LMFDB - Embedded newform 656.2.u.h.529.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [656,2,Mod(305,656)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(656, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("656.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.u (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.23818637260$
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} - 2 x^{19} + 7 x^{18} - 6 x^{17} + 60 x^{16} - 92 x^{15} + 603 x^{14} - 690 x^{13} + 2935 x^{12} + \cdots + 4096 $ x^20 - 2x^19 + 7x^18 - 6x^17 + 60x^16 - 92x^15 + 603x^14 - 690x^13 + 2935x^12 - 3168x^11 + 7811x^10 - 7928x^9 + 15482x^8 - 24314x^7 + 44829x^6 - 45930x^5 + 53273x^4 - 47528x^3 + 33216x^2 - 12800*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 328)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			529.4
Root			$1.02434 - 0.744226i$ of defining polynomial
Character	$\chi$	$=$	656.529
Dual form			656.2.u.h.625.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.26615 q^{3} +(-0.537278 + 1.65357i) q^{5} +(-1.50744 - 1.09522i) q^{7} -1.39685 q^{9} +O(q^{10})$	\(q+1.26615 q^{3} +(-0.537278 + 1.65357i) q^{5} +(-1.50744 - 1.09522i) q^{7} -1.39685 q^{9} +(1.02169 + 3.14443i) q^{11} +(-4.97380 + 3.61368i) q^{13} +(-0.680277 + 2.09368i) q^{15} +(2.23986 + 6.89358i) q^{17} +(3.69070 + 2.68145i) q^{19} +(-1.90866 - 1.38672i) q^{21} +(6.53835 - 4.75039i) q^{23} +(1.59945 + 1.16207i) q^{25} -5.56709 q^{27} +(-1.63469 + 5.03105i) q^{29} +(-0.892470 - 2.74674i) q^{31} +(1.29361 + 3.98133i) q^{33} +(2.62095 - 1.90423i) q^{35} +(1.96587 - 6.05032i) q^{37} +(-6.29760 + 4.57547i) q^{39} +(-4.45310 - 4.60108i) q^{41} +(-5.31133 + 3.85891i) q^{43} +(0.750500 - 2.30980i) q^{45} +(-3.91268 + 2.84273i) q^{47} +(-1.09024 - 3.35542i) q^{49} +(2.83601 + 8.72833i) q^{51} +(0.108621 - 0.334302i) q^{53} -5.74847 q^{55} +(4.67300 + 3.39513i) q^{57} +(10.8545 - 7.88624i) q^{59} +(5.52421 + 4.01357i) q^{61} +(2.10568 + 1.52987i) q^{63} +(-3.30317 - 10.1661i) q^{65} +(-1.12534 + 3.46344i) q^{67} +(8.27856 - 6.01472i) q^{69} +(-1.51236 - 4.65456i) q^{71} +10.4019 q^{73} +(2.02515 + 1.47136i) q^{75} +(1.90371 - 5.85902i) q^{77} -11.8893 q^{79} -2.85823 q^{81} +2.74043 q^{83} -12.6025 q^{85} +(-2.06977 + 6.37008i) q^{87} +(5.12539 + 3.72381i) q^{89} +11.4555 q^{91} +(-1.13000 - 3.47779i) q^{93} +(-6.41692 + 4.66216i) q^{95} +(-4.66068 + 14.3441i) q^{97} +(-1.42715 - 4.39231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	$ 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.26615			0.731014			0.365507	−	0.930809i	$-0.380896\pi$
$3$	1.26615			0.731014			0.365507	+	0.930809i	$0.380896\pi$
$4$		0			0
$5$	−0.537278	+	1.65357i	−0.240278	+	0.739500i	0.756099	+	0.654457i	$0.227103\pi$
$5$	−0.537278	+	1.65357i	−0.240278	+	0.739500i	−0.996377	+	0.0850432i	$0.972897\pi$
$6$		0			0
$7$	−1.50744	−	1.09522i	−0.569760	−	0.413955i	0.265258	−	0.964178i	$-0.414543\pi$
$7$	−1.50744	−	1.09522i	−0.569760	−	0.413955i	−0.835018	+	0.550222i	$0.814543\pi$
$8$		0			0
$9$	−1.39685			−0.465618
$10$		0			0
$11$	1.02169	+	3.14443i	0.308050	+	0.948081i	0.978521	+	0.206145i	$0.0660919\pi$
$11$	1.02169	+	3.14443i	0.308050	+	0.948081i	−0.670471	+	0.741935i	$0.733908\pi$
$12$		0			0
$13$	−4.97380	+	3.61368i	−1.37948	+	1.00225i	−0.382556	+	0.923932i	$0.624956\pi$
$13$	−4.97380	+	3.61368i	−1.37948	+	1.00225i	−0.996928	+	0.0783221i	$0.975044\pi$
$14$		0			0
$15$	−0.680277	+	2.09368i	−0.175647	+	0.540585i
$16$		0			0
$17$	2.23986	+	6.89358i	0.543246	+	1.67194i	0.725125	+	0.688618i	$0.241782\pi$
$17$	2.23986	+	6.89358i	0.543246	+	1.67194i	−0.181879	+	0.983321i	$0.558218\pi$
$18$		0			0
$19$	3.69070	+	2.68145i	0.846706	+	0.615168i	0.924236	−	0.381822i	$-0.124703\pi$
$19$	3.69070	+	2.68145i	0.846706	+	0.615168i	−0.0775300	+	0.996990i	$0.524703\pi$
$20$		0			0
$21$	−1.90866	−	1.38672i	−0.416503	−	0.302607i
$22$		0			0
$23$	6.53835	−	4.75039i	1.36334	−	0.990525i	0.365116	−	0.930962i	$-0.381029\pi$
$23$	6.53835	−	4.75039i	1.36334	−	0.990525i	0.998225	−	0.0595630i	$-0.0189707\pi$
$24$		0			0
$25$	1.59945	+	1.16207i	0.319890	+	0.232414i
$26$		0			0
$27$	−5.56709			−1.07139
$28$		0			0
$29$	−1.63469	+	5.03105i	−0.303554	+	0.934243i	0.676659	+	0.736297i	$0.263427\pi$
$29$	−1.63469	+	5.03105i	−0.303554	+	0.934243i	−0.980213	+	0.197946i	$0.936573\pi$
$30$		0			0
$31$	−0.892470	−	2.74674i	−0.160292	−	0.493329i	0.838366	−	0.545107i	$-0.183511\pi$
$31$	−0.892470	−	2.74674i	−0.160292	−	0.493329i	−0.998659	+	0.0517783i	$0.983511\pi$
$32$		0			0
$33$	1.29361	+	3.98133i	0.225189	+	0.693060i
$34$		0			0
$35$	2.62095	−	1.90423i	0.443021	−	0.321874i
$36$		0			0
$37$	1.96587	−	6.05032i	0.323187	−	0.994666i	−0.649066	−	0.760732i	$-0.724840\pi$
$37$	1.96587	−	6.05032i	0.323187	−	0.994666i	0.972252	−	0.233934i	$-0.0751600\pi$
$38$		0			0
$39$	−6.29760	+	4.57547i	−1.00842	+	0.732662i
$40$		0			0
$41$	−4.45310	−	4.60108i	−0.695457	−	0.718568i
$41$	−4.45310	−	4.60108i	−0.695457	−	0.718568i
$42$		0			0
$43$	−5.31133	+	3.85891i	−0.809970	+	0.588478i	−0.913822	−	0.406115i	$-0.866883\pi$
$43$	−5.31133	+	3.85891i	−0.809970	+	0.588478i	0.103852	+	0.994593i	$0.466883\pi$
$44$		0			0
$45$	0.750500	−	2.30980i	0.111878	−	0.344325i
$46$		0			0
$47$	−3.91268	+	2.84273i	−0.570724	+	0.414655i	−0.835368	−	0.549691i	$-0.814745\pi$
$47$	−3.91268	+	2.84273i	−0.570724	+	0.414655i	0.264644	+	0.964346i	$0.414745\pi$
$48$		0			0
$49$	−1.09024	−	3.35542i	−0.155749	−	0.479346i
$50$		0			0
$51$	2.83601	+	8.72833i	0.397120	+	1.22221i
$52$		0			0
$53$	0.108621	−	0.334302i	0.0149203	−	0.0459199i	−0.943319	−	0.331887i	$-0.892315\pi$
$53$	0.108621	−	0.334302i	0.0149203	−	0.0459199i	0.958239	+	0.285967i	$0.0923148\pi$
$54$		0			0
$55$	−5.74847			−0.775124
$56$		0			0
$57$	4.67300	+	3.39513i	0.618954	+	0.449696i
$58$		0			0
$59$	10.8545	−	7.88624i	1.41313	−	1.02670i	0.420276	−	0.907397i	$-0.361933\pi$
$59$	10.8545	−	7.88624i	1.41313	−	1.02670i	0.992858	−	0.119305i	$-0.0380666\pi$
$60$		0			0
$61$	5.52421	+	4.01357i	0.707302	+	0.513885i	0.882302	−	0.470683i	$-0.155993\pi$
$61$	5.52421	+	4.01357i	0.707302	+	0.513885i	−0.175000	+	0.984568i	$0.555993\pi$
$62$		0			0
$63$	2.10568	+	1.52987i	0.265291	+	0.192745i
$64$		0			0
$65$	−3.30317	−	10.1661i	−0.409707	−	1.26095i
$66$		0			0
$67$	−1.12534	+	3.46344i	−0.137482	+	0.423127i	−0.995968	−	0.0897109i	$-0.971406\pi$
$67$	−1.12534	+	3.46344i	−0.137482	+	0.423127i	0.858486	+	0.512838i	$0.171406\pi$
$68$		0			0
$69$	8.27856	−	6.01472i	0.996621	−	0.724088i
$70$		0			0
$71$	−1.51236	−	4.65456i	−0.179484	−	0.552395i	0.820326	−	0.571896i	$-0.193792\pi$
$71$	−1.51236	−	4.65456i	−0.179484	−	0.552395i	−0.999810	+	0.0195016i	$0.993792\pi$
