LMFDB - Embedded newform 961.2.g.a.816.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(235,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([26]))

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

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

chi := DirichletCharacter("961.235");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.g (of order $15$, degree $8$, 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:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			816.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	961.816
Dual form			961.2.g.a.338.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30902 - 0.951057i) q^{2} +(0.338261 + 3.21834i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.230909 - 0.0490813i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-7.30885 + 1.55354i) q^{9} +O(q^{10})$	\(q+(-1.30902 - 0.951057i) q^{2} +(0.338261 + 3.21834i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.230909 - 0.0490813i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-7.30885 + 1.55354i) q^{9} +(-0.169131 + 1.60917i) q^{10} +(1.33826 - 1.48629i) q^{11} +(-1.82709 + 0.813473i) q^{12} +(-2.95630 - 1.31623i) q^{13} +(0.255585 + 0.283856i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.511170 + 0.567712i) q^{17} +(11.0449 + 4.91752i) q^{18} +(-2.04275 + 0.909491i) q^{19} +(0.413545 - 0.459289i) q^{20} +(0.0798526 - 0.759747i) q^{21} +(-3.16535 + 0.672816i) q^{22} +(1.76393 - 5.42882i) q^{23} +(-7.07794 - 1.50446i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} +(-4.47214 - 13.7638i) q^{27} +(-0.0152505 - 0.145099i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(-0.129204 - 1.22930i) q^{34} +(0.0729490 + 0.224514i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(3.53897 + 0.752232i) q^{38} +(3.23607 - 9.95959i) q^{39} +(2.18720 - 0.464905i) q^{40} +(-0.731699 + 6.96165i) q^{41} +(-0.827091 + 0.918578i) q^{42} +(1.12920 - 0.502754i) q^{43} +(1.12920 + 0.502754i) q^{44} +(4.99983 + 5.55288i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(10.5108 + 11.6735i) q^{48} +(-6.34391 - 2.82449i) q^{49} +(-5.91259 + 2.63245i) q^{50} +(-1.65418 + 1.83716i) q^{51} +(0.209057 - 1.98904i) q^{52} +(10.2433 - 2.17728i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(-1.95630 - 0.415823i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +(1.38197 + 4.25325i) q^{58} +(-0.233733 - 2.22382i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(0.338261 + 3.21834i) q^{65} +(-3.23607 - 9.95959i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(18.0685 + 3.84057i) q^{69} +(0.118034 - 0.363271i) q^{70} +(8.97973 - 1.90870i) q^{71} +(1.74648 - 16.6167i) q^{72} +(5.66897 - 6.29602i) q^{73} +(-2.95630 + 1.31623i) q^{74} +(11.8252 + 5.26491i) q^{75} +(-0.924716 - 1.02700i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(-7.83432 - 8.70089i) q^{79} +(-4.43444 - 1.97434i) q^{80} +(22.3055 - 9.93105i) q^{81} +(7.57873 - 8.41704i) q^{82} +(1.56210 - 14.8624i) q^{83} +(0.461819 - 0.0981626i) q^{84} +(0.236068 - 0.726543i) q^{85} +(-1.95630 - 0.415823i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +(3.61803 + 11.1352i) q^{89} +(-1.26377 - 12.0239i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(-1.14399 - 10.8843i) q^{96} +(-4.92705 - 15.1639i) q^{97} +(5.61803 + 9.73072i) q^{98} +(-7.47214 + 12.9421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 32 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{30} - 36 q^{32} + 24 q^{33} + 4 q^{34} + 14 q^{35} - 14 q^{36} + 8 q^{37} + 8 q^{39} + 5 q^{40} + 7 q^{41} + 6 q^{42} + 4 q^{43} + 4 q^{44} - 7 q^{45} - 24 q^{46} - 16 q^{47} - 6 q^{48} - 18 q^{49} - 12 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 40 q^{54} + 2 q^{55} + 20 q^{56} - 20 q^{57} + 20 q^{58} + 5 q^{59} + 4 q^{60} - 24 q^{61} + 32 q^{63} - 14 q^{64} - 6 q^{65} - 8 q^{66} - 32 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 27 q^{71} - 25 q^{72} - 6 q^{73} - 6 q^{74} + 24 q^{75} - 5 q^{76} - 12 q^{77} - 56 q^{78} + 10 q^{79} - 9 q^{80} + 41 q^{81} - 14 q^{82} - 26 q^{83} + 14 q^{84} - 16 q^{85} + 2 q^{86} + 20 q^{89} + 19 q^{90} - 4 q^{91} + 64 q^{92} + 32 q^{94} + 10 q^{95} + 22 q^{96} - 26 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

Coefficient data

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

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

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

$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	0.0193004	−	0.999814i	$-0.493856\pi$
$2$	−1.30902	−	0.951057i	−0.925615	−	0.672499i	−0.944915	+	0.327315i	$0.893856\pi$
$3$	0.338261	+	3.21834i	0.195295	+	1.85811i	0.452515	+	0.891757i	$0.350527\pi$
$3$	0.338261	+	3.21834i	0.195295	+	1.85811i	−0.257220	+	0.966353i	$0.582806\pi$
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	2.61803	−	4.53457i	1.06881	−	1.85123i
$7$	−0.230909	−	0.0490813i	−0.0872755	−	0.0185510i	0.164067	−	0.986449i	$-0.447539\pi$
$7$	−0.230909	−	0.0490813i	−0.0872755	−	0.0185510i	−0.251342	+	0.967898i	$0.580872\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	−7.30885	+	1.55354i	−2.43628	+	0.517848i
$10$	−0.169131	+	1.60917i	−0.0534838	+	0.508864i
$11$	1.33826	−	1.48629i	0.403501	−	0.448133i	−0.506810	−	0.862058i	$-0.669176\pi$
$11$	1.33826	−	1.48629i	0.403501	−	0.448133i	0.910311	+	0.413924i	$0.135842\pi$
$12$	−1.82709	+	0.813473i	−0.527436	+	0.234830i
$13$	−2.95630	−	1.31623i	−0.819929	−	0.365056i	−0.0464836	−	0.998919i	$-0.514802\pi$
$13$	−2.95630	−	1.31623i	−0.819929	−	0.365056i	−0.773445	+	0.633863i	$0.781468\pi$
$14$	0.255585	+	0.283856i	0.0683080	+	0.0758637i
$15$	2.61803	−	1.90211i	0.675973	−	0.491123i
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	0.511170	+	0.567712i	0.123977	+	0.137690i	0.801938	−	0.597408i	$-0.203803\pi$
$17$	0.511170	+	0.567712i	0.123977	+	0.137690i	−0.677961	+	0.735098i	$0.737136\pi$
$18$	11.0449	+	4.91752i	2.60331	+	1.15907i
$19$	−2.04275	+	0.909491i	−0.468639	+	0.208651i	−0.627449	−	0.778658i	$-0.715901\pi$
$19$	−2.04275	+	0.909491i	−0.468639	+	0.208651i	0.158810	+	0.987309i	$0.449234\pi$
$20$	0.413545	−	0.459289i	0.0924716	−	0.102700i
$21$	0.0798526	−	0.759747i	0.0174253	−	0.165790i
$22$	−3.16535	+	0.672816i	−0.674855	+	0.143445i
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	−0.580400	−	0.814331i	$-0.697104\pi$
$23$	1.76393	−	5.42882i	0.367805	−	1.13199i	0.948206	−	0.317657i	$-0.102896\pi$
$24$	−7.07794	−	1.50446i	−1.44478	−	0.307097i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	2.61803	+	4.53457i	0.513439	+	0.889302i
$27$	−4.47214	−	13.7638i	−0.860663	−	2.64885i
$28$	−0.0152505	−	0.145099i	−0.00288207	−	0.0274211i
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	0.360487	−	0.932764i	$-0.382610\pi$
$29$	−2.23607	−	1.62460i	−0.415227	−	0.301680i	−0.775715	+	0.631084i	$0.782610\pi$
$30$	−5.23607			−0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	5.23607	+	3.80423i	0.911482	+	0.662231i
$34$	−0.129204	−	1.22930i	−0.0221584	−	0.210823i
$35$	0.0729490	+	0.224514i	0.0123306	+	0.0379498i
$36$	−2.30902	−	3.99933i	−0.384836	−	0.666556i
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	3.53897	+	0.752232i	0.574097	+	0.122028i
$39$	3.23607	−	9.95959i	0.518186	−	1.59481i
$40$	2.18720	−	0.464905i	0.345827	−	0.0735079i
$41$	−0.731699	+	6.96165i	−0.114272	+	1.08723i	0.775665	+	0.631145i	$0.217415\pi$
$41$	−0.731699	+	6.96165i	−0.114272	+	1.08723i	−0.889937	+	0.456083i	$0.849252\pi$
$42$	−0.827091	+	0.918578i	−0.127623	+	0.141740i
$43$	1.12920	−	0.502754i	0.172202	−	0.0766693i	−0.318825	−	0.947814i	$-0.603288\pi$
$43$	1.12920	−	0.502754i	0.172202	−	0.0766693i	0.491027	+	0.871144i	$0.336622\pi$
$44$	1.12920	+	0.502754i	0.170234	+	0.0757930i
$45$	4.99983	+	5.55288i	0.745331	+	0.827774i
$46$	−7.47214	+	5.42882i	−1.10171	+	0.800437i
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	−0.724018	−	0.689782i	$-0.757707\pi$
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	0.432288	+	0.901736i	$0.357707\pi$
$48$	10.5108	+	11.6735i	1.51711	+	1.68492i
$49$	−6.34391	−	2.82449i	−0.906273	−	0.403499i
$50$	−5.91259	+	2.63245i	−0.836167	+	0.372285i
$51$	−1.65418	+	1.83716i	−0.231632	+	0.257253i
$52$	0.209057	−	1.98904i	0.0289910	−	0.275831i
$53$	10.2433	−	2.17728i	1.40702	−	0.299072i	0.559061	−	0.829127i	$-0.311162\pi$
$53$	10.2433	−	2.17728i	1.40702	−	0.299072i	0.847964	+	0.530054i	$0.177828\pi$
$54$	−7.23607	+	22.2703i	−0.984704	+	3.03061i
$55$	−1.95630	−	0.415823i	−0.263787	−	0.0560696i
$56$	0.263932	−	0.457144i	0.0352694	−	0.0610884i
$57$	−3.61803	−	6.26662i	−0.479220	−	0.830034i
$58$	1.38197	+	4.25325i	0.181461	+	0.558480i
$59$	−0.233733	−	2.22382i	−0.0304294	−	0.289517i	−0.999145	−	0.0413430i	$-0.986836\pi$
$59$	−0.233733	−	2.22382i	−0.0304294	−	0.289517i	0.968716	−	0.248174i	$-0.0798303\pi$
$60$	1.61803	+	1.17557i	0.208887	+	0.151765i
$61$	8.18034			1.04739			0.523693	−	0.851907i	$-0.324554\pi$
$61$	8.18034			1.04739			0.523693	+	0.851907i	$0.324554\pi$
$62$		0			0
$63$	1.76393			0.222235
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	0.338261	+	3.21834i	0.0419561	+	0.399186i
$66$	−3.23607	−	9.95959i	−0.398332	−	1.22594i
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−0.236068	+	0.408882i	−0.0286274	+	0.0495842i
$69$	18.0685	+	3.84057i	2.17519	+	0.462351i
$70$	0.118034	−	0.363271i	0.0141078	−	0.0434192i
$71$	8.97973	−	1.90870i	1.06570	−	0.226521i	0.358495	−	0.933532i	$-0.383290\pi$
$71$	8.97973	−	1.90870i	1.06570	−	0.226521i	0.707203	+	0.707011i	$0.249957\pi$
$72$	1.74648	−	16.6167i	0.205825	−	1.95829i
$73$	5.66897	−	6.29602i	0.663502	−	0.736894i	−0.313626	−	0.949547i	$-0.601544\pi$
