LMFDB - Embedded newform 961.2.g.a.235.1

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			235.1
Root			$0.669131 + 0.743145i$ of defining polynomial
Character	$\chi$	$=$	961.235
Dual form			961.2.g.a.732.1

$q$-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} +(-2.95630 + 1.31623i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(0.157960 + 0.175433i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(4.99983 - 5.55288i) q^{9} +(1.47815 + 0.658114i) q^{10} +(-1.95630 + 0.415823i) q^{11} +(0.209057 + 1.98904i) q^{12} +(0.338261 - 3.21834i) q^{13} +(-0.373619 - 0.0794152i) q^{14} +(2.61803 + 1.90211i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-0.747238 - 0.158830i) q^{17} +(-1.26377 + 12.0239i) q^{18} +(0.233733 + 2.22382i) q^{19} +(-0.604528 + 0.128496i) q^{20} +(-0.697887 - 0.310719i) q^{21} +(2.16535 - 2.40487i) q^{22} +(1.76393 + 5.42882i) q^{23} +(4.84187 + 5.37745i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} +(-4.47214 + 13.7638i) q^{27} +(0.133284 - 0.0593421i) q^{28} +(-2.23607 + 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 - 3.80423i) q^{33} +(1.12920 - 0.502754i) q^{34} +(0.0729490 - 0.224514i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-2.42094 - 2.68872i) q^{38} +(3.23607 + 9.95959i) q^{39} +(-1.49622 + 1.66172i) q^{40} +(6.39482 + 2.84716i) q^{41} +(1.20906 - 0.256993i) q^{42} +(-0.129204 - 1.22930i) q^{43} +(-0.129204 + 1.22930i) q^{44} +(-7.30885 - 1.55354i) q^{45} +(-7.47214 - 5.42882i) q^{46} +(-2.00000 - 1.45309i) q^{47} +(-15.3649 - 3.26592i) q^{48} +(0.725874 - 6.90623i) q^{49} +(0.676522 + 6.43668i) q^{50} +(2.41811 - 0.513986i) q^{51} +(-1.82709 - 0.813473i) q^{52} +(-7.00723 + 7.78231i) q^{53} +(-7.23607 - 22.2703i) q^{54} +(1.33826 + 1.48629i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +(1.38197 - 4.25325i) q^{58} +(2.04275 - 0.909491i) q^{59} +(1.61803 - 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 + 2.48990i) q^{64} +(-2.95630 + 1.31623i) q^{65} +(-3.23607 + 9.95959i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(-12.3603 - 13.7275i) q^{69} +(0.118034 + 0.363271i) q^{70} +(-6.14285 + 6.82232i) q^{71} +(-15.2637 - 6.79584i) q^{72} +(-8.28700 + 1.76146i) q^{73} +(0.338261 + 3.21834i) q^{74} +(-1.35304 + 12.8734i) q^{75} +(1.35177 + 0.287327i) q^{76} +(-0.381966 - 0.277515i) q^{77} +(-13.7082 - 9.95959i) q^{78} +(11.4524 + 2.43427i) q^{79} +(0.507392 - 4.82751i) q^{80} +(-2.55221 - 24.2827i) q^{81} +(-11.0787 + 2.35486i) q^{82} +(-13.6523 - 6.07838i) q^{83} +(-0.315921 + 0.350865i) q^{84} +(0.236068 + 0.726543i) q^{85} +(1.33826 + 1.48629i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +(3.61803 - 11.1352i) q^{89} +(11.0449 - 4.91752i) q^{90} +(0.618034 - 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 - 1.31433i) q^{95} +(9.99809 - 4.45144i) 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} + 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}+ \cdots - 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