$72$		0			0
$73$	10.4019			1.21745			0.608725	−	0.793381i	$-0.291681\pi$
$73$	10.4019			1.21745			0.608725	+	0.793381i	$0.291681\pi$
$74$		0			0
$75$	2.02515	+	1.47136i	0.233844	+	0.169898i
$76$		0			0
$77$	1.90371	−	5.85902i	0.216948	−	0.667698i
$78$		0			0
$79$	−11.8893			−1.33765			−0.668825	−	0.743420i	$-0.733203\pi$
$79$	−11.8893			−1.33765			−0.668825	+	0.743420i	$0.733203\pi$
$80$		0			0
$81$	−2.85823			−0.317581
$82$		0			0
$83$	2.74043			0.300802			0.150401	−	0.988625i	$-0.451944\pi$
$83$	2.74043			0.300802			0.150401	+	0.988625i	$0.451944\pi$
$84$		0			0
$85$	−12.6025			−1.36693
$86$		0			0
$87$	−2.06977	+	6.37008i	−0.221902	+	0.682945i
$88$		0			0
$89$	5.12539	+	3.72381i	0.543290	+	0.394723i	0.825305	−	0.564687i	$-0.191003\pi$
$89$	5.12539	+	3.72381i	0.543290	+	0.394723i	−0.282015	+	0.959410i	$0.591003\pi$
$90$		0			0
$91$	11.4555			1.20086
$92$		0			0
$93$	−1.13000	−	3.47779i	−0.117176	−	0.360630i
$94$		0			0
$95$	−6.41692	+	4.66216i	−0.658362	+	0.478328i
$96$		0			0
$97$	−4.66068	+	14.3441i	−0.473221	+	1.45642i	0.375122	+	0.926976i	$0.377601\pi$
$97$	−4.66068	+	14.3441i	−0.473221	+	1.45642i	−0.848342	+	0.529448i	$0.822399\pi$
$98$		0			0
$99$	−1.42715	−	4.39231i	−0.143434	−	0.441444i
$100$		0			0
$101$	6.75691	+	4.90919i	0.672338	+	0.488482i	0.870807	−	0.491625i	$-0.163597\pi$
$101$	6.75691	+	4.90919i	0.672338	+	0.488482i	−0.198469	+	0.980107i	$0.563597\pi$
$102$		0			0
$103$	−3.47858	−	2.52734i	−0.342755	−	0.249026i	0.403069	−	0.915170i	$-0.367944\pi$
$103$	−3.47858	−	2.52734i	−0.342755	−	0.249026i	−0.745823	+	0.666144i	$0.767944\pi$
$104$		0			0
$105$	3.31852	−	2.41105i	0.323855	−	0.235294i
$106$		0			0
$107$	0.136554	+	0.0992124i	0.0132012	+	0.00959123i	0.594366	−	0.804194i	$-0.297403\pi$
$107$	0.136554	+	0.0992124i	0.0132012	+	0.00959123i	−0.581165	+	0.813786i	$0.697403\pi$
$108$		0			0
$109$	−0.535470			−0.0512887			−0.0256444	−	0.999671i	$-0.508164\pi$
$109$	−0.535470			−0.0512887			−0.0256444	+	0.999671i	$0.508164\pi$
$110$		0			0
$111$	2.48909	−	7.66063i	0.236254	−	0.727115i
$112$		0			0
$113$	−4.55123	−	14.0072i	−0.428143	−	1.31769i	−0.899952	−	0.435989i	$-0.856399\pi$
$113$	−4.55123	−	14.0072i	−0.428143	−	1.31769i	0.471809	−	0.881701i	$-0.343601\pi$
$114$		0			0
$115$	4.34220	+	13.3639i	0.404913	+	1.24619i
$116$		0			0
$117$	6.94768	−	5.04779i	0.642313	−	0.466668i
$118$		0			0
$119$	4.17354	−	12.8448i	0.382588	−	1.17748i
$120$		0			0
$121$	0.0556046	−	0.0403991i	0.00505496	−	0.00367265i
$122$		0			0
$123$	−5.63831	−	5.82567i	−0.508389	−	0.525283i
$124$		0			0
$125$	−9.81398	+	7.13027i	−0.877789	+	0.637751i
$126$		0			0
$127$	−2.76442	+	8.50801i	−0.245303	+	0.754964i	0.750284	+	0.661116i	$0.229917\pi$
$127$	−2.76442	+	8.50801i	−0.245303	+	0.754964i	−0.995587	+	0.0938480i	$0.970083\pi$
$128$		0			0
$129$	−6.72496	+	4.88597i	−0.592099	+	0.430185i
$130$		0			0
$131$	−4.64308	−	14.2899i	−0.405668	−	1.24852i	−0.920336	−	0.391128i	$-0.872085\pi$
$131$	−4.64308	−	14.2899i	−0.405668	−	1.24852i	0.514669	−	0.857389i	$-0.327915\pi$
$132$		0			0
$133$	−2.62674	−	8.08429i	−0.227768	−	0.700996i
$134$		0			0
$135$	2.99108	−	9.20560i	0.257431	−	0.792292i
$136$		0			0
$137$	−1.46168			−0.124880			−0.0624400	−	0.998049i	$-0.519888\pi$
$137$	−1.46168			−0.124880			−0.0624400	+	0.998049i	$0.519888\pi$
$138$		0			0
$139$	10.8040	+	7.84957i	0.916384	+	0.665792i	0.942621	−	0.333864i	$-0.108353\pi$
$139$	10.8040	+	7.84957i	0.916384	+	0.665792i	−0.0262374	+	0.999656i	$0.508353\pi$
$140$		0			0
$141$	−4.95406	+	3.59933i	−0.417207	+	0.303119i
$142$		0			0
$143$	−16.4446	−	11.9477i	−1.37517	−	0.999118i
$144$		0			0
$145$	−7.44093	−	5.40615i	−0.617936	−	0.448956i
$146$		0			0
$147$	−1.38041	−	4.24848i	−0.113855	−	0.350409i
$148$		0			0
$149$	−0.893557	+	2.75009i	−0.0732030	+	0.225296i	−0.980963	−	0.194194i	$-0.937791\pi$
$149$	−0.893557	+	2.75009i	−0.0732030	+	0.225296i	0.907760	+	0.419490i	$0.137791\pi$
$150$		0			0
$151$	7.59156	−	5.51559i	0.617793	−	0.448853i	−0.234357	−	0.972151i	$-0.575299\pi$
$151$	7.59156	−	5.51559i	0.617793	−	0.448853i	0.852150	+	0.523298i	$0.175299\pi$
$152$		0			0
$153$	−3.12876	−	9.62933i	−0.252945	−	0.778485i
$154$		0			0
$155$	5.02144			0.403332
$156$		0			0
$157$	10.5081	+	7.63460i	0.838639	+	0.609307i	0.921990	−	0.387213i	$-0.126562\pi$
$157$	10.5081	+	7.63460i	0.838639	+	0.609307i	−0.0833510	+	0.996520i	$0.526562\pi$
$158$		0			0
$159$	0.137531	−	0.423277i	0.0109069	−	0.0335681i
$160$		0			0
$161$	−15.0589			−1.18681
$162$		0			0
$163$	15.1777			1.18881			0.594406	−	0.804165i	$-0.297387\pi$
$163$	15.1777			1.18881			0.594406	+	0.804165i	$0.297387\pi$
$164$		0			0
$165$	−7.27845			−0.566626
$166$		0			0
$167$	12.9949			1.00558			0.502788	−	0.864410i	$-0.332308\pi$
$167$	12.9949			1.00558			0.502788	+	0.864410i	$0.332308\pi$
$168$		0			0
$169$	7.66281	−	23.5837i	0.589447	−	1.81413i
$170$		0			0
$171$	−5.15538	−	3.74560i	−0.394242	−	0.286433i
$172$		0			0
$173$	9.84312			0.748359			0.374179	−	0.927356i	$-0.377924\pi$
$173$	9.84312			0.748359			0.374179	+	0.927356i	$0.377924\pi$
$174$		0			0
$175$	−1.13836	−	3.50350i	−0.0860518	−	0.264840i
$176$		0			0
$177$	13.7434	−	9.98520i	1.03302	−	0.750533i
$178$		0			0
$179$	4.69314	−	14.4440i	0.350782	−	1.07960i	−0.607633	−	0.794218i	$-0.707881\pi$
$179$	4.69314	−	14.4440i	0.350782	−	1.07960i	0.958415	−	0.285378i	$-0.0921192\pi$
$180$		0			0
$181$	2.09840	+	6.45821i	0.155973	+	0.480035i	0.998258	−	0.0589971i	$-0.0187903\pi$
$181$	2.09840	+	6.45821i	0.155973	+	0.480035i	−0.842285	+	0.539032i	$0.818790\pi$
$182$		0			0
$183$	6.99450	+	5.08180i	0.517048	+	0.375657i
$184$		0			0
$185$	8.94843	+	6.50141i	0.657901	+	0.477993i
$186$		0			0
$187$	−19.3879	+	14.0862i	−1.41779	+	1.03008i
$188$		0			0
$189$	8.39208	+	6.09721i	0.610434	+	0.443507i
$190$		0			0
$191$	11.5755			0.837572			0.418786	−	0.908085i	$-0.362456\pi$
$191$	11.5755			0.837572			0.418786	+	0.908085i	$0.362456\pi$
$192$		0			0
$193$	−5.09361	+	15.6765i	−0.366646	+	1.12842i	0.582298	+	0.812975i	$0.302154\pi$
$193$	−5.09361	+	15.6765i	−0.366646	+	1.12842i	−0.948944	+	0.315444i	$0.897846\pi$
$194$		0			0
$195$	−4.18232	−	12.8718i	−0.299502	−	0.921772i
$196$		0			0
$197$	1.59514	+	4.90933i	0.113649	+	0.349775i	0.991663	−	0.128860i	$-0.0411317\pi$
$197$	1.59514	+	4.90933i	0.113649	+	0.349775i	−0.878014	+	0.478635i	$0.841132\pi$
$198$		0			0
$199$	−17.5083	+	12.7206i	−1.24113	+	0.901736i	−0.997673	−	0.0681744i	$-0.978283\pi$
$199$	−17.5083	+	12.7206i	−1.24113	+	0.901736i	−0.243460	+	0.969911i	$0.578283\pi$
$200$		0			0
$201$	−1.42485	+	4.38525i	−0.100501	+	0.309312i
$202$		0			0
$203$	7.97432	−	5.79368i	0.559688	−	0.406637i
$204$		0			0