$73$	5.66897	−	6.29602i	0.663502	−	0.736894i	0.977128	+	0.212653i	$0.0682103\pi$
$74$	−2.95630	+	1.31623i	−0.343662	+	0.153008i
$75$	11.8252	+	5.26491i	1.36545	+	0.607939i
$76$	−0.924716	−	1.02700i	−0.106072	−	0.117805i
$77$	−0.381966	+	0.277515i	−0.0435291	+	0.0316257i
$78$	−13.7082	+	9.95959i	−1.55215	+	1.12770i
$79$	−7.83432	−	8.70089i	−0.881430	−	0.978927i	0.118472	−	0.992957i	$-0.462200\pi$
$79$	−7.83432	−	8.70089i	−0.881430	−	0.978927i	−0.999902	+	0.0140307i	$0.995534\pi$
$80$	−4.43444	−	1.97434i	−0.495786	−	0.220738i
$81$	22.3055	−	9.93105i	2.47839	−	1.10345i
$82$	7.57873	−	8.41704i	0.836931	−	0.929506i
$83$	1.56210	−	14.8624i	0.171463	−	1.63136i	−0.483249	−	0.875483i	$-0.660544\pi$
$83$	1.56210	−	14.8624i	0.171463	−	1.63136i	0.654712	−	0.755878i	$-0.272790\pi$
$84$	0.461819	−	0.0981626i	0.0503885	−	0.0107104i
$85$	0.236068	−	0.726543i	0.0256052	−	0.0788046i
$86$	−1.95630	−	0.415823i	−0.210953	−	0.0448394i
$87$	4.47214	−	7.74597i	0.479463	−	0.830455i
$88$	2.23607	+	3.87298i	0.238366	+	0.412861i
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	0.937555	+	0.347838i	$0.113084\pi$
$89$	3.61803	+	11.1352i	0.383511	+	1.18032i	−0.554044	+	0.832487i	$0.686916\pi$
$90$	−1.26377	−	12.0239i	−0.133213	−	1.26743i
$91$	0.618034	+	0.449028i	0.0647876	+	0.0470709i
$92$	3.52786			0.367805
$93$		0			0
$94$	4.00000			0.412568
$95$	1.80902	+	1.31433i	0.185601	+	0.134847i
$96$	−1.14399	−	10.8843i	−0.116758	−	1.11088i
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	−0.808586	−	0.588378i	$-0.799767\pi$
$97$	−4.92705	−	15.1639i	−0.500266	−	1.53966i	0.308320	−	0.951283i	$-0.400233\pi$
$98$	5.61803	+	9.73072i	0.567507	+	0.982951i
$99$	−7.47214	+	12.9421i	−0.750978	+	1.30073i
$100$	2.41811	+	0.513986i	0.241811	+	0.0513986i
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	−0.986526	−	0.163605i	$-0.947688\pi$
$101$	−0.927051	+	2.85317i	−0.0922450	+	0.283901i	0.894281	+	0.447506i	$0.147688\pi$
$102$	3.91259	−	0.831647i	0.387404	−	0.0823453i
$103$	−0.651847	+	6.20191i	−0.0642284	+	0.611092i	0.914308	+	0.405019i	$0.132735\pi$
$103$	−0.651847	+	6.20191i	−0.0642284	+	0.611092i	−0.978537	+	0.206073i	$0.933932\pi$
$104$	4.84187	−	5.37745i	0.474785	−	0.527302i
$105$	−0.697887	+	0.310719i	−0.0681068	+	0.0303231i
$106$	−15.4794	−	6.89186i	−1.50349	−	0.669396i
$107$	3.85682	+	4.28344i	0.372853	+	0.414095i	0.900146	−	0.435588i	$-0.143460\pi$
$107$	3.85682	+	4.28344i	0.372853	+	0.414095i	−0.527293	+	0.849684i	$0.676793\pi$
$108$	7.23607	−	5.25731i	0.696291	−	0.505885i
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.102762	−	0.994706i	$-0.467232\pi$
$109$	11.2812	−	8.19624i	1.08054	−	0.785057i	0.977777	+	0.209649i	$0.0672321\pi$
$110$	2.16535	+	2.40487i	0.206458	+	0.229295i
$111$	5.91259	+	2.63245i	0.561198	+	0.249862i
$112$	−1.04683	+	0.466079i	−0.0989161	+	0.0440403i
$113$	2.32331	−	2.58030i	0.218559	−	0.242734i	−0.623888	−	0.781514i	$-0.714448\pi$
$113$	2.32331	−	2.58030i	0.218559	−	0.242734i	0.842447	+	0.538780i	$0.181114\pi$
$114$	−1.22384	+	11.6441i	−0.114623	+	1.09057i
$115$	−5.58347	+	1.18680i	−0.520661	+	0.110670i
$116$	0.527864	−	1.62460i	0.0490109	−	0.150840i
$117$	23.6519	+	5.02738i	2.18662	+	0.464781i
$118$	−1.80902	+	3.13331i	−0.166534	+	0.288445i
$119$	−0.0901699	−	0.156179i	−0.00826587	−	0.0143169i
$120$	2.23607	+	6.88191i	0.204124	+	0.628230i
$121$	0.731699	+	6.96165i	0.0665181	+	0.632878i
$122$	−10.7082	−	7.77997i	−0.969475	−	0.704365i
$123$	−22.6525			−2.04250
$124$		0			0
$125$	−9.00000			−0.804984
$126$	−2.30902	−	1.67760i	−0.205704	−	0.149452i
$127$	−1.30369	−	12.4038i	−0.115684	−	1.10066i	−0.886220	−	0.463264i	$-0.846678\pi$
$127$	−1.30369	−	12.4038i	−0.115684	−	1.10066i	0.770536	−	0.637396i	$-0.219989\pi$
$128$	4.20820	+	12.9515i	0.371956	+	1.14476i
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	2.61803	−	4.53457i	0.229617	−	0.397708i
$131$	−11.7378	−	2.49494i	−1.02553	−	0.217984i	−0.335713	−	0.941964i	$-0.608977\pi$
$131$	−11.7378	−	2.49494i	−1.02553	−	0.217984i	−0.689821	+	0.723980i	$0.742311\pi$
$132$	−1.23607	+	3.80423i	−0.107586	+	0.331115i
$133$	0.516329	−	0.109749i	0.0447714	−	0.00951645i
$134$	−1.35304	+	12.8734i	−0.116885	+	1.11209i
$135$	−9.68375	+	10.7549i	−0.833444	+	0.925634i
$136$	−1.56052	+	0.694789i	−0.133814	+	0.0595777i
$137$	5.74784	+	2.55910i	0.491071	+	0.218639i	0.637306	−	0.770611i	$-0.280049\pi$
$137$	5.74784	+	2.55910i	0.491071	+	0.218639i	−0.146235	+	0.989250i	$0.546715\pi$
$138$	−19.9993	−	22.2115i	−1.70246	−	1.89077i
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	−0.943681	−	0.330855i	$-0.892663\pi$
$139$	−10.8541	+	7.88597i	−0.920633	+	0.668879i	0.0230486	+	0.999734i	$0.492663\pi$
$140$	−0.118034	+	0.0857567i	−0.00997569	+	0.00724777i
$141$	−5.35304	−	5.94516i	−0.450808	−	0.500673i
$142$	−13.5699	−	6.04171i	−1.13876	−	0.507009i
$143$	−5.91259	+	2.63245i	−0.494436	+	0.220137i
$144$	−24.2697	+	26.9542i	−2.02248	+	2.24619i
$145$	−0.288910	+	2.74879i	−0.0239926	+	0.228275i
$146$	−13.4086	+	2.85010i	−1.10971	+	0.235876i
$147$	6.94427	−	21.3723i	0.572754	−	1.76276i
$148$	1.20906	+	0.256993i	0.0993839	+	0.0211247i
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−10.4721	−	18.1383i	−0.855046	−	1.48098i
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	−0.955076	−	0.296360i	$-0.904227\pi$
$151$	−4.38197	−	13.4863i	−0.356599	−	1.09750i	0.598477	−	0.801140i	$-0.295773\pi$
$152$	−0.522642	−	4.97261i	−0.0423919	−	0.403332i
$153$	−4.61803	−	3.35520i	−0.373346	−	0.271252i
$154$	0.763932			0.0615594
$155$		0			0
$156$	6.47214			0.518186
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.999075	−	0.0430003i	$-0.986308\pi$
$157$	−16.8992	−	12.2780i	−1.34870	−	0.979889i	−0.349627	−	0.936889i	$-0.613692\pi$
$158$	1.98022	+	18.8405i	0.157537	+	1.49887i
$159$	10.4721	+	32.2299i	0.830494	+	2.55600i
$160$	1.69098	+	2.92887i	0.133684	+	0.231547i
$161$	−0.673762	+	1.16699i	−0.0530999	+	0.0919717i
$162$	−38.6433	−	8.21388i	−3.03610	−	0.645343i
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	−0.733795	−	0.679371i	$-0.762253\pi$
$163$	3.30902	−	10.1841i	0.259182	−	0.797681i	0.992977	−	0.118309i	$-0.0377475\pi$
$164$	−4.23170	+	0.899475i	−0.330440	+	0.0702372i
$165$	0.676522	−	6.43668i	0.0526672	−	0.501095i
$166$	−16.1798	+	17.9695i	−1.25580	+	1.39470i
$167$	−5.91259	+	2.63245i	−0.457530	+	0.203705i	−0.622542	−	0.782586i	$-0.713900\pi$
$167$	−5.91259	+	2.63245i	−0.457530	+	0.203705i	0.165013	+	0.986291i	$0.447234\pi$
$168$	1.56052	+	0.694789i	0.120397	+	0.0536041i
$169$	−1.69147	−	1.87857i	−0.130113	−	0.144505i
$170$	−1.00000	+	0.726543i	−0.0766965	+	0.0557233i
$171$	13.5172	−	9.82084i	1.03369	−	0.751018i
$172$	0.511170	+	0.567712i	0.0389764	+	0.0432876i
$173$	2.68973	+	1.19754i	0.204496	+	0.0910475i	0.506429	−	0.862282i	$-0.330965\pi$
$173$	2.68973	+	1.19754i	0.204496	+	0.0910475i	−0.301933	+	0.953329i	$0.597632\pi$
$174$	−13.2210	+	5.88635i	−1.00228	+	0.446243i
$175$	−0.631841	+	0.701731i	−0.0477627	+	0.0530459i
$176$	1.01478	−	9.65502i	0.0764922	−	0.727775i
$177$	7.07794	−	1.50446i	0.532011	−	0.113082i
$178$	5.85410	−	18.0171i	0.438783	−	1.35044i
$179$	−1.67088	−	0.355156i	−0.124887	−	0.0265456i	0.145044	−	0.989425i	$-0.453668\pi$
$179$	−1.67088	−	0.355156i	−0.124887	−	0.0265456i	−0.269931	+	0.962880i	$0.587001\pi$
$180$	−2.30902	+	3.99933i	−0.172104	+	0.298093i
$181$	2.09017	+	3.62028i	0.155361	+	0.269093i	0.933190	−	0.359382i	$-0.117013\pi$
$181$	2.09017	+	3.62028i	0.155361	+	0.269093i	−0.777829	+	0.628476i	$0.783679\pi$
$182$	−0.381966	−	1.17557i	−0.0283132	−	0.0871391i
$183$	2.76709	+	26.3271i	0.204549	+	1.94616i
$184$	10.3262	+	7.50245i	0.761260	+	0.553088i
$185$	−2.00000			−0.147043
$186$		0			0
$187$	1.52786			0.111728
$188$	−1.23607	−	0.898056i	−0.0901495	−	0.0654975i
$189$	0.357112	+	3.39769i	0.0259761	+	0.247146i
$190$	−1.11803	−	3.44095i	−0.0811107	−	0.249633i
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	0.970543	+	0.240927i	$0.0774514\pi$
$191$	9.59017	+	16.6107i	0.693920	+	1.20191i	−0.276623	+	0.960979i	$0.589215\pi$
$192$	6.85410	−	11.8717i	0.494652	−	0.856763i
$193$	−3.39626	−	0.721898i	−0.244468	−	0.0519633i	0.0840478	−	0.996462i	$-0.473215\pi$
$193$	−3.39626	−	0.721898i	−0.244468	−	0.0519633i	−0.328516	+	0.944498i	$0.606548\pi$
$194$	−7.97214	+	24.5357i	−0.572366	+	1.76156i
$195$	−10.2433	+	2.17728i	−0.733538	+	0.155918i
$196$	0.448615	−	4.26829i	0.0320439	−	0.304878i
$197$	7.63907	−	8.48404i	0.544261	−	0.604463i	−0.406781	−	0.913526i	$-0.633349\pi$
$197$	7.63907	−	8.48404i	0.544261	−	0.604463i	0.951042	+	0.309063i	$0.100015\pi$
$198$	22.0898	−	9.83503i	1.56986	−	0.698945i
$199$	−17.3065	−	7.70533i	−1.22682	−	0.546216i	−0.312003	−	0.950081i	$-0.601000\pi$
$199$	−17.3065	−	7.70533i	−1.22682	−	0.546216i	−0.914819	+	0.403865i	$0.867667\pi$
$200$	5.98489	+	6.64689i	0.423195	+	0.470006i
$201$	20.9443	−	15.2169i	1.47730	−	1.07332i
$202$	3.92705	−	2.85317i	0.276306	−	0.200748i
$203$	0.436592	+	0.484884i	0.0306427	+	0.0340322i
$204$	−1.39577	−	0.621438i	−0.0977237	−	0.0435094i
$205$	6.39482	−	2.84716i	0.446633	−	0.198854i
$206$	6.75164	−	7.49846i	0.470409	−	0.522442i
$207$	−4.45840	+	42.4188i	−0.309880	+	2.94831i
$208$	−15.3649	+	3.26592i	−1.06537	+	0.226451i
$209$	−1.38197	+	4.25325i	−0.0955926	+	0.294204i
$210$	1.20906	+	0.256993i	0.0834329	+	0.0177342i
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	0.123081	+	0.992397i	$0.460723\pi$
$211$	−11.5902	+	20.0748i	−0.797900	+	1.38200i	−0.920981	+	0.389607i	$0.872611\pi$
$212$	3.23607	+	5.60503i	0.222254	+	0.384955i
$213$	9.18034	+	28.2542i	0.629027	+	1.93594i
$214$	−0.974857	−	9.27515i	−0.0666399	−	0.634036i
$215$	−1.00000	−	0.726543i	−0.0681994	−	0.0495498i
$216$	32.3607			2.20187