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

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	−0.944915	−	0.327315i	$-0.893856\pi$
$2$	−1.30902	+	0.951057i	−0.925615	+	0.672499i	0.0193004	+	0.999814i	$0.493856\pi$
$3$	−2.95630	+	1.31623i	−1.70682	+	0.759924i	−0.708276	+	0.705935i	$0.750527\pi$
$3$	−2.95630	+	1.31623i	−1.70682	+	0.759924i	−0.998542	+	0.0539889i	$0.982806\pi$
$4$	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
$7$	0.157960	+	0.175433i	0.0597034	+	0.0663073i	0.772257	−	0.635311i	$-0.219128\pi$
$7$	0.157960	+	0.175433i	0.0597034	+	0.0663073i	−0.712553	+	0.701618i	$0.752461\pi$
$8$	−0.690983	−	2.12663i	−0.244299	−	0.751876i
$9$	4.99983	−	5.55288i	1.66661	−	1.85096i
$10$	1.47815	+	0.658114i	0.467431	+	0.208114i
$11$	−1.95630	+	0.415823i	−0.589845	+	0.125375i	−0.493159	−	0.869939i	$-0.664158\pi$
$11$	−1.95630	+	0.415823i	−0.589845	+	0.125375i	−0.0966866	+	0.995315i	$0.530824\pi$
$12$	0.209057	+	1.98904i	0.0603495	+	0.574187i
$13$	0.338261	−	3.21834i	0.0938168	−	0.892607i	−0.841847	−	0.539716i	$-0.818532\pi$
$13$	0.338261	−	3.21834i	0.0938168	−	0.892607i	0.935664	−	0.352892i	$-0.114802\pi$
$14$	−0.373619	−	0.0794152i	−0.0998539	−	0.0212246i
$15$	2.61803	+	1.90211i	0.675973	+	0.491123i
$16$	3.92705	+	2.85317i	0.981763	+	0.713292i
$17$	−0.747238	−	0.158830i	−0.181232	−	0.0385220i	0.116402	−	0.993202i	$-0.462864\pi$
$17$	−0.747238	−	0.158830i	−0.181232	−	0.0385220i	−0.297634	+	0.954680i	$0.596197\pi$
$18$	−1.26377	+	12.0239i	−0.297873	+	2.83407i
$19$	0.233733	+	2.22382i	0.0536220	+	0.510179i	0.988062	+	0.154058i	$0.0492342\pi$
$19$	0.233733	+	2.22382i	0.0536220	+	0.510179i	−0.934440	+	0.356121i	$0.884099\pi$
$20$	−0.604528	+	0.128496i	−0.135177	+	0.0287327i
$21$	−0.697887	−	0.310719i	−0.152291	−	0.0678045i
$22$	2.16535	−	2.40487i	0.461655	−	0.512719i
$23$	1.76393	+	5.42882i	0.367805	+	1.13199i	0.948206	+	0.317657i	$0.102896\pi$
$23$	1.76393	+	5.42882i	0.367805	+	1.13199i	−0.580400	+	0.814331i	$0.697104\pi$
$24$	4.84187	+	5.37745i	0.988344	+	1.09767i
$25$	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
$28$	0.133284	−	0.0593421i	0.0251884	−	0.0112146i
$29$	−2.23607	+	1.62460i	−0.415227	+	0.301680i	−0.775715	−	0.631084i	$-0.782610\pi$
$29$	−2.23607	+	1.62460i	−0.415227	+	0.301680i	0.360487	+	0.932764i	$0.382610\pi$
$30$	−5.23607			−0.955971
$31$		0			0
$31$		0			0
$32$	−3.38197			−0.597853
$33$	5.23607	−	3.80423i	0.911482	−	0.662231i
$34$	1.12920	−	0.502754i	0.193657	−	0.0862216i
$35$	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	$0.114098\pi$
$38$	−2.42094	−	2.68872i	−0.392728	−	0.436169i