$205$	10.0008	−	4.89146i	0.698484	−	0.341635i
$206$		0			0
$207$	−9.13313	+	6.63561i	−0.634796	+	0.461207i
$208$		0			0
$209$	−4.66089	+	14.3448i	−0.322401	+	0.992248i
$210$		0			0
$211$	15.4114	−	11.1970i	1.06096	−	0.770834i	0.0866956	−	0.996235i	$-0.472369\pi$
$211$	15.4114	−	11.1970i	1.06096	−	0.770834i	0.974266	+	0.225401i	$0.0723693\pi$
$212$		0			0
$213$	−1.91488	−	5.89339i	−0.131205	−	0.403808i
$214$		0			0
$215$	−3.52732	−	10.8560i	−0.240561	−	0.740371i
$216$		0			0
$217$	−1.66294	+	5.11801i	−0.112888	+	0.347433i
$218$		0			0
$219$	13.1704			0.889973
$220$		0			0
$221$	−36.0518	−	26.1932i	−2.42511	−	1.76194i
$222$		0			0
$223$	13.3249	−	9.68108i	0.892299	−	0.648293i	−0.0441775	−	0.999024i	$-0.514067\pi$
$223$	13.3249	−	9.68108i	0.892299	−	0.648293i	0.936476	+	0.350731i	$0.114067\pi$
$224$		0			0
$225$	−2.23420	−	1.62324i	−0.148947	−	0.108216i
$226$		0			0
$227$	−0.931682	−	0.676906i	−0.0618379	−	0.0449279i	0.556437	−	0.830890i	$-0.312168\pi$
$227$	−0.931682	−	0.676906i	−0.0618379	−	0.0449279i	−0.618275	+	0.785962i	$0.712168\pi$
$228$		0			0
$229$	−1.55976	−	4.80045i	−0.103072	−	0.317223i	0.886201	−	0.463301i	$-0.153335\pi$
$229$	−1.55976	−	4.80045i	−0.103072	−	0.317223i	−0.989273	+	0.146078i	$0.953335\pi$
$230$		0			0
$231$	2.41039	−	7.41842i	0.158592	−	0.488097i
$232$		0			0
$233$	1.30500	−	0.948136i	0.0854932	−	0.0621145i	−0.544218	−	0.838944i	$-0.683173\pi$
$233$	1.30500	−	0.948136i	0.0854932	−	0.0621145i	0.629711	+	0.776830i	$0.283173\pi$
$234$		0			0
$235$	−2.59846	−	7.99725i	−0.169505	−	0.521683i
$236$		0			0
$237$	−15.0537			−0.977842
$238$		0			0
$239$	12.2854	+	8.92585i	0.794675	+	0.577365i	0.909347	−	0.416038i	$-0.136582\pi$
$239$	12.2854	+	8.92585i	0.794675	+	0.577365i	−0.114672	+	0.993403i	$0.536582\pi$
$240$		0			0
$241$	1.79949	−	5.53826i	0.115915	−	0.356751i	−0.876221	−	0.481909i	$-0.839944\pi$
$241$	1.79949	−	5.53826i	0.115915	−	0.356751i	0.992137	+	0.125158i	$0.0399437\pi$
$242$		0			0
$243$	13.0823			0.839231
$244$		0			0
$245$	6.13420			0.391900
$246$		0			0
$247$	−28.0467			−1.78457
$248$		0			0
$249$	3.46981			0.219890
$250$		0			0
$251$	−6.96196	+	21.4267i	−0.439435	+	1.35244i	0.449038	+	0.893512i	$0.351767\pi$
$251$	−6.96196	+	21.4267i	−0.439435	+	1.35244i	−0.888473	+	0.458929i	$0.848233\pi$
$252$		0			0
$253$	21.6174	+	15.7060i	1.35907	+	0.987426i
$254$		0			0
$255$	−15.9567			−0.999245
$256$		0			0
$257$	−1.57368	−	4.84330i	−0.0981636	−	0.302117i	0.889902	−	0.456152i	$-0.150773\pi$
$257$	−1.57368	−	4.84330i	−0.0981636	−	0.302117i	−0.988065	+	0.154036i	$0.950773\pi$
$258$		0			0
$259$	−9.58988	+	6.96746i	−0.595886	+	0.432937i
$260$		0			0
$261$	2.28342	−	7.02765i	0.141340	−	0.435001i
$262$		0			0
$263$	−7.57832	−	23.3237i	−0.467299	−	1.43820i	−0.856068	−	0.516863i	$-0.827100\pi$
$263$	−7.57832	−	23.3237i	−0.467299	−	1.43820i	0.388769	−	0.921335i	$-0.372900\pi$
$264$		0			0
$265$	0.494432	+	0.359226i	0.0303727	+	0.0220671i
$266$		0			0
$267$	6.48953	+	4.71492i	0.397153	+	0.288548i
$268$		0			0
$269$	2.51222	−	1.82524i	0.153173	−	0.111287i	−0.508559	−	0.861027i	$-0.669822\pi$
$269$	2.51222	−	1.82524i	0.153173	−	0.111287i	0.661732	+	0.749740i	$0.269822\pi$
$270$		0			0
$271$	7.95278	+	5.77803i	0.483097	+	0.350990i	0.802523	−	0.596621i	$-0.203490\pi$
$271$	7.95278	+	5.77803i	0.483097	+	0.350990i	−0.319427	+	0.947611i	$0.603490\pi$
$272$		0			0
$273$	14.5044			0.877849
$274$		0			0
$275$	−2.01990	+	6.21662i	−0.121805	+	0.374876i
$276$		0			0
$277$	6.42332	+	19.7689i	0.385940	+	1.18780i	0.935796	+	0.352541i	$0.114682\pi$
$277$	6.42332	+	19.7689i	0.385940	+	1.18780i	−0.549857	+	0.835259i	$0.685318\pi$
$278$		0			0
$279$	1.24665	+	3.83680i	0.0746350	+	0.229703i
$280$		0			0
$281$	−8.30370	+	6.03299i	−0.495357	+	0.359898i	−0.807241	−	0.590222i	$-0.799040\pi$
$281$	−8.30370	+	6.03299i	−0.495357	+	0.359898i	0.311884	+	0.950120i	$0.399040\pi$
$282$		0			0
$283$	−3.58518	+	11.0341i	−0.213117	+	0.655907i	0.786165	+	0.618017i	$0.212064\pi$
$283$	−3.58518	+	11.0341i	−0.213117	+	0.655907i	−0.999282	+	0.0378899i	$0.987936\pi$
$284$		0			0
$285$	−8.12480	+	5.90301i	−0.481272	+	0.349664i
$286$		0			0
$287$	1.67359	+	11.8130i	0.0987890	+	0.697299i
$288$		0			0
$289$	−28.7512	+	20.8889i	−1.69125	+	1.22876i
$290$		0			0
$291$	−5.90114	+	18.1618i	−0.345931	+	1.06467i
$292$		0			0
$293$	23.6862	−	17.2090i	1.38376	−	1.00536i	0.387246	−	0.921976i	$-0.373426\pi$
$293$	23.6862	−	17.2090i	1.38376	−	1.00536i	0.996517	−	0.0833870i	$-0.0265738\pi$
$294$		0			0
$295$	7.20860	+	22.1858i	0.419701	+	1.29171i
$296$		0			0
$297$	−5.68782	−	17.5053i	−0.330041	−	1.01576i
$298$		0			0
$299$	−15.3541	+	47.2550i	−0.887950	+	2.73283i
$300$		0			0
$301$	12.2329			0.705092
$302$		0			0
$303$	8.55529	+	6.21578i	0.491489	+	0.357087i
$304$		0			0
$305$	−9.60477	+	6.97828i	−0.549968	+	0.399575i
$306$		0			0
$307$	−8.64370	−	6.28001i	−0.493322	−	0.358419i	0.313139	−	0.949707i	$-0.398620\pi$
$307$	−8.64370	−	6.28001i	−0.493322	−	0.358419i	−0.806460	+	0.591288i	$0.798620\pi$
$308$		0			0
$309$	−4.40442	−	3.20000i	−0.250559	−	0.182041i
$310$		0			0
$311$	−8.08136	−	24.8719i	−0.458252	−	1.41035i	−0.867275	−	0.497830i	$-0.834130\pi$
$311$	−8.08136	−	24.8719i	−0.458252	−	1.41035i	0.409023	−	0.912524i	$-0.365870\pi$
$312$		0			0
$313$	5.65737	−	17.4116i	0.319774	−	0.984162i	−0.653971	−	0.756519i	$-0.726898\pi$
$313$	5.65737	−	17.4116i	0.319774	−	0.984162i	0.973745	−	0.227642i	$-0.0731017\pi$
$314$		0			0
$315$	−3.66108	+	2.65993i	−0.206279	+	0.149870i
$316$		0			0
$317$	6.75469	+	20.7888i	0.379381	+	1.16762i	0.940475	+	0.339864i	$0.110381\pi$
$317$	6.75469	+	20.7888i	0.379381	+	1.16762i	−0.561093	+	0.827753i	$0.689619\pi$
$318$		0			0
$319$	−17.4899			−0.979247
$320$		0			0
$321$	0.172899	+	0.125618i	0.00965026	+	0.00701132i
$322$		0			0
$323$	−10.2182	+	31.4482i	−0.568553	+	1.74983i
$324$		0			0
$325$	−12.1547			−0.674220
$326$		0			0
$327$	−0.677987			−0.0374928
$328$		0			0
$329$	9.01158			0.496824
$330$		0			0
$331$	7.22431			0.397084			0.198542	−	0.980092i	$-0.436379\pi$
$331$	7.22431			0.397084			0.198542	+	0.980092i	$0.436379\pi$
$332$		0			0
$333$	−2.74603	+	8.45142i	−0.150482	+	0.463135i
$334$		0			0
$335$	−5.12243	−	3.72167i	−0.279868	−	0.203336i
$336$		0			0
$337$	13.1349			0.715506			0.357753	−	0.933816i	$-0.383543\pi$
$337$	13.1349			0.715506			0.357753	+	0.933816i	$0.383543\pi$
$338$		0			0
$339$	−5.76255	−	17.7353i	−0.312979	−	0.963250i
$340$		0			0
$341$	7.72510	−	5.61261i	0.418338	−	0.303940i
$342$		0			0
$343$	−6.06200	+	18.6569i	−0.327317	+	1.00738i
$344$		0			0
$345$	5.49790	+	16.9208i	0.295997	+	0.910984i
$346$		0			0
$347$	−20.1368	−	14.6303i	−1.08100	−	0.785394i	−0.103144	−	0.994666i	$-0.532890\pi$
