LMFDB - Embedded newform 656.2.u.h.305.2

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			305.2
Root			$0.596104 + 1.83462i$ of defining polynomial
Character	$\chi$	$=$	656.305
Dual form			656.2.u.h.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92903 q^{3} +(-3.33100 + 2.42011i) q^{5} +(0.669598 - 2.06081i) q^{7} +0.721162 q^{9} +O(q^{10})$	\(q-1.92903 q^{3} +(-3.33100 + 2.42011i) q^{5} +(0.669598 - 2.06081i) q^{7} +0.721162 q^{9} +(-2.97764 - 2.16338i) q^{11} +(0.806270 + 2.48144i) q^{13} +(6.42560 - 4.66847i) q^{15} +(1.33047 + 0.966643i) q^{17} +(-0.968612 + 2.98108i) q^{19} +(-1.29168 + 3.97537i) q^{21} +(-1.16389 - 3.58209i) q^{23} +(3.69353 - 11.3675i) q^{25} +4.39595 q^{27} +(6.94926 - 5.04893i) q^{29} +(7.05672 + 5.12701i) q^{31} +(5.74395 + 4.17323i) q^{33} +(2.75697 + 8.48507i) q^{35} +(6.25029 - 4.54110i) q^{37} +(-1.55532 - 4.78678i) q^{39} +(-4.88420 + 4.14060i) q^{41} +(0.357294 + 1.09964i) q^{43} +(-2.40219 + 1.74530i) q^{45} +(-2.21658 - 6.82193i) q^{47} +(1.86454 + 1.35467i) q^{49} +(-2.56652 - 1.86468i) q^{51} +(-4.36314 + 3.17001i) q^{53} +15.1541 q^{55} +(1.86848 - 5.75060i) q^{57} +(-3.04255 - 9.36399i) q^{59} +(3.09805 - 9.53482i) q^{61} +(0.482889 - 1.48618i) q^{63} +(-8.69106 - 6.31442i) q^{65} +(-0.772918 + 0.561558i) q^{67} +(2.24518 + 6.90996i) q^{69} +(1.89727 + 1.37845i) q^{71} +12.6712 q^{73} +(-7.12493 + 21.9283i) q^{75} +(-6.45213 + 4.68775i) q^{77} -7.14371 q^{79} -10.6434 q^{81} -1.54479 q^{83} -6.77118 q^{85} +(-13.4053 + 9.73955i) q^{87} +(1.79501 - 5.52448i) q^{89} +5.65366 q^{91} +(-13.6126 - 9.89016i) q^{93} +(-3.98811 - 12.2741i) q^{95} +(-7.59771 + 5.52006i) q^{97} +(-2.14736 - 1.56015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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
$3$	−1.92903			−1.11373			−0.556863	−	0.830604i	$-0.687995\pi$
$3$	−1.92903			−1.11373			−0.556863	+	0.830604i	$0.687995\pi$
$4$		0			0
$5$	−3.33100	+	2.42011i	−1.48967	+	1.08231i	−0.515391	+	0.856955i	$0.672353\pi$
$5$	−3.33100	+	2.42011i	−1.48967	+	1.08231i	−0.974277	+	0.225353i	$0.927647\pi$
$6$		0			0
$7$	0.669598	−	2.06081i	0.253084	−	0.778914i	−0.741117	−	0.671376i	$-0.765703\pi$
$7$	0.669598	−	2.06081i	0.253084	−	0.778914i	0.994201	−	0.107537i	$-0.0342965\pi$
$8$		0			0
$9$	0.721162			0.240387
$10$		0			0
$11$	−2.97764	−	2.16338i	−0.897791	−	0.652283i	0.0401068	−	0.999195i	$-0.487230\pi$
$11$	−2.97764	−	2.16338i	−0.897791	−	0.652283i	−0.937898	+	0.346912i	$0.887230\pi$
$12$		0			0
$13$	0.806270	+	2.48144i	0.223619	+	0.688228i	0.998429	+	0.0560341i	$0.0178456\pi$
$13$	0.806270	+	2.48144i	0.223619	+	0.688228i	−0.774810	+	0.632194i	$0.782154\pi$
$14$		0			0
$15$	6.42560	−	4.66847i	1.65908	−	1.20540i
$16$		0			0
$17$	1.33047	+	0.966643i	0.322686	+	0.234445i	0.737321	−	0.675543i	$-0.236091\pi$
$17$	1.33047	+	0.966643i	0.322686	+	0.234445i	−0.414635	+	0.909988i	$0.636091\pi$
$18$		0			0
$19$	−0.968612	+	2.98108i	−0.222215	+	0.683907i	0.776348	+	0.630305i	$0.217070\pi$
$19$	−0.968612	+	2.98108i	−0.222215	+	0.683907i	−0.998562	+	0.0536017i	$0.982930\pi$
$20$		0			0
$21$	−1.29168	+	3.97537i	−0.281867	+	0.867497i
$22$		0			0
$23$	−1.16389	−	3.58209i	−0.242688	−	0.746917i	−0.996008	−	0.0892627i	$-0.971549\pi$
$23$	−1.16389	−	3.58209i	−0.242688	−	0.746917i	0.753320	−	0.657654i	$-0.228451\pi$
$24$		0			0
$25$	3.69353	−	11.3675i	0.738706	−	2.27350i
$26$		0			0
$27$	4.39595			0.846001
$28$		0			0
$29$	6.94926	−	5.04893i	1.29044	−	0.937563i	0.290631	−	0.956835i	$-0.406135\pi$
$29$	6.94926	−	5.04893i	1.29044	−	0.937563i	0.999814	+	0.0192723i	$0.00613495\pi$
$30$		0			0
$31$	7.05672	+	5.12701i	1.26743	+	0.920838i	0.999097	−	0.0424894i	$-0.0135289\pi$
$31$	7.05672	+	5.12701i	1.26743	+	0.920838i	0.268328	+	0.963328i	$0.413529\pi$
$32$		0			0
$33$	5.74395	+	4.17323i	0.999894	+	0.726465i
$34$		0			0
$35$	2.75697	+	8.48507i	0.466012	+	1.43424i
$36$		0			0
$37$	6.25029	−	4.54110i	1.02754	−	0.746553i	0.0597264	−	0.998215i	$-0.480977\pi$
$37$	6.25029	−	4.54110i	1.02754	−	0.746553i	0.967815	+	0.251662i	$0.0809772\pi$
$38$		0			0
$39$	−1.55532	−	4.78678i	−0.249050	−	0.766499i
$40$		0			0
$41$	−4.88420	+	4.14060i	−0.762784	+	0.646654i
$41$	−4.88420	+	4.14060i	−0.762784	+	0.646654i
$42$		0			0
$43$	0.357294	+	1.09964i	0.0544868	+	0.167693i	0.974597	−	0.223967i	$-0.0719008\pi$
$43$	0.357294	+	1.09964i	0.0544868	+	0.167693i	−0.920110	+	0.391660i	$0.871901\pi$
$44$		0			0
$45$	−2.40219	+	1.74530i	−0.358098	+	0.260173i
$46$		0			0
$47$	−2.21658	−	6.82193i	−0.323321	−	0.995080i	−0.972193	−	0.234182i	$-0.924759\pi$
$47$	−2.21658	−	6.82193i	−0.323321	−	0.995080i	0.648872	−	0.760898i	$-0.275241\pi$
$48$		0			0
$49$	1.86454	+	1.35467i	0.266362	+	0.193524i
$50$		0			0
$51$	−2.56652	−	1.86468i	−0.359384	−	0.261108i
$52$		0			0
$53$	−4.36314	+	3.17001i	−0.599324	+	0.435434i	−0.845639	−	0.533756i	$-0.820780\pi$
$53$	−4.36314	+	3.17001i	−0.599324	+	0.435434i	0.246315	+	0.969190i	$0.420780\pi$
$54$		0			0
$55$	15.1541			2.04338
$56$		0			0
$57$	1.86848	−	5.75060i	0.247487	−	0.761685i
$58$		0			0
$59$	−3.04255	−	9.36399i	−0.396106	−	1.21909i	−0.928097	−	0.372338i	$-0.878556\pi$
$59$	−3.04255	−	9.36399i	−0.396106	−	1.21909i	0.531991	−	0.846750i	$-0.321444\pi$
$60$		0			0
$61$	3.09805	−	9.53482i	0.396665	−	1.22081i	−0.530993	−	0.847376i	$-0.678181\pi$
$61$	3.09805	−	9.53482i	0.396665	−	1.22081i	0.927658	−	0.373432i	$-0.121819\pi$
$62$		0			0
$63$	0.482889	−	1.48618i	0.0608383	−	0.187241i
$64$		0			0
$65$	−8.69106	−	6.31442i	−1.07799	−	0.783208i
$66$		0			0
$67$	−0.772918	+	0.561558i	−0.0944269	+	0.0686052i	−0.633997	−	0.773336i	$-0.718587\pi$
$67$	−0.772918	+	0.561558i	−0.0944269	+	0.0686052i	0.539570	+	0.841941i	$0.318587\pi$
$68$		0			0
$69$	2.24518	+	6.90996i	0.270288	+	0.831861i
$70$		0			0
$71$	1.89727	+	1.37845i	0.225165	+	0.163592i	0.694649	−	0.719349i	$-0.255560\pi$
$71$	1.89727	+	1.37845i	0.225165	+	0.163592i	−0.469484	+	0.882941i	$0.655560\pi$
$72$		0			0
$73$	12.6712			1.48305			0.741527	−	0.670923i	$-0.234102\pi$
$73$	12.6712			1.48305			0.741527	+	0.670923i	$0.234102\pi$
$74$		0			0
$75$	−7.12493	+	21.9283i	−0.822717	+	2.53206i
$76$		0			0
$77$	−6.45213	+	4.68775i	−0.735289	+	0.534219i
$78$		0			0
$79$	−7.14371			−0.803730			−0.401865	−	0.915699i	$-0.631638\pi$
$79$	−7.14371			−0.803730			−0.401865	+	0.915699i	$0.631638\pi$
$80$		0			0
$81$	−10.6434			−1.18260
$82$		0			0
$83$	−1.54479			−0.169562			−0.0847811	−	0.996400i	$-0.527019\pi$