$217$		0			0
$218$	−22.5623			−1.52811
$219$	22.1803	+	16.1150i	1.49881	+	1.08895i
$220$	−0.129204	−	1.22930i	−0.00871095	−	0.0828792i
$221$	−0.763932	−	2.35114i	−0.0513876	−	0.158155i
$222$	−5.23607	−	9.06914i	−0.351422	−	0.608681i
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$	0.780927	+	0.165991i	0.0521779	+	0.0110908i
$225$	−9.23607	+	28.4257i	−0.615738	+	1.89505i
$226$	−5.49527	+	1.16805i	−0.365540	+	0.0776979i
$227$	0.676522	−	6.43668i	0.0449024	−	0.427218i	−0.948860	−	0.315698i	$-0.897761\pi$
$227$	0.676522	−	6.43668i	0.0449024	−	0.427218i	0.993762	−	0.111520i	$-0.0355719\pi$
$228$	2.99244	−	3.32344i	0.198179	−	0.220101i
$229$	−12.2565	+	5.45694i	−0.809932	+	0.360605i	−0.769556	−	0.638579i	$-0.779522\pi$
$229$	−12.2565	+	5.45694i	−0.809932	+	0.360605i	−0.0403763	+	0.999185i	$0.512856\pi$
$230$	8.43757	+	3.75665i	0.556357	+	0.247706i
$231$	−1.02234	−	1.13542i	−0.0672651	−	0.0747054i
$232$	5.00000	−	3.63271i	0.328266	−	0.238499i
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	−0.951056	−	0.309018i	$-0.900000\pi$
$233$	−14.5172	+	10.5474i	−0.951055	+	0.690982i	1.33829e−6		1.00000i	$0.500000\pi$
$234$	−26.1795	−	29.0753i	−1.71141	−	1.90071i
$235$	2.25841	+	1.00551i	0.147322	+	0.0655921i
$236$	1.26249	−	0.562096i	0.0821810	−	0.0365893i
$237$	25.3524	−	28.1567i	1.64681	−	1.82897i
$238$	−0.0305010	+	0.290198i	−0.00197709	+	0.0188107i
$239$	11.4524	−	2.43427i	0.740791	−	0.157460i	0.177967	−	0.984037i	$-0.443048\pi$
$239$	11.4524	−	2.43427i	0.740791	−	0.157460i	0.562824	+	0.826577i	$0.309715\pi$
$240$	4.85410	−	14.9394i	0.313331	−	0.964333i
$241$	−14.0469	−	2.98575i	−0.904838	−	0.192329i	−0.268083	−	0.963396i	$-0.586390\pi$
$241$	−14.0469	−	2.98575i	−0.904838	−	0.192329i	−0.636755	+	0.771066i	$0.719724\pi$
$242$	5.66312	−	9.80881i	0.364039	−	0.630534i
$243$	17.7984	+	30.8277i	1.14177	+	1.97760i
$244$	1.56231	+	4.80828i	0.100016	+	0.307819i
$245$	0.725874	+	6.90623i	0.0463744	+	0.441223i
$246$	29.6525	+	21.5438i	1.89057	+	1.37358i
$247$	7.23607			0.460420
$248$		0			0
$249$	48.3607			3.06473
$250$	11.7812	+	8.55951i	0.745106	+	0.541351i
$251$	0.190206	+	1.80969i	0.0120057	+	0.114227i	0.998883	−	0.0472426i	$-0.0150434\pi$
$251$	0.190206	+	1.80969i	0.0120057	+	0.114227i	−0.986878	+	0.161469i	$0.948377\pi$
$252$	0.336881	+	1.03681i	0.0212215	+	0.0653131i
$253$	−5.70820	−	9.88690i	−0.358872	−	0.621584i
$254$	−10.0902	+	17.4767i	−0.633114	+	1.09658i
$255$	2.41811	+	0.513986i	0.151428	+	0.0321870i
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	−1.90178	+	0.404237i	−0.118630	+	0.0252156i	−0.266844	−	0.963740i	$-0.585981\pi$
$257$	−1.90178	+	0.404237i	−0.118630	+	0.0252156i	0.148214	+	0.988955i	$0.452648\pi$
$258$	0.676522	−	6.43668i	0.0421184	−	0.400730i
$259$	−0.315921	+	0.350865i	−0.0196304	+	0.0218017i
$260$	−1.82709	+	0.813473i	−0.113311	+	0.0504495i
$261$	18.8670	+	8.40012i	1.16784	+	0.519954i
$262$	12.9921	+	14.4292i	0.802655	+	0.891439i
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.169486	−	0.985533i	$-0.445789\pi$
$263$	18.7984	−	13.6578i	1.15916	−	0.842177i	0.989671	+	0.143355i	$0.0457892\pi$
$264$	−11.7082	+	8.50651i	−0.720590	+	0.523539i
$265$	−7.00723	−	7.78231i	−0.430451	−	0.478064i
$266$	−0.780261	−	0.347395i	−0.0478409	−	0.0213001i
$267$	−34.6129	+	15.4107i	−2.11828	+	0.943117i
$268$	3.30836	−	3.67431i	0.202090	−	0.224444i
$269$	1.15564	−	10.9952i	0.0704605	−	0.670387i	−0.901103	−	0.433606i	$-0.857241\pi$
$269$	1.15564	−	10.9952i	0.0704605	−	0.670387i	0.971563	−	0.236781i	$-0.0760924\pi$
$270$	22.9047	−	4.86854i	1.39394	−	0.296290i
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	0.725232	+	0.688504i	$0.241732\pi$
$271$	−4.38197	+	13.4863i	−0.266185	+	0.819235i	−0.991418	+	0.130731i	$0.958268\pi$
$272$	3.62717	+	0.770979i	0.219930	+	0.0467475i
$273$	−1.23607	+	2.14093i	−0.0748102	+	0.129575i
$274$	−5.09017	−	8.81643i	−0.307508	−	0.532620i
$275$	−2.47214	−	7.60845i	−0.149075	−	0.458807i
$276$	1.19334	+	11.3539i	0.0718306	+	0.683423i
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	0.851180	−	0.524873i	$-0.175887\pi$
$277$	10.2361	+	7.43694i	0.615026	+	0.446842i	−0.236155	+	0.971715i	$0.575887\pi$
$278$	21.7082			1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	0.0963896	−	0.995344i	$-0.469271\pi$
$281$	−13.7533	−	9.99235i	−0.820452	−	0.596094i	−0.916842	+	0.399250i	$0.869271\pi$
$282$	1.35304	+	12.8734i	0.0805726	+	0.766598i
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	−0.993806	−	0.111130i	$-0.964553\pi$
$283$	−4.29180	−	13.2088i	−0.255121	−	0.785181i	0.738685	−	0.674051i	$-0.235447\pi$
$284$	2.83688	+	4.91362i	0.168338	+	0.291570i
$285$	−3.61803	+	6.26662i	−0.214314	+	0.371202i
$286$	10.2433	+	2.17728i	0.605699	+	0.128745i
$287$	0.510643	−	1.57160i	0.0301423	−	0.0927685i
$288$	24.7183	−	5.25403i	1.45654	−	0.309597i
$289$	1.71598	−	16.3265i	0.100940	−	0.960381i
$290$	2.99244	−	3.32344i	0.175722	−	0.195159i
$291$	47.1360	−	20.9863i	2.76316	−	1.23024i
$292$	4.78339	+	2.12970i	0.279926	+	0.124631i
$293$	−0.315921	−	0.350865i	−0.0184563	−	0.0204978i	0.733846	−	0.679316i	$-0.237723\pi$
$293$	−0.315921	−	0.350865i	−0.0184563	−	0.0204978i	−0.752302	+	0.658818i	$0.771057\pi$
$294$	−29.4164	+	21.3723i	−1.71560	+	1.24646i
$295$	−1.80902	+	1.31433i	−0.105325	+	0.0765231i
$296$	2.99244	+	3.32344i	0.173932	+	0.193171i
$297$	−26.4419	−	11.7727i	−1.53432	−	0.683121i
$298$	14.7815	−	6.58114i	0.856268	−	0.381235i
$299$	−12.3603	+	13.7275i	−0.714813	+	0.793880i
$300$	−0.836228	+	7.95618i	−0.0482796	+	0.459350i
$301$	−0.285420	+	0.0606678i	−0.0164513	+	0.00349683i
$302$	−7.09017	+	21.8213i	−0.407993	+	1.25567i
$303$	−9.49606	−	2.01845i	−0.545534	−	0.115957i
$304$	−5.42705	+	9.39993i	−0.311263	+	0.539123i
$305$	−4.09017	−	7.08438i	−0.234202	−	0.405651i
$306$	2.85410	+	8.78402i	0.163158	+	0.502149i
$307$	3.00082	+	28.5509i	0.171266	+	1.62949i	0.655954	+	0.754801i	$0.272267\pi$
$307$	3.00082	+	28.5509i	0.171266	+	1.62949i	−0.484688	+	0.874687i	$0.661067\pi$
$308$	−0.236068	−	0.171513i	−0.0134512	−	0.00977288i
$309$	−20.1803			−1.14802
$310$		0			0
$311$	−29.1803			−1.65467			−0.827333	−	0.561712i	$-0.810143\pi$
$311$	−29.1803			−1.65467			−0.827333	+	0.561712i	$0.810143\pi$
$312$	18.9443	+	13.7638i	1.07251	+	0.779223i
$313$	−1.75231	−	16.6721i	−0.0990463	−	0.942363i	−0.925344	−	0.379129i	$-0.876224\pi$
$313$	−1.75231	−	16.6721i	−0.0990463	−	0.942363i	0.826298	−	0.563234i	$-0.190443\pi$
$314$	10.4443	+	32.1442i	0.589404	+	1.81400i
$315$	−0.881966	−	1.52761i	−0.0496932	−	0.0860711i
$316$	3.61803	−	6.26662i	0.203530	−	0.352525i
$317$	−3.96710	−	0.843233i	−0.222815	−	0.0473607i	0.0951515	−	0.995463i	$-0.469666\pi$
$317$	−3.96710	−	0.843233i	−0.222815	−	0.0473607i	−0.317966	+	0.948102i	$0.603000\pi$
$318$	16.9443	−	52.1491i	0.950188	−	2.92438i
$319$	−5.40707	+	1.14931i	−0.302738	+	0.0643489i
$320$	−0.442790	+	4.21286i	−0.0247527	+	0.235506i
$321$	−12.4809	+	13.8615i	−0.696618	+	0.773673i
$322$	1.99184	−	0.886824i	0.111001	−	0.0494208i
$323$	−1.56052	−	0.694789i	−0.0868298	−	0.0386591i
$324$	10.0973	+	11.2142i	0.560961	+	0.623010i
$325$	−10.4721	+	7.60845i	−0.580890	+	0.422041i
$326$	−14.0172	+	10.1841i	−0.776342	+	0.564046i
$327$	30.1943	+	33.5341i	1.66975	+	1.85444i
$328$	−14.2992	−	6.36644i	−0.789544	−	0.351528i
$329$	0.533138	−	0.237368i	0.0293928	−	0.0130865i
$330$	−7.00723	+	7.78231i	−0.385735	+	0.428402i
$331$	−0.209057	+	1.98904i	−0.0114908	+	0.109328i	−0.998764	−	0.0497066i	$-0.984171\pi$
$331$	−0.209057	+	1.98904i	−0.0114908	+	0.109328i	0.987273	+	0.159034i	$0.0508380\pi$
$332$	9.03424	−	1.92029i	0.495818	−	0.105389i
$333$	−4.61803	+	14.2128i	−0.253067	+	0.778859i
$334$	10.2433	+	2.17728i	0.560488	+	0.119135i
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$	−1.85410	−	3.21140i	−0.101150	−	0.175196i
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	−0.995037	−	0.0995083i	$-0.968273\pi$
$337$	−4.56231	−	14.0413i	−0.248525	−	0.764880i	0.746512	−	0.665372i	$-0.231727\pi$
$338$	0.427539	+	4.06776i	0.0232551	+	0.221257i
$339$	9.09017	+	6.60440i	0.493710	+	0.358702i
$340$	0.472136			0.0256052
$341$		0			0
$342$	−27.0344			−1.46186
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$	0.288910	+	2.74879i	0.0155770	+	0.148205i
$345$	−5.70820	−	17.5680i	−0.307319	−	0.945832i
$346$	−2.38197	−	4.12569i	−0.128055	−	0.221798i
$347$	−12.0902	+	20.9408i	−0.649034	+	1.12416i	0.334320	+	0.942460i	$0.391494\pi$
$347$	−12.0902	+	20.9408i	−0.649034	+	1.12416i	−0.983354	+	0.181701i	$0.941840\pi$
$348$	5.40707	+	1.14931i	0.289849	+	0.0616094i
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	−0.994861	−	0.101252i	$-0.967715\pi$
$349$	−2.43769	+	7.50245i	−0.130487	+	0.401597i	0.864374	+	0.502849i	$0.167715\pi$
$350$	1.49448	−	0.317661i	0.0798831	−	0.0169797i
$351$	−4.89536	+	46.5763i	−0.261295	+	2.48606i
$352$	−4.52595	+	5.02658i	−0.241234	+	0.267918i
$353$	6.77523	−	3.01652i	0.360609	−	0.160553i	−0.218431	−	0.975852i	$-0.570094\pi$
$353$	6.77523	−	3.01652i	0.360609	−	0.160553i	0.579040	+	0.815299i	$0.303427\pi$
$354$	−10.6960	−	4.76216i	−0.568485	−	0.253106i
$355$	−6.14285	−	6.82232i	−0.326028	−	0.362091i
$356$	−5.85410	+	4.25325i	−0.310267	+	0.225422i
$357$	0.472136	−	0.343027i	0.0249881	−	0.0181549i
$358$	1.84943	+	2.05400i	0.0977455	+	0.108557i
$359$	20.3137	+	9.04422i	1.07211	+	0.477336i	0.865408	−	0.501067i	$-0.167059\pi$
$359$	20.3137	+	9.04422i	1.07211	+	0.477336i	0.206706	+	0.978403i	$0.433726\pi$
$360$	−15.2637	+	6.79584i	−0.804468	+	0.358172i
$361$	−9.36783	+	10.4040i	−0.493044	+	0.547580i
$362$	0.707023	−	6.72688i	0.0371603	−	0.353557i
$363$	−22.1575	+	4.70971i	−1.16297	+	0.247196i
$364$	−0.145898	+	0.449028i	−0.00764713	+	0.0235355i