$347$	−20.1368	−	14.6303i	−1.08100	−	0.785394i	−0.977857	+	0.209273i	$0.932890\pi$
$348$		0			0
$349$	0.652305	+	0.473927i	0.0349171	+	0.0253687i	0.605107	−	0.796144i	$-0.293130\pi$
$349$	0.652305	+	0.473927i	0.0349171	+	0.0253687i	−0.570190	+	0.821513i	$0.693130\pi$
$350$		0			0
$351$	27.6896	−	20.1177i	1.47796	−	1.07380i
$352$		0			0
$353$	22.3554	+	16.2421i	1.18986	+	0.864481i	0.993249	−	0.116002i	$-0.0370077\pi$
$353$	22.3554	+	16.2421i	1.18986	+	0.864481i	0.196607	+	0.980482i	$0.437008\pi$
$354$		0			0
$355$	8.50922			0.451622
$356$		0			0
$357$	5.28434	−	16.2635i	0.279677	−	0.860757i
$358$		0			0
$359$	6.78160	+	20.8716i	0.357919	+	1.10156i	0.954298	+	0.298858i	$0.0966057\pi$
$359$	6.78160	+	20.8716i	0.357919	+	1.10156i	−0.596379	+	0.802703i	$0.703394\pi$
$360$		0			0
$361$	0.559783	+	1.72284i	0.0294623	+	0.0906756i
$362$		0			0
$363$	0.0704040	−	0.0511515i	0.00369525	−	0.00268476i
$364$		0			0
$365$	−5.58871	+	17.2003i	−0.292527	+	0.900305i
$366$		0			0
$367$	−26.4018	+	19.1821i	−1.37817	+	1.00130i	−0.381116	+	0.924527i	$0.624460\pi$
$367$	−26.4018	+	19.1821i	−1.37817	+	1.00130i	−0.997049	+	0.0767683i	$0.975540\pi$
$368$		0			0
$369$	6.22033	+	6.42704i	0.323817	+	0.334578i
$370$		0			0
$371$	−0.529875	+	0.384977i	−0.0275097	+	0.0199870i
$372$		0			0
$373$	0.215204	−	0.662329i	0.0111428	−	0.0342941i	−0.945331	−	0.326114i	$-0.894261\pi$
$373$	0.215204	−	0.662329i	0.0111428	−	0.0342941i	0.956473	+	0.291820i	$0.0942607\pi$
$374$		0			0
$375$	−12.4260	+	9.02802i	−0.641676	+	0.466205i
$376$		0			0
$377$	−10.0500	−	30.9307i	−0.517601	−	1.59301i
$378$		0			0
$379$	−0.882180	−	2.71507i	−0.0453145	−	0.139464i	0.925839	−	0.377917i	$-0.123360\pi$
$379$	−0.882180	−	2.71507i	−0.0453145	−	0.139464i	−0.971154	+	0.238453i	$0.923360\pi$
$380$		0			0
$381$	−3.50018	+	10.7724i	−0.179320	+	0.551889i
$382$		0			0
$383$	13.4097			0.685204			0.342602	−	0.939481i	$-0.388692\pi$
$383$	13.4097			0.685204			0.342602	+	0.939481i	$0.388692\pi$
$384$		0			0
$385$	8.66550	+	6.29586i	0.441635	+	0.320866i
$386$		0			0
$387$	7.41915	−	5.39033i	0.377137	−	0.274006i
$388$		0			0
$389$	−5.10837	−	3.71145i	−0.259005	−	0.188178i	0.450703	−	0.892674i	$-0.351173\pi$
$389$	−5.10837	−	3.71145i	−0.259005	−	0.188178i	−0.709708	+	0.704496i	$0.751173\pi$
$390$		0			0
$391$	47.3922	+	34.4324i	2.39673	+	1.74132i
$392$		0			0
$393$	−5.87885	−	18.0932i	−0.296549	−	0.912684i
$394$		0			0
$395$	6.38787	−	19.6598i	0.321408	−	0.989193i
$396$		0			0
$397$	−28.9144	+	21.0076i	−1.45117	+	1.05434i	−0.465619	+	0.884985i	$0.654168\pi$
$397$	−28.9144	+	21.0076i	−1.45117	+	1.05434i	−0.985555	+	0.169355i	$0.945832\pi$
$398$		0			0
$399$	−3.32586	−	10.2359i	−0.166501	−	0.512438i
$400$		0			0
$401$	−8.66951			−0.432935			−0.216467	−	0.976290i	$-0.569454\pi$
$401$	−8.66951			−0.432935			−0.216467	+	0.976290i	$0.569454\pi$
$402$		0			0
$403$	14.3648	+	10.4366i	0.715562	+	0.519886i
$404$		0			0
$405$	1.53567	−	4.72630i	0.0763079	−	0.234852i
$406$		0			0
$407$	21.0333			1.04258
$408$		0			0
$409$	17.6317			0.871832			0.435916	−	0.899987i	$-0.356424\pi$
$409$	17.6317			0.871832			0.435916	+	0.899987i	$0.356424\pi$
$410$		0			0
$411$	−1.85071			−0.0912890
$412$		0			0
$413$	−24.9997			−1.23016
$414$		0			0
$415$	−1.47238	+	4.53151i	−0.0722761	+	0.222443i
$416$		0			0
$417$	13.6795	+	9.93876i	0.669890	+	0.486703i
$418$		0			0
$419$	−19.4926			−0.952275			−0.476137	−	0.879371i	$-0.657964\pi$
$419$	−19.4926			−0.952275			−0.476137	+	0.879371i	$0.657964\pi$
$420$		0			0
$421$	3.16598	+	9.74389i	0.154301	+	0.474888i	0.998089	−	0.0617871i	$-0.0196800\pi$
$421$	3.16598	+	9.74389i	0.154301	+	0.474888i	−0.843789	+	0.536675i	$0.819680\pi$
$422$		0			0
$423$	5.46545	−	3.97088i	0.265739	−	0.193071i
$424$		0			0
$425$	−4.42826	+	13.6288i	−0.214802	+	0.661094i
$426$		0			0
$427$	−3.93168	−	12.1005i	−0.190267	−	0.585583i
$428$		0			0
$429$	−20.8214	−	15.1276i	−1.00527	−	0.730369i
$430$		0			0
$431$	11.7077	+	8.50616i	0.563941	+	0.409727i	0.832899	−	0.553424i	$-0.186679\pi$
$431$	11.7077	+	8.50616i	0.563941	+	0.409727i	−0.268958	+	0.963152i	$0.586679\pi$
$432$		0			0
$433$	−14.7555	+	10.7205i	−0.709102	+	0.515193i	−0.882884	−	0.469591i	$-0.844401\pi$
$433$	−14.7555	+	10.7205i	−0.709102	+	0.515193i	0.173782	+	0.984784i	$0.444401\pi$
$434$		0			0
$435$	−9.42136	−	6.84502i	−0.451720	−	0.328194i
$436$		0			0
$437$	36.8691			1.76369
$438$		0			0
$439$	11.5541	−	35.5599i	0.551447	−	1.69718i	−0.153699	−	0.988118i	$-0.549119\pi$
$439$	11.5541	−	35.5599i	0.551447	−	1.69718i	0.705146	−	0.709062i	$-0.250881\pi$
$440$		0			0
$441$	1.52291	+	4.68704i	0.0725196	+	0.223192i
$442$		0			0
$443$	−3.15018	−	9.69526i	−0.149670	−	0.460636i	0.847912	−	0.530136i	$-0.177859\pi$
$443$	−3.15018	−	9.69526i	−0.149670	−	0.460636i	−0.997582	+	0.0695010i	$0.977859\pi$
$444$		0			0
$445$	−8.91136	+	6.47448i	−0.422439	+	0.306920i
$446$		0			0
$447$	−1.13138	+	3.48203i	−0.0535124	+	0.164694i
$448$		0			0
$449$	12.3571	−	8.97793i	0.583166	−	0.423695i	−0.256698	−	0.966492i	$-0.582635\pi$
$449$	12.3571	−	8.97793i	0.583166	−	0.423695i	0.839864	+	0.542797i	$0.182635\pi$
$450$		0			0
$451$	9.91809	−	18.7033i	0.467025	−	0.880704i
$452$		0			0
$453$	9.61209	−	6.98359i	0.451615	−	0.328118i
$454$		0			0
$455$	−6.15480	+	18.9425i	−0.288542	+	0.888039i
$456$		0			0
$457$	−29.5807	+	21.4916i	−1.38373	+	1.00534i	−0.387205	+	0.921994i	$0.626559\pi$
$457$	−29.5807	+	21.4916i	−1.38373	+	1.00534i	−0.996521	+	0.0833417i	$0.973441\pi$
$458$		0			0
$459$	−12.4695	−	38.3772i	−0.582027	−	1.79129i
$460$		0			0
$461$	−5.03489	−	15.4958i	−0.234498	−	0.721711i	−0.997188	−	0.0749460i	$-0.976122\pi$
$461$	−5.03489	−	15.4958i	−0.234498	−	0.721711i	0.762690	−	0.646765i	$-0.223878\pi$
$462$		0			0
$463$	1.26708	−	3.89966i	0.0588861	−	0.181233i	−0.917287	−	0.398227i	$-0.869625\pi$
$463$	1.26708	−	3.89966i	0.0588861	−	0.181233i	0.976173	+	0.216995i	$0.0696255\pi$
$464$		0			0
$465$	6.35791			0.294841
$466$		0			0
$467$	−21.1881	−	15.3941i	−0.980471	−	0.712354i	−0.0226569	−	0.999743i	$-0.507213\pi$
$467$	−21.1881	−	15.3941i	−0.980471	−	0.712354i	−0.957814	+	0.287390i	$0.907213\pi$
$468$		0			0
$469$	5.48963	−	3.98845i	0.253487	−	0.184169i
$470$		0			0
$471$	13.3049	+	9.66657i	0.613057	+	0.445412i
$472$		0			0
$473$	−17.5606	−	12.7585i	−0.807435	−	0.586636i
$474$		0			0
$475$	2.78706	+	8.57770i	0.127879	+	0.393572i
$476$		0			0
$477$	−0.151728	+	0.466971i	−0.00694715	+	0.0213811i
$478$		0			0
$479$	4.39370	−	3.19221i	0.200753	−	0.145856i	−0.482867	−	0.875694i	$-0.660405\pi$
$479$	4.39370	−	3.19221i	0.200753	−	0.145856i	0.683620	+	0.729838i	$0.260405\pi$
$480$		0			0
$481$	12.0861	+	37.1971i	0.551077	+	1.69604i