$83$	−1.54479			−0.169562			−0.0847811	+	0.996400i	$0.527019\pi$
$84$		0			0
$85$	−6.77118			−0.734437
$86$		0			0
$87$	−13.4053	+	9.73955i	−1.43720	+	1.04419i
$88$		0			0
$89$	1.79501	−	5.52448i	0.190271	−	0.585593i	−0.809728	−	0.586805i	$-0.800386\pi$
$89$	1.79501	−	5.52448i	0.190271	−	0.585593i	0.999999	+	0.00121147i	$0.000385621\pi$
$90$		0			0
$91$	5.65366			0.592665
$92$		0			0
$93$	−13.6126	−	9.89016i	−1.41157	−	1.02556i
$94$		0			0
$95$	−3.98811	−	12.2741i	−0.409171	−	1.25930i
$96$		0			0
$97$	−7.59771	+	5.52006i	−0.771431	+	0.560477i	−0.902395	−	0.430910i	$-0.858193\pi$
$97$	−7.59771	+	5.52006i	−0.771431	+	0.560477i	0.130964	+	0.991387i	$0.458193\pi$
$98$		0			0
$99$	−2.14736	−	1.56015i	−0.215818	−	0.156801i
$100$		0			0
$101$	2.41604	−	7.43581i	0.240405	−	0.739890i	−0.755953	−	0.654626i	$-0.772826\pi$
$101$	2.41604	−	7.43581i	0.240405	−	0.739890i	0.996358	−	0.0852649i	$-0.0271737\pi$
$102$		0			0
$103$	−4.03052	+	12.4047i	−0.397139	+	1.22227i	0.530145	+	0.847907i	$0.322138\pi$
$103$	−4.03052	+	12.4047i	−0.397139	+	1.22227i	−0.927283	+	0.374360i	$0.877862\pi$
$104$		0			0
$105$	−5.31827	−	16.3680i	−0.519010	−	1.59735i
$106$		0			0
$107$	−4.03924	+	12.4315i	−0.390488	+	1.20180i	0.541933	+	0.840422i	$0.317693\pi$
$107$	−4.03924	+	12.4315i	−0.390488	+	1.20180i	−0.932420	+	0.361376i	$0.882307\pi$
$108$		0			0
$109$	2.85551			0.273508			0.136754	−	0.990605i	$-0.456333\pi$
$109$	2.85551			0.273508			0.136754	+	0.990605i	$0.456333\pi$
$110$		0			0
$111$	−12.0570	+	8.75993i	−1.14440	+	0.831456i
$112$		0			0
$113$	11.5385	+	8.38319i	1.08545	+	0.788624i	0.978625	−	0.205654i	$-0.0659322\pi$
$113$	11.5385	+	8.38319i	1.08545	+	0.788624i	0.106823	+	0.994278i	$0.465932\pi$
$114$		0			0
$115$	12.5460	+	9.11518i	1.16992	+	0.849995i
$116$		0			0
$117$	0.581451	+	1.78952i	0.0537552	+	0.165442i
$118$		0			0
$119$	2.88295	−	2.09458i	0.264279	−	0.192010i
$120$		0			0
$121$	0.786917	+	2.42188i	0.0715379	+	0.220171i
$122$		0			0
$123$	9.42177	−	7.98736i	0.849533	−	0.720196i
$124$		0			0
$125$	8.84588	+	27.2248i	0.791200	+	2.43506i
$126$		0			0
$127$	15.6017	−	11.3353i	1.38443	−	1.00584i	0.387975	−	0.921670i	$-0.373175\pi$
$127$	15.6017	−	11.3353i	1.38443	−	1.00584i	0.996451	−	0.0841743i	$-0.0268252\pi$
$128$		0			0
$129$	−0.689231	−	2.12124i	−0.0606834	−	0.186764i
$130$		0			0
$131$	4.53322	+	3.29358i	0.396069	+	0.287761i	0.767938	−	0.640524i	$-0.221283\pi$
$131$	4.53322	+	3.29358i	0.396069	+	0.287761i	−0.371869	+	0.928285i	$0.621283\pi$
$132$		0			0
$133$	5.49486	+	3.99225i	0.476465	+	0.346172i
$134$		0			0
$135$	−14.6429	+	10.6387i	−1.26026	+	0.915633i
$136$		0			0
$137$	−16.5392			−1.41304			−0.706521	−	0.707692i	$-0.749736\pi$
$137$	−16.5392			−1.41304			−0.706521	+	0.707692i	$0.749736\pi$
$138$		0			0
$139$	4.04182	−	12.4395i	0.342823	−	1.05510i	−0.619916	−	0.784668i	$-0.712833\pi$
$139$	4.04182	−	12.4395i	0.342823	−	1.05510i	0.962739	−	0.270432i	$-0.0871667\pi$
$140$		0			0
$141$	4.27585	+	13.1597i	0.360091	+	1.10825i
$142$		0			0
$143$	2.96752	−	9.13310i	0.248157	−	0.763748i
$144$		0			0
$145$	−10.9290	+	33.6360i	−0.907604	+	2.79332i
$146$		0			0
$147$	−3.59675	−	2.61319i	−0.296655	−	0.215532i
$148$		0			0
$149$	13.0549	−	9.48494i	1.06950	−	0.777036i	0.0936768	−	0.995603i	$-0.470138\pi$
$149$	13.0549	−	9.48494i	1.06950	−	0.777036i	0.975822	+	0.218566i	$0.0701379\pi$
$150$		0			0
$151$	−5.83870	−	17.9697i	−0.475147	−	1.46235i	−0.845760	−	0.533563i	$-0.820853\pi$
$151$	−5.83870	−	17.9697i	−0.475147	−	1.46235i	0.370614	−	0.928787i	$-0.379147\pi$
$152$		0			0
$153$	0.959485	+	0.697106i	0.0775697	+	0.0563577i
$154$		0			0
$155$	−35.9139			−2.88467
$156$		0			0
$157$	3.25083	−	10.0050i	0.259445	−	0.798488i	−0.733477	−	0.679714i	$-0.762104\pi$
$157$	3.25083	−	10.0050i	0.259445	−	0.798488i	0.992921	−	0.118774i	$-0.0378963\pi$
$158$		0			0
$159$	8.41664	−	6.11505i	0.667483	−	0.484955i
$160$		0			0
$161$	−8.16134			−0.643204
$162$		0			0
$163$	−13.4214			−1.05125			−0.525623	−	0.850717i	$-0.676168\pi$
$163$	−13.4214			−1.05125			−0.525623	+	0.850717i	$0.676168\pi$
$164$		0			0
$165$	−29.2328			−2.27577
$166$		0			0
$167$	24.2911			1.87970			0.939851	−	0.341585i	$-0.110964\pi$
$167$	24.2911			1.87970			0.939851	+	0.341585i	$0.110964\pi$
$168$		0			0
$169$	5.00973	−	3.63978i	0.385364	−	0.279983i
$170$		0			0
$171$	−0.698526	+	2.14984i	−0.0534176	+	0.164403i
$172$		0			0
$173$	2.76844			0.210480			0.105240	−	0.994447i	$-0.466439\pi$
$173$	2.76844			0.210480			0.105240	+	0.994447i	$0.466439\pi$
$174$		0			0
$175$	−20.9531	−	15.2233i	−1.58391	−	1.15078i
$176$		0			0
$177$	5.86917	+	18.0634i	0.441154	+	1.35773i
$178$		0			0
$179$	−1.66498	+	1.20968i	−0.124446	+	0.0904157i	−0.648267	−	0.761413i	$-0.724506\pi$
$179$	−1.66498	+	1.20968i	−0.124446	+	0.0904157i	0.523821	+	0.851828i	$0.324506\pi$
$180$		0			0
$181$	−15.9991	−	11.6240i	−1.18920	−	0.864006i	−0.196022	−	0.980599i	$-0.562802\pi$
$181$	−15.9991	−	11.6240i	−1.18920	−	0.864006i	−0.993180	+	0.116594i	$0.962802\pi$
$182$		0			0
$183$	−5.97624	+	18.3930i	−0.441776	+	1.35965i
$184$		0			0
$185$	−9.82974	+	30.2528i	−0.722697	+	2.22423i
$186$		0			0
$187$	−1.87044	−	5.75662i	−0.136780	−	0.420966i
$188$		0			0
$189$	2.94352	−	9.05922i	0.214110	−	0.658961i
$190$		0			0
$191$	5.30024			0.383512			0.191756	−	0.981443i	$-0.438582\pi$
$191$	5.30024			0.383512			0.191756	+	0.981443i	$0.438582\pi$
$192$		0			0
$193$	−0.696605	+	0.506113i	−0.0501427	+	0.0364308i	−0.612574	−	0.790413i	$-0.709866\pi$
$193$	−0.696605	+	0.506113i	−0.0501427	+	0.0364308i	0.562432	+	0.826844i	$0.309866\pi$
$194$		0			0
$195$	16.7653	+	12.1807i	1.20059	+	0.872280i
$196$		0			0
$197$	12.7106	+	9.23478i	0.905592	+	0.657951i	0.939896	−	0.341460i	$-0.110922\pi$
$197$	12.7106	+	9.23478i	0.905592	+	0.657951i	−0.0343044	+	0.999411i	$0.510922\pi$
$198$		0			0
$199$	−3.70452	−	11.4013i	−0.262606	−	0.808220i	−0.992235	−	0.124376i	$-0.960307\pi$
$199$	−3.70452	−	11.4013i	−0.262606	−	0.808220i	0.729629	−	0.683844i	$-0.239693\pi$
$200$		0			0
$201$	1.49098	−	1.08326i	0.105166	−	0.0764074i
$202$		0			0
$203$	−5.75169	−	17.7019i	−0.403689	−	1.24243i
$204$		0			0
$205$	6.24854	−	25.6127i	0.436417	−	1.78887i
$206$		0			0
$207$	−0.839354	−	2.58327i	−0.0583391	−	0.179549i
$208$		0			0
$209$	9.33338	−	6.78109i	0.645603	−	0.469058i
$210$		0			0
$211$	6.21667	+	19.1329i	0.427973	+	1.31717i	0.900119	+	0.435645i	$0.143480\pi$
