.73603	−	5.34295i	−0.0921390	−	0.283575i
$356$		0			0
$357$	0.0735594	+	0.0534441i	0.00389318	+	0.00282856i
$358$		0			0
$359$	0.833832	−	2.56627i	0.0440080	−	0.135443i	−0.926638	−	0.375954i	$-0.877315\pi$
$359$	0.833832	−	2.56627i	0.0440080	−	0.135443i	0.970646	+	0.240511i	$0.0773151\pi$
$360$		0			0
$361$	11.1367	−	8.09130i	0.586143	−	0.425858i
$362$		0			0
$363$	9.95020	+	4.68972i	0.522250	+	0.246147i
$364$		0			0
$365$	3.51801	−	2.55598i	0.184141	−	0.133786i
$366$		0			0
$367$	0.500409	−	1.54010i	0.0261212	−	0.0803926i	−0.937146	−	0.348937i	$-0.886543\pi$
$367$	0.500409	−	1.54010i	0.0261212	−	0.0803926i	0.963267	+	0.268545i	$0.0865427\pi$
$368$		0			0
$369$	−5.38736	−	3.91415i	−0.280455	−	0.203762i
$370$		0			0
$371$	0.599826	+	1.84608i	0.0311414	+	0.0958435i
$372$		0			0
$373$	5.85788			0.303309			0.151655	−	0.988434i	$-0.451540\pi$
$373$	5.85788			0.303309			0.151655	+	0.988434i	$0.451540\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	−0.919595	−	2.83022i	−0.0473615	−	0.145764i
$378$		0			0
$379$	18.6964	+	13.5837i	0.960367	+	0.697748i	0.953236	−	0.302227i	$-0.0977300\pi$
$379$	18.6964	+	13.5837i	0.960367	+	0.697748i	0.00713143	+	0.999975i	$0.497730\pi$
$380$		0			0
$381$	−3.93001	+	12.0953i	−0.201340	+	0.619662i
$382$		0			0
$383$	−14.0323	+	10.1951i	−0.717019	+	0.520945i	−0.885430	−	0.464772i	$-0.846136\pi$
$383$	−14.0323	+	10.1951i	−0.717019	+	0.520945i	0.168412	+	0.985717i	$0.446136\pi$
$384$		0			0
$385$	0.451188	+	0.267020i	0.0229947	+	0.0136086i
$386$		0			0
$387$	0.00985277	−	0.00715846i	0.000500845	−	0.000363885i
$388$		0			0
$389$	6.64641	−	20.4555i	0.336986	−	1.03714i	−0.628749	−	0.777608i	$-0.716433\pi$
$389$	6.64641	−	20.4555i	0.336986	−	1.03714i	0.965735	−	0.259529i	$-0.0835673\pi$
$390$		0			0
$391$	−0.917475	−	0.666585i	−0.0463987	−	0.0337106i
$392$		0			0
$393$	3.46709	+	10.6706i	0.174891	+	0.538260i
$394$		0			0
$395$	12.1738			0.612528
$396$		0			0
$397$	6.53614			0.328040			0.164020	−	0.986457i	$-0.447554\pi$
$397$	6.53614			0.328040			0.164020	+	0.986457i	$0.447554\pi$
$398$		0			0
$399$	−0.111758	−	0.343955i	−0.00559489	−	0.0172193i
$400$		0			0
$401$	0.133855	+	0.0972512i	0.00668439	+	0.00485649i	0.591122	−	0.806582i	$-0.298685\pi$
$401$	0.133855	+	0.0972512i	0.00668439	+	0.00485649i	−0.584438	+	0.811438i	$0.698685\pi$
$402$		0			0
$403$	8.03944	−	24.7429i	0.400473	−	1.23253i
$404$		0			0
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$		0			0
$407$	−27.4067	+	2.58215i	−1.35850	+	0.127992i
$408$		0			0
$409$	−8.81836	+	6.40691i	−0.436040	+	0.316801i	−0.784059	−	0.620686i	$-0.786854\pi$
$409$	−8.81836	+	6.40691i	−0.436040	+	0.316801i	0.348020	+	0.937487i	$0.386854\pi$
$410$		0			0
$411$	3.54655	−	10.9152i	0.174939	−	0.538406i
$412$		0			0
$413$	−0.218291	−	0.158598i	−0.0107414	−	0.00780409i
$414$		0			0
$415$	1.03589	+	3.18815i	0.0508500	+	0.156500i
$416$		0			0
$417$	−16.4596			−0.806032
$418$		0			0
$419$	26.9225			1.31525			0.657626	−	0.753345i	$-0.271561\pi$
$419$	26.9225			1.31525			0.657626	+	0.753345i	$0.271561\pi$
$420$		0			0
$421$	0.482283	+	1.48432i	0.0235051	+	0.0723411i	0.962121	−	0.272623i	$-0.0878911\pi$
$421$	0.482283	+	1.48432i	0.0235051	+	0.0723411i	−0.938616	+	0.344964i	$0.887891\pi$
$422$		0			0
$423$	0.675747	+	0.490959i	0.0328560	+	0.0238713i
$424$		0			0
$425$	−0.177744	+	0.547040i	−0.00862185	+	0.0265353i
$426$		0			0
$427$	−1.76155	+	1.27984i	−0.0852472	+	0.0619357i
$428$		0			0
$429$	−1.74103	+	7.77765i	−0.0840579	+	0.375508i
$430$		0			0
$431$	−18.8041	+	13.6620i	−0.905763	+	0.658075i	−0.939940	−	0.341340i	$-0.889119\pi$
$431$	−18.8041	+	13.6620i	−0.905763	+	0.658075i	0.0341767	+	0.999416i	$0.489119\pi$
$432$		0			0
$433$	6.49412	−	19.9868i	0.312087	−	0.960506i	−0.664849	−	0.746977i	$-0.731504\pi$
$433$	6.49412	−	19.9868i	0.312087	−	0.960506i	0.976937	−	0.213529i	$-0.0684957\pi$
$434$		0			0
$435$	−1.00185	−	0.727887i	−0.0480350	−	0.0348995i
$436$		0			0
$437$	1.39391	+	4.29001i	0.0666796	+	0.205219i
$438$		0			0
$439$	−29.1154			−1.38960			−0.694800	−	0.719203i	$-0.744507\pi$
$439$	−29.1154			−1.38960			−0.694800	+	0.719203i	$0.744507\pi$