$482$		0			0
$483$	−19.0669			−0.867575
$484$		0			0
$485$	−21.2149	−	15.4136i	−0.963321	−	0.699894i
$486$		0			0
$487$	−5.78078	+	17.7914i	−0.261952	+	0.806205i	0.730428	+	0.682990i	$0.239321\pi$
$487$	−5.78078	+	17.7914i	−0.261952	+	0.806205i	−0.992380	+	0.123215i	$0.960679\pi$
$488$		0			0
$489$	19.2173			0.869038
$490$		0			0
$491$	20.0033			0.902736			0.451368	−	0.892338i	$-0.350936\pi$
$491$	20.0033			0.902736			0.451368	+	0.892338i	$0.350936\pi$
$492$		0			0
$493$	−38.3434			−1.72690
$494$		0			0
$495$	8.02978			0.360912
$496$		0			0
$497$	−2.81798	+	8.67286i	−0.126404	+	0.389031i
$498$		0			0
$499$	−4.09170	−	2.97280i	−0.183170	−	0.133081i	0.492422	−	0.870357i	$-0.336112\pi$
$499$	−4.09170	−	2.97280i	−0.183170	−	0.133081i	−0.675592	+	0.737276i	$0.736112\pi$
$500$		0			0
$501$	16.4536			0.735091
$502$		0			0
$503$	−0.742563	−	2.28537i	−0.0331092	−	0.101900i	0.933136	−	0.359523i	$-0.117061\pi$
$503$	−0.742563	−	2.28537i	−0.0331092	−	0.101900i	−0.966245	+	0.257623i	$0.917061\pi$
$504$		0			0
$505$	−11.7480	+	8.53545i	−0.522781	+	0.379823i
$506$		0			0
$507$	9.70230	−	29.8606i	0.430894	−	1.32616i
$508$		0			0
$509$	7.07502	+	21.7747i	0.313595	+	0.965146i	0.976329	+	0.216291i	$0.0693960\pi$
$509$	7.07502	+	21.7747i	0.313595	+	0.965146i	−0.662734	+	0.748855i	$0.730604\pi$
$510$		0			0
$511$	−15.6803	−	11.3924i	−0.693655	−	0.503970i
$512$		0			0
$513$	−20.5465	−	14.9279i	−0.907150	−	0.659083i
$514$		0			0
$515$	6.04810	−	4.39420i	0.266511	−	0.193632i
$516$		0			0
$517$	−12.9363	−	9.39877i	−0.568938	−	0.413357i
$518$		0			0
$519$	12.4629			0.547061
$520$		0			0
$521$	−0.300837	+	0.925880i	−0.0131799	+	0.0405635i	−0.957430	−	0.288665i	$-0.906789\pi$
$521$	−0.300837	+	0.925880i	−0.0131799	+	0.0405635i	0.944250	+	0.329228i	$0.106789\pi$
$522$		0			0
$523$	−11.1745	−	34.3917i	−0.488629	−	1.50385i	−0.826655	−	0.562708i	$-0.809759\pi$
$523$	−11.1745	−	34.3917i	−0.488629	−	1.50385i	0.338027	−	0.941137i	$-0.390241\pi$
$524$		0			0
$525$	−1.44134	−	4.43598i	−0.0629051	−	0.193602i
$526$		0			0
$527$	16.9359	−	12.3046i	0.737737	−	0.535998i
$528$		0			0
$529$	13.0764	−	40.2452i	0.568541	−	1.74979i
$530$		0			0
$531$	−15.1621	+	11.0159i	−0.657981	+	0.478051i
$532$		0			0
$533$	38.7756	+	6.79279i	1.67956	+	0.294228i
$534$		0			0
$535$	−0.237423	+	0.172498i	−0.0102647	+	0.00745772i
$536$		0			0
$537$	5.94224	−	18.2883i	0.256427	−	0.789200i
$538$		0			0
$539$	9.43699	−	6.85638i	0.406480	−	0.295325i
$540$		0			0
$541$	−7.99195	−	24.5967i	−0.343601	−	1.05749i	−0.962329	−	0.271889i	$-0.912352\pi$
$541$	−7.99195	−	24.5967i	−0.343601	−	1.05749i	0.618728	−	0.785605i	$-0.287648\pi$
$542$		0			0
$543$	2.65689	+	8.17708i	0.114018	+	0.350912i
$544$		0			0
$545$	0.287696	−	0.885439i	0.0123236	−	0.0379280i
$546$		0			0
$547$	−12.1985			−0.521570			−0.260785	−	0.965397i	$-0.583981\pi$
$547$	−12.1985			−0.521570			−0.260785	+	0.965397i	$0.583981\pi$
$548$		0			0
$549$	−7.71652	−	5.60638i	−0.329333	−	0.239274i
$550$		0			0
$551$	−19.5237	+	14.1848i	−0.831737	+	0.604292i
$552$		0			0
$553$	17.9225	+	13.0214i	0.762141	+	0.553728i
$554$		0			0
$555$	11.3301	+	8.23179i	0.480935	+	0.349420i
$556$		0			0
$557$	−7.91551	−	24.3614i	−0.335391	−	1.03223i	−0.966529	−	0.256557i	$-0.917412\pi$
$557$	−7.91551	−	24.3614i	−0.335391	−	1.03223i	0.631138	−	0.775670i	$-0.282588\pi$
$558$		0			0
$559$	12.4726	−	38.3869i	0.527537	−	1.62359i
$560$		0			0
$561$	−24.5481	+	17.8352i	−1.03642	+	0.753004i
$562$		0			0
$563$	2.48959	+	7.66218i	0.104924	+	0.322922i	0.989713	−	0.143070i	$-0.0456974\pi$
$563$	2.48959	+	7.66218i	0.104924	+	0.322922i	−0.884789	+	0.465992i	$0.845697\pi$
$564$		0			0
$565$	25.6073			1.07731
$566$		0			0
$567$	4.30863	+	3.13040i	0.180945	+	0.131464i
$568$		0			0
$569$	12.6316	−	38.8760i	0.529544	−	1.62977i	−0.225609	−	0.974218i	$-0.572437\pi$
$569$	12.6316	−	38.8760i	0.529544	−	1.62977i	0.755152	−	0.655549i	$-0.227563\pi$
$570$		0			0
$571$	−13.7848			−0.576877			−0.288439	−	0.957498i	$-0.593136\pi$
$571$	−13.7848			−0.576877			−0.288439	+	0.957498i	$0.593136\pi$
$572$		0			0
$573$	14.6563			0.612277
$574$		0			0
$575$	15.9780			0.666330
$576$		0			0
$577$	−38.5939			−1.60668			−0.803342	−	0.595518i	$-0.796947\pi$
$577$	−38.5939			−1.60668			−0.803342	+	0.595518i	$0.796947\pi$
$578$		0			0
$579$	−6.44929	+	19.8489i	−0.268023	+	0.824891i
$580$		0			0
$581$	−4.13105	−	3.00139i	−0.171385	−	0.124518i
$582$		0			0
$583$	1.16216			0.0481319
$584$		0			0
$585$	4.61404	+	14.2006i	0.190767	+	0.587121i
$586$		0			0
$587$	−17.6578	+	12.8291i	−0.728813	+	0.529514i	−0.889188	−	0.457542i	$-0.848730\pi$
$587$	−17.6578	+	12.8291i	−0.728813	+	0.529514i	0.160374	+	0.987056i	$0.448730\pi$
$588$		0			0
$589$	4.07141	−	12.5305i	0.167760	−	0.516311i
$590$		0			0
$591$	2.01969	+	6.21596i	0.0830789	+	0.255691i
$592$		0			0
$593$	23.4260	+	17.0200i	0.961991	+	0.698928i	0.953612	−	0.301037i	$-0.0973328\pi$
$593$	23.4260	+	17.0200i	0.961991	+	0.698928i	0.00837909	+	0.999965i	$0.497333\pi$
$594$		0			0
$595$	18.9975	+	13.8025i	0.778822	+	0.565847i
$596$		0			0
$597$	−22.1683	+	16.1062i	−0.907286	+	0.659182i
$598$		0			0
$599$	7.56654	+	5.49741i	0.309160	+	0.224618i	0.731536	−	0.681803i	$-0.238804\pi$
$599$	7.56654	+	5.49741i	0.309160	+	0.224618i	−0.422376	+	0.906421i	$0.638804\pi$
$600$		0			0
$601$	−6.51007			−0.265551			−0.132776	−	0.991146i	$-0.542389\pi$
$601$	−6.51007			−0.265551			−0.132776	+	0.991146i	$0.542389\pi$
$602$		0			0
$603$	1.57194	−	4.83793i	0.0640142	−	0.197016i
$604$		0			0
$605$	0.0369277	+	0.113652i	0.00150133	+	0.00462060i
$606$		0			0
$607$	1.20667	+	3.71375i	0.0489772	+	0.150736i	0.972554	−	0.232677i	$-0.0747485\pi$
$607$	1.20667	+	3.71375i	0.0489772	+	0.150736i	−0.923577	+	0.383413i	$0.874748\pi$
$608$		0			0
$609$	10.0967	−	7.33569i	0.409140	−	0.297257i
$610$		0			0
$611$	9.18820	−	28.2784i	0.371715	−	1.14402i
$612$		0			0
$613$	−35.5676	+	25.8414i	−1.43656	+	1.04372i	−0.447815	+	0.894126i	$0.647798\pi$
$613$	−35.5676	+	25.8414i	−1.43656	+	1.04372i	−0.988747	+	0.149597i	$0.952202\pi$
$614$		0			0
$615$	12.6625	−	6.19334i	0.510602	−	0.249740i
$616$		0			0
$617$	7.70678	−	5.59930i	0.310263	−	0.225419i	−0.421746	−	0.906714i	$-0.638583\pi$
$617$	7.70678	−	5.59930i	0.310263	−	0.225419i	0.732009	+	0.681295i	$0.238583\pi$
$618$		0			0
$619$	−5.65549	+	17.4058i	−0.227314	+	0.699599i	0.770735	+	0.637156i	$0.219889\pi$
$619$	−5.65549	+	17.4058i	−0.227314	+	0.699599i	−0.998049	+	0.0624433i	$0.980111\pi$
$620$		0			0
$621$	−36.3996	+	26.4459i	−1.46067	+	1.06124i
$622$		0			0
$623$	−3.64783	−	11.2269i	−0.146147	−	0.449795i
$624$		0			0
$625$	−3.46291	−	10.6578i	−0.138517	−	0.426310i
$626$		0			0