$365$	−8.28700	−	1.76146i	−0.433761	−	0.0921988i
$366$	21.4164	−	37.0943i	1.11945	−	1.93895i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−8.56231	−	26.3521i	−0.446341	−	1.37370i
$369$	−5.46736	−	52.0184i	−0.284619	−	2.70797i
$370$	2.61803	+	1.90211i	0.136105	+	0.0988861i
$371$	−2.47214			−0.128347
$372$		0			0
$373$	19.0000			0.983783			0.491891	−	0.870657i	$-0.336306\pi$
$373$	19.0000			0.983783			0.491891	+	0.870657i	$0.336306\pi$
$374$	−2.00000	−	1.45309i	−0.103418	−	0.0751372i
$375$	−3.04435	−	28.9651i	−0.157210	−	1.49575i
$376$	−1.70820	−	5.25731i	−0.0880939	−	0.271125i
$377$	4.47214	+	7.74597i	0.230327	+	0.398938i
$378$	2.76393	−	4.78727i	0.142161	−	0.246231i
$379$	2.06532	+	0.438996i	0.106088	+	0.0225497i	0.260650	−	0.965433i	$-0.416063\pi$
$379$	2.06532	+	0.438996i	0.106088	+	0.0225497i	−0.154562	+	0.987983i	$0.549397\pi$
$380$	−0.427051	+	1.31433i	−0.0219073	+	0.0674236i
$381$	39.4787	−	8.39146i	2.02256	−	0.429907i
$382$	3.24398	−	30.8644i	0.165977	−	1.57916i
$383$	−15.9846	+	17.7526i	−0.816773	+	0.907118i	−0.997070	−	0.0764942i	$-0.975627\pi$
$383$	−15.9846	+	17.7526i	−0.816773	+	0.907118i	0.180297	+	0.983612i	$0.442294\pi$
$384$	−40.2589	+	17.9244i	−2.05445	+	0.914702i
$385$	0.431318	+	0.192035i	0.0219820	+	0.00978701i
$386$	3.75920	+	4.17501i	0.191338	+	0.212503i
$387$	−7.47214	+	5.42882i	−0.379830	+	0.275963i
$388$	7.97214	−	5.79210i	0.404724	−	0.294049i
$389$	−11.9698	−	13.2938i	−0.606892	−	0.674021i	0.358890	−	0.933380i	$-0.383155\pi$
$389$	−11.9698	−	13.2938i	−0.606892	−	0.674021i	−0.965781	+	0.259359i	$0.916489\pi$
$390$	15.4794	+	6.89186i	0.783828	+	0.348983i
$391$	3.98368	−	1.77365i	0.201463	−	0.0896972i
$392$	10.3902	−	11.5395i	0.524783	−	0.582830i
$393$	4.05913	−	38.6201i	0.204756	−	1.94813i
$394$	−18.0685	+	3.84057i	−0.910277	+	0.193485i
$395$	−3.61803	+	11.1352i	−0.182043	+	0.560271i
$396$	−9.03424	−	1.92029i	−0.453988	−	0.0964980i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$	15.3262	+	26.5458i	0.768235	+	1.33062i
$399$	0.527864	+	1.62460i	0.0264263	+	0.0813317i
$400$	−2.02957	−	19.3100i	−0.101478	−	0.965502i
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.948743	−	0.316048i	$-0.897644\pi$
$401$	−30.8885	−	22.4418i	−1.54250	−	1.12069i	−0.593757	−	0.804644i	$-0.702356\pi$
$402$	−41.8885			−2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	−19.7533	−	14.3516i	−0.981549	−	0.713137i
$406$	−0.110354	−	1.04994i	−0.00547676	−	0.0521079i
$407$	−1.23607	−	3.80423i	−0.0612696	−	0.188568i
$408$	−2.76393	−	4.78727i	−0.136835	−	0.237005i
$409$	1.90983	−	3.30792i	0.0944350	−	0.163566i	−0.814938	−	0.579549i	$-0.803229\pi$
$409$	1.90983	−	3.30792i	0.0944350	−	0.163566i	0.909373	+	0.415982i	$0.136562\pi$
$410$	−11.0787	−	2.35486i	−0.547140	−	0.116298i
$411$	−6.29180	+	19.3642i	−0.310351	+	0.955163i
$412$	−3.76988	+	0.801313i	−0.185729	+	0.0394779i
$413$	−0.0551768	+	0.524972i	−0.00271507	+	0.0258322i
$414$	46.1788	−	51.2868i	2.26956	−	2.52061i
$415$	−13.6523	+	6.07838i	−0.670164	+	0.298376i
$416$	9.99809	+	4.45144i	0.490197	+	0.218250i
$417$	−29.0512	−	32.2647i	−1.42265	−	1.58001i
$418$	5.85410	−	4.25325i	0.286333	−	0.208033i
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	−0.369449	−	0.929251i	$-0.620453\pi$
$419$	8.19098	−	5.95110i	0.400156	−	0.290730i	0.769604	+	0.638521i	$0.220453\pi$
$420$	−0.315921	−	0.350865i	−0.0154153	−	0.0171205i
$421$	26.8223	+	11.9421i	1.30724	+	0.582021i	0.937781	−	0.347227i	$-0.112877\pi$
$421$	26.8223	+	11.9421i	1.30724	+	0.582021i	0.369458	+	0.929247i	$0.379543\pi$
$422$	34.2640	−	15.2553i	1.66794	−	0.742616i
$423$	12.3603	−	13.7275i	0.600977	−	0.667453i
$424$	−2.44768	+	23.2881i	−0.118870	+	1.13097i
$425$	2.98895	−	0.635322i	0.144986	−	0.0308176i
$426$	14.8541	−	45.7162i	0.719684	−	2.21496i
$427$	−1.88892	−	0.401502i	−0.0914111	−	0.0194300i
$428$	−1.78115	+	3.08505i	−0.0860953	+	0.149121i
$429$	−10.4721	−	18.1383i	−0.505599	−	0.875724i
$430$	0.618034	+	1.90211i	0.0298042	+	0.0917280i
$431$	−1.25434	−	11.9343i	−0.0604195	−	0.574853i	−0.982292	−	0.187359i	$-0.940007\pi$
$431$	−1.25434	−	11.9343i	−0.0604195	−	0.574853i	0.921872	−	0.387494i	$-0.126659\pi$
$432$	−56.8328	−	41.2915i	−2.73437	−	1.98664i
$433$	10.1803			0.489236			0.244618	−	0.969620i	$-0.421337\pi$
$433$	10.1803			0.489236			0.244618	+	0.969620i	$0.421337\pi$
$434$		0			0
$435$	−8.94427			−0.428845
$436$	6.97214	+	5.06555i	0.333905	+	0.242596i
$437$	1.33419	+	12.6940i	0.0638232	+	0.607237i
$438$	−13.7082	−	42.1895i	−0.655003	−	2.01589i
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	0.879765	−	0.475408i	$-0.157700\pi$
$439$	0.590170	+	1.02220i	0.0281673	+	0.0487872i	−0.851598	+	0.524195i	$0.824366\pi$
$440$	2.23607	−	3.87298i	0.106600	−	0.184637i
$441$	50.7547	+	10.7882i	2.41689	+	0.513725i
$442$	−1.23607	+	3.80423i	−0.0587938	+	0.180949i
$443$	−30.0372	+	6.38459i	−1.42711	+	0.303341i	−0.855763	−	0.517368i	$-0.826912\pi$
$443$	−30.0372	+	6.38459i	−1.42711	+	0.303341i	−0.571346	+	0.820710i	$0.693578\pi$
$444$	−0.418114	+	3.97809i	−0.0198428	+	0.188792i
$445$	7.83432	−	8.70089i	0.371382	−	0.412462i
$446$	5.91259	−	2.63245i	0.279969	−	0.124650i
$447$	−29.5630	−	13.1623i	−1.39828	−	0.622554i
$448$	0.669131	+	0.743145i	0.0316134	+	0.0351103i
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.201413	−	0.979506i	$-0.435447\pi$
$449$	25.3262	−	18.4006i	1.19522	−	0.868377i	0.993806	+	0.111129i	$0.0354466\pi$
$450$	39.1246	−	28.4257i	1.84435	−	1.34000i
$451$	9.36783	+	10.4040i	0.441114	+	0.489907i
$452$	1.96038	+	0.872815i	0.0922083	+	0.0410538i
$453$	41.9213	−	18.6646i	1.96963	−	0.876937i
$454$	−7.00723	+	7.78231i	−0.328865	+	0.365242i
$455$	0.0798526	−	0.759747i	0.00374355	−	0.0356175i
$456$	15.8268	−	3.36408i	0.741156	−	0.157538i
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	−0.970710	−	0.240254i	$-0.922769\pi$
$457$	−0.944272	+	2.90617i	−0.0441712	+	0.135945i	0.926539	+	0.376199i	$0.122769\pi$
$458$	21.2338	+	4.51339i	0.992192	+	0.210897i
$459$	5.52786	−	9.57454i	0.258019	−	0.446901i
$460$	−1.76393	−	3.05522i	−0.0822438	−	0.142450i
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	0.817686	+	0.575664i	$0.195256\pi$
$461$	10.6180	+	32.6789i	0.494531	+	1.52201i	−0.323155	+	0.946346i	$0.604744\pi$
$462$	0.258409	+	2.45859i	0.0120223	+	0.114384i
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	0.635294	−	0.772270i	$-0.280879\pi$
$463$	2.09017	+	1.51860i	0.0971384	+	0.0705752i	−0.538156	+	0.842845i	$0.680879\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	0.496157	−	0.868233i	$-0.334744\pi$
$467$	−3.80902	−	2.76741i	−0.176260	−	0.128061i	−0.672417	+	0.740172i	$0.734744\pi$
$468$	1.56210	+	14.8624i	0.0722082	+	0.687015i
$469$	0.583592	+	1.79611i	0.0269478	+	0.0829367i
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	33.7984	−	58.5405i	1.55735	−	2.69740i
$472$	4.89074	+	1.03956i	0.225114	+	0.0478496i
$473$	0.763932	−	2.35114i	0.0351256	−	0.108106i
$474$	−59.9653	+	12.7460i	−2.75430	+	0.585444i
$475$	−0.934931	+	8.89527i	−0.0428976	+	0.408143i
$476$	0.0745787	−	0.0828281i	0.00341831	−	0.00379642i
$477$	−71.4842	+	31.8268i	−3.27304	+	1.45725i
$478$	−17.3065	−	7.70533i	−0.791579	−	0.352434i
$479$	15.5853	+	17.3092i	0.712108	+	0.790877i	0.985254	−	0.171096i	$-0.0547309\pi$
$479$	15.5853	+	17.3092i	0.712108	+	0.790877i	−0.273146	+	0.961973i	$0.588064\pi$
$480$	−8.85410	+	6.43288i	−0.404133	+	0.293620i
$481$	−5.23607	+	3.80423i	−0.238744	+	0.173458i
$482$	15.5480	+	17.2678i	0.708190	+	0.786525i
$483$	−3.98368	−	1.77365i	−0.181264	−	0.0807038i
$484$	−3.95222	+	1.75964i	−0.179646	+	0.0799836i
$485$	−10.6688	+	11.8489i	−0.484445	+	0.538031i
$486$	6.02050	−	57.2812i	0.273095	−	2.59833i
$487$	18.8157	−	3.99940i	0.852621	−	0.181230i	0.239185	−	0.970974i	$-0.423120\pi$
$487$	18.8157	−	3.99940i	0.852621	−	0.181230i	0.613437	+	0.789744i	$0.289787\pi$
$488$	−5.65248	+	17.3965i	−0.255876	+	0.787504i
$489$	33.8952	+	7.20465i	1.53280	+	0.325806i
$490$	5.61803	−	9.73072i	0.253797	−	0.439589i
$491$	−2.18034	−	3.77646i	−0.0983974	−	0.170429i	0.812624	−	0.582788i	$-0.198038\pi$
$491$	−2.18034	−	3.77646i	−0.0983974	−	0.170429i	−0.911021	+	0.412359i	$0.864705\pi$
$492$	−4.32624	−	13.3148i	−0.195042	−	0.600277i
$493$	−0.220707	−	2.09989i	−0.00994016	−	0.0945743i
$494$	−9.47214	−	6.88191i	−0.426172	−	0.309632i
$495$	14.9443			0.671695
$496$		0			0
$497$	−2.16718			−0.0972115
$498$	−63.3050	−	45.9937i	−2.83676	−	2.06103i
$499$	0.688173	+	6.54753i	0.0308068	+	0.293108i	0.999068	+	0.0431665i	$0.0137446\pi$
$499$	0.688173	+	6.54753i	0.0308068	+	0.293108i	−0.968261	+	0.249941i	$0.919589\pi$
$500$	−1.71885	−	5.29007i	−0.0768692	−	0.236579i
$501$	−10.4721	−	18.1383i	−0.467861	−	0.810358i
$502$	1.47214	−	2.54981i	0.0657046	−	0.113804i
$503$	−29.0045	−	6.16510i	−1.29325	−	0.274888i	−0.490622	−	0.871373i	$-0.663230\pi$
$503$	−29.0045	−	6.16510i	−1.29325	−	0.274888i	−0.802625	+	0.596484i	$0.796564\pi$
$504$	−1.21885	+	3.75123i	−0.0542918	+	0.167093i
$505$	2.93444	−	0.623735i	0.130581	−	0.0277558i
$506$	−1.93086	+	18.3709i	−0.0858374	+	0.816688i
$507$	5.47372	−	6.07918i	0.243096	−	0.269986i
$508$	7.04179	−	3.13521i	0.312429	−	0.139102i
$509$	27.0380	+	12.0381i	1.19844	+	0.533579i	0.906234	−	0.422778i	$-0.138945\pi$
$509$	27.0380	+	12.0381i	1.19844	+	0.533579i	0.292204	+	0.956356i	$0.405611\pi$
$510$	−2.67652	−	2.97258i	−0.118518	−	0.131628i
$511$	−1.61803	+	1.17557i	−0.0715776	+	0.0520042i
$512$	4.28115	−	3.11044i	0.189202	−	0.137463i
$513$	21.6535	+	24.0487i	0.956026	+	1.06177i
$514$	2.87392	+	1.27955i	0.126763	+	0.0564386i
$515$	5.69693	−	2.53644i	0.251037	−	0.111769i
$516$	−1.65418	+	1.83716i	−0.0728213	+	0.0808762i
$517$	−0.516817	+	4.91719i	−0.0227296	+	0.216258i