$440$		0			0
$441$	−6.97501			−0.332143
$442$		0			0
$443$	−6.81362	−	20.9702i	−0.323725	−	0.996323i	−0.972013	−	0.234928i	$-0.924515\pi$
$443$	−6.81362	−	20.9702i	−0.323725	−	0.996323i	0.648288	−	0.761395i	$-0.275485\pi$
$444$		0			0
$445$	−8.14454	−	5.91735i	−0.386088	−	0.280509i
$446$		0			0
$447$	4.16932	−	12.8318i	0.197202	−	0.606925i
$448$		0			0
$449$	29.1522	−	21.1803i	1.37578	−	0.999560i	0.378516	−	0.925595i	$-0.376435\pi$
$449$	29.1522	−	21.1803i	1.37578	−	0.999560i	0.997261	−	0.0739653i	$-0.0235654\pi$
$450$		0			0
$451$	−16.5714	+	14.6005i	−0.780316	+	0.687512i
$452$		0			0
$453$	9.20775	−	6.68982i	0.432618	−	0.314315i
$454$		0			0
$455$	−0.117387	+	0.361280i	−0.00550318	+	0.0169370i
$456$		0			0
$457$	19.3761	+	14.0776i	0.906377	+	0.658521i	0.940096	−	0.340910i	$-0.110735\pi$
$457$	19.3761	+	14.0776i	0.906377	+	0.658521i	−0.0337192	+	0.999431i	$0.510735\pi$
$458$		0			0
$459$	0.177744	+	0.547040i	0.00829638	+	0.0255336i
$460$		0			0
$461$	−13.9008			−0.647427			−0.323714	−	0.946155i	$-0.604931\pi$
$461$	−13.9008			−0.647427			−0.323714	+	0.946155i	$0.604931\pi$
$462$		0			0
$463$	31.5713			1.46724			0.733621	−	0.679559i	$-0.237829\pi$
$463$	31.5713			1.46724			0.733621	+	0.679559i	$0.237829\pi$
$464$		0			0
$465$	−3.34547	−	10.2963i	−0.155142	−	0.477479i
$466$		0			0
$467$	31.3997	+	22.8132i	1.45301	+	1.05567i	0.985117	+	0.171884i	$0.0549854\pi$
$467$	31.3997	+	22.8132i	1.45301	+	1.05567i	0.467889	+	0.883787i	$0.345015\pi$
$468$		0			0
$469$	0.0234308	−	0.0721125i	0.00108193	−	0.00332984i
$470$		0			0
$471$	2.19960	−	1.59810i	0.101352	−	0.0736366i
$472$		0			0
$473$	−0.0160302	−	0.0370751i	−0.000737070	−	0.00170471i
$474$		0			0
$475$	1.85091	−	1.34476i	0.0849256	−	0.0617020i
$476$		0			0
$477$	−3.79453	+	11.6784i	−0.173739	+	0.534715i
$478$		0			0
$479$	−2.03000	−	1.47488i	−0.0927529	−	0.0673889i	0.540442	−	0.841381i	$-0.318257\pi$
$479$	−2.03000	−	1.47488i	−0.0927529	−	0.0673889i	−0.633195	+	0.773992i	$0.718257\pi$
$480$		0			0
$481$	−6.16355	−	18.9695i	−0.281034	−	0.864933i
$482$		0			0
$483$	−0.311668			−0.0141814
$484$		0			0
$485$	8.22574			0.373511
$486$		0			0
$487$	−1.69241	−	5.20871i	−0.0766906	−	0.236029i	0.905361	−	0.424643i	$-0.139600\pi$
$487$	−1.69241	−	5.20871i	−0.0766906	−	0.236029i	−0.982051	+	0.188614i	$0.939600\pi$
$488$		0			0
$489$	−10.8583	−	7.88900i	−0.491028	−	0.356753i
$490$		0			0
$491$	−12.4641	+	38.3605i	−0.562496	+	1.73118i	0.112780	+	0.993620i	$0.464024\pi$
$491$	−12.4641	+	38.3605i	−0.562496	+	1.73118i	−0.675276	+	0.737565i	$0.735976\pi$
$492$		0			0
$493$	−0.576256	+	0.418674i	−0.0259533	+	0.0188561i
$494$		0			0
$495$	1.31625	+	3.04425i	0.0591610	+	0.136829i
$496$		0			0
$497$	−0.718457	+	0.521990i	−0.0322272	+	0.0234144i
$498$		0			0
$499$	−5.22932	+	16.0942i	−0.234096	+	0.720474i	0.763144	+	0.646229i	$0.223655\pi$
$499$	−5.22932	+	16.0942i	−0.234096	+	0.720474i	−0.997240	+	0.0742455i	$0.976345\pi$
$500$		0			0
$501$	9.85918	+	7.16312i	0.440476	+	0.320024i
$502$		0			0
$503$	0.536615	+	1.65153i	0.0239265	+	0.0736382i	0.962307	−	0.271966i	$-0.0876739\pi$
$503$	0.536615	+	1.65153i	0.0239265	+	0.0736382i	−0.938380	+	0.345604i	$0.887674\pi$
$504$		0			0
$505$	−2.66429			−0.118559
$506$		0			0
$507$	7.22518			0.320882
$508$		0			0
$509$	0.0568804	+	0.175060i	0.00252118	+	0.00775940i	0.952309	−	0.305135i	$-0.0987015\pi$
$509$	0.0568804	+	0.175060i	0.00252118	+	0.00775940i	−0.949788	+	0.312894i	$0.898701\pi$
$510$		0			0
$511$	−0.556115	−	0.404042i	−0.0246011	−	0.0178737i
$512$		0			0
$513$	0.706985	−	2.17587i	0.0312141	−	0.0960672i
$514$		0			0
$515$	1.51135	−	1.09806i	0.0665981	−	0.0483863i
$516$		0			0
$517$	2.07858	−	1.83137i	0.0914159	−	0.0805438i
$518$		0			0
$519$	−17.0105	+	12.3589i	−0.746680	+	0.542495i
$520$		0			0
$521$	6.87601	−	21.1622i	0.301244	−	0.927132i	−0.679809	−	0.733389i	$-0.737937\pi$
$521$	6.87601	−	21.1622i	0.301244	−	0.927132i	0.981052	−	0.193743i	$-0.0620627\pi$
$522$		0			0
$523$	26.8958	+	19.5409i	1.17607	+	0.854466i	0.991723	−	0.128395i	$-0.0409827\pi$
$523$	26.8958	+	19.5409i	1.17607	+	0.854466i	0.184348	+	0.982861i	$0.440983\pi$