$627$	−5.90141	+	18.1627i	−0.235680	+	0.725347i
$628$		0			0
$629$	46.1116			1.83859
$630$		0			0
$631$	−18.4780	−	13.4251i	−0.735598	−	0.534444i	0.155731	−	0.987799i	$-0.450227\pi$
$631$	−18.4780	−	13.4251i	−0.735598	−	0.534444i	−0.891330	+	0.453356i	$0.850227\pi$
$632$		0			0
$633$	19.5131	−	14.1771i	0.775578	−	0.563490i
$634$		0			0
$635$	−12.5834	−	9.14234i	−0.499355	−	0.362803i
$636$		0			0
$637$	17.5481	+	12.7494i	0.695280	+	0.505150i
$638$		0			0
$639$	2.11255	+	6.50175i	0.0835710	+	0.257205i
$640$		0			0
$641$	−0.780976	+	2.40360i	−0.0308467	+	0.0949363i	−0.965295	−	0.261164i	$-0.915894\pi$
$641$	−0.780976	+	2.40360i	−0.0308467	+	0.0949363i	0.934448	+	0.356100i	$0.115894\pi$
$642$		0			0
$643$	19.5603	−	14.2114i	0.771383	−	0.560443i	−0.130997	−	0.991383i	$-0.541818\pi$
$643$	19.5603	−	14.2114i	0.771383	−	0.560443i	0.902381	+	0.430940i	$0.141818\pi$
$644$		0			0
$645$	−4.46613	−	13.7453i	−0.175854	−	0.541222i
$646$		0			0
$647$	12.6600			0.497718			0.248859	−	0.968540i	$-0.419944\pi$
$647$	12.6600			0.497718			0.248859	+	0.968540i	$0.419944\pi$
$648$		0			0
$649$	35.8876	+	26.0739i	1.40871	+	1.02349i
$650$		0			0
$651$	−2.10554	+	6.48019i	−0.0825226	+	0.253979i
$652$		0			0
$653$	−1.28238			−0.0501835			−0.0250918	−	0.999685i	$-0.507988\pi$
$653$	−1.28238			−0.0501835			−0.0250918	+	0.999685i	$0.507988\pi$
$654$		0			0
$655$	26.1241			1.02075
$656$		0			0
$657$	−14.5299			−0.566867
$658$		0			0
$659$	1.69507			0.0660304			0.0330152	−	0.999455i	$-0.489489\pi$
$659$	1.69507			0.0660304			0.0330152	+	0.999455i	$0.489489\pi$
$660$		0			0
$661$	5.98339	−	18.4150i	0.232727	−	0.716260i	−0.764688	−	0.644401i	$-0.777107\pi$
$661$	5.98339	−	18.4150i	0.232727	−	0.716260i	0.997415	−	0.0718592i	$-0.0228932\pi$
$662$		0			0
$663$	−45.6471	−	33.1646i	−1.77279	−	1.28801i
$664$		0			0
$665$	14.7793			0.573115
$666$		0			0
$667$	13.2113	+	40.6602i	0.511543	+	1.57437i
$668$		0			0
$669$	16.8713	−	12.2577i	0.652283	−	0.473911i
$670$		0			0
$671$	−6.97638	+	21.4711i	−0.269320	+	0.828882i
$672$		0			0
$673$	−13.8135	−	42.5136i	−0.532472	−	1.63878i	−0.749049	−	0.662515i	$-0.769489\pi$
$673$	−13.8135	−	42.5136i	−0.532472	−	1.63878i	0.216577	−	0.976266i	$-0.430511\pi$
$674$		0			0
$675$	−8.90428	−	6.46934i	−0.342726	−	0.249005i
$676$		0			0
$677$	−3.88913	−	2.82562i	−0.149471	−	0.108597i	0.510536	−	0.859856i	$-0.329447\pi$
$677$	−3.88913	−	2.82562i	−0.149471	−	0.108597i	−0.660008	+	0.751259i	$0.729447\pi$
$678$		0			0
$679$	22.7357	−	16.5185i	0.872517	−	0.633920i
$680$		0			0
$681$	−1.17965	−	0.857068i	−0.0452044	−	0.0328429i
$682$		0			0
$683$	−43.0048			−1.64553			−0.822766	−	0.568380i	$-0.807570\pi$
$683$	−43.0048			−1.64553			−0.822766	+	0.568380i	$0.807570\pi$
$684$		0			0
$685$	0.785330	−	2.41700i	0.0300059	−	0.0923488i
$686$		0			0
$687$	−1.97490	−	6.07811i	−0.0753471	−	0.231894i
$688$		0			0
$689$	0.667798	+	2.05527i	0.0254411	+	0.0782996i
$690$		0			0
$691$	−15.6096	+	11.3411i	−0.593819	+	0.431434i	−0.843679	−	0.536847i	$-0.819615\pi$
$691$	−15.6096	+	11.3411i	−0.593819	+	0.431434i	0.249861	+	0.968282i	$0.419615\pi$
$692$		0			0
$693$	−2.65921	+	8.18421i	−0.101015	+	0.310892i
$694$		0			0
$695$	−18.7846	+	13.6478i	−0.712541	+	0.517691i
$696$		0			0
$697$	21.7436	−	41.0035i	0.823597	−	1.55312i
$698$		0			0
$699$	1.65233	−	1.20049i	0.0624968	−	0.0454066i
$700$		0			0
$701$	4.76216	−	14.6564i	0.179864	−	0.553565i	−0.819958	−	0.572424i	$-0.806003\pi$
$701$	4.76216	−	14.6564i	0.179864	−	0.553565i	0.999822	+	0.0188587i	$0.00600328\pi$
$702$		0			0
$703$	23.4791	−	17.0586i	0.885531	−	0.643376i
$704$		0			0
$705$	−3.29005	−	10.1257i	−0.123911	−	0.381358i
$706$		0			0
$707$	−4.80902	−	14.8006i	−0.180862	−	0.556636i
$708$		0			0
$709$	5.78129	−	17.7930i	0.217121	−	0.668229i	−0.781875	−	0.623435i	$-0.785737\pi$
$709$	5.78129	−	17.7930i	0.217121	−	0.668229i	0.998996	−	0.0447946i	$-0.0142633\pi$
$710$		0			0
$711$	16.6076			0.622835
$712$		0			0
$713$	−18.8834	−	13.7196i	−0.707188	−	0.513802i
$714$		0			0
$715$	28.5918	−	20.7731i	1.06927	−	0.776871i
$716$		0			0
$717$	15.5552	+	11.3015i	0.580919	+	0.422062i
$718$		0			0
$719$	0.445612	+	0.323756i	0.0166185	+	0.0120741i	0.596064	−	0.802937i	$-0.296731\pi$
$719$	0.445612	+	0.323756i	0.0166185	+	0.0120741i	−0.579445	+	0.815011i	$0.696731\pi$
$720$		0			0
$721$	2.47577	+	7.61964i	0.0922025	+	0.283770i
$722$		0			0
$723$	2.27843	−	7.01229i	0.0847358	−	0.260790i
$724$		0			0
$725$	−8.46102	+	6.14729i	−0.314234	+	0.228305i
$726$		0			0
$727$	−3.13691	−	9.65441i	−0.116341	−	0.358062i	0.875883	−	0.482524i	$-0.160280\pi$
$727$	−3.13691	−	9.65441i	−0.116341	−	0.358062i	−0.992224	+	0.124461i	$0.960280\pi$
$728$		0			0
$729$	25.1389			0.931071
$730$		0			0
$731$	−38.4983	−	27.9707i	−1.42391	−	1.03453i
$732$		0			0
$733$	−0.223804	+	0.688797i	−0.00826638	+	0.0254413i	−0.955105	−	0.296269i	$-0.904258\pi$
$733$	−0.223804	+	0.688797i	−0.00826638	+	0.0254413i	0.946838	+	0.321710i	$0.104258\pi$
$734$		0			0
$735$	7.76684			0.286484
$736$		0			0
$737$	−12.0403			−0.443510
$738$		0			0
$739$	−30.4123			−1.11873			−0.559367	−	0.828920i	$-0.688956\pi$
$739$	−30.4123			−1.11873			−0.559367	+	0.828920i	$0.688956\pi$
$740$		0			0
$741$	−35.5115			−1.30455
$742$		0			0
$743$	−9.43894	+	29.0501i	−0.346281	+	1.06574i	0.614613	+	0.788828i	$0.289312\pi$
$743$	−9.43894	+	29.0501i	−0.346281	+	1.06574i	−0.960894	+	0.276915i	$0.910688\pi$
$744$		0			0
$745$	−4.06738	−	2.95512i	−0.149017	−	0.108267i
$746$		0			0
$747$	−3.82799			−0.140059
$748$		0			0
$749$	−0.0971882	−	0.299114i	−0.00355118	−	0.0109294i
$750$		0			0
$751$	−6.70945	+	4.87470i	−0.244831	+	0.177880i	−0.703433	−	0.710762i	$-0.748350\pi$
$751$	−6.70945	+	4.87470i	−0.244831	+	0.177880i	0.458602	+	0.888642i	$0.348350\pi$
$752$		0			0
$753$	−8.81491	+	27.1295i	−0.321233	+	0.988654i
$754$		0			0
$755$	5.04165	+	15.5166i	0.183485	+	0.564707i
$756$		0			0
$757$	17.5125	+	12.7235i	0.636501	+	0.462445i	0.858646	−	0.512568i	$-0.171306\pi$
$757$	17.5125	+	12.7235i	0.636501	+	0.462445i	−0.222145	+	0.975014i	$0.571306\pi$
$758$		0			0
$759$	27.3710	+	19.8862i	0.993503	+	0.721822i
$760$		0			0
$761$	16.6541	−	12.0999i	0.603712	−	0.438622i	−0.243483	−	0.969905i	$-0.578290\pi$
$761$	16.6541	−	12.0999i	0.603712	−	0.438622i	0.847195	+	0.531283i	$0.178290\pi$
$762$		0			0
$763$	0.807191	+	0.586459i	0.0292223	+	0.0212312i
$764$		0			0
$765$	17.6038			0.636467
$766$		0			0
$767$	−25.4897	+	78.4492i	−0.920380	+	2.83264i
$768$		0			0
$769$	0.209310	+	0.644191i	0.00754792	+	0.0232301i	0.954760	−	0.297379i	$-0.0961124\pi$
$769$	0.209310	+	0.644191i	0.00754792	+	0.0232301i	−0.947212	+	0.320609i	$0.896112\pi$
$770$		0			0
$771$	−1.99252	−	6.13236i	−0.0717590	−	0.220851i