$518$	0.747238	−	0.158830i	0.0328318	−	0.00697861i
$519$	−2.94427	+	9.06154i	−0.129239	+	0.397757i
$520$	−7.07794	−	1.50446i	−0.310388	−	0.0659751i
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	−0.887099	−	0.461579i	$-0.847283\pi$
$521$	−1.00000	+	1.73205i	−0.0438108	+	0.0758825i	0.843288	+	0.537461i	$0.180617\pi$
$522$	−16.7082	−	28.9395i	−0.731298	−	1.26665i
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	−0.996525	−	0.0832966i	$-0.973455\pi$
$523$	−5.47214	−	16.8415i	−0.239280	−	0.736427i	0.757245	−	0.653131i	$-0.226545\pi$
$524$	−0.775226	−	7.37578i	−0.0338659	−	0.322212i
$525$	−2.47214	−	1.79611i	−0.107893	−	0.0783888i
$526$	−37.5967			−1.63930
$527$		0			0
$528$	31.4164			1.36722
$529$	−7.75329	−	5.63309i	−0.337100	−	0.244917i
$530$	1.77116	+	16.8514i	0.0769342	+	0.731980i
$531$	5.16312	+	15.8904i	0.224060	+	0.689587i
$532$	0.163119	+	0.282530i	0.00707210	+	0.0122492i
$533$	11.3262	−	19.6176i	0.490594	−	0.849733i
$534$	59.9653	+	12.7460i	2.59495	+	0.551574i
$535$	1.78115	−	5.48183i	0.0770060	−	0.237000i
$536$	17.4976	−	3.71924i	0.755783	−	0.160647i
$537$	0.577819	−	5.49758i	0.0249347	−	0.237238i
$538$	−11.9698	+	13.2938i	−0.516054	+	0.573135i
$539$	−12.6878	+	5.64898i	−0.546503	+	0.243319i
$540$	−8.17100	−	3.63796i	−0.351624	−	0.156553i
$541$	−16.9696	−	18.8467i	−0.729580	−	0.810281i	0.258207	−	0.966090i	$-0.416868\pi$
$541$	−16.9696	−	18.8467i	−0.729580	−	0.810281i	−0.987787	+	0.155809i	$0.950202\pi$
$542$	18.5623	−	13.4863i	0.797319	−	0.579286i
$543$	−10.9443	+	7.95148i	−0.469664	+	0.341231i
$544$	−1.72876	−	1.91998i	−0.0741200	−	0.0823186i
$545$	−12.7387	−	5.67165i	−0.545667	−	0.242947i
$546$	3.65418	−	1.62695i	0.156385	−	0.0696269i
$547$	−8.11295	+	9.01034i	−0.346885	+	0.385254i	−0.891188	−	0.453634i	$-0.850127\pi$
$547$	−8.11295	+	9.01034i	−0.346885	+	0.385254i	0.544303	+	0.838888i	$0.316794\pi$
$548$	−0.406464	+	3.86724i	−0.0173633	+	0.165200i
$549$	−59.7889	+	12.7085i	−2.55173	+	0.542386i
$550$	−4.00000	+	12.3107i	−0.170561	+	0.524931i
$551$	6.04528	+	1.28496i	0.257538	+	0.0547413i
$552$	−20.6525	+	35.7711i	−0.879028	+	1.52252i
$553$	1.38197	+	2.39364i	0.0587672	+	0.101788i
$554$	−6.32624	−	19.4702i	−0.268776	−	0.827208i
$555$	−0.676522	−	6.43668i	−0.0287168	−	0.273222i
$556$	−6.70820	−	4.87380i	−0.284491	−	0.206695i
$557$	−12.0000			−0.508456			−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000			−0.508456			−0.254228	+	0.967144i	$0.581821\pi$
$558$		0			0
$559$	−4.00000			−0.169182
$560$	0.927051	+	0.673542i	0.0391751	+	0.0284623i
$561$	0.516817	+	4.91719i	0.0218200	+	0.207604i
$562$	8.50000	+	26.1603i	0.358551	+	1.10351i
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	−0.995437	−	0.0954238i	$-0.969579\pi$
$563$	−13.7705	−	23.8512i	−0.580358	−	1.00521i	0.415079	−	0.909785i	$-0.363754\pi$
$564$	2.47214	−	4.28187i	0.104096	−	0.180299i
$565$	−3.39626	−	0.721898i	−0.142882	−	0.0303705i
$566$	−6.94427	+	21.3723i	−0.291890	+	0.898344i
$567$	−5.63798	+	1.19839i	−0.236773	+	0.0503276i
$568$	−2.14575	+	20.4154i	−0.0900335	+	0.856612i
$569$	3.69886	−	4.10800i	0.155064	−	0.172216i	−0.660607	−	0.750732i	$-0.729701\pi$
$569$	3.69886	−	4.10800i	0.155064	−	0.172216i	0.815671	+	0.578515i	$0.196368\pi$
$570$	10.6960	−	4.76216i	0.448005	−	0.199465i
$571$	25.7440	+	11.4620i	1.07735	+	0.479669i	0.867180	−	0.497995i	$-0.165930\pi$
$571$	25.7440	+	11.4620i	1.07735	+	0.479669i	0.210174	+	0.977664i	$0.432597\pi$
$572$	−2.67652	−	2.97258i	−0.111911	−	0.124290i
$573$	−50.2148	+	36.4832i	−2.09775	+	1.52411i
$574$	−2.16312	+	1.57160i	−0.0902868	+	0.0655972i
$575$	−15.2781	−	16.9681i	−0.637142	−	0.707618i
$576$	28.9160	+	12.8742i	1.20483	+	0.536426i
$577$	−26.3401	+	11.7274i	−1.09655	+	0.488216i	−0.873616	−	0.486616i	$-0.838231\pi$
$577$	−26.3401	+	11.7274i	−1.09655	+	0.488216i	−0.222936	+	0.974833i	$0.571564\pi$
$578$	−17.7737	+	19.7396i	−0.739286	+	0.821061i
$579$	1.17449	−	11.1745i	0.0488101	−	0.464397i
$580$	−1.67088	+	0.355156i	−0.0693793	+	0.0147470i
$581$	−1.09017	+	3.35520i	−0.0452279	+	0.139197i
$582$	−81.6609	−	17.3576i	−3.38495	−	0.719494i
$583$	10.4721	−	18.1383i	0.433712	−	0.751210i
$584$	9.47214	+	16.4062i	0.391960	+	0.678894i
$585$	−7.47214	−	22.9969i	−0.308935	−	0.950804i
$586$	0.0798526	+	0.759747i	0.00329868	+	0.0313849i
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	0.690576	−	0.723259i	$-0.257357\pi$
$587$	5.23607	+	3.80423i	0.216116	+	0.157017i	−0.474461	+	0.880277i	$0.657357\pi$
$588$	13.8885			0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	29.8885	+	21.7153i	1.22945	+	0.893248i
$592$	−1.01478	−	9.65502i	−0.0417074	−	0.396819i
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	0.901056	−	0.433702i	$-0.142793\pi$
$593$	−2.01722	−	6.20837i	−0.0828373	−	0.254947i	−0.983894	+	0.178755i	$0.942793\pi$
$594$	23.4164	+	40.5584i	0.960787	+	1.66413i
$595$	−0.0901699	+	0.156179i	−0.00369661	+	0.00640271i
$596$	−6.04528	−	1.28496i	−0.247625	−	0.0526342i
$597$	18.9443	−	58.3045i	0.775337	−	2.38624i
$598$	29.2354	−	6.21418i	1.19552	−	0.254117i
$599$	1.52578	−	14.5168i	0.0623415	−	0.593140i	−0.918103	−	0.396343i	$-0.870279\pi$
$599$	1.52578	−	14.5168i	0.0623415	−	0.593140i	0.980444	−	0.196797i	$-0.0630541\pi$
$600$	−19.3675	+	21.5098i	−0.790675	+	0.878133i
$601$	27.9006	−	12.4222i	1.13809	−	0.506710i	0.250853	−	0.968025i	$-0.419289\pi$
$601$	27.9006	−	12.4222i	1.13809	−	0.506710i	0.887236	+	0.461315i	$0.152622\pi$
$602$	0.431318	+	0.192035i	0.0175792	+	0.00782676i
$603$	39.9987	+	44.4230i	1.62887	+	1.80905i
$604$	7.09017	−	5.15131i	0.288495	−	0.209604i
$605$	5.66312	−	4.11450i	0.230239	−	0.167278i
$606$	10.5108	+	11.6735i	0.426974	+	0.474202i
$607$	20.5293	+	9.14024i	0.833259	+	0.370991i	0.778605	−	0.627514i	$-0.215928\pi$
$607$	20.5293	+	9.14024i	0.833259	+	0.370991i	0.0546543	+	0.998505i	$0.482594\pi$
$608$	6.90851	−	3.07587i	0.280177	−	0.124743i
$609$	−1.41284	+	1.56912i	−0.0572512	+	0.0635839i
$610$	−1.38355	+	13.1636i	−0.0560181	+	0.532977i
$611$	7.82518	−	1.66329i	0.316573	−	0.0672897i
$612$	1.09017	−	3.35520i	0.0440675	−	0.135626i
$613$	42.9295	+	9.12494i	1.73391	+	0.368553i	0.963231	−	0.268676i	$-0.0865861\pi$
$613$	42.9295	+	9.12494i	1.73391	+	0.368553i	0.770675	+	0.637229i	$0.219919\pi$
$614$	23.2254	−	40.2276i	0.937302	−	1.62345i
$615$	11.3262	+	19.6176i	0.456718	+	0.791059i
$616$	−0.326238	−	1.00406i	−0.0131445	−	0.0404546i
$617$	−3.39426	−	32.2943i	−0.136648	−	1.30012i	−0.820984	−	0.570951i	$-0.806575\pi$
$617$	−3.39426	−	32.2943i	−0.136648	−	1.30012i	0.684336	−	0.729167i	$-0.260092\pi$
$618$	26.4164	+	19.1926i	1.06262	+	0.772041i
$619$	6.18034			0.248409			0.124204	−	0.992257i	$-0.460362\pi$
$619$	6.18034			0.248409			0.124204	+	0.992257i	$0.460362\pi$
$620$		0			0
$621$	−82.6099			−3.31502
$622$	38.1976	+	27.7522i	1.53158	+	1.11276i
$623$	−0.288910	−	2.74879i	−0.0115749	−	0.110128i
$624$	−15.7082	−	48.3449i	−0.628831	−	1.93534i
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−13.5623	+	23.4906i	−0.542059	+	0.938873i
$627$	−14.1559	−	3.00893i	−0.565332	−	0.120165i
$628$	3.98936	−	12.2780i	0.159193	−	0.489945i
$629$	1.49448	−	0.317661i	0.0595887	−	0.0126660i
$630$	−0.298335	+	2.83847i	−0.0118859	+	0.113087i
$631$	22.9918	−	25.5350i	0.915288	−	1.01653i	−0.0845094	−	0.996423i	$-0.526932\pi$
$631$	22.9918	−	25.5350i	0.915288	−	1.01653i	0.999798	−	0.0201081i	$-0.00640103\pi$
$632$	23.9169	−	10.6485i	0.951364	−	0.423575i
$633$	−68.5279	−	30.5106i	−2.72374	−	1.21269i
$634$	4.39104	+	4.87674i	0.174390	+	0.193680i
$635$	−10.0902	+	7.33094i	−0.400416	+	0.290919i
$636$	−16.9443	+	12.3107i	−0.671884	+	0.488152i
$637$	15.0368	+	16.7001i	0.595779	+	0.661680i
$638$	8.17100	+	3.63796i	0.323493	+	0.144028i
$639$	−62.6662	+	27.9008i	−2.47904	+	1.10374i
$640$	9.11224	−	10.1202i	0.360193	−	0.400035i
$641$	−1.25434	+	11.9343i	−0.0495435	+	0.471375i	0.941419	+	0.337238i	$0.109493\pi$
$641$	−1.25434	+	11.9343i	−0.0495435	+	0.471375i	−0.990963	+	0.134137i	$0.957174\pi$
$642$	29.5208	−	6.27485i	1.16509	−	0.247648i
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	−0.758738	−	0.651396i	$-0.774184\pi$
$643$	6.03444	−	18.5721i	0.237975	−	0.732412i	0.996713	−	0.0810159i	$-0.0258165\pi$
$644$	−0.814617	−	0.173152i	−0.0321004	−	0.00682315i
$645$	2.00000	−	3.46410i	0.0787499	−	0.136399i
$646$	1.38197	+	2.39364i	0.0543727	+	0.0941763i
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	0.945157	−	0.326617i	$-0.105909\pi$
$647$	−0.291796	−	0.898056i	−0.0114717	−	0.0353062i	−0.956629	+	0.291311i	$0.905909\pi$
$648$	5.70691	+	54.2977i	0.224189	+	2.13301i
$649$	−3.61803	−	2.62866i	−0.142020	−	0.103184i
$650$	20.9443			0.821502
$651$		0			0
$652$	6.61803			0.259182
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.971309	+	0.237820i	$0.0764329\pi$
$653$	38.2705	+	27.8052i	1.49764	+	1.08810i	0.526332	+	0.850279i	$0.323567\pi$
$654$	−7.63195	−	72.6132i	−0.298433	−	2.83940i
$655$	3.70820	+	11.4127i	0.144892	+	0.445930i
$656$	16.9894	+	29.4264i	0.663323	+	1.14891i
$657$	−31.6525	+	54.8237i	−1.23488	+	2.13888i
$658$	−0.923637	−	0.196325i	−0.0360071	−	0.00765355i
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	−0.669440	−	0.742866i	$-0.733466\pi$
$659$	7.92705	−	24.3970i	0.308794	−	0.950370i	0.978234	−	0.207504i	$-0.0665341\pi$
$660$	3.91259	−	0.831647i	0.152297	−	0.0323718i
$661$	0.0668272	−	0.635818i	0.00259928	−	0.0247305i	−0.993145	−	0.116886i	$-0.962709\pi$
$661$	0.0668272	−	0.635818i	0.00259928	−	0.0247305i	0.995745	+	0.0921552i	$0.0293756\pi$
$662$	2.16535	−	2.40487i	0.0841588	−	0.0934678i
$663$	7.30836	−	3.25389i	0.283833	−	0.126371i
$664$	30.5274	+	13.5917i	1.18469	+	0.527459i
$665$	−0.353210	−	0.392279i	−0.0136969	−	0.0152119i