$524$		0			0
$525$	0.0488484	+	0.150340i	0.00213192	+	0.00656137i
$526$		0			0
$527$	−6.22712			−0.271258
$528$		0			0
$529$	−19.1127			−0.830987
$530$		0			0
$531$	−0.527464	−	1.62337i	−0.0228900	−	0.0704481i
$532$		0			0
$533$	−12.9463	−	9.40603i	−0.560766	−	0.407420i
$534$		0			0
$535$	0.0388088	−	0.119441i	0.00167785	−	0.00516389i
$536$		0			0
$537$	0.587511	−	0.426851i	0.0253530	−	0.0184200i
$538$		0			0
$539$	−5.05339	+	22.5748i	−0.217665	+	0.972366i
$540$		0			0
$541$	−1.18728	+	0.862609i	−0.0510451	+	0.0370864i	−0.613015	−	0.790071i	$-0.710044\pi$
$541$	−1.18728	+	0.862609i	−0.0510451	+	0.0370864i	0.561970	+	0.827158i	$0.310044\pi$
$542$		0			0
$543$	−5.01931	+	15.4478i	−0.215399	+	0.662930i
$544$		0			0
$545$	9.30462	+	6.76020i	0.398566	+	0.289575i
$546$		0			0
$547$	−1.85290	−	5.70265i	−0.0792245	−	0.243828i	0.903598	−	0.428382i	$-0.140916\pi$
$547$	−1.85290	−	5.70265i	−0.0792245	−	0.243828i	−0.982822	+	0.184554i	$0.940916\pi$
$548$		0			0
$549$	−13.7743			−0.587871
$550$		0			0
$551$	2.83317			0.120697
$552$		0			0
$553$	−0.594669	−	1.83020i	−0.0252879	−	0.0778281i
$554$		0			0
$555$	−6.71486	−	4.87863i	−0.285030	−	0.207087i
$556$		0			0
$557$	−12.6146	+	38.8238i	−0.534498	+	1.64502i	0.210233	+	0.977651i	$0.432578\pi$
$557$	−12.6146	+	38.8238i	−0.534498	+	1.64502i	−0.744731	+	0.667364i	$0.767422\pi$
$558$		0			0
$559$	0.0236770	−	0.0172024i	0.00100143	−	0.000727583i
$560$		0			0
$561$	1.89928	−	0.178943i	0.0801879	−	0.00755498i
$562$		0			0
$563$	−19.7736	+	14.3663i	−0.833356	+	0.605468i	−0.920507	−	0.390727i	$-0.872224\pi$
$563$	−19.7736	+	14.3663i	−0.833356	+	0.605468i	0.0871509	+	0.996195i	$0.472224\pi$
$564$		0			0
$565$	−0.649173	+	1.99795i	−0.0273109	+	0.0840544i
$566$		0			0
$567$	0.127887	+	0.0929152i	0.00537074	+	0.00390207i
$568$		0			0
$569$	6.17982	+	19.0195i	0.259071	+	0.797340i	0.993000	+	0.118113i	$0.0376846\pi$
$569$	6.17982	+	19.0195i	0.259071	+	0.797340i	−0.733929	+	0.679227i	$0.762315\pi$
$570$		0			0
$571$	20.1690			0.844047			0.422024	−	0.906585i	$-0.361320\pi$
$571$	20.1690			0.844047			0.422024	+	0.906585i	$0.361320\pi$
$572$		0			0
$573$	13.8426			0.578283
$574$		0			0
$575$	−0.609265	−	1.87513i	−0.0254081	−	0.0781981i
$576$		0			0
$577$	17.0357	+	12.3771i	0.709204	+	0.515267i	0.882917	−	0.469530i	$-0.155576\pi$
$577$	17.0357	+	12.3771i	0.709204	+	0.515267i	−0.173713	+	0.984796i	$0.555576\pi$
$578$		0			0
$579$	5.47761	−	16.8583i	0.227642	−	0.700609i
$580$		0			0
$581$	0.428705	−	0.311472i	0.0177857	−	0.0129221i
$582$		0			0
$583$	35.0482	+	20.7420i	1.45155	+	0.859048i
$584$		0			0
$585$	−1.94414	+	1.41250i	−0.0803801	+	0.0583996i
$586$		0			0
$587$	0.132027	−	0.406336i	0.00544932	−	0.0167713i	−0.948295	−	0.317391i	$-0.897193\pi$
$587$	0.132027	−	0.406336i	0.00544932	−	0.0167713i	0.953744	+	0.300619i	$0.0971934\pi$
$588$		0			0
$589$	20.0382	+	14.5586i	0.825661	+	0.599878i
$590$		0			0
$591$	3.92594	+	12.0828i	0.161492	+	0.497021i
$592$		0			0
$593$	−17.8084			−0.731302			−0.365651	−	0.930752i	$-0.619154\pi$
$593$	−17.8084			−0.731302			−0.365651	+	0.930752i	$0.619154\pi$
$594$		0			0
$595$	0.0909244			0.00372754
$596$		0			0
$597$	5.43029	+	16.7127i	0.222247	+	0.684006i
$598$		0			0
$599$	25.4201	+	18.4688i	1.03864	+	0.754615i	0.970019	−	0.243028i	$-0.0781407\pi$
$599$	25.4201	+	18.4688i	1.03864	+	0.754615i	0.0686190	+	0.997643i	$0.478141\pi$
$600$		0			0
$601$	11.1787	−	34.4046i	0.455991	−	1.40339i	−0.413978	−	0.910287i	$-0.635861\pi$
$601$	11.1787	−	34.4046i	0.455991	−	1.40339i	0.869968	−	0.493108i	$-0.164139\pi$
$602$		0			0
$603$	0.388055	−	0.281939i	0.0158028	−	0.0114814i
$604$		0			0
$605$	10.8064	−	2.05451i	0.439344	−	0.0835279i
$606$		0			0
$607$	2.97992	−	2.16504i	0.120951	−	0.0878762i	−0.525665	−	0.850692i	$-0.676184\pi$
$607$	2.97992	−	2.16504i	0.120951	−	0.0878762i	0.646616	+	0.762815i	$0.276184\pi$
$608$		0			0
$609$	−0.0604916	+	0.186174i	−0.00245124	+	0.00754416i
$610$		0			0
$611$	1.62388	+	1.17982i	0.0656951	+	0.0477303i
$612$		0			0
$613$	0.469001	+	1.44344i	0.0189428	+	0.0582999i	0.960081	−	0.279722i	$-0.0902423\pi$