$39$	3.23607	+	9.95959i	0.518186	+	1.59481i
$40$	−1.49622	+	1.66172i	−0.236573	+	0.262741i
$41$	6.39482	+	2.84716i	0.998703	+	0.444651i	0.839948	−	0.542667i	$-0.182585\pi$
$41$	6.39482	+	2.84716i	0.998703	+	0.444651i	0.158755	+	0.987318i	$0.449252\pi$
$42$	1.20906	−	0.256993i	0.186562	−	0.0396549i
$43$	−0.129204	−	1.22930i	−0.0197035	−	0.187466i	0.980243	−	0.197796i	$-0.0633784\pi$
$43$	−0.129204	−	1.22930i	−0.0197035	−	0.187466i	−0.999947	+	0.0103302i	$0.996712\pi$
$44$	−0.129204	+	1.22930i	−0.0194783	+	0.185323i
$45$	−7.30885	−	1.55354i	−1.08954	−	0.231589i
$46$	−7.47214	−	5.42882i	−1.10171	−	0.800437i
$47$	−2.00000	−	1.45309i	−0.291730	−	0.211954i	0.432288	−	0.901736i	$-0.357707\pi$
$47$	−2.00000	−	1.45309i	−0.291730	−	0.211954i	−0.724018	+	0.689782i	$0.757707\pi$
$48$	−15.3649	−	3.26592i	−2.21774	−	0.471395i
$49$	0.725874	−	6.90623i	0.103696	−	0.986604i
$50$	0.676522	+	6.43668i	0.0956747	+	0.910284i
$51$	2.41811	−	0.513986i	0.338604	−	0.0719724i
$52$	−1.82709	−	0.813473i	−0.253372	−	0.112808i
$53$	−7.00723	+	7.78231i	−0.962517	+	1.06898i	0.0350585	+	0.999385i	$0.488838\pi$
$53$	−7.00723	+	7.78231i	−0.962517	+	1.06898i	−0.997575	+	0.0695977i	$0.977828\pi$
$54$	−7.23607	−	22.2703i	−0.984704	−	3.03061i
$55$	1.33826	+	1.48629i	0.180451	+	0.200411i
$56$	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
$59$	2.04275	−	0.909491i	0.265943	−	0.118406i	−0.269433	−	0.963019i	$-0.586836\pi$
$59$	2.04275	−	0.909491i	0.265943	−	0.118406i	0.535377	+	0.844613i	$0.320170\pi$
$60$	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
$65$	−2.95630	+	1.31623i	−0.366683	+	0.163258i
$66$	−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
$69$	−12.3603	−	13.7275i	−1.48800	−	1.65259i
$70$	0.118034	+	0.363271i	0.0141078	+	0.0434192i
$71$	−6.14285	+	6.82232i	−0.729022	+	0.809661i	−0.987710	−	0.156300i	$-0.950043\pi$
$71$	−6.14285	+	6.82232i	−0.729022	+	0.809661i	0.258688	+	0.965961i	$0.416710\pi$
$72$	−15.2637	−	6.79584i	−1.79884	−	0.800897i
$73$	−8.28700	+	1.76146i	−0.969920	+	0.206163i	−0.665519	−	0.746381i	$-0.731790\pi$
$73$	−8.28700	+	1.76146i	−0.969920	+	0.206163i	−0.304401	+	0.952544i	$0.598456\pi$
$74$	0.338261	+	3.21834i	0.0393221	+	0.374124i
$75$	−1.35304	+	12.8734i	−0.156236	+	1.48649i
$76$	1.35177	+	0.287327i	0.155058	+	0.0329587i
$77$	−0.381966	−	0.277515i	−0.0435291	−	0.0316257i
$78$	−13.7082	−	9.95959i	−1.55215	−	1.12770i
$79$	11.4524	+	2.43427i	1.28849	+	0.273877i	0.800690	−	0.599078i	$-0.204466\pi$
$79$	11.4524	+	2.43427i	1.28849	+	0.273877i	0.487800	+	0.872955i	$0.337800\pi$
$80$	0.507392	−	4.82751i	0.0567281	−	0.539732i
$81$	−2.55221	−	24.2827i	−0.283579	−	2.69807i
$82$	−11.0787	+	2.35486i	−1.22344	+	0.260050i
$83$	−13.6523	−	6.07838i	−1.49853	−	0.667189i	−0.516566	−	0.856248i	$-0.672790\pi$