$211$	6.21667	+	19.1329i	0.427973	+	1.31717i	−0.472146	+	0.881521i	$0.656520\pi$
$212$		0			0
$213$	−3.65990	−	2.65907i	−0.250772	−	0.182197i
$214$		0			0
$215$	−3.85139	−	2.79820i	−0.262663	−	0.190836i
$216$		0			0
$217$	15.2910	−	11.1095i	1.03802	−	0.754165i
$218$		0			0
$219$	−24.4432			−1.65172
$220$		0			0
$221$	−1.32595	+	4.08086i	−0.0891931	+	0.274508i
$222$		0			0
$223$	1.39807	+	4.30283i	0.0936220	+	0.288139i	0.986892	−	0.161381i	$-0.0515949\pi$
$223$	1.39807	+	4.30283i	0.0936220	+	0.288139i	−0.893270	+	0.449520i	$0.851595\pi$
$224$		0			0
$225$	2.66363	−	8.19783i	0.177576	−	0.546522i
$226$		0			0
$227$	−2.71423	+	8.35353i	−0.180150	+	0.554443i	−0.999831	−	0.0183761i	$-0.994150\pi$
$227$	−2.71423	+	8.35353i	−0.180150	+	0.554443i	0.819682	+	0.572819i	$0.194150\pi$
$228$		0			0
$229$	−11.2746	−	8.19148i	−0.745047	−	0.541309i	0.149240	−	0.988801i	$-0.452317\pi$
$229$	−11.2746	−	8.19148i	−0.745047	−	0.541309i	−0.894288	+	0.447492i	$0.852317\pi$
$230$		0			0
$231$	12.4464	−	9.04282i	0.818911	−	0.594974i
$232$		0			0
$233$	−4.56905	−	14.0621i	−0.299329	−	0.921239i	−0.981733	−	0.190264i	$-0.939066\pi$
$233$	−4.56905	−	14.0621i	−0.299329	−	0.921239i	0.682404	−	0.730975i	$-0.260934\pi$
$234$		0			0
$235$	23.8933	+	17.3595i	1.55862	+	1.13241i
$236$		0			0
$237$	13.7804			0.895136
$238$		0			0
$239$	5.62470	−	17.3110i	0.363831	−	1.11976i	−0.586878	−	0.809675i	$-0.699643\pi$
$239$	5.62470	−	17.3110i	0.363831	−	1.11976i	0.950710	−	0.310082i	$-0.100357\pi$
$240$		0			0
$241$	−5.48374	+	3.98417i	−0.353238	+	0.256643i	−0.750226	−	0.661181i	$-0.770055\pi$
$241$	−5.48374	+	3.98417i	−0.353238	+	0.256643i	0.396988	+	0.917824i	$0.370055\pi$
$242$		0			0
$243$	7.34363			0.471094
$244$		0			0
$245$	−9.48922			−0.606244
$246$		0			0
$247$	−8.17834			−0.520375
$248$		0			0
$249$	2.97994			0.188846
$250$		0			0
$251$	13.0608	−	9.48921i	0.824389	−	0.598953i	−0.0935776	−	0.995612i	$-0.529830\pi$
$251$	13.0608	−	9.48921i	0.824389	−	0.598953i	0.917966	+	0.396659i	$0.129830\pi$
$252$		0			0
$253$	−4.28377	+	13.1841i	−0.269318	+	0.828876i
$254$		0			0
$255$	13.0618			0.817963
$256$		0			0
$257$	15.6450	+	11.3667i	0.975906	+	0.709037i	0.956790	−	0.290780i	$-0.0939148\pi$
$257$	15.6450	+	11.3667i	0.975906	+	0.709037i	0.0191160	+	0.999817i	$0.493915\pi$
$258$		0			0
$259$	−5.17317	−	15.9214i	−0.321445	−	0.989307i
$260$		0			0
$261$	5.01154	−	3.64110i	0.310207	−	0.225378i
$262$		0			0
$263$	15.3145	+	11.1266i	0.944330	+	0.686096i	0.949459	−	0.313891i	$-0.101633\pi$
$263$	15.3145	+	11.1266i	0.944330	+	0.686096i	−0.00512935	+	0.999987i	$0.501633\pi$
$264$		0			0
$265$	6.86185	−	21.1186i	0.421520	−	1.29731i
$266$		0			0
$267$	−3.46263	+	10.6569i	−0.211910	+	0.652191i
$268$		0			0
$269$	−3.72706	−	11.4707i	−0.227243	−	0.699381i	−0.998056	−	0.0623200i	$-0.980150\pi$
$269$	−3.72706	−	11.4707i	−0.227243	−	0.699381i	0.770814	−	0.637061i	$-0.219850\pi$
$270$		0			0
$271$	4.73440	−	14.5710i	0.287594	−	0.885124i	−0.698015	−	0.716083i	$-0.745933\pi$
$271$	4.73440	−	14.5710i	0.287594	−	0.885124i	0.985609	−	0.169041i	$-0.0540669\pi$
$272$		0			0
$273$	−10.9061			−0.660067
$274$		0			0
$275$	−35.5902	+	25.8578i	−2.14617	+	1.55928i
$276$		0			0
$277$	2.87488	+	2.08872i	0.172735	+	0.125499i	0.670794	−	0.741644i	$-0.265954\pi$
$277$	2.87488	+	2.08872i	0.172735	+	0.125499i	−0.498059	+	0.867143i	$0.665954\pi$
$278$		0			0
$279$	5.08904	+	3.69741i	0.304673	+	0.221358i
$280$		0			0
$281$	4.50314	+	13.8592i	0.268635	+	0.826773i	0.990834	+	0.135087i	$0.0431315\pi$
$281$	4.50314	+	13.8592i	0.268635	+	0.826773i	−0.722199	+	0.691685i	$0.756868\pi$
$282$		0			0
$283$	6.79983	−	4.94036i	0.404208	−	0.293674i	−0.367045	−	0.930203i	$-0.619630\pi$
$283$	6.79983	−	4.94036i	0.404208	−	0.293674i	0.771253	+	0.636529i	$0.219630\pi$
$284$		0			0
$285$	7.69318	+	23.6772i	0.455705	+	1.40252i
$286$		0			0
$287$	5.26255	+	12.8380i	0.310639	+	0.757800i
$288$		0			0
$289$	−4.41754	−	13.5958i	−0.259855	−	0.799752i
$290$		0			0
$291$	14.6562	−	10.6484i	0.859163	−	0.624218i
$292$		0			0
$293$	−1.83586	−	5.65019i	−0.107252	−	0.330088i	0.883000	−	0.469372i	$-0.155520\pi$
$293$	−1.83586	−	5.65019i	−0.107252	−	0.330088i	−0.990252	+	0.139284i	$0.955520\pi$
$294$		0			0
$295$	32.7966	+	23.8282i	1.90949	+	1.38733i
$296$		0			0
$297$	−13.0895	−	9.51010i	−0.759532	−	0.551832i
$298$		0			0
$299$	7.95033	−	5.77625i	0.459780	−	0.334049i
$300$		0			0
$301$	2.50539			0.144408
$302$		0			0
$303$	−4.66062	+	14.3439i	−0.267745	+	0.824036i
$304$		0			0
$305$	12.7557	+	39.2581i	0.730391	+	2.24791i
$306$		0			0
$307$	−2.21408	+	6.81424i	−0.126364	+	0.388909i	−0.994147	−	0.108034i	$-0.965544\pi$
$307$	−2.21408	+	6.81424i	−0.126364	+	0.388909i	0.867783	+	0.496943i	$0.165544\pi$
$308$		0			0
$309$	7.77499	−	23.9290i	0.442304	−	1.36127i
$310$		0			0
$311$	14.6342	+	10.6324i	0.829830	+	0.602907i	0.919511	−	0.393064i	$-0.128585\pi$
$311$	14.6342	+	10.6324i	0.829830	+	0.602907i	−0.0896814	+	0.995971i	$0.528585\pi$
$312$		0			0
$313$	7.24196	−	5.26159i	0.409340	−	0.297403i	−0.363995	−	0.931401i	$-0.618587\pi$
$313$	7.24196	−	5.26159i	0.409340	−	0.297403i	0.773334	+	0.633998i	$0.218587\pi$
$314$		0			0
$315$	1.98822	+	6.11911i	0.112024	+	0.344773i
$316$		0			0
$317$	17.7914	+	12.9262i	0.999263	+	0.726007i	0.961930	−	0.273296i	$-0.0881137\pi$
$317$	17.7914	+	12.9262i	0.999263	+	0.726007i	0.0373333	+	0.999303i	$0.488114\pi$
$318$		0			0
$319$	−31.6151			−1.77011
$320$		0			0
$321$	7.79181	−	23.9807i	0.434897	−	1.33847i
$322$		0			0
$323$	−4.17035	+	3.02993i	−0.232044	+	0.168590i
$324$		0			0
$325$	31.1858			1.72988
$326$		0			0
$327$	−5.50836			−0.304613
$328$		0			0
$329$	−15.5429			−0.856909
$330$		0			0
$331$	−8.29991			−0.456204			−0.228102	−	0.973637i	$-0.573252\pi$
$331$	−8.29991			−0.456204			−0.228102	+	0.973637i	$0.573252\pi$
$332$		0			0
$333$	4.50748	−	3.27487i	0.247008	−	0.179462i
$334$		0			0
$335$	1.21556	−	3.74110i	0.0664129	−	0.204398i
$336$		0			0
$337$	1.22525			0.0667434			0.0333717	−	0.999443i	$-0.489375\pi$
$337$	1.22525			0.0667434			0.0333717	+	0.999443i	$0.489375\pi$
$338$		0			0
$339$	−22.2581	−	16.1714i	−1.20889	−	0.878311i
$340$		0			0
$341$	−9.92069	−	30.5327i	−0.537235	−	1.65344i
$342$		0			0
$343$	16.3114	−	11.8509i	0.880734	−	0.639891i
$344$		0			0
$345$	−24.2016	−	17.5835i	−1.30297	−	0.946662i
$346$		0			0
$347$	7.00176	−	21.5492i	0.375874	−	1.15682i	−0.567013	−	0.823709i	$-0.691901\pi$