$613$	0.469001	+	1.44344i	0.0189428	+	0.0582999i	−0.941138	+	0.338022i	$0.890242\pi$
$614$		0			0
$615$	−6.65914			−0.268523
$616$		0			0
$617$	−11.6630			−0.469535			−0.234767	−	0.972052i	$-0.575433\pi$
$617$	−11.6630			−0.469535			−0.234767	+	0.972052i	$0.575433\pi$
$618$		0			0
$619$	−12.6760	−	39.0127i	−0.509491	−	1.56805i	−0.793088	−	0.609107i	$-0.791528\pi$
$619$	−12.6760	−	39.0127i	−0.509491	−	1.56805i	0.283597	−	0.958944i	$-0.408472\pi$
$620$		0			0
$621$	−1.59508	−	1.15889i	−0.0640082	−	0.0465047i
$622$		0			0
$623$	−0.491767	+	1.51350i	−0.0197022	+	0.0606372i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−6.53007	−	3.86459i	−0.260786	−	0.154337i
$628$		0			0
$629$	−3.86234	+	2.80615i	−0.154001	+	0.111889i
$630$		0			0
$631$	−6.28841	+	19.3537i	−0.250338	+	0.770460i	0.744375	+	0.667762i	$0.232748\pi$
$631$	−6.28841	+	19.3537i	−0.250338	+	0.770460i	−0.994713	+	0.102698i	$0.967252\pi$
$632$		0			0
$633$	15.0004	+	10.8984i	0.596213	+	0.433174i
$634$		0			0
$635$	3.93001	+	12.0953i	0.155958	+	0.479988i
$636$		0			0
$637$	−16.7615			−0.664117
$638$		0			0
$639$	−5.61792			−0.222241
$640$		0			0
$641$	−9.68745	−	29.8149i	−0.382631	−	1.17762i	−0.938184	−	0.346137i	$-0.887493\pi$
$641$	−9.68745	−	29.8149i	−0.382631	−	1.17762i	0.555553	−	0.831481i	$-0.312507\pi$
$642$		0			0
$643$	8.03218	+	5.83572i	0.316758	+	0.230138i	0.734791	−	0.678294i	$-0.237280\pi$
$643$	8.03218	+	5.83572i	0.316758	+	0.230138i	−0.418033	+	0.908432i	$0.637280\pi$
$644$		0			0
$645$	0.00376342	−	0.0115826i	0.000148185	−	0.000456066i
$646$		0			0
$647$	11.1472	−	8.09895i	0.438244	−	0.318403i	−0.346693	−	0.937979i	$-0.612695\pi$
$647$	11.1472	−	8.09895i	0.438244	−	0.318403i	0.784937	+	0.619576i	$0.212695\pi$
$648$		0			0
$649$	−5.63622	+	0.531022i	−0.221241	+	0.0208444i
$650$		0			0
$651$	−1.38452	+	1.00591i	−0.0542637	+	0.0394249i
$652$		0			0
$653$	−14.8148	+	45.5954i	−0.579749	+	1.78428i	0.0396564	+	0.999213i	$0.487374\pi$
$653$	−14.8148	+	45.5954i	−0.579749	+	1.78428i	−0.619406	+	0.785071i	$0.712626\pi$
$654$		0			0
$655$	9.07695	+	6.59479i	0.354666	+	0.257680i
$656$		0			0
$657$	−1.34376	−	4.13567i	−0.0524251	−	0.161348i
$658$		0			0
$659$	45.9928			1.79162			0.895812	−	0.444433i	$-0.146595\pi$
$659$	45.9928			1.79162			0.895812	+	0.444433i	$0.146595\pi$
$660$		0			0
$661$	9.36152			0.364121			0.182061	−	0.983287i	$-0.441723\pi$
$661$	9.36152			0.364121			0.182061	+	0.983287i	$0.441723\pi$
$662$		0			0
$663$	0.427134	+	1.31458i	0.0165885	+	0.0510542i
$664$		0			0
$665$	−0.292586	−	0.212576i	−0.0113460	−	0.00824334i
$666$		0			0
$667$	0.754486	−	2.32207i	0.0292138	−	0.0899109i
$668$		0			0
$669$	−20.2974	+	14.7469i	−0.784743	+	0.570149i
$670$		0			0
$671$	−9.97945	+	44.5807i	−0.385252	+	1.72102i
$672$		0			0
$673$	−29.9827	+	21.7837i	−1.15575	+	0.839701i	−0.989235	−	0.146337i	$-0.953251\pi$
$673$	−29.9827	+	21.7837i	−1.15575	+	0.839701i	−0.166515	+	0.986039i	$0.553251\pi$
$674$		0			0
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$		0			0
$677$	−4.94545	−	3.59308i	−0.190069	−	0.138093i	0.488681	−	0.872462i	$-0.337478\pi$
$677$	−4.94545	−	3.59308i	−0.190069	−	0.138093i	−0.678750	+	0.734369i	$0.737478\pi$
$678$		0			0
$679$	−0.401814	−	1.23666i	−0.0154202	−	0.0474585i
$680$		0			0
$681$	−22.1317			−0.848089
$682$		0			0
$683$	−35.9156			−1.37427			−0.687137	−	0.726528i	$-0.741133\pi$
$683$	−35.9156			−1.37427			−0.687137	+	0.726528i	$0.741133\pi$
$684$		0			0
$685$	−3.54655	−	10.9152i	−0.135507	−	0.417047i
$686$		0			0
$687$	5.46467	+	3.97032i	0.208490	+	0.151477i
$688$		0			0
$689$	−9.11857	+	28.0641i	−0.347390	+	1.06916i
$690$		0			0
$691$	−6.99506	+	5.08221i	−0.266105	+	0.193336i	−0.712834	−	0.701333i	$-0.752589\pi$
$691$	−6.99506	+	5.08221i	−0.266105	+	0.193336i	0.446729	+	0.894669i	$0.352589\pi$
$692$		0			0
$693$	0.393376	−	0.346592i	0.0149431	−	0.0131659i
$694$		0			0
$695$	−13.3161	+	9.67473i	−0.505109	+	0.366984i
$696$		0			0
$697$	−1.18362	+	3.64282i	−0.0448329	+	0.137982i
$698$		0			0
$699$	3.65449	+	2.65515i	0.138226	+	0.100427i
$700$		0			0
$701$	−6.28290	−	19.3368i	−0.237302	−	0.730340i	−0.996808	−	0.0798398i	$-0.974559\pi$