$83$	−13.6523	−	6.07838i	−1.49853	−	0.667189i	−0.981966	+	0.189058i	$0.939456\pi$
$84$	−0.315921	+	0.350865i	−0.0344698	+	0.0382826i
$85$	0.236068	+	0.726543i	0.0256052	+	0.0788046i
$86$	1.33826	+	1.48629i	0.144308	+	0.160271i
$87$	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	−0.554044	−	0.832487i	$-0.686916\pi$
$89$	3.61803	−	11.1352i	0.383511	−	1.18032i	0.937555	−	0.347838i	$-0.113084\pi$
$90$	11.0449	−	4.91752i	1.16424	−	0.518352i
$91$	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
$96$	9.99809	−	4.45144i	1.02043	−	0.454323i
$97$	−4.92705	+	15.1639i	−0.500266	+	1.53966i	0.308320	+	0.951283i	$0.400233\pi$
$97$	−4.92705	+	15.1639i	−0.500266	+	1.53966i	−0.808586	+	0.588378i	$0.799767\pi$
$98$	5.61803	+	9.73072i	0.567507	+	0.982951i
$99$	−7.47214	+	12.9421i	−0.750978	+	1.30073i
$100$	−1.65418	−	1.83716i	−0.165418	−	0.183716i
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	0.894281	−	0.447506i	$-0.147688\pi$
$101$	−0.927051	−	2.85317i	−0.0922450	−	0.283901i	−0.986526	+	0.163605i	$0.947688\pi$
$102$	−2.67652	+	2.97258i	−0.265015	+	0.294329i
$103$	5.69693	+	2.53644i	0.561335	+	0.249923i	0.667733	−	0.744401i	$-0.267265\pi$
$103$	5.69693	+	2.53644i	0.561335	+	0.249923i	−0.106397	+	0.994324i	$0.533932\pi$
$104$	−7.07794	+	1.50446i	−0.694049	+	0.147525i
$105$	0.0798526	+	0.759747i	0.00779282	+	0.0741437i
$106$	1.77116	−	16.8514i	0.172030	−	1.63676i
$107$	−5.63798	−	1.19839i	−0.545044	−	0.115853i	−0.0728426	−	0.997343i	$-0.523207\pi$
$107$	−5.63798	−	1.19839i	−0.545044	−	0.115853i	−0.472201	+	0.881491i	$0.656540\pi$
$108$	7.23607	+	5.25731i	0.696291	+	0.505885i
$109$	11.2812	+	8.19624i	1.08054	+	0.785057i	0.977777	−	0.209649i	$-0.0672321\pi$
$109$	11.2812	+	8.19624i	1.08054	+	0.785057i	0.102762	+	0.994706i	$0.467232\pi$
$110$	−3.16535	−	0.672816i	−0.301804	−	0.0641505i
$111$	−0.676522	+	6.43668i	−0.0642127	+	0.610943i
$112$	0.119779	+	1.13962i	0.0113180	+	0.107684i
$113$	−3.39626	+	0.721898i	−0.319493	+	0.0679104i	−0.364867	−	0.931060i	$-0.618886\pi$
$113$	−3.39626	+	0.721898i	−0.319493	+	0.0679104i	0.0453735	+	0.998970i	$0.485552\pi$
$114$	10.6960	+	4.76216i	1.00177	+	0.446017i
$115$	3.81953	−	4.24202i	0.356173	−	0.395571i
$116$	0.527864	+	1.62460i	0.0490109	+	0.150840i
$117$	−16.1798	−	17.9695i	−1.49582	−	1.66128i
$118$	−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
$121$	−6.39482	+	2.84716i	−0.581347	+	0.258832i
$122$	−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
$127$	11.3939	−	5.07287i	1.01104	−	0.450145i	0.166733	−	0.986002i	$-0.446678\pi$
$127$	11.3939	−	5.07287i	1.01104	−	0.450145i	0.844309	+	0.535857i	$0.180011\pi$
$128$	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
$131$	8.02957	+	8.91774i	0.701547	+	0.779146i	0.983622	−	0.180246i	$-0.0576894\pi$