$666$	19.5623	−	14.2128i	0.758024	−	0.550737i
$667$	−12.7639	+	9.27354i	−0.494221	+	0.359073i
$668$	−2.67652	−	2.97258i	−0.103558	−	0.115013i
$669$	−11.8252	−	5.26491i	−0.457188	−	0.203553i
$670$	11.8252	−	5.26491i	0.456847	−	0.203401i
$671$	10.9474	−	12.1584i	0.422621	−	0.469368i
$672$	−0.270059	+	2.56944i	−0.0104177	+	0.0991183i
$673$	28.3791	−	6.03217i	1.09394	−	0.232523i	0.374601	−	0.927186i	$-0.377780\pi$
$673$	28.3791	−	6.03217i	1.09394	−	0.232523i	0.719335	+	0.694663i	$0.244447\pi$
$674$	−7.38197	+	22.7194i	−0.284343	+	0.875117i
$675$	−56.6235	−	12.0357i	−2.17944	−	0.463255i
$676$	0.781153	−	1.35300i	0.0300443	−	0.0520383i
$677$	23.3607	+	40.4619i	0.897824	+	1.55508i	0.830270	+	0.557361i	$0.188186\pi$
$677$	23.3607	+	40.4619i	0.897824	+	1.55508i	0.0675535	+	0.997716i	$0.478481\pi$
$678$	−5.61803	−	17.2905i	−0.215759	−	0.664039i
$679$	0.393438	+	3.74331i	0.0150988	+	0.143655i
$680$	1.38197	+	1.00406i	0.0529960	+	0.0385038i
$681$	20.9443			0.802586
$682$		0			0
$683$	5.18034			0.198220			0.0991101	−	0.995076i	$-0.468400\pi$
$683$	5.18034			0.198220			0.0991101	+	0.995076i	$0.468400\pi$
$684$	8.35410	+	6.06961i	0.319427	+	0.232077i
$685$	−0.657672	−	6.25733i	−0.0251283	−	0.239080i
$686$	−1.64590	−	5.06555i	−0.0628407	−	0.193404i
$687$	−21.7082	−	37.5997i	−0.828220	−	1.43452i
$688$	3.00000	−	5.19615i	0.114374	−	0.198101i
$689$	−33.1480	−	7.04582i	−1.26284	−	0.268425i
$690$	−9.23607	+	28.4257i	−0.351611	+	1.08215i
$691$	−3.11084	+	0.661230i	−0.118342	+	0.0251544i	−0.266702	−	0.963779i	$-0.585934\pi$
$691$	−3.11084	+	0.661230i	−0.118342	+	0.0251544i	0.148360	+	0.988933i	$0.452601\pi$
$692$	−0.190206	+	1.80969i	−0.00723056	+	0.0687942i
$693$	2.36060	−	2.62171i	0.0896718	−	0.0995907i
$694$	35.7421	−	15.9134i	1.35675	−	0.604065i
$695$	12.2565	+	5.45694i	0.464915	+	0.206994i
$696$	13.3826	+	14.8629i	0.507267	+	0.563377i
$697$	−4.32624	+	3.14320i	−0.163868	+	0.119057i
$698$	10.3262	−	7.50245i	0.390854	−	0.283972i
$699$	−38.8557	−	43.1536i	−1.46966	−	1.63222i
$700$	−0.533138	−	0.237368i	−0.0201507	−	0.00897168i
$701$	6.39482	−	2.84716i	0.241529	−	0.107536i	−0.282403	−	0.959296i	$-0.591131\pi$
$701$	6.39482	−	2.84716i	0.241529	−	0.107536i	0.523932	+	0.851760i	$0.324465\pi$
$702$	50.7048	−	56.3134i	1.91373	−	2.12541i
$703$	−0.467465	+	4.44764i	−0.0176308	+	0.167746i
$704$	−8.28700	+	1.76146i	−0.312328	+	0.0663874i
$705$	−2.47214	+	7.60845i	−0.0931060	+	0.286551i
$706$	−11.7378	−	2.49494i	−0.441757	−	0.0938983i
$707$	0.354102	−	0.613323i	0.0133174	−	0.0230664i
$708$	2.23607	+	3.87298i	0.0840366	+	0.145556i
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	0.982795	+	0.184699i	$0.0591310\pi$
$709$	7.88854	+	24.2784i	0.296260	+	0.911796i	−0.686535	+	0.727097i	$0.740869\pi$
$710$	1.55268	+	14.7727i	0.0582709	+	0.554411i
$711$	70.7771	+	51.4226i	2.65435	+	1.92850i
$712$	−26.1803			−0.981150
$713$		0			0
$714$	−0.944272			−0.0353385
$715$	5.23607	+	3.80423i	0.195818	+	0.142270i
$716$	−0.110354	−	1.04994i	−0.00412411	−	0.0392383i
$717$	11.7082	+	36.0341i	0.437251	+	1.34572i
$718$	−17.9894	−	31.1585i	−0.671357	−	1.16282i
$719$	6.90983	−	11.9682i	0.257693	−	0.446338i	−0.707930	−	0.706282i	$-0.750371\pi$
$719$	6.90983	−	11.9682i	0.257693	−	0.446338i	0.965624	+	0.259945i	$0.0837043\pi$
$720$	35.4779	+	7.54106i	1.32218	+	0.281039i
$721$	0.454915	−	1.40008i	0.0169419	−	0.0521419i
$722$	22.1575	−	4.70971i	0.824615	−	0.175277i
$723$	4.85766	−	46.2176i	0.180658	−	1.71885i
$724$	−1.72876	+	1.91998i	−0.0642489	+	0.0713556i
$725$	−10.0999	+	4.49677i	−0.375101	+	0.167006i
$726$	33.4837	+	14.9079i	1.24270	+	0.553284i
$727$	−29.5997	−	32.8738i	−1.09779	−	1.21922i	−0.973912	−	0.226925i	$-0.927133\pi$
$727$	−29.5997	−	32.8738i	−1.09779	−	1.21922i	−0.123880	−	0.992297i	$-0.539534\pi$
$728$	−1.38197	+	1.00406i	−0.0512191	+	0.0372128i
$729$	−33.9336	+	24.6542i	−1.25680	+	0.913119i
$730$	9.17258	+	10.1872i	0.339492	+	0.377044i
$731$	0.862635	+	0.384070i	0.0319057	+	0.0142053i
$732$	−14.9462	+	6.65449i	−0.552428	+	0.245957i
$733$	2.32331	−	2.58030i	0.0858135	−	0.0953056i	−0.698709	−	0.715406i	$-0.746242\pi$
$733$	2.32331	−	2.58030i	0.0858135	−	0.0953056i	0.784522	+	0.620101i	$0.212908\pi$
$734$	−3.04435	+	28.9651i	−0.112369	+	1.06912i
$735$	−21.9811	+	4.67222i	−0.810784	+	0.172337i
$736$	−5.96556	+	18.3601i	−0.219893	+	0.676762i
$737$	−15.6504	−	3.32659i	−0.576488	−	0.122536i
$738$	−42.3156	+	73.2928i	−1.55766	+	2.69794i
$739$	−3.09017	−	5.35233i	−0.113674	−	0.196889i	0.803575	−	0.595203i	$-0.202929\pi$
$739$	−3.09017	−	5.35233i	−0.113674	−	0.196889i	−0.917249	+	0.398315i	$0.869595\pi$
$740$	−0.381966	−	1.17557i	−0.0140413	−	0.0432148i
$741$	2.44768	+	23.2881i	0.0899178	+	0.855511i
$742$	3.23607	+	2.35114i	0.118800	+	0.0863131i
$743$	50.1803			1.84094			0.920469	−	0.390815i	$-0.127807\pi$
$743$	50.1803			1.84094			0.920469	+	0.390815i	$0.127807\pi$
$744$		0			0
$745$	10.0000			0.366372
$746$	−24.8713	−	18.0701i	−0.910604	−	0.661592i
$747$	11.6722	+	111.054i	0.427065	+	4.06325i
$748$	0.291796	+	0.898056i	0.0106691	+	0.0328362i
$749$	−0.680340	−	1.17838i	−0.0248591	−	0.0430572i
$750$	−23.5623	+	40.8111i	−0.860374	+	1.49021i
$751$	21.0703	+	4.47863i	0.768866	+	0.163428i	0.575614	−	0.817722i	$-0.304763\pi$
$751$	21.0703	+	4.47863i	0.768866	+	0.163428i	0.193252	+	0.981149i	$0.438096\pi$
$752$	−3.70820	+	11.4127i	−0.135224	+	0.416178i
$753$	−5.75987	+	1.22430i	−0.209901	+	0.0446159i
$754$	1.51275	−	14.3929i	0.0550911	−	0.524157i
$755$	−9.48850	+	10.5380i	−0.345322	+	0.383519i
$756$	−1.92891	+	0.858807i	−0.0701538	+	0.0312345i
$757$	7.90443	+	3.51928i	0.287291	+	0.127910i	0.545323	−	0.838226i	$-0.316407\pi$
$757$	7.90443	+	3.51928i	0.287291	+	0.127910i	−0.258031	+	0.966137i	$0.583074\pi$
$758$	−2.28602	−	2.53889i	−0.0830321	−	0.0922165i
$759$	29.8885	−	21.7153i	1.08489	−	0.788215i
$760$	−4.04508	+	2.93893i	−0.146731	+	0.106606i
$761$	1.33826	+	1.48629i	0.0485119	+	0.0538780i	0.766912	−	0.641752i	$-0.221792\pi$
$761$	1.33826	+	1.48629i	0.0485119	+	0.0538780i	−0.718400	+	0.695630i	$0.755125\pi$
$762$	−59.6590	−	26.5619i	−2.16122	−	0.962237i
$763$	−3.00721	+	1.33889i	−0.108868	+	0.0484712i
$764$	−7.93194	+	8.80931i	−0.286968	+	0.318710i
$765$	−0.596670	+	5.67693i	−0.0215726	+	0.205250i
$766$	37.8078	−	8.03630i	1.36605	−	0.290363i
$767$	−2.23607	+	6.88191i	−0.0807397	+	0.248491i
$768$	42.9295	+	9.12494i	1.54908	+	0.329268i
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	−0.0236947	−	0.999719i	$-0.507543\pi$
$769$	23.6803	−	41.0156i	0.853935	−	1.47906i	0.877630	−	0.479339i	$-0.159124\pi$
$770$	−0.381966	−	0.661585i	−0.0137651	−	0.0238419i
$771$	−1.94427	−	5.98385i	−0.0700212	−	0.215503i
$772$	−0.224307	−	2.13414i	−0.00807300	−	0.0768095i
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	0.737756	−	0.675068i	$-0.235886\pi$
$773$	9.00000	+	6.53888i	0.323708	+	0.235187i	−0.414048	+	0.910255i	$0.635886\pi$
$774$	14.9443			0.537161
$775$		0			0
$776$	35.6525			1.27985
$777$	−1.23607	−	0.898056i	−0.0443437	−	0.0322176i
$778$	3.02550	+	28.7857i	0.108469	+	1.03202i
$779$	−4.83688	−	14.8864i	−0.173299	−	0.533360i
$780$	−3.23607	−	5.60503i	−0.115870	−	0.200692i
$781$	9.18034	−	15.9008i	0.328498	−	0.568976i
$782$	−6.90154	−	1.46697i	−0.246799	−	0.0524587i
$783$	−12.3607	+	38.0423i	−0.441735	+	1.35952i
$784$	−32.9716	+	7.00833i	−1.17756	+	0.250297i
$785$	−2.18345	+	20.7741i	−0.0779306	+	0.741460i
$786$	−42.0434	+	46.6939i	−1.49964	+	1.66552i
$787$	6.71230	−	2.98851i	0.239268	−	0.106529i	−0.283600	−	0.958943i	$-0.591529\pi$
$787$	6.71230	−	2.98851i	0.239268	−	0.106529i	0.522868	+	0.852414i	$0.324862\pi$
$788$	6.44573	+	2.86982i	0.229620	+	0.102233i
$789$	50.3143	+	55.8797i	1.79124	+	1.98937i
$790$	15.3262	−	11.1352i	0.545283	−	0.396171i
$791$	−0.663119	+	0.481784i	−0.0235778	+	0.0171303i
$792$	−22.3599	−	24.8332i	−0.794526	−	0.882410i
$793$	−24.1835	−	10.7672i	−0.858781	−	0.382354i
$794$	−10.3470	+	4.60680i	−0.367202	+	0.163489i
$795$	22.6759	−	25.1841i	0.804230	−	0.893188i
$796$	1.22384	−	11.6441i	0.0433779	−	0.412713i
$797$	54.2054	−	11.5217i	1.92005	−	0.408120i	0.920193	−	0.391464i	$-0.128031\pi$
$797$	54.2054	−	11.5217i	1.92005	−	0.408120i	0.999861	−	0.0166563i	$-0.00530210\pi$
$798$	0.854102	−	2.62866i	0.0302349	−	0.0930534i
$799$	−1.84727	−	0.392650i	−0.0653519	−	0.0138910i
$800$	−6.76393	+	11.7155i	−0.239141	+	0.414205i
$801$	−43.7426	−	75.7645i	−1.54557	−	2.67701i
$802$	19.0902	+	58.7535i	0.674097	+	2.07466i
$803$	−1.77116	−	16.8514i	−0.0625028	−	0.594675i
$804$	12.9443	+	9.40456i	0.456509	+	0.331673i
$805$	1.34752			0.0474940
$806$		0			0
$807$	35.7771			1.25941
$808$	−5.42705	−	3.94298i	−0.190923	−	0.138714i
$809$	−2.44768	−	23.2881i	−0.0860559	−	0.818767i	−0.949383	−	0.314122i	$-0.898290\pi$
$809$	−2.44768	−	23.2881i	−0.0860559	−	0.818767i	0.863327	−	0.504645i	$-0.168377\pi$
$810$	12.2082	+	37.5730i	0.428953	+	1.32018i
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	0.999953	−	0.00966502i	$-0.00307652\pi$
$811$	14.0000	+	24.2487i	0.491606	+	0.851487i	−0.508347	+	0.861152i	$0.669743\pi$
$812$	−0.201626	+	0.349227i	−0.00707569	+	0.0122555i
$813$	−44.8858	−	9.54076i	−1.57421	−	0.334609i
$814$	−2.00000	+	6.15537i	−0.0701000	+	0.215746i
$815$	−10.4742	+	2.22636i	−0.366895	+	0.0779860i
$816$	−1.25434	+	11.9343i	−0.0439107	+	0.417783i
$817$	−1.84943	+	2.05400i	−0.0647034	+	0.0718604i
$818$	−5.64602	+	2.51377i	−0.197409	+	0.0878919i
$819$	−5.21470	−	2.32174i	−0.182216	−	0.0811280i
$820$	2.89482	+	3.21502i	0.101091	+	0.112273i
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	−0.928516	−	0.371293i	$-0.878915\pi$
$821$	−24.7082	+	17.9516i	−0.862322	+	0.626514i	0.0661935	+	0.997807i	$0.478915\pi$