$701$	−6.28290	−	19.3368i	−0.237302	−	0.730340i	0.759506	−	0.650501i	$-0.225441\pi$
$702$		0			0
$703$	18.9892			0.716192
$704$		0			0
$705$	0.835270			0.0314581
$706$		0			0
$707$	0.130146	+	0.400549i	0.00489466	+	0.0150642i
$708$		0			0
$709$	−4.68420	−	3.40327i	−0.175919	−	0.127812i	0.496342	−	0.868127i	$-0.334676\pi$
$709$	−4.68420	−	3.40327i	−0.175919	−	0.127812i	−0.672260	+	0.740315i	$0.734676\pi$
$710$		0			0
$711$	3.76190	−	11.5779i	0.141082	−	0.434207i
$712$		0			0
$713$	17.2686	−	12.5463i	0.646712	−	0.469864i
$714$		0			0
$715$	3.16306	+	7.31560i	0.118292	+	0.273588i
$716$		0			0
$717$	−5.33323	+	3.87481i	−0.199173	+	0.144708i
$718$		0			0
$719$	−9.23164	+	28.4121i	−0.344282	+	1.05959i	0.617685	+	0.786425i	$0.288071\pi$
$719$	−9.23164	+	28.4121i	−0.344282	+	1.05959i	−0.961967	+	0.273165i	$0.911929\pi$
$720$		0			0
$721$	−0.238909	−	0.173578i	−0.00889745	−	0.00646438i
$722$		0			0
$723$	2.10879	+	6.49019i	0.0784268	+	0.241373i
$724$		0			0
$725$	−1.23835			−0.0459913
$726$		0			0
$727$	22.1061			0.819869			0.409934	−	0.912115i	$-0.365552\pi$
$727$	22.1061			0.819869			0.409934	+	0.912115i	$0.365552\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	−0.00566723	−	0.00411749i	−0.000209610	−	0.000152291i
$732$		0			0
$733$	−1.73003	+	5.32448i	−0.0639001	+	0.196664i	−0.977909	−	0.209029i	$-0.932970\pi$
$733$	−1.73003	+	5.32448i	−0.0639001	+	0.196664i	0.914009	+	0.405693i	$0.132970\pi$
$734$		0			0
$735$	−5.64290	+	4.09981i	−0.208142	+	0.151224i
$736$		0			0
$737$	−0.631356	−	1.46022i	−0.0232563	−	0.0537877i
$738$		0			0
$739$	26.7422	−	19.4293i	0.983728	−	0.714720i	0.0251889	−	0.999683i	$-0.491981\pi$
$739$	26.7422	−	19.4293i	0.983728	−	0.714720i	0.958539	+	0.284963i	$0.0919813\pi$
$740$		0			0
$741$	1.69894	−	5.22881i	0.0624123	−	0.192085i
$742$		0			0
$743$	−14.4316	−	10.4852i	−0.529445	−	0.384664i	0.290705	−	0.956813i	$-0.406110\pi$
$743$	−14.4316	−	10.4852i	−0.529445	−	0.384664i	−0.820150	+	0.572149i	$0.806110\pi$
$744$		0			0
$745$	−4.16932	−	12.8318i	−0.152752	−	0.470122i
$746$		0			0
$747$	3.35222			0.122651
$748$		0			0
$749$	−0.0198525			−0.000725395
$750$		0			0
$751$	−1.25950	−	3.87634i	−0.0459598	−	0.141450i	0.925443	−	0.378886i	$-0.123693\pi$
$751$	−1.25950	−	3.87634i	−0.0459598	−	0.141450i	−0.971403	+	0.237437i	$0.923693\pi$
$752$		0			0
$753$	−6.52317	−	4.73936i	−0.237718	−	0.172712i
$754$		0			0
$755$	3.51705	−	10.8244i	0.127999	−	0.393939i
$756$		0			0
$757$	32.5022	−	23.6142i	1.18131	−	0.858274i	0.188993	−	0.981978i	$-0.439477\pi$
$757$	32.5022	−	23.6142i	1.18131	−	0.858274i	0.992319	+	0.123705i	$0.0394775\pi$
$758$		0			0
$759$	−4.90641	+	4.32289i	−0.178092	+	0.156911i
$760$		0			0
$761$	−25.5076	+	18.5323i	−0.924649	+	0.671797i	−0.944677	−	0.328003i	$-0.893624\pi$
$761$	−25.5076	+	18.5323i	−0.924649	+	0.671797i	0.0200279	+	0.999799i	$0.493624\pi$
$762$		0			0
$763$	0.561812	−	1.72908i	0.0203390	−	0.0625969i
$764$		0			0
$765$	0.465340	+	0.338089i	0.0168244	+	0.0122236i
$766$		0			0
$767$	−1.26754	−	3.90109i	−0.0457682	−	0.140860i
$768$		0			0
$769$	−6.96374			−0.251119			−0.125559	−	0.992086i	$-0.540073\pi$
$769$	−6.96374			−0.251119			−0.125559	+	0.992086i	$0.540073\pi$
$770$		0			0
$771$	8.28576			0.298404
$772$		0			0
$773$	−12.3865	−	38.1217i	−0.445511	−	1.37114i	−0.881922	−	0.471395i	$-0.843751\pi$
$773$	−12.3865	−	38.1217i	−0.445511	−	1.37114i	0.436411	−	0.899747i	$-0.356249\pi$
$774$		0			0
$775$	−8.75855	−	6.36346i	−0.314616	−	0.228582i
$776$		0			0
$777$	−0.405443	+	1.24783i	−0.0145452	+	0.0447655i
$778$		0			0
$779$	12.3255	−	8.95498i	0.441606	−	0.320845i
$780$		0			0
$781$	−4.07018	+	18.1825i	−0.145642	+	0.650622i
$782$		0			0
$783$	−1.00185	+	0.727887i	−0.0358032	+	0.0260125i
$784$		0			0
$785$	0.840171	−	2.58578i	0.0299870	−	0.0922905i
$786$		0			0
$787$	−10.9734	−	7.97265i	−0.391160	−	0.284194i	0.374771	−	0.927118i	$-0.377721\pi$
$787$	−10.9734	−	7.97265i	−0.391160	−	0.284194i	−0.765931	+	0.642923i	$0.777721\pi$
$788$		0			0
$789$	−1.97817	−	6.08819i	−0.0704248	−	0.216745i
$790$		0			0
$791$	0.332083			0.0118075
$792$		0			0
$793$	−33.1007			−1.17544
$794$		0			0