$347$	7.00176	−	21.5492i	0.375874	−	1.15682i	0.942887	−	0.333113i	$-0.108099\pi$
$348$		0			0
$349$	−2.52301	+	7.76504i	−0.135054	+	0.415653i	−0.995598	−	0.0937222i	$-0.970123\pi$
$349$	−2.52301	+	7.76504i	−0.135054	+	0.415653i	0.860545	+	0.509375i	$0.170123\pi$
$350$		0			0
$351$	3.54432	+	10.9083i	0.189182	+	0.582242i
$352$		0			0
$353$	9.24359	−	28.4488i	0.491986	−	1.51418i	−0.329614	−	0.944116i	$-0.606919\pi$
$353$	9.24359	−	28.4488i	0.491986	−	1.51418i	0.821601	−	0.570063i	$-0.193081\pi$
$354$		0			0
$355$	−9.65582			−0.512478
$356$		0			0
$357$	−5.56130	+	4.04052i	−0.294335	+	0.213847i
$358$		0			0
$359$	1.98330	+	1.44095i	0.104674	+	0.0760505i	0.638891	−	0.769297i	$-0.279393\pi$
$359$	1.98330	+	1.44095i	0.104674	+	0.0760505i	−0.534217	+	0.845348i	$0.679393\pi$
$360$		0			0
$361$	7.42269	+	5.39290i	0.390668	+	0.283837i
$362$		0			0
$363$	−1.51799	−	4.67189i	−0.0796737	−	0.245210i
$364$		0			0
$365$	−42.2078	+	30.6658i	−2.20926	+	1.60512i
$366$		0			0
$367$	10.9643	+	33.7446i	0.572331	+	1.76145i	0.645092	+	0.764105i	$0.276819\pi$
$367$	10.9643	+	33.7446i	0.572331	+	1.76145i	−0.0727603	+	0.997349i	$0.523181\pi$
$368$		0			0
$369$	−3.52230	+	2.98605i	−0.183364	+	0.155447i
$370$		0			0
$371$	3.61124	+	11.1142i	0.187486	+	0.577023i
$372$		0			0
$373$	18.0867	−	13.1408i	0.936494	−	0.680403i	−0.0110801	−	0.999939i	$-0.503527\pi$
$373$	18.0867	−	13.1408i	0.936494	−	0.680403i	0.947574	+	0.319536i	$0.103527\pi$
$374$		0			0
$375$	−17.0640	−	52.5175i	−0.881180	−	2.71199i
$376$		0			0
$377$	18.1316	+	13.1734i	0.933826	+	0.678464i
$378$		0			0
$379$	1.17160	+	0.851214i	0.0601808	+	0.0437239i	0.617469	−	0.786595i	$-0.288158\pi$
$379$	1.17160	+	0.851214i	0.0601808	+	0.0437239i	−0.557288	+	0.830319i	$0.688158\pi$
$380$		0			0
$381$	−30.0961	+	21.8661i	−1.54187	+	1.12024i
$382$		0			0
$383$	−13.7131			−0.700706			−0.350353	−	0.936618i	$-0.613938\pi$
$383$	−13.7131			−0.700706			−0.350353	+	0.936618i	$0.613938\pi$
$384$		0			0
$385$	10.1472	−	31.2298i	0.517148	−	1.59162i
$386$		0			0
$387$	0.257667	+	0.793017i	0.0130979	+	0.0403113i
$388$		0			0
$389$	6.24605	−	19.2234i	0.316687	−	0.974664i	−0.658367	−	0.752697i	$-0.728752\pi$
$389$	6.24605	−	19.2234i	0.316687	−	0.974664i	0.975054	−	0.221967i	$-0.0712476\pi$
$390$		0			0
$391$	1.91408	−	5.89092i	0.0967990	−	0.297917i
$392$		0			0
$393$	−8.74473	−	6.35342i	−0.441113	−	0.320487i
$394$		0			0
$395$	23.7957	−	17.2886i	1.19729	−	0.869884i
$396$		0			0
$397$	8.01026	+	24.6531i	0.402024	+	1.23730i	0.923355	+	0.383947i	$0.125436\pi$
$397$	8.01026	+	24.6531i	0.402024	+	1.23730i	−0.521331	+	0.853354i	$0.674564\pi$
$398$		0			0
$399$	−10.5998	−	7.70118i	−0.530652	−	0.385541i
$400$		0			0
$401$	−26.0765			−1.30220			−0.651099	−	0.758993i	$-0.725692\pi$
$401$	−26.0765			−1.30220			−0.651099	+	0.758993i	$0.725692\pi$
$402$		0			0
$403$	−7.03276	+	21.6446i	−0.350327	+	1.07819i
$404$		0			0
$405$	35.4532	−	25.7583i	1.76168	−	1.27994i
$406$		0			0
$407$	−28.4352			−1.40948
$408$		0			0
$409$	−32.7564			−1.61970			−0.809849	−	0.586638i	$-0.800451\pi$
$409$	−32.7564			−1.61970			−0.809849	+	0.586638i	$0.800451\pi$
$410$		0			0
$411$	31.9047			1.57374
$412$		0			0
$413$	−21.3347			−1.04981
$414$		0			0
$415$	5.14568	−	3.73856i	0.252592	−	0.183519i
$416$		0			0
$417$	−7.79680	+	23.9961i	−0.381811	+	1.17509i
$418$		0			0
$419$	18.0892			0.883715			0.441858	−	0.897085i	$-0.354320\pi$
$419$	18.0892			0.883715			0.441858	+	0.897085i	$0.354320\pi$
$420$		0			0
$421$	−0.979889	−	0.711931i	−0.0477569	−	0.0346974i	0.563651	−	0.826013i	$-0.309396\pi$
$421$	−0.979889	−	0.711931i	−0.0477569	−	0.0346974i	−0.611408	+	0.791316i	$0.709396\pi$
$422$		0			0
$423$	−1.59851	−	4.91972i	−0.0777224	−	0.239205i
$424$		0			0
$425$	15.9025	−	11.5538i	0.771382	−	0.560442i
$426$		0			0
$427$	−17.5750	−	12.7690i	−0.850514	−	0.617935i
$428$		0			0
$429$	−5.72445	+	17.6180i	−0.276379	+	0.850607i
$430$		0			0
$431$	−9.93461	+	30.5756i	−0.478533	+	1.47277i	0.362599	+	0.931945i	$0.381890\pi$
$431$	−9.93461	+	30.5756i	−0.478533	+	1.47277i	−0.841132	+	0.540829i	$0.818110\pi$
$432$		0			0
$433$	8.18005	+	25.1756i	0.393108	+	1.20986i	0.930425	+	0.366482i	$0.119438\pi$
$433$	8.18005	+	25.1756i	0.393108	+	1.20986i	−0.537317	+	0.843380i	$0.680562\pi$
$434$		0			0
$435$	21.0824	−	64.8849i	1.01082	−	3.11099i
$436$		0			0
$437$	11.8058			0.564750
$438$		0			0
$439$	11.4728	−	8.33549i	0.547567	−	0.397831i	−0.279320	−	0.960198i	$-0.590109\pi$
$439$	11.4728	−	8.33549i	0.547567	−	0.397831i	0.826888	+	0.562367i	$0.190109\pi$
$440$		0			0
$441$	1.34463	+	0.976934i	0.0640302	+	0.0465207i
$442$		0			0
$443$	11.2846	+	8.19871i	0.536146	+	0.389533i	0.822652	−	0.568546i	$-0.192494\pi$
$443$	11.2846	+	8.19871i	0.536146	+	0.389533i	−0.286506	+	0.958078i	$0.592494\pi$
$444$		0			0
$445$	7.39068	+	22.7462i	0.350352	+	1.07827i
$446$		0			0
$447$	−25.1833	+	18.2967i	−1.19113	+	0.865406i
$448$		0			0
$449$	−11.4239	−	35.1591i	−0.539126	−	1.65926i	−0.734560	−	0.678543i	$-0.762612\pi$
$449$	−11.4239	−	35.1591i	−0.539126	−	1.65926i	0.195434	−	0.980717i	$-0.437388\pi$
$450$		0			0
$451$	23.5011	−	1.76284i	1.10662	−	0.0830088i
$452$		0			0
$453$	11.2630	+	34.6641i	0.529183	+	1.62866i
$454$		0			0
$455$	−18.8324	+	13.6825i	−0.882874	+	0.641446i
$456$		0			0
$457$	−5.25210	−	16.1643i	−0.245683	−	0.756134i	−0.995523	−	0.0945152i	$-0.969870\pi$
$457$	−5.25210	−	16.1643i	−0.245683	−	0.756134i	0.749841	−	0.661618i	$-0.230130\pi$
$458$		0			0
$459$	5.84868	+	4.24931i	0.272993	+	0.198341i
$460$		0			0
$461$	0.780415	+	0.567005i	0.0363475	+	0.0264080i	0.605811	−	0.795609i	$-0.292849\pi$
$461$	0.780415	+	0.567005i	0.0363475	+	0.0264080i	−0.569463	+	0.822017i	$0.692849\pi$
$462$		0			0
$463$	5.81477	−	4.22468i	0.270235	−	0.196337i	−0.444412	−	0.895823i	$-0.646587\pi$
$463$	5.81477	−	4.22468i	0.270235	−	0.196337i	0.714647	+	0.699485i	$0.246587\pi$
$464$		0			0
$465$	69.2790			3.21274
$466$		0			0
$467$	−1.56656	+	4.82138i	−0.0724918	+	0.223107i	−0.980737	−	0.195331i	$-0.937422\pi$
$467$	−1.56656	+	4.82138i	−0.0724918	+	0.223107i	0.908246	+	0.418437i	$0.137422\pi$
$468$		0			0
$469$	0.639720	+	1.96886i	0.0295395	+	0.0909133i
$470$		0			0
$471$	−6.27095	+	19.3000i	−0.288950	+	0.889298i
$472$		0			0
$473$	1.31504	−	4.04728i	0.0604657	−	0.186094i
$474$		0			0
$475$	30.3099	+	22.0214i	1.39071	+	1.01041i
$476$		0			0
$477$	−3.14653	+	2.28609i	−0.144070	+	0.104673i
$478$		0			0