$822$	26.6525	−	19.3642i	0.929612	−	0.675403i
$823$	−9.56308	−	10.6209i	−0.333348	−	0.370220i	0.553047	−	0.833150i	$-0.313465\pi$
$823$	−9.56308	−	10.6209i	−0.333348	−	0.370220i	−0.886395	+	0.462930i	$0.846798\pi$
$824$	−12.7387	−	5.67165i	−0.443775	−	0.197581i
$825$	23.6504	−	10.5298i	0.823400	−	0.366601i
$826$	0.571506	−	0.634721i	0.0198852	−	0.0220848i
$827$	−1.81331	+	17.2525i	−0.0630550	+	0.599928i	0.916679	+	0.399624i	$0.130859\pi$
$827$	−1.81331	+	17.2525i	−0.0630550	+	0.599928i	−0.979734	+	0.200303i	$0.935807\pi$
$828$	−25.7846	+	5.48069i	−0.896078	+	0.190467i
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	−0.819187	−	0.573527i	$-0.805575\pi$
$829$	5.20163	−	16.0090i	0.180660	−	0.556014i	0.999847	+	0.0175128i	$0.00557479\pi$
$830$	23.6519	+	5.02738i	0.820971	+	0.174503i
$831$	−20.4721	+	35.4588i	−0.710171	+	1.23005i
$832$	6.85410	+	11.8717i	0.237623	+	0.411576i
$833$	−1.63932	−	5.04531i	−0.0567991	−	0.174810i
$834$	7.34304	+	69.8644i	0.254269	+	2.41921i
$835$	5.23607	+	3.80423i	0.181202	+	0.131651i
$836$	−2.76393			−0.0955926
$837$		0			0
$838$	−16.3820			−0.565906
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	0.104949	−	0.994478i	$-0.466532\pi$
$839$	−23.4164	−	17.0130i	−0.808424	−	0.587355i	−0.913373	+	0.407123i	$0.866532\pi$
$840$	−0.178556	−	1.69885i	−0.00616076	−	0.0586158i
$841$	−6.60081	−	20.3152i	−0.227614	−	0.700525i
$842$	−23.7533	−	41.1419i	−0.818592	−	1.41784i
$843$	27.5066	−	47.6428i	0.947377	−	1.64090i
$844$	−14.0132	−	2.97859i	−0.482353	−	0.102527i
$845$	−0.781153	+	2.40414i	−0.0268725	+	0.0827050i
$846$	−29.2354	+	6.21418i	−1.00513	+	0.213648i
$847$	0.172731	−	1.64342i	0.00593510	−	0.0564687i
$848$	34.0138	−	37.7761i	1.16804	−	1.29724i
$849$	41.0586	−	18.2805i	1.40913	−	0.627385i
$850$	−4.51682	−	2.01102i	−0.154926	−	0.0689773i
$851$	−7.63907	−	8.48404i	−0.261864	−	0.290829i
$852$	−14.8541	+	10.7921i	−0.508893	+	0.369733i
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	−0.724640	−	0.689127i	$-0.757994\pi$
$853$	−8.56231	+	6.22088i	−0.293168	+	0.212999i	0.431473	+	0.902126i	$0.357994\pi$
$854$	2.09077	+	2.32204i	0.0715448	+	0.0794585i
$855$	−15.2637	−	6.79584i	−0.522008	−	0.232413i
$856$	−11.7743	+	5.24224i	−0.402436	+	0.179176i
$857$	−37.2476	+	41.3676i	−1.27235	+	1.41309i	−0.405834	+	0.913947i	$0.633019\pi$
$857$	−37.2476	+	41.3676i	−1.27235	+	1.41309i	−0.866519	+	0.499144i	$0.833648\pi$
$858$	−3.54232	+	33.7029i	−0.120933	+	1.15060i
$859$	−2.06532	+	0.438996i	−0.0704677	+	0.0149784i	−0.243011	−	0.970024i	$-0.578135\pi$
$859$	−2.06532	+	0.438996i	−0.0704677	+	0.0149784i	0.172543	+	0.985002i	$0.444802\pi$
$860$	0.236068	−	0.726543i	0.00804985	−	0.0247749i
$861$	5.23067	+	1.11181i	0.178261	+	0.0378905i
$862$	−9.70820	+	16.8151i	−0.330663	+	0.572725i
$863$	4.90983	+	8.50408i	0.167133	+	0.289482i	0.937411	−	0.348226i	$-0.113216\pi$
$863$	4.90983	+	8.50408i	0.167133	+	0.289482i	−0.770278	+	0.637708i	$0.779883\pi$
$864$	15.1246	+	46.5488i	0.514550	+	1.58362i
$865$	−0.307760	−	2.92814i	−0.0104642	−	0.0995598i
$866$	−13.3262	−	9.68208i	−0.452844	−	0.329010i
$867$	53.1246			1.80421
$868$		0			0
$869$	−23.4164			−0.794347
$870$	11.7082	+	8.50651i	0.396945	+	0.288398i
$871$	2.70609	+	25.7467i	0.0916924	+	0.872394i
$872$	9.63525	+	29.6543i	0.326291	+	1.00422i
$873$	59.5689	+	103.176i	2.01610	+	3.49199i
$874$	10.3262	−	17.8856i	0.349290	−	0.604988i
$875$	2.07818	+	0.441732i	0.0702554	+	0.0149333i
$876$	−5.23607	+	16.1150i	−0.176910	+	0.544474i
$877$	17.6612	−	3.75400i	0.596375	−	0.126763i	0.100172	−	0.994970i	$-0.468061\pi$
$877$	17.6612	−	3.75400i	0.596375	−	0.126763i	0.496203	+	0.868207i	$0.334727\pi$
$878$	0.199632	−	1.89937i	0.00673724	−	0.0641006i
$879$	1.02234	−	1.13542i	0.0344827	−	0.0382969i
$880$	−8.86889	+	3.94868i	−0.298970	+	0.133110i
$881$	−18.6004	−	8.28143i	−0.626664	−	0.279009i	0.0687326	−	0.997635i	$-0.478104\pi$
$881$	−18.6004	−	8.28143i	−0.626664	−	0.279009i	−0.695396	+	0.718626i	$0.744771\pi$
$882$	−56.1785	−	62.3925i	−1.89163	−	2.10087i
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	−0.0641312	−	0.997941i	$-0.520428\pi$
$883$	25.7082	−	18.6781i	0.865150	−	0.628568i	0.929281	+	0.369373i	$0.120428\pi$
$884$	1.23607	−	0.898056i	0.0415735	−	0.0302049i
$885$	−4.84187	−	5.37745i	−0.162758	−	0.180761i
$886$	45.3913	+	20.2095i	1.52495	+	0.678951i
$887$	24.7287	−	11.0099i	0.830307	−	0.369676i	0.0528421	−	0.998603i	$-0.483172\pi$
$887$	24.7287	−	11.0099i	0.830307	−	0.369676i	0.777465	+	0.628926i	$0.216505\pi$
$888$	−9.68375	+	10.7549i	−0.324965	+	0.360911i
$889$	−0.307760	+	2.92814i	−0.0103219	+	0.0982068i
$890$	−18.5303	+	3.93874i	−0.621137	+	0.132027i
$891$	15.0902	−	46.4428i	0.505540	−	1.55589i
$892$	−2.41811	−	0.513986i	−0.0809644	−	0.0172095i
$893$	2.76393	−	4.78727i	0.0924915	−	0.160200i
$894$	26.1803	+	45.3457i	0.875602	+	1.51659i
$895$	0.527864	+	1.62460i	0.0176445	+	0.0543043i
$896$	−0.336036	−	3.19717i	−0.0112262	−	0.106810i
$897$	−48.3607	−	35.1361i	−1.61472	−	1.17316i
$898$	−50.6525			−1.69030
$899$		0			0
$900$	−18.4721			−0.615738
$901$	6.47214	+	4.70228i	0.215618	+	0.156656i
$902$	−2.36783	−	22.5284i	−0.0788401	−	0.750113i
$903$	−0.291796	−	0.898056i	−0.00971037	−	0.0298854i
$904$	3.88197	+	6.72376i	0.129112	+	0.223629i
$905$	2.09017	−	3.62028i	0.0694796	−	0.120342i
$906$	−72.6267	−	15.4373i	−2.41286	−	0.512869i
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	0.746329	+	0.665577i	$0.231814\pi$
$907$	−7.48936	+	23.0499i	−0.248680	+	0.765358i	−0.995009	+	0.0997816i	$0.968186\pi$
$908$	3.91259	−	0.831647i	0.129844	−	0.0275992i
$909$	2.34315	−	22.2936i	0.0777175	−	0.739432i
$910$	−0.827091	+	0.918578i	−0.0274178	+	0.0304505i
$911$	16.6086	−	7.39461i	0.550266	−	0.244994i	−0.112719	−	0.993627i	$-0.535956\pi$
$911$	16.6086	−	7.39461i	0.550266	−	0.244994i	0.662985	+	0.748633i	$0.269289\pi$
$912$	−32.0879	−	14.2865i	−1.06254	−	0.473072i
$913$	−19.9993	−	22.2115i	−0.661882	−	0.735094i
$914$	4.00000	−	2.90617i	0.132308	−	0.0961276i
$915$	21.4164	−	15.5599i	0.708005	−	0.514395i
$916$	−5.54829	−	6.16201i	−0.183321	−	0.203598i
$917$	2.58791	+	1.15221i	0.0854602	+	0.0380493i
$918$	−16.3420	+	7.27593i	−0.539366	+	0.240141i
$919$	−9.68375	+	10.7549i	−0.319437	+	0.354771i	−0.881382	−	0.472403i	$-0.843387\pi$
$919$	−9.68375	+	10.7549i	−0.319437	+	0.354771i	0.561945	+	0.827175i	$0.310053\pi$
$920$	1.33419	−	12.6940i	0.0439871	−	0.418509i
$921$	−90.8716	+	19.3153i	−2.99432	+	0.636462i
$922$	17.1803	−	52.8756i	0.565804	−	1.74137i
$923$	−29.0590	−	6.17668i	−0.956489	−	0.203308i
$924$	0.472136	−	0.817763i	0.0155321	−	0.0269024i
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	−1.29180	−	3.97574i	−0.0424511	−	0.130651i
$927$	−4.87069	−	46.3415i	−0.159974	−	1.52205i
$928$	7.56231	+	5.49434i	0.248245	+	0.180360i
$929$	−20.0000			−0.656179			−0.328089	−	0.944647i	$-0.606405\pi$
$929$	−20.0000			−0.656179			−0.328089	+	0.944647i	$0.606405\pi$
$930$		0			0
$931$	15.5279			0.508905
$932$	−8.97214	−	6.51864i	−0.293892	−	0.213525i
$933$	−9.87058	−	93.9123i	−0.323148	−	3.07455i
$934$	2.35410	+	7.24518i	0.0770286	+	0.237070i
$935$	−0.763932	−	1.32317i	−0.0249832	−	0.0432723i
$936$	−27.0344	+	46.8250i	−0.883648	+	1.53052i
$937$	−8.85784	−	1.88279i	−0.289373	−	0.0615081i	0.0609381	−	0.998142i	$-0.480591\pi$
$937$	−8.85784	−	1.88279i	−0.289373	−	0.0615081i	−0.350311	+	0.936633i	$0.613924\pi$
$938$	0.944272	−	2.90617i	0.0308316	−	0.0948898i
$939$	53.0637	−	11.2790i	1.73167	−	0.368078i
$940$	−0.159705	+	1.51949i	−0.00520901	+	0.0495604i
$941$	−25.4270	+	28.2395i	−0.828895	+	0.920581i	−0.997883	−	0.0650367i	$-0.979284\pi$
$941$	−25.4270	+	28.2395i	−0.828895	+	0.920581i	0.168988	+	0.985618i	$0.445950\pi$
$942$	−99.9180	+	44.4863i	−3.25550	+	1.44944i
$943$	36.5029	+	16.2521i	1.18870	+	0.529243i
$944$	−7.26281	−	8.06617i	−0.236384	−	0.262531i
$945$	2.76393	−	2.00811i	0.0899107	−	0.0653240i
$946$	−3.23607	+	2.35114i	−0.105214	+	0.0764422i
$947$	−8.73599	−	9.70230i	−0.283881	−	0.315282i	0.584292	−	0.811544i	$-0.301372\pi$
$947$	−8.73599	−	9.70230i	−0.283881	−	0.315282i	−0.868173	+	0.496261i	$0.834706\pi$
$948$	21.3920	+	9.52431i	0.694778	+	0.309335i
$949$	−25.0461	+	11.1513i	−0.813032	+	0.361985i
$950$	9.68375	−	10.7549i	0.314182	−	0.348935i
$951$	1.37190	−	13.0527i	0.0444868	−	0.423263i
$952$	0.394440	−	0.0838409i	0.0127839	−	0.00271730i
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	−0.410585	−	0.911822i	$-0.634675\pi$
$953$	14.1246	−	43.4711i	0.457541	−	1.40817i	0.868126	−	0.496344i	$-0.165325\pi$
$954$	123.843	+	26.3237i	4.00957	+	0.852261i
$955$	9.59017	−	16.6107i	0.310331	−	0.537508i
$956$	3.61803	+	6.26662i	0.117016	+	0.202677i
$957$	−5.52786	−	17.0130i	−0.178690	−	0.549953i
$958$	−3.93936	−	37.4805i	−0.127275	−	1.21094i
$959$	−1.20163	−	0.873032i	−0.0388025	−	0.0281917i
$960$	−13.7082			−0.442430
$961$		0			0
$962$	10.4721			0.337635
$963$	−34.8435	−	25.3153i	−1.12281	−	0.815773i
$964$	−0.927731	−	8.82677i	−0.0298802	−	0.284291i
$965$	1.07295	+	3.30220i	0.0345395	+	0.106301i
$966$	3.52786	+	6.11044i	0.113507	+	0.196600i
$967$	−30.1803	+	52.2739i	−0.970534	+	1.68101i	−0.276587	+	0.960989i	$0.589203\pi$
$967$	−30.1803	+	52.2739i	−0.970534	+	1.68101i	−0.693947	+	0.720026i	$0.744130\pi$
$968$	−15.3104	−	3.25433i	−0.492096	−	0.104598i
$969$	1.70820	−	5.25731i	0.0548754	−	0.168889i
$970$	25.2346	−	5.36378i	0.810235	−	0.172221i
$971$	2.92680	−	27.8466i	0.0939254	−	0.893640i	−0.841534	−	0.540205i	$-0.818347\pi$
$971$	2.92680	−	27.8466i	0.0939254	−	0.893640i	0.935459	−	0.353435i	$-0.114987\pi$
$972$	−14.7209	+	16.3492i	−0.472172	+	0.524400i
$973$	2.89337	−	1.28821i	0.0927571	−	0.0412981i
$974$	−28.4337	−	12.6595i	−0.911076	−	0.405637i