$795$	3.79453	+	11.6784i	0.134578	+	0.414188i
$796$		0			0
$797$	−1.46631	−	1.06534i	−0.0519393	−	0.0377361i	0.561513	−	0.827468i	$-0.310220\pi$
$797$	−1.46631	−	1.06534i	−0.0519393	−	0.0377361i	−0.613452	+	0.789732i	$0.710220\pi$
$798$		0			0
$799$	0.148464	−	0.456926i	0.00525229	−	0.0161649i
$800$		0			0
$801$	−8.14454	+	5.91735i	−0.287773	+	0.209079i
$802$		0			0
$803$	−14.3588	+	1.35282i	−0.506709	+	0.0477401i
$804$		0			0
$805$	−0.252145	+	0.183194i	−0.00888693	+	0.00645673i
$806$		0			0
$807$	2.40815	−	7.41152i	0.0847709	−	0.260898i
$808$		0			0
$809$	14.0763	+	10.2271i	0.494898	+	0.359564i	0.807065	−	0.590463i	$-0.201055\pi$
$809$	14.0763	+	10.2271i	0.494898	+	0.359564i	−0.312167	+	0.950027i	$0.601055\pi$
$810$		0			0
$811$	11.8390	+	36.4368i	0.415725	+	1.27947i	0.911601	+	0.411076i	$0.134847\pi$
$811$	11.8390	+	36.4368i	0.415725	+	1.27947i	−0.495876	+	0.868393i	$0.665153\pi$
$812$		0			0
$813$	15.7542			0.552525
$814$		0			0
$815$	−13.4216			−0.470137
$816$		0			0
$817$	0.00861015	+	0.0264993i	0.000301231	+	0.000927094i
$818$		0			0
$819$	0.307323	+	0.223283i	0.0107387	+	0.00780214i
$820$		0			0
$821$	−13.1605	+	40.5038i	−0.459304	+	1.41359i	0.406703	+	0.913560i	$0.366678\pi$
$821$	−13.1605	+	40.5038i	−0.459304	+	1.41359i	−0.866007	+	0.500031i	$0.833322\pi$
$822$		0			0
$823$	26.0294	−	18.9115i	0.907329	−	0.659213i	−0.0330086	−	0.999455i	$-0.510509\pi$
$823$	26.0294	−	18.9115i	0.907329	−	0.659213i	0.940338	+	0.340242i	$0.110509\pi$
$824$		0			0
$825$	2.85424	+	1.68918i	0.0993718	+	0.0588098i
$826$		0			0
$827$	6.87560	−	4.99541i	0.239088	−	0.173708i	−0.461789	−	0.886990i	$-0.652792\pi$
$827$	6.87560	−	4.99541i	0.239088	−	0.173708i	0.700877	+	0.713282i	$0.252792\pi$
$828$		0			0
$829$	5.21111	−	16.0381i	0.180989	−	0.557027i	−0.818867	−	0.573983i	$-0.805397\pi$
$829$	5.21111	−	16.0381i	0.180989	−	0.557027i	0.999856	+	0.0169558i	$0.00539746\pi$
$830$		0			0
$831$	12.2302	+	8.88578i	0.424262	+	0.308244i
$832$		0			0
$833$	1.23977	+	3.81561i	0.0429554	+	0.132203i
$834$		0			0
$835$	12.1866			0.421735
$836$		0			0
$837$	−10.8262			−0.374207
$838$		0			0
$839$	0.166253	+	0.511675i	0.00573970	+	0.0176650i	0.953885	−	0.300171i	$-0.0970438\pi$
$839$	0.166253	+	0.511675i	0.00573970	+	0.0176650i	−0.948146	+	0.317836i	$0.897044\pi$
$840$		0			0
$841$	22.2208	+	16.1444i	0.766236	+	0.556703i
$842$		0			0
$843$	−1.57330	+	4.84213i	−0.0541874	+	0.166772i
$844$		0			0
$845$	5.84530	−	4.24686i	0.201084	−	0.146096i
$846$		0			0
$847$	−0.836752	−	1.52428i	−0.0287512	−	0.0523748i
$848$		0			0
$849$	−19.7891	+	14.3776i	−0.679159	+	0.493438i
$850$		0			0
$851$	5.05692	−	15.5636i	0.173349	−	0.533513i
$852$		0			0
$853$	40.4553	+	29.3925i	1.38516	+	1.00638i	0.996377	+	0.0850513i	$0.0271054\pi$
$853$	40.4553	+	29.3925i	1.38516	+	1.00638i	0.388786	+	0.921328i	$0.372895\pi$
$854$		0			0
$855$	−0.706985	−	2.17587i	−0.0241784	−	0.0744133i
$856$		0			0
$857$	2.07718			0.0709552			0.0354776	−	0.999370i	$-0.488705\pi$
$857$	2.07718			0.0709552			0.0354776	+	0.999370i	$0.488705\pi$
$858$		0			0
$859$	35.2650			1.20322			0.601612	−	0.798788i	$-0.294525\pi$
$859$	35.2650			1.20322			0.601612	+	0.798788i	$0.294525\pi$
$860$		0			0
$861$	0.325288	+	1.00113i	0.0110858	+	0.0341186i
$862$		0			0
$863$	13.9948	+	10.1678i	0.476387	+	0.346115i	0.799925	−	0.600100i	$-0.204872\pi$
$863$	13.9948	+	10.1678i	0.476387	+	0.346115i	−0.323538	+	0.946215i	$0.604872\pi$
$864$		0			0
$865$	−6.49745	+	19.9971i	−0.220920	+	0.679922i
$866$		0			0
$867$	−13.4856	+	9.79788i	−0.457996	+	0.332754i
$868$		0			0
$869$	−34.7468	−	20.5637i	−1.17870	−	0.697576i
$870$		0			0
$871$	0.932530	−	0.677523i	0.0315976	−	0.0229570i
$872$		0			0
$873$	2.54189	−	7.82314i	0.0860300	−	0.264773i
$874$		0			0
$875$	0.127887	+	0.0929152i	0.00432336	+	0.00314111i
$876$		0			0
$877$	14.5900	+	44.9034i	0.492669	+	1.51628i	0.820558	+	0.571563i	$0.193663\pi$
$877$	14.5900	+	44.9034i	0.492669	+	1.51628i	−0.327890	+	0.944716i	$0.606337\pi$
$878$		0			0
$879$	−29.1778			−0.984143
$880$		0			0
$881$	13.4761			0.454021			0.227010	−	0.973892i	$-0.427105\pi$
$881$	13.4761			0.454021			0.227010	+	0.973892i	$0.427105\pi$