$479$	8.62600	+	26.5481i	0.394132	+	1.21301i	0.929636	+	0.368480i	$0.120122\pi$
$479$	8.62600	+	26.5481i	0.394132	+	1.21301i	−0.535504	+	0.844533i	$0.679878\pi$
$480$		0			0
$481$	16.3079	+	11.8484i	0.743577	+	0.540240i
$482$		0			0
$483$	15.7435			0.716353
$484$		0			0
$485$	11.9488	−	36.7746i	0.542567	−	1.66985i
$486$		0			0
$487$	−14.6417	+	10.6378i	−0.663479	+	0.482046i	−0.867836	−	0.496851i	$-0.834490\pi$
$487$	−14.6417	+	10.6378i	−0.663479	+	0.482046i	0.204357	+	0.978896i	$0.434490\pi$
$488$		0			0
$489$	25.8903			1.17080
$490$		0			0
$491$	6.94381			0.313370			0.156685	−	0.987649i	$-0.449919\pi$
$491$	6.94381			0.313370			0.156685	+	0.987649i	$0.449919\pi$
$492$		0			0
$493$	14.1263			0.636216
$494$		0			0
$495$	10.9286			0.491203
$496$		0			0
$497$	4.11113	−	2.98691i	0.184410	−	0.133981i
$498$		0			0
$499$	5.75662	−	17.7171i	0.257702	−	0.793125i	−0.735583	−	0.677434i	$-0.763092\pi$
$499$	5.75662	−	17.7171i	0.257702	−	0.793125i	0.993285	−	0.115691i	$-0.0369081\pi$
$500$		0			0
$501$	−46.8583			−2.09347
$502$		0			0
$503$	−23.2283	−	16.8764i	−1.03570	−	0.752480i	−0.0662588	−	0.997802i	$-0.521106\pi$
$503$	−23.2283	−	16.8764i	−1.03570	−	0.752480i	−0.969442	+	0.245322i	$0.921106\pi$
$504$		0			0
$505$	9.94767	+	30.6158i	0.442665	+	1.36238i
$506$		0			0
$507$	−9.66393	+	7.02126i	−0.429190	+	0.311825i
$508$		0			0
$509$	−21.3754	−	15.5301i	−0.947447	−	0.688361i	0.00275453	−	0.999996i	$-0.499123\pi$
$509$	−21.3754	−	15.5301i	−0.947447	−	0.688361i	−0.950202	+	0.311636i	$0.899123\pi$
$510$		0			0
$511$	8.48463	−	26.1130i	0.375338	−	1.15517i
$512$		0			0
$513$	−4.25797	+	13.1047i	−0.187994	+	0.578586i
$514$		0			0
$515$	−16.5950	−	51.0742i	−0.731264	−	2.25060i
$516$		0			0
$517$	−8.15825	+	25.1085i	−0.358799	+	1.10427i
$518$		0			0
$519$	−5.34040			−0.234418
$520$		0			0
$521$	2.05709	−	1.49456i	0.0901227	−	0.0654780i	−0.541811	−	0.840500i	$-0.682261\pi$
$521$	2.05709	−	1.49456i	0.0901227	−	0.0654780i	0.631934	+	0.775022i	$0.282261\pi$
$522$		0			0
$523$	−23.9846	−	17.4258i	−1.04877	−	0.761978i	−0.0767942	−	0.997047i	$-0.524468\pi$
$523$	−23.9846	−	17.4258i	−1.04877	−	0.761978i	−0.971979	+	0.235069i	$0.924468\pi$
$524$		0			0
$525$	40.4192	+	29.3663i	1.76404	+	1.28165i
$526$		0			0
$527$	4.43277	+	13.6427i	0.193094	+	0.594284i
$528$		0			0
$529$	7.13069	−	5.18075i	0.310030	−	0.225250i
$530$		0			0
$531$	−2.19417	−	6.75296i	−0.0952189	−	0.293054i
$532$		0			0
$533$	−14.2127	−	8.78142i	−0.615618	−	0.380365i
$534$		0			0
$535$	−16.6309	−	51.1847i	−0.719017	−	2.21291i
$536$		0			0
$537$	3.21180	−	2.33351i	0.138599	−	0.100698i
$538$		0			0
$539$	−2.62126	−	8.06740i	−0.112906	−	0.347487i
$540$		0			0
$541$	−9.56326	−	6.94812i	−0.411157	−	0.298723i	0.362913	−	0.931823i	$-0.381782\pi$
$541$	−9.56326	−	6.94812i	−0.411157	−	0.298723i	−0.774070	+	0.633100i	$0.781782\pi$
$542$		0			0
$543$	30.8627	+	22.4231i	1.32445	+	0.962266i
$544$		0			0
$545$	−9.51169	+	6.91065i	−0.407436	+	0.296020i
$546$		0			0
$547$	−9.30351			−0.397789			−0.198895	−	0.980021i	$-0.563735\pi$
$547$	−9.30351			−0.397789			−0.198895	+	0.980021i	$0.563735\pi$
$548$		0			0
$549$	2.23420	−	6.87615i	0.0953532	−	0.293467i
$550$		0			0
$551$	8.32014	+	25.6067i	0.354450	+	1.09088i
$552$		0			0
$553$	−4.78342	+	14.7218i	−0.203412	+	0.626037i
$554$		0			0
$555$	18.9619	−	58.3587i	0.804887	−	2.47719i
$556$		0			0
$557$	10.5013	+	7.62967i	0.444956	+	0.323280i	0.787601	−	0.616185i	$-0.211323\pi$
$557$	10.5013	+	7.62967i	0.444956	+	0.323280i	−0.342645	+	0.939465i	$0.611323\pi$
$558$		0			0
$559$	−2.44061	+	1.77321i	−0.103227	+	0.0749987i
$560$		0			0
$561$	3.60813	+	11.1047i	0.152336	+	0.468841i
$562$		0			0
$563$	−8.73756	−	6.34821i	−0.368244	−	0.267545i	0.388238	−	0.921559i	$-0.373084\pi$
$563$	−8.73756	−	6.34821i	−0.368244	−	0.267545i	−0.756482	+	0.654014i	$0.773084\pi$
$564$		0			0
$565$	−58.7229			−2.47049
$566$		0			0
$567$	−7.12681	+	21.9341i	−0.299298	+	0.921144i
$568$		0			0
$569$	−23.8433	+	17.3232i	−0.999562	+	0.726224i	−0.961994	−	0.273070i	$-0.911961\pi$
$569$	−23.8433	+	17.3232i	−0.999562	+	0.726224i	−0.0375678	+	0.999294i	$0.511961\pi$
$570$		0			0
$571$	16.7196			0.699692			0.349846	−	0.936807i	$-0.386234\pi$
$571$	16.7196			0.699692			0.349846	+	0.936807i	$0.386234\pi$
$572$		0			0
$573$	−10.2243			−0.427128
$574$		0			0
$575$	−45.0183			−1.87739
$576$		0			0
$577$	19.0760			0.794142			0.397071	−	0.917788i	$-0.370027\pi$
$577$	19.0760			0.794142			0.397071	+	0.917788i	$0.370027\pi$
$578$		0			0
$579$	1.34377	−	0.976308i	0.0558453	−	0.0405740i
$580$		0			0
$581$	−1.03439	+	3.18351i	−0.0429136	+	0.132074i
$582$		0			0
$583$	19.8498			0.822094
$584$		0			0
$585$	−6.26767	−	4.55373i	−0.259136	−	0.188273i
$586$		0			0
$587$	4.65087	+	14.3139i	0.191962	+	0.590798i	0.999999	+	0.00166599i	$0.000530302\pi$
$587$	4.65087	+	14.3139i	0.191962	+	0.590798i	−0.808037	+	0.589132i	$0.799470\pi$
$588$		0			0
$589$	−22.1193	+	16.0706i	−0.911408	+	0.662177i
$590$		0			0
$591$	−24.5191	−	17.8142i	−1.00858	−	0.732778i
$592$		0			0
$593$	−5.13293	+	15.7975i	−0.210784	+	0.648727i	0.788642	+	0.614853i	$0.210785\pi$
$593$	−5.13293	+	15.7975i	−0.210784	+	0.648727i	−0.999426	+	0.0338745i	$0.989215\pi$
$594$		0			0
$595$	−4.53397	+	13.9541i	−0.185875	+	0.572063i
$596$		0			0
$597$	7.14614	+	21.9935i	0.292472	+	0.900136i
$598$		0			0
$599$	−2.44414	+	7.52229i	−0.0998649	+	0.307353i	−0.988491	−	0.151280i	$-0.951661\pi$
$599$	−2.44414	+	7.52229i	−0.0998649	+	0.307353i	0.888626	+	0.458632i	$0.151661\pi$
$600$		0			0
$601$	−6.71507			−0.273913			−0.136957	−	0.990577i	$-0.543732\pi$
$601$	−6.71507			−0.273913			−0.136957	+	0.990577i	$0.543732\pi$
$602$		0			0
$603$	−0.557399	+	0.404974i	−0.0226991	+	0.0164918i
$604$		0			0
$605$	−8.48245	−	6.16286i	−0.344861	−	0.250556i
$606$		0			0
$607$	16.6172	+	12.0731i	0.674469	+	0.490031i	0.871518	−	0.490363i	$-0.163136\pi$
$607$	16.6172	+	12.0731i	0.674469	+	0.490031i	−0.197049	+	0.980394i	$0.563136\pi$
$608$		0			0
$609$	11.0952	+	34.1475i	0.449599	+	1.38372i
$610$		0			0
$611$	15.1411	−	11.0006i	0.612542	−	0.445038i
$612$		0			0
$613$	−2.21238	−	6.80901i	−0.0893573	−	0.275013i	0.896385	−	0.443277i	$-0.146184\pi$
$613$	−2.21238	−	6.80901i	−0.0893573	−	0.275013i	−0.985742	+	0.168263i	$0.946184\pi$
$614$		0			0
$615$	−12.0536	+	49.4076i	−0.486049	+	1.99231i
$616$		0			0
$617$	−9.83846	−	30.2797i	−0.396082	−	1.21901i	−0.928116	−	0.372291i	$-0.878572\pi$
$617$	−9.83846	−	30.2797i	−0.396082	−	1.21901i	0.532035	−	0.846723i	$-0.321428\pi$