$772$		0			0
$773$	33.1165	−	24.0605i	1.19112	−	0.865397i	0.197735	−	0.980256i	$-0.436642\pi$
$773$	33.1165	−	24.0605i	1.19112	−	0.865397i	0.993382	+	0.114859i	$0.0366415\pi$
$774$		0			0
$775$	1.76444	−	5.43038i	0.0633804	−	0.195065i
$776$		0			0
$777$	−12.1423	+	8.82187i	−0.435601	+	0.316483i
$778$		0			0
$779$	−4.09749	−	28.9220i	−0.146808	−	1.03624i
$780$		0			0
$781$	13.0908	−	9.51101i	0.468425	−	0.340331i
$782$		0			0
$783$	9.10046	−	28.0083i	0.325224	−	1.00094i
$784$		0			0
$785$	−18.2701	+	13.2740i	−0.652090	+	0.473771i
$786$		0			0
$787$	3.88312	+	11.9510i	0.138418	+	0.426007i	0.996106	−	0.0881634i	$-0.0280998\pi$
$787$	3.88312	+	11.9510i	0.138418	+	0.426007i	−0.857688	+	0.514171i	$0.828100\pi$
$788$		0			0
$789$	−9.59531	−	29.5313i	−0.341602	−	1.05134i
$790$		0			0
$791$	−8.48032	+	26.0997i	−0.301525	+	0.928000i
$792$		0			0
$793$	−41.9801			−1.49076
$794$		0			0
$795$	0.626027	+	0.454835i	0.0222029	+	0.0161314i
$796$		0			0
$797$	−32.3523	+	23.5053i	−1.14598	+	0.832600i	−0.987941	−	0.154833i	$-0.950516\pi$
$797$	−32.3523	+	23.5053i	−1.14598	+	0.832600i	−0.158035	+	0.987433i	$0.550516\pi$
$798$		0			0
$799$	−28.3605	−	20.6051i	−1.00332	−	0.728955i
$800$		0			0
$801$	−7.15942	−	5.20163i	−0.252966	−	0.183790i
$802$		0			0
$803$	10.6275	+	32.7080i	0.375035	+	1.15424i
$804$		0			0
$805$	8.09084	−	24.9011i	0.285165	−	0.877647i
$806$		0			0
$807$	3.18086	−	2.31103i	0.111972	−	0.0813521i
$808$		0			0
$809$	−7.08158	−	21.7949i	−0.248975	−	0.766267i	−0.994957	−	0.100301i	$-0.968020\pi$
$809$	−7.08158	−	21.7949i	−0.248975	−	0.766267i	0.745982	−	0.665966i	$-0.231980\pi$
$810$		0			0
$811$	33.8845			1.18984			0.594922	−	0.803783i	$-0.297183\pi$
$811$	33.8845			1.18984			0.594922	+	0.803783i	$0.297183\pi$
$812$		0			0
$813$	10.0694	+	7.31588i	0.353151	+	0.256579i
$814$		0			0
$815$	−8.15467	+	25.0975i	−0.285646	+	0.879127i
$816$		0			0
$817$	−29.9500			−1.04782
$818$		0			0
$819$	−16.0017			−0.559144
$820$		0			0
$821$	−7.00101			−0.244337			−0.122168	−	0.992509i	$-0.538985\pi$
$821$	−7.00101			−0.244337			−0.122168	+	0.992509i	$0.538985\pi$
$822$		0			0
$823$	−42.7437			−1.48995			−0.744976	−	0.667092i	$-0.767539\pi$
$823$	−42.7437			−1.48995			−0.744976	+	0.667092i	$0.767539\pi$
$824$		0			0
$825$	−2.55751	+	7.87120i	−0.0890410	+	0.274040i
$826$		0			0
$827$	3.87085	+	2.81234i	0.134603	+	0.0977945i	0.653049	−	0.757316i	$-0.273489\pi$
$827$	3.87085	+	2.81234i	0.134603	+	0.0977945i	−0.518447	+	0.855110i	$0.673489\pi$
$828$		0			0
$829$	30.6677			1.06513			0.532567	−	0.846388i	$-0.321227\pi$
$829$	30.6677			1.06513			0.532567	+	0.846388i	$0.321227\pi$
$830$		0			0
$831$	8.13291	+	25.0305i	0.282127	+	0.868299i
$832$		0			0
$833$	20.6889	−	15.0313i	0.716827	−	0.520805i
$834$		0			0
$835$	−6.98189	+	21.4880i	−0.241618	+	0.743624i
$836$		0			0
$837$	4.96846	+	15.2914i	0.171735	+	0.528547i
$838$		0			0
$839$	18.6566	+	13.5548i	0.644097	+	0.467964i	0.861255	−	0.508173i	$-0.169679\pi$
$839$	18.6566	+	13.5548i	0.644097	+	0.467964i	−0.217158	+	0.976136i	$0.569679\pi$
$840$		0			0
$841$	0.822217	+	0.597376i	0.0283523	+	0.0205992i
$842$		0			0
$843$	−10.5138	+	7.63869i	−0.362113	+	0.263091i
$844$		0			0
$845$	34.8803	+	25.3420i	1.19992	+	0.871793i
$846$		0			0
$847$	−0.128067			−0.00440043
$848$		0			0
$849$	−4.53939	+	13.9708i	−0.155792	+	0.479477i
$850$		0			0
$851$	−15.8878	−	48.8978i	−0.544628	−	1.67619i
$852$		0			0
$853$	12.7551	+	39.2561i	0.436726	+	1.34410i	0.891308	+	0.453399i	$0.149789\pi$
$853$	12.7551	+	39.2561i	0.436726	+	1.34410i	−0.454582	+	0.890705i	$0.650211\pi$
$854$		0			0
$855$	8.96350	−	6.51236i	0.306545	−	0.222718i
$856$		0			0
$857$	2.83201	−	8.71604i	0.0967397	−	0.297734i	−0.890963	−	0.454075i	$-0.849970\pi$
$857$	2.83201	−	8.71604i	0.0967397	−	0.297734i	0.987703	+	0.156341i	$0.0499698\pi$
$858$		0			0
$859$	32.0827	−	23.3095i	1.09465	−	0.795309i	0.114470	−	0.993427i	$-0.463483\pi$
$859$	32.0827	−	23.3095i	1.09465	−	0.795309i	0.980178	+	0.198118i	$0.0634829\pi$
$860$		0			0
$861$	2.11902	+	14.9571i	0.0722162	+	0.509736i
$862$		0			0
$863$	29.2873	−	21.2785i	0.996951	−	0.724327i	0.0355186	−	0.999369i	$-0.488692\pi$
$863$	29.2873	−	21.2785i	0.996951	−	0.724327i	0.961432	+	0.275042i	$0.0886917\pi$
$864$		0			0
$865$	−5.28850	+	16.2763i	−0.179814	+	0.553412i
$866$		0			0
$867$	−36.4034	+	26.4486i	−1.23632	+	0.898242i
$868$		0			0
$869$	−12.1471	−	37.3850i	−0.412063	−	1.26820i
$870$		0			0
$871$	−6.91854	−	21.2931i	−0.234426	−	0.721489i
$872$		0			0
$873$	6.51030	−	20.0366i	0.220340	−	0.678137i
$874$		0			0
$875$	22.6033			0.764130
$876$		0			0
$877$	30.5531	+	22.1981i	1.03170	+	0.749577i	0.968649	−	0.248434i	$-0.0799157\pi$
$877$	30.5531	+	22.1981i	1.03170	+	0.749577i	0.0630547	+	0.998010i	$0.479916\pi$
$878$		0			0
$879$	29.9904	−	21.7893i	1.01155	−	0.734935i
$880$		0			0
$881$	1.76986	+	1.28588i	0.0596280	+	0.0433223i	0.617200	−	0.786806i	$-0.288267\pi$
$881$	1.76986	+	1.28588i	0.0596280	+	0.0433223i	−0.557572	+	0.830129i	$0.688267\pi$
$882$		0			0
$883$	−12.6222	−	9.17058i	−0.424771	−	0.308615i	0.354783	−	0.934949i	$-0.384555\pi$
$883$	−12.6222	−	9.17058i	−0.424771	−	0.308615i	−0.779555	+	0.626334i	$0.784555\pi$
$884$		0			0
$885$	9.12720	+	28.0906i	0.306807	+	0.944256i
$886$		0			0
$887$	7.59394	−	23.3717i	0.254980	−	0.784746i	−0.738854	−	0.673865i	$-0.764633\pi$
$887$	7.59394	−	23.3717i	0.254980	−	0.784746i	0.993834	−	0.110881i	$-0.0353673\pi$
$888$		0			0
$889$	13.4854	−	9.79770i	0.452285	−	0.328604i
$890$		0			0
$891$	−2.92022	−	8.98750i	−0.0978309	−	0.301093i
$892$		0			0
$893$	−22.0632			−0.738317
$894$		0			0
$895$	21.3627	+	15.5209i	0.714077	+	0.518807i
$896$		0			0
$897$	−19.4406	+	59.8321i	−0.649104	+	1.99774i
$898$		0			0
$899$	15.2779			0.509546
$900$		0			0
$901$	2.54783			0.0848805
$902$		0			0
$903$	15.4887			0.515432
$904$		0			0
$905$	−11.8065			−0.392463
$906$		0			0
$907$	−16.4751	+	50.7052i	−0.547047	+	1.68364i	0.169024	+	0.985612i	$0.445938\pi$
$907$	−16.4751	+	50.7052i	−0.547047	+	1.68364i	−0.716072	+	0.698027i	$0.754062\pi$
$908$		0			0
$909$	−9.43843	−	6.85742i	−0.313053	−	0.227446i
$910$		0			0
$911$	30.3599			1.00587			0.502935	−	0.864324i	$-0.332254\pi$
$911$	30.3599			1.00587			0.502935	+	0.864324i	$0.332254\pi$
$912$		0			0
$913$	2.79987	+	8.61710i	0.0926620	+	0.285184i
$914$		0			0
$915$	−12.1611	+	8.83557i	−0.402034	+	0.292095i
$916$		0			0
$917$	−8.65147	+	26.6265i	−0.285697	+	0.879284i
$918$		0			0
$919$	−12.0949	−	37.2242i	−0.398973	−	1.22791i	−0.925824	−	0.377956i	$-0.876627\pi$
$919$	−12.0949	−	37.2242i	−0.398973	−	1.22791i	0.526850	−	0.849958i	$-0.323373\pi$
$920$		0			0
$921$	−10.9442	−	7.95146i	−0.360625	−	0.262010i