$131$	8.02957	+	8.91774i	0.701547	+	0.779146i	−0.282075	+	0.959392i	$0.591023\pi$
$132$	−1.23607	−	3.80423i	−0.107586	−	0.331115i
$133$	−0.353210	+	0.392279i	−0.0306272	+	0.0340149i
$134$	11.8252	+	5.26491i	1.02154	+	0.454819i
$135$	14.1559	−	3.00893i	1.21834	−	0.258967i
$136$	0.178556	+	1.69885i	0.0153110	+	0.145675i
$137$	−0.657672	+	6.25733i	−0.0561887	+	0.534600i	0.929833	+	0.367982i	$0.119951\pi$
$137$	−0.657672	+	6.25733i	−0.0561887	+	0.534600i	−0.986022	+	0.166618i	$0.946715\pi$
$138$	29.2354	+	6.21418i	2.48868	+	0.528986i
$139$	−10.8541	−	7.88597i	−0.920633	−	0.668879i	0.0230486	−	0.999734i	$-0.492663\pi$
$139$	−10.8541	−	7.88597i	−0.920633	−	0.668879i	−0.943681	+	0.330855i	$0.892663\pi$
$140$	−0.118034	−	0.0857567i	−0.00997569	−	0.00724777i
$141$	7.82518	+	1.66329i	0.658999	+	0.140075i
$142$	1.55268	−	14.7727i	0.130298	−	1.23970i
$143$	0.676522	+	6.43668i	0.0565736	+	0.538262i
$144$	35.4779	−	7.54106i	2.95649	−	0.628422i
$145$	2.52498	+	1.12419i	0.209688	+	0.0933591i
$146$	9.17258	−	10.1872i	0.759128	−	0.843097i
$147$	6.94427	+	21.3723i	0.572754	+	1.76276i
$148$	−0.827091	−	0.918578i	−0.0679865	−	0.0755066i
$149$	−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	0.598477	+	0.801140i	$0.295773\pi$
$151$	−4.38197	+	13.4863i	−0.356599	+	1.09750i	−0.955076	+	0.296360i	$0.904227\pi$
$152$	4.56773	−	2.03368i	0.370492	−	0.164953i
$153$	−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	−0.349627	+	0.936889i	$0.613692\pi$
$157$	−16.8992	+	12.2780i	−1.34870	+	0.979889i	−0.999075	+	0.0430003i	$0.986308\pi$
$158$	−17.3065	+	7.70533i	−1.37683	+	0.613003i
$159$	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
$162$	26.4351	+	29.3591i	2.07693	+	2.30667i
$163$	3.30902	+	10.1841i	0.259182	+	0.797681i	0.992977	+	0.118309i	$0.0377475\pi$
$163$	3.30902	+	10.1841i	0.259182	+	0.797681i	−0.733795	+	0.679371i	$0.762253\pi$
$164$	2.89482	−	3.21502i	0.226047	−	0.251051i
$165$	−5.91259	−	2.63245i	−0.460295	−	0.204936i
$166$	23.6519	−	5.02738i	1.83575	−	0.390200i
$167$	0.676522	+	6.43668i	0.0523509	+	0.498085i	0.989011	+	0.147845i	$0.0472336\pi$
$167$	0.676522	+	6.43668i	0.0523509	+	0.498085i	−0.936660	+	0.350241i	$0.886100\pi$
$168$	−0.178556	+	1.69885i	−0.0137759	+	0.131069i
$169$	2.47262	+	0.525572i	0.190202	+	0.0404287i
$170$	−1.00000	−	0.726543i	−0.0766965	−	0.0557233i
$171$	13.5172	+	9.82084i	1.03369	+	0.751018i
$172$	−0.747238	−	0.158830i	−0.0569764	−	0.0121107i
$173$	−0.307760	+	2.92814i	−0.0233986	+	0.222623i	0.976574	+	0.215183i	$0.0690348\pi$
$173$	−0.307760	+	2.92814i	−0.0233986	+	0.222623i	−0.999972	+	0.00743961i	$0.997632\pi$
$174$	1.51275	+	14.3929i	0.114681	+	1.09112i
$175$	0.923637	−	0.196325i	0.0698204	−	0.0148408i
$176$	−8.86889	−	3.94868i	−0.668517	−	0.297643i
$177$	−4.84187	+	5.37745i	−0.363938	+	0.404194i