$618$		0			0
$619$	−17.8285	+	12.9531i	−0.716587	+	0.520631i	−0.885292	−	0.465036i	$-0.846041\pi$
$619$	−17.8285	+	12.9531i	−0.716587	+	0.520631i	0.168705	+	0.985667i	$0.446041\pi$
$620$		0			0
$621$	−5.11640	−	15.7467i	−0.205314	−	0.631892i
$622$		0			0
$623$	−10.1830	−	7.39836i	−0.407972	−	0.296409i
$624$		0			0
$625$	−47.0039	−	34.1503i	−1.88016	−	1.36601i
$626$		0			0
$627$	−18.0044	+	13.0809i	−0.719026	+	0.522403i
$628$		0			0
$629$	12.7054			0.506599
$630$		0			0
$631$	−3.70319	+	11.3972i	−0.147422	+	0.453717i	−0.997314	−	0.0732386i	$-0.976667\pi$
$631$	−3.70319	+	11.3972i	−0.147422	+	0.453717i	0.849893	+	0.526955i	$0.176667\pi$
$632$		0			0
$633$	−11.9921	−	36.9080i	−0.476645	−	1.46696i
$634$		0			0
$635$	−24.5365	+	75.5157i	−0.973703	+	2.99675i
$636$		0			0
$637$	−1.85821	+	5.71897i	−0.0736248	+	0.226594i
$638$		0			0
$639$	1.36824	+	0.994086i	0.0541268	+	0.0393254i
$640$		0			0
$641$	4.35217	−	3.16204i	0.171900	−	0.124893i	−0.498508	−	0.866885i	$-0.666119\pi$
$641$	4.35217	−	3.16204i	0.171900	−	0.124893i	0.670409	+	0.741992i	$0.266119\pi$
$642$		0			0
$643$	−5.06426	−	15.5862i	−0.199715	−	0.614659i	−0.999889	−	0.0148914i	$-0.995260\pi$
$643$	−5.06426	−	15.5862i	−0.199715	−	0.614659i	0.800174	−	0.599767i	$-0.204740\pi$
$644$		0			0
$645$	7.42946	+	5.39782i	0.292535	+	0.212539i
$646$		0			0
$647$	−45.9801			−1.80767			−0.903833	−	0.427886i	$-0.859259\pi$
$647$	−45.9801			−1.80767			−0.903833	+	0.427886i	$0.859259\pi$
$648$		0			0
$649$	−11.1983	+	34.4647i	−0.439571	+	1.35286i
$650$		0			0
$651$	−29.4968	+	21.4307i	−1.15607	+	0.839934i
$652$		0			0
$653$	−25.2859			−0.989514			−0.494757	−	0.869031i	$-0.664743\pi$
$653$	−25.2859			−0.989514			−0.494757	+	0.869031i	$0.664743\pi$
$654$		0			0
$655$	−23.0710			−0.901458
$656$		0			0
$657$	9.13801			0.356508
$658$		0			0
$659$	31.9184			1.24336			0.621681	−	0.783270i	$-0.286450\pi$
$659$	31.9184			1.24336			0.621681	+	0.783270i	$0.286450\pi$
$660$		0			0
$661$	−19.6877	+	14.3040i	−0.765763	+	0.556360i	−0.900673	−	0.434498i	$-0.856926\pi$
$661$	−19.6877	+	14.3040i	−0.765763	+	0.556360i	0.134909	+	0.990858i	$0.456926\pi$
$662$		0			0
$663$	2.55780	−	7.87210i	0.0993368	−	0.305727i
$664$		0			0
$665$	−27.9651			−1.08444
$666$		0			0
$667$	−26.1739	−	19.0164i	−1.01346	−	0.736319i
$668$		0			0
$669$	−2.69693	−	8.30030i	−0.104269	−	0.320908i
$670$		0			0
$671$	−29.8523	+	21.6890i	−1.15243	+	0.837293i
$672$		0			0
$673$	−27.1273	−	19.7091i	−1.04568	−	0.759730i	−0.0742927	−	0.997236i	$-0.523670\pi$
$673$	−27.1273	−	19.7091i	−1.04568	−	0.759730i	−0.971386	+	0.237506i	$0.923670\pi$
$674$		0			0
$675$	16.2366	−	49.9710i	0.624946	−	1.92339i
$676$		0			0
$677$	−1.12510	+	3.46269i	−0.0432410	+	0.133082i	−0.970346	−	0.241719i	$-0.922289\pi$
$677$	−1.12510	+	3.46269i	−0.0432410	+	0.133082i	0.927105	+	0.374801i	$0.122289\pi$
$678$		0			0
$679$	6.28839	+	19.3537i	0.241326	+	0.742726i
$680$		0			0
$681$	5.23583	−	16.1142i	0.200637	−	0.617499i
$682$		0			0
$683$	−37.8589			−1.44863			−0.724314	−	0.689470i	$-0.757844\pi$
$683$	−37.8589			−1.44863			−0.724314	+	0.689470i	$0.757844\pi$
$684$		0			0
$685$	55.0922	−	40.0268i	2.10496	−	1.52935i
$686$		0			0
$687$	21.7491	+	15.8016i	0.829779	+	0.602870i
$688$		0			0
$689$	−11.3841	−	8.27101i	−0.433698	−	0.315100i
$690$		0			0
$691$	−0.917417	−	2.82352i	−0.0349002	−	0.107412i	0.932089	−	0.362230i	$-0.117984\pi$
$691$	−0.917417	−	2.82352i	−0.0349002	−	0.107412i	−0.966989	+	0.254818i	$0.917984\pi$
$692$		0			0
$693$	−4.65304	+	3.38063i	−0.176754	+	0.128419i
$694$		0			0
$695$	16.6416	+	51.2175i	0.631251	+	1.94279i
$696$		0			0
$697$	−10.5008	+	0.787672i	−0.397745	+	0.0298352i
$698$		0			0
$699$	8.81384	+	27.1262i	0.333370	+	1.02601i
$700$		0			0
$701$	18.3718	−	13.3479i	0.693893	−	0.504143i	−0.184045	−	0.982918i	$-0.558919\pi$
$701$	18.3718	−	13.3479i	0.693893	−	0.504143i	0.877938	+	0.478775i	$0.158919\pi$
$702$		0			0
$703$	7.48328	+	23.0312i	0.282237	+	0.868637i
$704$		0			0
$705$	−46.0908	−	33.4870i	−1.73588	−	1.26119i
$706$		0			0
$707$	−13.7060	−	9.95801i	−0.515468	−	0.374509i
$708$		0			0
$709$	32.7329	−	23.7818i	1.22931	−	0.893145i	0.232470	−	0.972604i	$-0.425319\pi$
$709$	32.7329	−	23.7818i	1.22931	−	0.893145i	0.996838	+	0.0794590i	$0.0253193\pi$
$710$		0			0
$711$	−5.15178			−0.193207
$712$		0			0
$713$	10.1521	−	31.2451i	0.380201	−	1.17014i
$714$		0			0
$715$	12.2183	+	37.6041i	0.456939	+	1.40631i
$716$		0			0
$717$	−10.8502	+	33.3935i	−0.405209	+	1.24710i
$718$		0			0
$719$	−1.37649	+	4.23640i	−0.0513344	+	0.157991i	−0.973437	−	0.228954i	$-0.926470\pi$
$719$	−1.37649	+	4.23640i	−0.0513344	+	0.157991i	0.922103	+	0.386945i	$0.126470\pi$
$720$		0			0
$721$	22.8648	+	16.6123i	0.851531	+	0.618673i
$722$		0			0
$723$	10.5783	−	7.68558i	0.393411	−	0.285830i
$724$		0			0
$725$	−31.7265	−	97.6442i	−1.17829	−	3.62641i
$726$		0			0
$727$	−32.1431	−	23.3533i	−1.19212	−	0.866128i	−0.198635	−	0.980073i	$-0.563651\pi$
$727$	−32.1431	−	23.3533i	−1.19212	−	0.866128i	−0.993487	+	0.113946i	$0.963651\pi$
$728$		0			0
$729$	17.7641			0.657931
$730$		0			0
$731$	−0.587588	+	1.80841i	−0.0217327	+	0.0668864i
$732$		0			0
$733$	2.59816	−	1.88768i	0.0959653	−	0.0697229i	−0.538768	−	0.842454i	$-0.681110\pi$
$733$	2.59816	−	1.88768i	0.0959653	−	0.0697229i	0.634733	+	0.772731i	$0.281110\pi$
$734$		0			0
$735$	18.3050			0.675190
$736$		0			0
$737$	3.51633			0.129526
$738$		0			0
$739$	7.53633			0.277228			0.138614	−	0.990346i	$-0.455735\pi$
$739$	7.53633			0.277228			0.138614	+	0.990346i	$0.455735\pi$
$740$		0			0
$741$	15.7763			0.579556
$742$		0			0
$743$	−15.7651	+	11.4540i	−0.578366	+	0.420207i	−0.838134	−	0.545464i	$-0.816354\pi$
$743$	−15.7651	+	11.4540i	−0.578366	+	0.420207i	0.259769	+	0.965671i	$0.416354\pi$
$744$		0			0
$745$	−20.5312	+	63.1887i	−0.752207	+	2.31505i
$746$		0			0
$747$	−1.11404			−0.0407607
$748$		0			0
$749$	22.9143	+	16.6482i	0.837270	+	0.608312i
$750$		0			0
$751$	3.22857	+	9.93653i	0.117812	+	0.362589i	0.992523	−	0.122056i	$-0.0389487\pi$
$751$	3.22857	+	9.93653i	0.117812	+	0.362589i	−0.874711	+	0.484645i	$0.838949\pi$
$752$		0			0
$753$	−25.1946	+	18.3050i	−0.918144	+	0.667071i
$754$		0			0
$755$	62.9373	+	45.7266i	2.29052	+	1.66416i
$756$		0			0
$757$	0.114252	−	0.351632i	0.00415256	−	0.0127803i	−0.948959	−	0.315400i	$-0.897861\pi$
$757$	0.114252	−	0.351632i	0.00415256	−	0.0127803i	0.953111	+	0.302620i	$0.0978613\pi$