$882$		0			0
$883$	−0.304094	−	0.935906i	−0.0102336	−	0.0314957i	0.945809	−	0.324722i	$-0.105271\pi$
$883$	−0.304094	−	0.935906i	−0.0102336	−	0.0314957i	−0.956043	+	0.293227i	$0.905271\pi$
$884$		0			0
$885$	−1.38092	−	1.00330i	−0.0464191	−	0.0337254i
$886$		0			0
$887$	−3.43370	+	10.5679i	−0.115292	+	0.354834i	−0.992008	−	0.126176i	$-0.959730\pi$
$887$	−3.43370	+	10.5679i	−0.115292	+	0.354834i	0.876715	+	0.481009i	$0.159730\pi$
$888$		0			0
$889$	1.62643	−	1.18167i	0.0545489	−	0.0396321i
$890$		0			0
$891$	3.30200	−	0.311101i	0.110621	−	0.0104223i
$892$		0			0
$893$	−1.54601	+	1.12324i	−0.0517352	+	0.0375878i
$894$		0			0
$895$	0.224409	−	0.690660i	0.00750117	−	0.0230862i
$896$		0			0
$897$	−3.83310	−	2.78491i	−0.127984	−	0.0929856i
$898$		0			0
$899$	−4.14288	−	12.7505i	−0.138173	−	0.425252i
$900$		0			0
$901$	7.06298			0.235302
$902$		0			0
$903$	−0.00192517			−6.40656e−5
$904$		0			0
$905$	5.01931	+	15.4478i	0.166847	+	0.513504i
$906$		0			0
$907$	7.41332	+	5.38609i	0.246155	+	0.178842i	0.704021	−	0.710179i	$-0.251386\pi$
$907$	7.41332	+	5.38609i	0.246155	+	0.178842i	−0.457866	+	0.889021i	$0.651386\pi$
$908$		0			0
$909$	−0.823311	+	2.53389i	−0.0273075	+	0.0840439i
$910$		0			0
$911$	40.6511	−	29.5347i	1.34683	−	0.978529i	0.347667	−	0.937618i	$-0.386974\pi$
$911$	40.6511	−	29.5347i	1.34683	−	0.978529i	0.999163	−	0.0409115i	$-0.0130262\pi$
$912$		0			0
$913$	2.42868	−	10.8496i	0.0803777	−	0.359068i
$914$		0			0
$915$	−11.1436	+	8.09631i	−0.368396	+	0.267656i
$916$		0			0
$917$	0.548066	−	1.68677i	0.0180987	−	0.0557021i
$918$		0			0
$919$	−7.76156	−	5.63910i	−0.256030	−	0.186017i	0.452365	−	0.891833i	$-0.350580\pi$
$919$	−7.76156	−	5.63910i	−0.256030	−	0.186017i	−0.708395	+	0.705816i	$0.750580\pi$
$920$		0			0
$921$	0.389056	+	1.19739i	0.0128198	+	0.0394554i
$922$		0			0
$923$	−13.5003			−0.444369
$924$		0			0
$925$	−8.30003			−0.272903
$926$		0			0
$927$	−0.577285	−	1.77670i	−0.0189605	−	0.0583545i
$928$		0			0
$929$	40.6339	+	29.5223i	1.33316	+	0.968595i	0.999666	+	0.0258411i	$0.00822641\pi$
$929$	40.6339	+	29.5223i	1.33316	+	0.968595i	0.333490	+	0.942754i	$0.391774\pi$
$930$		0			0
$931$	4.93123	−	15.1768i	0.161614	−	0.497398i
$932$		0			0
$933$	6.84969	−	4.97659i	0.224249	−	0.162926i
$934$		0			0
$935$	1.43137	−	1.26114i	0.0468109	−	0.0412437i
$936$		0			0
$937$	19.2959	−	14.0193i	0.630371	−	0.457991i	−0.226158	−	0.974091i	$-0.572616\pi$
$937$	19.2959	−	14.0193i	0.630371	−	0.457991i	0.856529	+	0.516099i	$0.172616\pi$
$938$		0			0
$939$	−4.40728	+	13.5642i	−0.143826	+	0.442652i
$940$		0			0
$941$	−8.05019	−	5.84881i	−0.262429	−	0.190666i	0.448788	−	0.893638i	$-0.351856\pi$
$941$	−8.05019	−	5.84881i	−0.262429	−	0.190666i	−0.711217	+	0.702972i	$0.751856\pi$
$942$		0			0
$943$	−4.05718	−	12.4867i	−0.132120	−	0.406624i
$944$		0			0
$945$	0.158077			0.00514224
$946$		0			0
$947$	−13.0778			−0.424973			−0.212487	−	0.977164i	$-0.568156\pi$
$947$	−13.0778			−0.424973			−0.212487	+	0.977164i	$0.568156\pi$
$948$		0			0
$949$	−3.22917	−	9.93836i	−0.104823	−	0.322613i
$950$		0			0
$951$	−12.8819	−	9.35924i	−0.417724	−	0.303494i
$952$		0			0
$953$	−13.9477	+	42.9265i	−0.451809	+	1.39053i	0.423031	+	0.906115i	$0.360966\pi$
$953$	−13.9477	+	42.9265i	−0.451809	+	1.39053i	−0.874841	+	0.484411i	$0.839034\pi$
$954$		0			0
$955$	11.1989	−	8.13648i	0.362388	−	0.263290i
$956$		0			0
$957$	1.62998	+	3.76987i	0.0526899	+	0.121862i
$958$		0			0
$959$	−1.46774	+	1.06638i	−0.0473959	+	0.0344351i
$960$		0			0
$961$	26.6390	−	81.9865i	0.859324	−	2.64473i
$962$		0			0
$963$	−0.101603	−	0.0738187i	−0.00327410	−	0.00237877i
$964$		0			0
$965$	−5.47761	−	16.8583i	−0.176330	−	0.542689i
$966$		0			0
$967$	−34.4522			−1.10791			−0.553955	−	0.832547i	$-0.686882\pi$
$967$	−34.4522			−1.10791			−0.553955	+	0.832547i	$0.686882\pi$
$968$		0			0
$969$	−1.31595			−0.0422745
$970$		0			0
$971$	3.98758	+	12.2725i	0.127968	+	0.393844i	0.994430	−	0.105398i	$-0.0336118\pi$
$971$	3.98758	+	12.2725i	0.127968	+	0.393844i	−0.866462	+	0.499242i	$0.833612\pi$
$972$		0			0
$973$	2.10497	+	1.52935i	0.0674822	+	0.0490287i
$974$		0			0