$975$	−28.0289	−	31.1293i	−0.897643	−	0.996934i
$976$	32.1246	−	23.3399i	1.02828	−	0.747092i
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.226599	−	0.973988i	$-0.427239\pi$
$977$	38.2254	−	27.7724i	1.22294	−	0.888518i	0.996341	+	0.0854705i	$0.0272393\pi$
$978$	−37.5174	−	41.6673i	−1.19967	−	1.33237i
$979$	21.3920	+	9.52431i	0.683690	+	0.304398i
$980$	−3.92075	+	1.74563i	−0.125244	+	0.0557621i
$981$	−69.7191	+	77.4309i	−2.22596	+	2.47218i
$982$	−0.737524	+	7.01708i	−0.0235353	+	0.223924i
$983$	−38.6641	+	8.21831i	−1.23319	+	0.262123i	−0.777997	−	0.628268i	$-0.783764\pi$
$983$	−38.6641	+	8.21831i	−1.23319	+	0.262123i	−0.455196	+	0.890391i	$0.650431\pi$
$984$	15.6525	−	48.1734i	0.498983	−	1.53571i
$985$	−11.1669	−	2.37360i	−0.355808	−	0.0756293i
$986$	−1.70820	+	2.95870i	−0.0544003	+	0.0942241i
$987$	0.944272	+	1.63553i	0.0300565	+	0.0520594i
$988$	1.38197	+	4.25325i	0.0439662	+	0.135314i
$989$	−0.737524	−	7.01708i	−0.0234519	−	0.223130i
$990$	−19.5623	−	14.2128i	−0.621731	−	0.451714i
$991$	−16.5410			−0.525443			−0.262721	−	0.964872i	$-0.584620\pi$
$991$	−16.5410			−0.525443			−0.262721	+	0.964872i	$0.584620\pi$
$992$		0			0
$993$	−6.47214			−0.205387
$994$	2.83688	+	2.06111i	0.0899804	+	0.0653746i
$995$	1.98022	+	18.8405i	0.0627771	+	0.597284i
$996$	9.23607	+	28.4257i	0.292656	+	0.900703i
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	0.999198	−	0.0400314i	$-0.0127458\pi$
$997$	14.6803	+	25.4271i	0.464931	+	0.805284i	−0.534267	+	0.845316i	$0.679412\pi$
$998$	5.32624	−	9.22531i	0.168599	−	0.292022i
$999$	−28.3118	−	6.01785i	−0.895745	−	0.190396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.a.816.1		8
31.2	even	5		961.2.g.h.846.1		8
31.3	odd	30		961.2.g.d.338.1		8
31.4	even	5		961.2.c.e.439.2		4
31.5	even	3		961.2.d.c.374.1		4
31.6	odd	6		961.2.g.d.732.1		8
31.7	even	15		961.2.c.e.521.2		4
31.8	even	5		961.2.g.h.547.1		8
31.9	even	15		961.2.d.d.531.1		4
31.10	even	15		961.2.d.d.628.1		4
31.11	odd	30		961.2.a.f.1.2		2
31.12	odd	30		961.2.g.e.448.1		8
31.13	odd	30		961.2.d.a.388.1		4
31.14	even	15		961.2.g.h.844.1		8
31.15	odd	10		961.2.g.d.235.1		8
31.16	even	5	inner	961.2.g.a.235.1		8
31.17	odd	30		961.2.g.e.844.1		8
31.18	even	15		961.2.d.c.388.1		4
31.19	even	15		961.2.g.h.448.1		8
31.20	even	15		31.2.a.a.1.2	✓	2
31.21	odd	30		961.2.d.g.628.1		4
31.22	odd	30		961.2.d.g.531.1		4
31.23	odd	10		961.2.g.e.547.1		8
31.24	odd	30		961.2.c.c.521.2		4
31.25	even	3	inner	961.2.g.a.732.1		8
31.26	odd	6		961.2.d.a.374.1		4
31.27	odd	10		961.2.c.c.439.2		4
31.28	even	15	inner	961.2.g.a.338.1		8
31.29	odd	10		961.2.g.e.846.1		8
31.30	odd	2		961.2.g.d.816.1		8
93.11	even	30		8649.2.a.c.1.1		2
93.20	odd	30		279.2.a.a.1.1		2
124.51	odd	30		496.2.a.i.1.2		2
155.82	odd	60		775.2.b.d.249.4		4
155.113	odd	60		775.2.b.d.249.1		4
155.144	even	30		775.2.a.d.1.1		2
217.20	odd	30		1519.2.a.a.1.2		2
248.51	odd	30		1984.2.a.n.1.1		2
248.237	even	30		1984.2.a.r.1.2		2
341.175	odd	30		3751.2.a.b.1.1		2
372.299	even	30		4464.2.a.bf.1.1		2
403.51	even	30		5239.2.a.f.1.1		2
465.299	odd	30		6975.2.a.y.1.2		2
527.237	even	30		8959.2.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.a.a.1.2	✓	2	31.20	even	15
279.2.a.a.1.1		2	93.20	odd	30
496.2.a.i.1.2		2	124.51	odd	30
775.2.a.d.1.1		2	155.144	even	30
775.2.b.d.249.1		4	155.113	odd	60
775.2.b.d.249.4		4	155.82	odd	60
961.2.a.f.1.2		2	31.11	odd	30
961.2.c.c.439.2		4	31.27	odd	10
961.2.c.c.521.2		4	31.24	odd	30
961.2.c.e.439.2		4	31.4	even	5
961.2.c.e.521.2		4	31.7	even	15
961.2.d.a.374.1		4	31.26	odd	6
961.2.d.a.388.1		4	31.13	odd	30
961.2.d.c.374.1		4	31.5	even	3
961.2.d.c.388.1		4	31.18	even	15
961.2.d.d.531.1		4	31.9	even	15
961.2.d.d.628.1		4	31.10	even	15
961.2.d.g.531.1		4	31.22	odd	30
961.2.d.g.628.1		4	31.21	odd	30
961.2.g.a.235.1		8	31.16	even	5	inner
961.2.g.a.338.1		8	31.28	even	15	inner
961.2.g.a.732.1		8	31.25	even	3	inner
961.2.g.a.816.1		8	1.1	even	1	trivial
961.2.g.d.235.1		8	31.15	odd	10
961.2.g.d.338.1		8	31.3	odd	30
961.2.g.d.732.1		8	31.6	odd	6
961.2.g.d.816.1		8	31.30	odd	2
961.2.g.e.448.1		8	31.12	odd	30
961.2.g.e.547.1		8	31.23	odd	10
961.2.g.e.844.1		8	31.17	odd	30
961.2.g.e.846.1		8	31.29	odd	10
961.2.g.h.448.1		8	31.19	even	15
961.2.g.h.547.1		8	31.8	even	5
961.2.g.h.844.1		8	31.14	even	15
961.2.g.h.846.1		8	31.2	even	5
1519.2.a.a.1.2		2	217.20	odd	30
1984.2.a.n.1.1		2	248.51	odd	30
1984.2.a.r.1.2		2	248.237	even	30
3751.2.a.b.1.1		2	341.175	odd	30
4464.2.a.bf.1.1		2	372.299	even	30
5239.2.a.f.1.1		2	403.51	even	30
6975.2.a.y.1.2		2	465.299	odd	30
8649.2.a.c.1.1		2	93.11	even	30
8959.2.a.b.1.2		2	527.237	even	30

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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.g (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30902 - 0.951057i) q^{2} +(0.338261 + 3.21834i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.230909 - 0.0490813i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-7.30885 + 1.55354i) q^{9} +O(q^{10})\)	\(q+(-1.30902 - 0.951057i) q^{2} +(0.338261 + 3.21834i) q^{3} +(0.190983 + 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(-0.230909 - 0.0490813i) q^{7} +(-0.690983 + 2.12663i) q^{8} +(-7.30885 + 1.55354i) q^{9} +(-0.169131 + 1.60917i) q^{10} +(1.33826 - 1.48629i) q^{11} +(-1.82709 + 0.813473i) q^{12} +(-2.95630 - 1.31623i) q^{13} +(0.255585 + 0.283856i) q^{14} +(2.61803 - 1.90211i) q^{15} +(3.92705 - 2.85317i) q^{16} +(0.511170 + 0.567712i) q^{17} +(11.0449 + 4.91752i) q^{18} +(-2.04275 + 0.909491i) q^{19} +(0.413545 - 0.459289i) q^{20} +(0.0798526 - 0.759747i) q^{21} +(-3.16535 + 0.672816i) q^{22} +(1.76393 - 5.42882i) q^{23} +(-7.07794 - 1.50446i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} +(-4.47214 - 13.7638i) q^{27} +(-0.0152505 - 0.145099i) q^{28} +(-2.23607 - 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 + 3.80423i) q^{33} +(-0.129204 - 1.22930i) q^{34} +(0.0729490 + 0.224514i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(3.53897 + 0.752232i) q^{38} +(3.23607 - 9.95959i) q^{39} +(2.18720 - 0.464905i) q^{40} +(-0.731699 + 6.96165i) q^{41} +(-0.827091 + 0.918578i) q^{42} +(1.12920 - 0.502754i) q^{43} +(1.12920 + 0.502754i) q^{44} +(4.99983 + 5.55288i) q^{45} +(-7.47214 + 5.42882i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(10.5108 + 11.6735i) q^{48} +(-6.34391 - 2.82449i) q^{49} +(-5.91259 + 2.63245i) q^{50} +(-1.65418 + 1.83716i) q^{51} +(0.209057 - 1.98904i) q^{52} +(10.2433 - 2.17728i) q^{53} +(-7.23607 + 22.2703i) q^{54} +(-1.95630 - 0.415823i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +(1.38197 + 4.25325i) q^{58} +(-0.233733 - 2.22382i) q^{59} +(1.61803 + 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 - 2.48990i) q^{64} +(0.338261 + 3.21834i) q^{65} +(-3.23607 - 9.95959i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(18.0685 + 3.84057i) q^{69} +(0.118034 - 0.363271i) q^{70} +(8.97973 - 1.90870i) q^{71} +(1.74648 - 16.6167i) q^{72} +(5.66897 - 6.29602i) q^{73} +(-2.95630 + 1.31623i) q^{74} +(11.8252 + 5.26491i) q^{75} +(-0.924716 - 1.02700i) q^{76} +(-0.381966 + 0.277515i) q^{77} +(-13.7082 + 9.95959i) q^{78} +(-7.83432 - 8.70089i) q^{79} +(-4.43444 - 1.97434i) q^{80} +(22.3055 - 9.93105i) q^{81} +(7.57873 - 8.41704i) q^{82} +(1.56210 - 14.8624i) q^{83} +(0.461819 - 0.0981626i) q^{84} +(0.236068 - 0.726543i) q^{85} +(-1.95630 - 0.415823i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +(3.61803 + 11.1352i) q^{89} +(-1.26377 - 12.0239i) q^{90} +(0.618034 + 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 + 1.31433i) q^{95} +(-1.14399 - 10.8843i) q^{96} +(-4.92705 - 15.1639i) q^{97} +(5.61803 + 9.73072i) q^{98} +(-7.47214 + 12.9421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20} + 2 q^{21} - 4 q^{22} + 32 q^{23} + 16 q^{25} + 12 q^{26} - 4 q^{28} - 24 q^{30} - 36 q^{32} + 24 q^{33} + 4 q^{34} + 14 q^{35} - 14 q^{36} + 8 q^{37} + 8 q^{39} + 5 q^{40} + 7 q^{41} + 6 q^{42} + 4 q^{43} + 4 q^{44} - 7 q^{45} - 24 q^{46} - 16 q^{47} - 6 q^{48} - 18 q^{49} - 12 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 40 q^{54} + 2 q^{55} + 20 q^{56} - 20 q^{57} + 20 q^{58} + 5 q^{59} + 4 q^{60} - 24 q^{61} + 32 q^{63} - 14 q^{64} - 6 q^{65} - 8 q^{66} - 32 q^{67} + 16 q^{68} - 4 q^{69} - 8 q^{70} + 27 q^{71} - 25 q^{72} - 6 q^{73} - 6 q^{74} + 24 q^{75} - 5 q^{76} - 12 q^{77} - 56 q^{78} + 10 q^{79} - 9 q^{80} + 41 q^{81} - 14 q^{82} - 26 q^{83} + 14 q^{84} - 16 q^{85} + 2 q^{86} + 20 q^{89} + 19 q^{90} - 4 q^{91} + 64 q^{92} + 32 q^{94} + 10 q^{95} + 22 q^{96} - 26 q^{97} + 36 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - 4 * q^5 + 12 * q^6 - 7 * q^7 - 10 * q^8 - 7 * q^9 + 3 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 4 * q^14 + 12 * q^15 + 18 * q^16 + 8 * q^17 + 19 * q^18 - 5 * q^19 - 3 * q^20 + 2 * q^21 - 4 * q^22 + 32 * q^23 + 16 * q^25 + 12 * q^26 - 4 * q^28 - 24 * q^30 - 36 * q^32 + 24 * q^33 + 4 * q^34 + 14 * q^35 - 14 * q^36 + 8 * q^37 + 8 * q^39 + 5 * q^40 + 7 * q^41 + 6 * q^42 + 4 * q^43 + 4 * q^44 - 7 * q^45 - 24 * q^46 - 16 * q^47 - 6 * q^48 - 18 * q^49 - 12 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 40 * q^54 + 2 * q^55 + 20 * q^56 - 20 * q^57 + 20 * q^58 + 5 * q^59 + 4 * q^60 - 24 * q^61 + 32 * q^63 - 14 * q^64 - 6 * q^65 - 8 * q^66 - 32 * q^67 + 16 * q^68 - 4 * q^69 - 8 * q^70 + 27 * q^71 - 25 * q^72 - 6 * q^73 - 6 * q^74 + 24 * q^75 - 5 * q^76 - 12 * q^77 - 56 * q^78 + 10 * q^79 - 9 * q^80 + 41 * q^81 - 14 * q^82 - 26 * q^83 + 14 * q^84 - 16 * q^85 + 2 * q^86 + 20 * q^89 + 19 * q^90 - 4 * q^91 + 64 * q^92 + 32 * q^94 + 10 * q^95 + 22 * q^96 - 26 * q^97 + 36 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more