$758$		0			0
$759$	8.26352	−	25.4325i	0.299947	−	0.923141i
$760$		0			0
$761$	5.04168	+	15.5167i	0.182761	+	0.562480i	0.999903	−	0.0139568i	$-0.00444274\pi$
$761$	5.04168	+	15.5167i	0.182761	+	0.562480i	−0.817142	+	0.576437i	$0.804443\pi$
$762$		0			0
$763$	1.91204	−	5.88466i	0.0692205	−	0.213039i
$764$		0			0
$765$	−4.88312			−0.176550
$766$		0			0
$767$	20.7831	−	15.0998i	0.750434	−	0.545222i
$768$		0			0
$769$	10.4368	+	7.58276i	0.376359	+	0.273441i	0.759843	−	0.650107i	$-0.225276\pi$
$769$	10.4368	+	7.58276i	0.376359	+	0.273441i	−0.383484	+	0.923548i	$0.625276\pi$
$770$		0			0
$771$	−30.1796	−	21.9268i	−1.08689	−	0.789674i
$772$		0			0
$773$	11.5325	+	35.4934i	0.414795	+	1.27661i	0.912434	+	0.409224i	$0.134200\pi$
$773$	11.5325	+	35.4934i	0.414795	+	1.27661i	−0.497639	+	0.867384i	$0.665800\pi$
$774$		0			0
$775$	84.3456	−	61.2807i	3.02978	−	2.20127i
$776$		0			0
$777$	9.97921	+	30.7129i	0.358002	+	1.10182i
$778$		0			0
$779$	−7.61258	−	18.5708i	−0.272749	−	0.665369i
$780$		0			0
$781$	−2.66728	−	8.20904i	−0.0954427	−	0.293742i
$782$		0			0
$783$	30.5486	−	22.1948i	1.09172	−	0.793179i
$784$		0			0
$785$	13.3848	+	41.1941i	0.477723	+	1.47028i
$786$		0			0
$787$	14.4081	+	10.4681i	0.513594	+	0.373148i	0.814185	−	0.580605i	$-0.197184\pi$
$787$	14.4081	+	10.4681i	0.513594	+	0.373148i	−0.300591	+	0.953753i	$0.597184\pi$
$788$		0			0
$789$	−29.5421	−	21.4636i	−1.05173	−	0.764123i
$790$		0			0
$791$	25.0023	−	18.1652i	0.888979	−	0.645881i
$792$		0			0
$793$	26.1580			0.928897
$794$		0			0
$795$	−13.2367	+	40.7384i	−0.469458	+	1.44484i
$796$		0			0
$797$	−0.364540	−	1.12194i	−0.0129127	−	0.0397411i	0.944393	−	0.328820i	$-0.106651\pi$
$797$	−0.364540	−	1.12194i	−0.0129127	−	0.0397411i	−0.957305	+	0.289079i	$0.906651\pi$
$798$		0			0
$799$	3.64528	−	11.2190i	0.128961	−	0.396900i
$800$		0			0
$801$	1.29449	−	3.98404i	0.0457387	−	0.140769i
$802$		0			0
$803$	−37.7303	−	27.4126i	−1.33147	−	0.967371i
$804$		0			0
$805$	27.1854	−	19.7514i	0.958161	−	0.696144i
$806$		0			0
$807$	7.18961	+	22.1273i	0.253086	+	0.778919i
$808$		0			0
$809$	−19.6139	−	14.2504i	−0.689589	−	0.501016i	0.186936	−	0.982372i	$-0.440144\pi$
$809$	−19.6139	−	14.2504i	−0.689589	−	0.501016i	−0.876525	+	0.481356i	$0.840144\pi$
$810$		0			0
$811$	26.3088			0.923826			0.461913	−	0.886925i	$-0.347163\pi$
$811$	26.3088			0.923826			0.461913	+	0.886925i	$0.347163\pi$
$812$		0			0
$813$	−9.13280	+	28.1079i	−0.320301	+	0.985786i
$814$		0			0
$815$	44.7067	−	32.4814i	1.56601	−	1.13777i
$816$		0			0
$817$	−3.62419			−0.126794
$818$		0			0
$819$	4.07721			0.142469
$820$		0			0
$821$	7.08991			0.247440			0.123720	−	0.992317i	$-0.460518\pi$
$821$	7.08991			0.247440			0.123720	+	0.992317i	$0.460518\pi$
$822$		0			0
$823$	−31.1395			−1.08545			−0.542727	−	0.839909i	$-0.682608\pi$
$823$	−31.1395			−1.08545			−0.542727	+	0.839909i	$0.682608\pi$
$824$		0			0
$825$	68.6547	−	49.8805i	2.39025	−	1.73662i
$826$		0			0
$827$	5.25425	−	16.1709i	0.182708	−	0.562318i	−0.817193	−	0.576364i	$-0.804471\pi$
$827$	5.25425	−	16.1709i	0.182708	−	0.562318i	0.999901	+	0.0140462i	$0.00447118\pi$
$828$		0			0
$829$	45.9767			1.59684			0.798418	−	0.602104i	$-0.205671\pi$
$829$	45.9767			1.59684			0.798418	+	0.602104i	$0.205671\pi$
$830$		0			0
$831$	−5.54573	−	4.02921i	−0.192379	−	0.139772i
$832$		0			0
$833$	1.17123	+	3.60468i	0.0405808	+	0.124895i
$834$		0			0
$835$	−80.9137	+	58.7872i	−2.80013	+	2.03442i
$836$		0			0
$837$	31.0210	+	22.5381i	1.07224	+	0.779030i
$838$		0			0
$839$	1.71363	−	5.27403i	0.0591612	−	0.182080i	−0.917108	−	0.398638i	$-0.869483\pi$
$839$	1.71363	−	5.27403i	0.0591612	−	0.182080i	0.976270	+	0.216558i	$0.0694831\pi$
$840$		0			0
$841$	13.8390	−	42.5920i	0.477206	−	1.46869i
$842$		0			0
$843$	−8.68670	−	26.7349i	−0.299186	−	0.920799i
$844$		0			0
$845$	−7.87873	+	24.2482i	−0.271037	+	0.834165i
$846$		0			0
$847$	5.51796			0.189599
$848$		0			0
$849$	−13.1171	+	9.53012i	−0.450177	+	0.327073i
$850$		0			0
$851$	−23.5413	−	17.1037i	−0.806984	−	0.586308i
$852$		0			0
$853$	32.0457	+	23.2826i	1.09722	+	0.797180i	0.980604	−	0.195997i	$-0.0627943\pi$
$853$	32.0457	+	23.2826i	1.09722	+	0.797180i	0.116619	+	0.993177i	$0.462794\pi$
$854$		0			0
$855$	−2.87607	−	8.85164i	−0.0983596	−	0.302720i
$856$		0			0
$857$	−34.5438	+	25.0975i	−1.17999	+	0.857315i	−0.992171	−	0.124888i	$-0.960143\pi$
$857$	−34.5438	+	25.0975i	−1.17999	+	0.857315i	−0.187822	+	0.982203i	$0.560143\pi$
$858$		0			0
$859$	−12.5059	−	38.4893i	−0.426697	−	1.31324i	−0.901360	−	0.433070i	$-0.857430\pi$
$859$	−12.5059	−	38.4893i	−0.426697	−	1.31324i	0.474664	−	0.880167i	$-0.342570\pi$
$860$		0			0
$861$	−10.1516	−	24.7648i	−0.345967	−	0.843983i
$862$		0			0
$863$	2.61554	+	8.04982i	0.0890341	+	0.274019i	0.985653	−	0.168784i	$-0.0539841\pi$
$863$	2.61554	+	8.04982i	0.0890341	+	0.274019i	−0.896619	+	0.442803i	$0.853984\pi$
$864$		0			0
$865$	−9.22167	+	6.69993i	−0.313546	+	0.227805i
$866$		0			0
$867$	8.52157	+	26.2267i	0.289408	+	0.890705i
$868$		0			0
$869$	21.2714	+	15.4546i	0.721582	+	0.524260i
$870$		0			0
$871$	−2.01665	−	1.46518i	−0.0683317	−	0.0496459i
$872$		0			0
$873$	−5.47918	+	3.98086i	−0.185442	+	0.134732i
$874$		0			0
$875$	62.0284			2.09694
$876$		0			0
$877$	−1.60800	+	4.94890i	−0.0542982	+	0.167113i	−0.974528	−	0.224266i	$-0.928002\pi$
$877$	−1.60800	+	4.94890i	−0.0542982	+	0.167113i	0.920230	+	0.391378i	$0.128002\pi$
$878$		0			0
$879$	3.54143	+	10.8994i	0.119449	+	0.367628i
$880$		0			0
$881$	1.65456	−	5.09220i	0.0557434	−	0.171560i	−0.919308	−	0.393538i	$-0.871251\pi$
$881$	1.65456	−	5.09220i	0.0557434	−	0.171560i	0.975052	+	0.221977i	$0.0712511\pi$
$882$		0			0
$883$	1.79434	−	5.52241i	0.0603843	−	0.185844i	−0.916314	−	0.400460i	$-0.868850\pi$
$883$	1.79434	−	5.52241i	0.0603843	−	0.185844i	0.976698	+	0.214617i	$0.0688502\pi$
$884$		0			0
$885$	−63.2658	−	45.9653i	−2.12666	−	1.54511i
$886$		0			0
$887$	−10.9690	+	7.96947i	−0.368304	+	0.267589i	−0.756507	−	0.653985i	$-0.773096\pi$
$887$	−10.9690	+	7.96947i	−0.368304	+	0.267589i	0.388203	+	0.921574i	$0.373096\pi$
$888$		0			0
$889$	−12.9130	−	39.7422i	−0.433089	−	1.33291i
$890$		0			0
$891$	31.6922	+	23.0257i	1.06173	+	0.771391i
$892$		0			0
$893$	22.4837			0.752389
$894$		0			0
$895$	2.61849	−	8.05888i	0.0875265	−	0.269379i
$896$		0			0
$897$	−15.3364	+	11.1426i	−0.512069	+	0.372040i
$898$		0			0
$899$	74.9249			2.49889
$900$		0			0
$901$	−8.86929			−0.295479