$975$	−0.742594	+	2.28547i	−0.0237820	+	0.0731936i
$976$		0			0
$977$	17.0571	−	12.3927i	0.545704	−	0.396477i	−0.280495	−	0.959855i	$-0.590499\pi$
$977$	17.0571	−	12.3927i	0.545704	−	0.396477i	0.826199	+	0.563379i	$0.190499\pi$
$978$		0			0
$979$	13.2509	+	30.6471i	0.423502	+	0.979486i
$980$		0			0
$981$	9.30462	−	6.76020i	0.297074	−	0.215837i
$982$		0			0
$983$	−16.6465	+	51.2326i	−0.530940	+	1.63407i	0.221322	+	0.975201i	$0.428963\pi$
$983$	−16.6465	+	51.2326i	−0.530940	+	1.63407i	−0.752262	+	0.658864i	$0.771037\pi$
$984$		0			0
$985$	10.2783	+	7.46759i	0.327492	+	0.237937i
$986$		0			0
$987$	−0.0408016	−	0.125574i	−0.00129873	−	0.00399708i
$988$		0			0
$989$	0.0240118			0.000763531
$990$		0			0
$991$	37.7220			1.19828			0.599139	−	0.800645i	$-0.295510\pi$
$991$	37.7220			1.19828			0.599139	+	0.800645i	$0.295510\pi$
$992$		0			0
$993$	−7.30208	−	22.4735i	−0.231725	−	0.713175i
$994$		0			0
$995$	14.2167	+	10.3290i	0.450699	+	0.327452i
$996$		0			0
$997$	19.3750	−	59.6302i	0.613613	−	1.88851i	0.193256	−	0.981148i	$-0.438095\pi$
$997$	19.3750	−	59.6302i	0.613613	−	1.88851i	0.420357	−	0.907359i	$-0.361905\pi$
$998$		0			0
$999$	−6.71486	+	4.87863i	−0.212449	+	0.154353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.2.bw.f.1081.2	yes	12
11.4	even	5	inner	1320.2.bw.f.961.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.2.bw.f.961.2	✓	12	11.4	even	5	inner
1320.2.bw.f.1081.2	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.bw (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0488484 + 0.150340i) q^{7} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{5} +(-0.0488484 + 0.150340i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(1.31625 + 3.04425i) q^{11} +(-1.94414 + 1.41250i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(0.465340 + 0.338089i) q^{17} +(-0.706985 - 2.17587i) q^{19} +0.158077 q^{21} -1.97162 q^{23} +(0.309017 + 0.951057i) q^{25} +(0.809017 + 0.587785i) q^{27} +(-0.382673 + 1.17775i) q^{29} +(-8.75855 + 6.36346i) q^{31} +(2.48851 - 2.19255i) q^{33} +(0.127887 - 0.0929152i) q^{35} +(-2.56485 + 7.89380i) q^{37} +(1.94414 + 1.41250i) q^{39} +(2.05779 + 6.33322i) q^{41} -0.0121787 q^{43} +1.00000 q^{45} +(-0.258113 - 0.794389i) q^{47} +(5.64290 + 4.09981i) q^{49} +(0.177744 - 0.547040i) q^{51} +(9.93420 - 7.21762i) q^{53} +(0.724500 - 3.23653i) q^{55} +(-1.85091 + 1.34476i) q^{57} +(-0.527464 + 1.62337i) q^{59} +(11.1436 + 8.09631i) q^{61} +(-0.0488484 - 0.150340i) q^{63} +2.40308 q^{65} -0.479663 q^{67} +(0.609265 + 1.87513i) q^{69} +(4.54499 + 3.30213i) q^{71} +(-1.34376 + 4.13567i) q^{73} +(0.809017 - 0.587785i) q^{75} +(-0.521970 + 0.0491779i) q^{77} +(-9.84878 + 7.15556i) q^{79} +(0.309017 - 0.951057i) q^{81} +(-2.71201 - 1.97039i) q^{83} +(-0.177744 - 0.547040i) q^{85} +1.23835 q^{87} +10.0672 q^{89} +(-0.117387 - 0.361280i) q^{91} +(8.75855 + 6.36346i) q^{93} +(-0.706985 + 2.17587i) q^{95} +(-6.65476 + 4.83497i) q^{97} +(-2.85424 - 1.68918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{5} - 3 q^{9} - 4 q^{11} + 3 q^{13} + 3 q^{15} + 12 q^{17} - 4 q^{19} - 10 q^{21} - 12 q^{23} - 3 q^{25} + 3 q^{27} + 16 q^{29} + 3 q^{31} + 4 q^{33} - 5 q^{35} - 19 q^{37} - 3 q^{39} + 22 q^{41} + 52 q^{43} + 12 q^{45} + 25 q^{47} - 11 q^{49} + 8 q^{51} - q^{53} - 4 q^{55} + 4 q^{57} - 9 q^{59} + 21 q^{61} - 12 q^{65} - 18 q^{67} - 8 q^{69} + 17 q^{71} + 37 q^{73} + 3 q^{75} - 13 q^{77} - 18 q^{79} - 3 q^{81} + 19 q^{83} - 8 q^{85} + 14 q^{87} + 2 q^{89} - 30 q^{91} - 3 q^{93} - 4 q^{95} + q^{97} + 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^5 - 3 * q^9 - 4 * q^11 + 3 * q^13 + 3 * q^15 + 12 * q^17 - 4 * q^19 - 10 * q^21 - 12 * q^23 - 3 * q^25 + 3 * q^27 + 16 * q^29 + 3 * q^31 + 4 * q^33 - 5 * q^35 - 19 * q^37 - 3 * q^39 + 22 * q^41 + 52 * q^43 + 12 * q^45 + 25 * q^47 - 11 * q^49 + 8 * q^51 - q^53 - 4 * q^55 + 4 * q^57 - 9 * q^59 + 21 * q^61 - 12 * q^65 - 18 * q^67 - 8 * q^69 + 17 * q^71 + 37 * q^73 + 3 * q^75 - 13 * q^77 - 18 * q^79 - 3 * q^81 + 19 * q^83 - 8 * q^85 + 14 * q^87 + 2 * q^89 - 30 * q^91 - 3 * q^93 - 4 * q^95 + q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more