$922$		0			0
$923$	24.3423	+	17.6857i	0.801235	+	0.582132i
$924$		0			0
$925$	10.1752	−	7.39270i	0.334558	−	0.243071i
$926$		0			0
$927$	4.85907	+	3.53032i	0.159593	+	0.115951i
$928$		0			0
$929$	−36.4929			−1.19729			−0.598646	−	0.801014i	$-0.704294\pi$
$929$	−36.4929			−1.19729			−0.598646	+	0.801014i	$0.704294\pi$
$930$		0			0
$931$	4.97364	−	15.3073i	0.163005	−	0.501677i
$932$		0			0
$933$	−10.2322	−	31.4916i	−0.334989	−	1.03099i
$934$		0			0
$935$	−12.8758	−	39.6275i	−0.421083	−	1.29596i
$936$		0			0
$937$	−13.9607	+	10.1430i	−0.456077	+	0.331359i	−0.791990	−	0.610534i	$-0.790955\pi$
$937$	−13.9607	+	10.1430i	−0.456077	+	0.331359i	0.335914	+	0.941893i	$0.390955\pi$
$938$		0			0
$939$	7.16310	−	22.0458i	0.233759	−	0.719436i
$940$		0			0
$941$	34.2893	−	24.9126i	1.11780	−	0.812128i	0.133924	−	0.990992i	$-0.457242\pi$
$941$	34.2893	−	24.9126i	1.11780	−	0.812128i	0.983874	+	0.178864i	$0.0572421\pi$
$942$		0			0
$943$	−50.9728	−	8.92952i	−1.65990	−	0.290785i
$944$		0			0
$945$	−14.5911	+	10.6010i	−0.474647	+	0.344851i
$946$		0			0
$947$	−14.0302	+	43.1805i	−0.455920	+	1.40318i	0.414133	+	0.910217i	$0.364085\pi$
$947$	−14.0302	+	43.1805i	−0.455920	+	1.40318i	−0.870052	+	0.492960i	$0.835915\pi$
$948$		0			0
$949$	−51.7370	+	37.5891i	−1.67945	+	1.22019i
$950$		0			0
$951$	8.55248	+	26.3218i	0.277333	+	0.853544i
$952$		0			0
$953$	1.99337	+	6.13495i	0.0645715	+	0.198731i	0.978137	−	0.207960i	$-0.0666825\pi$
$953$	1.99337	+	6.13495i	0.0645715	+	0.198731i	−0.913566	+	0.406691i	$0.866683\pi$
$954$		0			0
$955$	−6.21925	+	19.1409i	−0.201250	+	0.619385i
$956$		0			0
$957$	−22.1449			−0.715844
$958$		0			0
$959$	2.20340	+	1.60087i	0.0711517	+	0.0516947i
$960$		0			0
$961$	18.3315	−	13.3186i	0.591337	−	0.429632i
$962$		0			0
$963$	−0.190746	−	0.138585i	−0.00614672	−	0.00446585i
$964$		0			0
$965$	−23.1856	−	16.8453i	−0.746370	−	0.542269i
$966$		0			0
$967$	−13.3083	−	40.9589i	−0.427967	−	1.31715i	−0.900124	−	0.435634i	$-0.856524\pi$
$967$	−13.3083	−	40.9589i	−0.427967	−	1.31715i	0.472157	−	0.881515i	$-0.343476\pi$
$968$		0			0
$969$	−12.9378	+	39.8183i	−0.415621	+	1.27915i
$970$		0			0
$971$	−1.55646	+	1.13083i	−0.0499492	+	0.0362902i	−0.612480	−	0.790486i	$-0.709828\pi$
$971$	−1.55646	+	1.13083i	−0.0499492	+	0.0362902i	0.562531	+	0.826777i	$0.309828\pi$
$972$		0			0
$973$	−7.68941	−	23.6656i	−0.246511	−	0.758684i
$974$		0			0
$975$	−15.3897			−0.492865
$976$		0			0
$977$	43.4627	+	31.5775i	1.39050	+	1.01025i	0.995811	+	0.0914378i	$0.0291463\pi$
$977$	43.4627	+	31.5775i	1.39050	+	1.01025i	0.394685	+	0.918817i	$0.370854\pi$
$978$		0			0
$979$	−6.47272	+	19.9210i	−0.206869	+	0.636677i
$980$		0			0
$981$	0.747974			0.0238810
$982$		0			0
$983$	41.4706			1.32271			0.661353	−	0.750075i	$-0.269983\pi$
$983$	41.4706			1.32271			0.661353	+	0.750075i	$0.269983\pi$
$984$		0			0
$985$	−8.97497			−0.285966
$986$		0			0
$987$	11.4100			0.363186
$988$		0			0
$989$	−16.3960	+	50.4618i	−0.521363	+	1.60459i
$990$		0			0
$991$	−39.1925	−	28.4750i	−1.24499	−	0.904538i	−0.247070	−	0.968998i	$-0.579468\pi$
$991$	−39.1925	−	28.4750i	−1.24499	−	0.904538i	−0.997920	+	0.0644593i	$0.979468\pi$
$992$		0			0
$993$	9.14709			0.290274
$994$		0			0
$995$	−11.6275	−	35.7858i	−0.368617	−	1.13449i
$996$		0			0
$997$	40.7579	−	29.6124i	1.29082	−	0.937833i	0.290995	−	0.956725i	$-0.406014\pi$
$997$	40.7579	−	29.6124i	1.29082	−	0.937833i	0.999822	+	0.0188917i	$0.00601377\pi$
$998$		0			0
$999$	−10.9442	+	33.6827i	−0.346258	+	1.06567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.529.4		20
4.3	odd	2		328.2.m.c.201.2	✓	20
41.10	even	5	inner	656.2.u.h.625.4		20
164.51	odd	10		328.2.m.c.297.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.201.2	✓	20	4.3	odd	2
328.2.m.c.297.2	yes	20	164.51	odd	10
656.2.u.h.529.4		20	1.1	even	1	trivial
656.2.u.h.625.4		20	41.10	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:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.u (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+1.26615 q^{3} +(-0.537278 + 1.65357i) q^{5} +(-1.50744 - 1.09522i) q^{7} -1.39685 q^{9} +O(q^{10})\)	\(q+1.26615 q^{3} +(-0.537278 + 1.65357i) q^{5} +(-1.50744 - 1.09522i) q^{7} -1.39685 q^{9} +(1.02169 + 3.14443i) q^{11} +(-4.97380 + 3.61368i) q^{13} +(-0.680277 + 2.09368i) q^{15} +(2.23986 + 6.89358i) q^{17} +(3.69070 + 2.68145i) q^{19} +(-1.90866 - 1.38672i) q^{21} +(6.53835 - 4.75039i) q^{23} +(1.59945 + 1.16207i) q^{25} -5.56709 q^{27} +(-1.63469 + 5.03105i) q^{29} +(-0.892470 - 2.74674i) q^{31} +(1.29361 + 3.98133i) q^{33} +(2.62095 - 1.90423i) q^{35} +(1.96587 - 6.05032i) q^{37} +(-6.29760 + 4.57547i) q^{39} +(-4.45310 - 4.60108i) q^{41} +(-5.31133 + 3.85891i) q^{43} +(0.750500 - 2.30980i) q^{45} +(-3.91268 + 2.84273i) q^{47} +(-1.09024 - 3.35542i) q^{49} +(2.83601 + 8.72833i) q^{51} +(0.108621 - 0.334302i) q^{53} -5.74847 q^{55} +(4.67300 + 3.39513i) q^{57} +(10.8545 - 7.88624i) q^{59} +(5.52421 + 4.01357i) q^{61} +(2.10568 + 1.52987i) q^{63} +(-3.30317 - 10.1661i) q^{65} +(-1.12534 + 3.46344i) q^{67} +(8.27856 - 6.01472i) q^{69} +(-1.51236 - 4.65456i) q^{71} +10.4019 q^{73} +(2.02515 + 1.47136i) q^{75} +(1.90371 - 5.85902i) q^{77} -11.8893 q^{79} -2.85823 q^{81} +2.74043 q^{83} -12.6025 q^{85} +(-2.06977 + 6.37008i) q^{87} +(5.12539 + 3.72381i) q^{89} +11.4555 q^{91} +(-1.13000 - 3.47779i) q^{93} +(-6.41692 + 4.66216i) q^{95} +(-4.66068 + 14.3441i) q^{97} +(-1.42715 - 4.39231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9} - 9 q^{11} + 7 q^{13} - q^{15} - 8 q^{17} - q^{19} - 6 q^{21} + 11 q^{23} + 15 q^{25} - 2 q^{27} + 21 q^{29} + 5 q^{31} + 19 q^{33} - 4 q^{37} - 4 q^{39} + 9 q^{41} + 17 q^{43} + 11 q^{45} - 15 q^{47} - 25 q^{49} + 22 q^{51} + 10 q^{53} + 28 q^{55} - 20 q^{57} + 24 q^{59} + 15 q^{61} + 65 q^{63} - 29 q^{65} + 26 q^{67} - 47 q^{69} - 16 q^{71} + 14 q^{73} - 11 q^{75} + 12 q^{77} + 26 q^{79} - 60 q^{81} - 20 q^{83} - 94 q^{85} - 57 q^{87} + 5 q^{89} + 46 q^{91} + 43 q^{93} - 71 q^{95} - 22 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 + 2 * q^5 + 10 * q^9 - 9 * q^11 + 7 * q^13 - q^15 - 8 * q^17 - q^19 - 6 * q^21 + 11 * q^23 + 15 * q^25 - 2 * q^27 + 21 * q^29 + 5 * q^31 + 19 * q^33 - 4 * q^37 - 4 * q^39 + 9 * q^41 + 17 * q^43 + 11 * q^45 - 15 * q^47 - 25 * q^49 + 22 * q^51 + 10 * q^53 + 28 * q^55 - 20 * q^57 + 24 * q^59 + 15 * q^61 + 65 * q^63 - 29 * q^65 + 26 * q^67 - 47 * q^69 - 16 * q^71 + 14 * q^73 - 11 * q^75 + 12 * q^77 + 26 * q^79 - 60 * q^81 - 20 * q^83 - 94 * q^85 - 57 * q^87 + 5 * q^89 + 46 * q^91 + 43 * q^93 - 71 * q^95 - 22 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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