$902$		0			0
$903$	−4.83297			−0.160831
$904$		0			0
$905$	81.4244			2.70664
$906$		0			0
$907$	−16.4236	+	11.9325i	−0.545338	+	0.396211i	−0.826064	−	0.563577i	$-0.809425\pi$
$907$	−16.4236	+	11.9325i	−0.545338	+	0.396211i	0.280726	+	0.959788i	$0.409425\pi$
$908$		0			0
$909$	1.74236	−	5.36243i	0.0577904	−	0.177860i
$910$		0			0
$911$	37.5683			1.24469			0.622347	−	0.782741i	$-0.286179\pi$
$911$	37.5683			1.24469			0.622347	+	0.782741i	$0.286179\pi$
$912$		0			0
$913$	4.59981	+	3.34196i	0.152231	+	0.110603i
$914$		0			0
$915$	−24.6062	−	75.7301i	−0.813456	−	2.50356i
$916$		0			0
$917$	9.82288	−	7.13674i	0.324380	−	0.235676i
$918$		0			0
$919$	−48.2604	−	35.0632i	−1.59196	−	1.15663i	−0.901072	−	0.433671i	$-0.857218\pi$
$919$	−48.2604	−	35.0632i	−1.59196	−	1.15663i	−0.690892	−	0.722958i	$-0.742782\pi$
$920$		0			0
$921$	4.27103	−	13.1449i	0.140735	−	0.433138i
$922$		0			0
$923$	−1.89083	+	5.81938i	−0.0622374	+	0.191547i
$924$		0			0
$925$	−28.5354	−	87.8230i	−0.938239	−	2.88760i
$926$		0			0
$927$	−2.90666	+	8.94577i	−0.0954672	+	0.293818i
$928$		0			0
$929$	−8.08575			−0.265285			−0.132642	−	0.991164i	$-0.542346\pi$
$929$	−8.08575			−0.265285			−0.132642	+	0.991164i	$0.542346\pi$
$930$		0			0
$931$	−5.84438	+	4.24619i	−0.191542	+	0.139163i
$932$		0			0
$933$	−28.2298	−	20.5102i	−0.924204	−	0.671473i
$934$		0			0
$935$	20.1621	+	14.6486i	0.659371	+	0.479061i
$936$		0			0
$937$	0.392592	+	1.20827i	0.0128254	+	0.0394726i	0.957264	−	0.289214i	$-0.0933940\pi$
$937$	0.392592	+	1.20827i	0.0128254	+	0.0394726i	−0.944439	+	0.328687i	$0.893394\pi$
$938$		0			0
$939$	−13.9700	+	10.1498i	−0.455893	+	0.331225i
$940$		0			0
$941$	12.1076	+	37.2632i	0.394695	+	1.21475i	0.929199	+	0.369580i	$0.120499\pi$
$941$	12.1076	+	37.2632i	0.394695	+	1.21475i	−0.534504	+	0.845166i	$0.679501\pi$
$942$		0			0
$943$	20.5167	+	12.6764i	0.668115	+	0.412801i
$944$		0			0
$945$	12.1195	+	37.2999i	0.394247	+	1.21337i
$946$		0			0
$947$	35.6744	−	25.9190i	1.15926	−	0.842253i	0.169578	−	0.985517i	$-0.445760\pi$
$947$	35.6744	−	25.9190i	1.15926	−	0.842253i	0.989685	+	0.143264i	$0.0457596\pi$
$948$		0			0
$949$	10.2164	+	31.4429i	0.331639	+	1.02068i
$950$		0			0
$951$	−34.3201	−	24.9350i	−1.11291	−	0.808574i
$952$		0			0
$953$	−7.21774	−	5.24399i	−0.233806	−	0.169870i	0.464714	−	0.885461i	$-0.346157\pi$
$953$	−7.21774	−	5.24399i	−0.233806	−	0.169870i	−0.698519	+	0.715591i	$0.746157\pi$
$954$		0			0
$955$	−17.6551	+	12.8272i	−0.571306	+	0.415078i
$956$		0			0
$957$	60.9865			1.97141
$958$		0			0
$959$	−11.0746	+	34.0842i	−0.357619	+	1.10064i
$960$		0			0
$961$	13.9316	+	42.8770i	0.449406	+	1.38313i
$962$		0			0
$963$	−2.91295	+	8.96512i	−0.0938684	+	0.288897i
$964$		0			0
$965$	1.09554	−	3.37173i	0.0352667	−	0.108540i
$966$		0			0
$967$	−26.4167	−	19.1929i	−0.849504	−	0.617200i	0.0755055	−	0.997145i	$-0.475943\pi$
$967$	−26.4167	−	19.1929i	−0.849504	−	0.617200i	−0.925009	+	0.379945i	$0.875943\pi$
$968$		0			0
$969$	8.04473	−	5.84484i	0.258434	−	0.187763i
$970$		0			0
$971$	−12.4315	−	38.2603i	−0.398947	−	1.22783i	−0.925845	−	0.377903i	$-0.876645\pi$
$971$	−12.4315	−	38.2603i	−0.398947	−	1.22783i	0.526899	−	0.849928i	$-0.323355\pi$
$972$		0			0
$973$	−22.9290	−	16.6589i	−0.735069	−	0.534059i
$974$		0			0
$975$	−60.1584			−1.92661
$976$		0			0
$977$	4.40917	−	13.5700i	0.141062	−	0.434144i	−0.855422	−	0.517932i	$-0.826702\pi$
$977$	4.40917	−	13.5700i	0.141062	−	0.434144i	0.996484	+	0.0837883i	$0.0267020\pi$
$978$		0			0
$979$	−17.2964	+	12.5666i	−0.552796	+	0.401630i
$980$		0			0
$981$	2.05928			0.0657479
$982$		0			0
$983$	30.9900			0.988429			0.494214	−	0.869340i	$-0.335456\pi$
$983$	30.9900			0.988429			0.494214	+	0.869340i	$0.335456\pi$
$984$		0			0
$985$	−64.6882			−2.06114
$986$		0			0
$987$	29.9828			0.954363
$988$		0			0
$989$	3.52315	−	2.55971i	0.112029	−	0.0813942i
$990$		0			0
$991$	13.1632	−	40.5121i	0.418142	−	1.28691i	−0.491268	−	0.871008i	$-0.663466\pi$
$991$	13.1632	−	40.5121i	0.418142	−	1.28691i	0.909410	−	0.415900i	$-0.136534\pi$
$992$		0			0
$993$	16.0108			0.508087
$994$		0			0
$995$	39.9323	+	29.0125i	1.26594	+	0.919758i
$996$		0			0
$997$	1.30278	+	4.00955i	0.0412595	+	0.126984i	0.969565	−	0.244836i	$-0.0787340\pi$
$997$	1.30278	+	4.00955i	0.0412595	+	0.126984i	−0.928305	+	0.371819i	$0.878734\pi$
$998$		0			0
$999$	27.4760	−	19.9625i	0.869301	−	0.631584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.u.h.305.2		20
4.3	odd	2		328.2.m.c.305.4	yes	20
41.16	even	5	inner	656.2.u.h.385.2		20
164.139	odd	10		328.2.m.c.57.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
328.2.m.c.57.4	✓	20	164.139	odd	10
328.2.m.c.305.4	yes	20	4.3	odd	2
656.2.u.h.305.2		20	1.1	even	1	trivial
656.2.u.h.385.2		20	41.16	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)

\(f(q)\)	\(=\)	\(q-1.92903 q^{3} +(-3.33100 + 2.42011i) q^{5} +(0.669598 - 2.06081i) q^{7} +0.721162 q^{9} +O(q^{10})\)	\(q-1.92903 q^{3} +(-3.33100 + 2.42011i) q^{5} +(0.669598 - 2.06081i) q^{7} +0.721162 q^{9} +(-2.97764 - 2.16338i) q^{11} +(0.806270 + 2.48144i) q^{13} +(6.42560 - 4.66847i) q^{15} +(1.33047 + 0.966643i) q^{17} +(-0.968612 + 2.98108i) q^{19} +(-1.29168 + 3.97537i) q^{21} +(-1.16389 - 3.58209i) q^{23} +(3.69353 - 11.3675i) q^{25} +4.39595 q^{27} +(6.94926 - 5.04893i) q^{29} +(7.05672 + 5.12701i) q^{31} +(5.74395 + 4.17323i) q^{33} +(2.75697 + 8.48507i) q^{35} +(6.25029 - 4.54110i) q^{37} +(-1.55532 - 4.78678i) q^{39} +(-4.88420 + 4.14060i) q^{41} +(0.357294 + 1.09964i) q^{43} +(-2.40219 + 1.74530i) q^{45} +(-2.21658 - 6.82193i) q^{47} +(1.86454 + 1.35467i) q^{49} +(-2.56652 - 1.86468i) q^{51} +(-4.36314 + 3.17001i) q^{53} +15.1541 q^{55} +(1.86848 - 5.75060i) q^{57} +(-3.04255 - 9.36399i) q^{59} +(3.09805 - 9.53482i) q^{61} +(0.482889 - 1.48618i) q^{63} +(-8.69106 - 6.31442i) q^{65} +(-0.772918 + 0.561558i) q^{67} +(2.24518 + 6.90996i) q^{69} +(1.89727 + 1.37845i) q^{71} +12.6712 q^{73} +(-7.12493 + 21.9283i) q^{75} +(-6.45213 + 4.68775i) q^{77} -7.14371 q^{79} -10.6434 q^{81} -1.54479 q^{83} -6.77118 q^{85} +(-13.4053 + 9.73955i) q^{87} +(1.79501 - 5.52448i) q^{89} +5.65366 q^{91} +(-13.6126 - 9.89016i) q^{93} +(-3.98811 - 12.2741i) q^{95} +(-7.59771 + 5.52006i) q^{97} +(-2.14736 - 1.56015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} + 2 q^{5} + 10 q^{9}+O(q^{10}) \) 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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