$178$	5.85410	+	18.0171i	0.438783	+	1.35044i
$179$	1.14301	+	1.26944i	0.0854327	+	0.0948826i	0.784345	−	0.620324i	$-0.212999\pi$
$179$	1.14301	+	1.26944i	0.0854327	+	0.0948826i	−0.698913	+	0.715207i	$0.746332\pi$
$180$	−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
$183$	−24.1835	+	10.7672i	−1.78770	+	0.795933i
$184$	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
$189$	−3.12104	+	1.38958i	−0.227023	+	0.101077i
$190$	−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
$193$	2.32331	+	2.58030i	0.167236	+	0.185734i	0.820937	−	0.571018i	$-0.193452\pi$
$193$	2.32331	+	2.58030i	0.167236	+	0.185734i	−0.653702	+	0.756752i	$0.726785\pi$
$194$	−7.97214	−	24.5357i	−0.572366	−	1.76156i
$195$	7.00723	−	7.78231i	0.501798	−	0.557303i
$196$	−3.92075	−	1.74563i	−0.280054	−	0.124688i
$197$	−11.1669	+	2.37360i	−0.795611	+	0.169112i	−0.587746	−	0.809045i	$-0.699985\pi$
$197$	−11.1669	+	2.37360i	−0.795611	+	0.169112i	−0.207865	+	0.978158i	$0.566651\pi$
$198$	−2.52753	−	24.0479i	−0.179624	−	1.70901i
$199$	1.98022	−	18.8405i	0.140374	−	1.33557i	−0.666793	−	0.745243i	$-0.732333\pi$
$199$	1.98022	−	18.8405i	0.140374	−	1.33557i	0.807166	−	0.590324i	$-0.201000\pi$
$200$	−8.74882	−	1.85962i	−0.618635	−	0.131495i
$201$	20.9443	+	15.2169i	1.47730	+	1.07332i
$202$	3.92705	+	2.85317i	0.276306	+	0.200748i
$203$	−0.638218	−	0.135657i	−0.0447941	−	0.00952128i
$204$	0.159705	−	1.51949i	0.0111816	−	0.106386i
$205$	−0.731699	−	6.96165i	−0.0511041	−	0.486223i
$206$	−9.86968	+	2.09786i	−0.687653	+	0.146165i
$207$	38.9650	+	17.3483i	2.70825	+	1.20579i
$208$	10.5108	−	11.6735i	0.728796	−	0.809410i
$209$	−1.38197	−	4.25325i	−0.0955926	−	0.294204i
$210$	−0.827091	−	0.918578i	−0.0570747	−	0.0633879i
$211$	−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
$214$	8.51994	−	3.79332i	0.582411	−	0.259306i
$215$	−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
$220$	1.12920	−	0.502754i	0.0761309	−	0.0338957i
$221$	−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	$0.209426\pi$
$224$	−0.534216	−	0.593307i	−0.0356938	−	0.0396420i
$225$	−9.23607	−	28.4257i	−0.615738	−	1.89505i
$226$	3.75920	−	4.17501i	0.250058	−	0.277718i
$227$	−5.91259	−	2.63245i	−0.392432	−	0.174722i	0.201028	−	0.979586i	$-0.435572\pi$
$227$	−5.91259	−	2.63245i	−0.392432	−	0.174722i	−0.593460	+	0.804863i	$0.702239\pi$
$228$	−4.37441	+	0.929809i	−0.289702	+	0.0615781i
$229$	1.40240	+	13.3429i	0.0926730	+	0.881724i	0.937804	+	0.347165i	$0.112856\pi$
$229$	1.40240	+	13.3429i	0.0926730	+	0.881724i	−0.845131	+	0.534559i	$0.820478\pi$
$230$	−0.965432	+	9.18547i	−0.0636587	+	0.605672i
$231$	1.49448	+	0.317661i	0.0983293	+	0.0209005i
$232$	5.00000	+	3.63271i	0.328266	+	0.238499i
$233$	−14.5172	−	10.5474i	−0.951055	−	0.690982i	1.33829e−6	−	1.00000i	$-0.500000\pi$
$233$	−14.5172	−	10.5474i	−0.951055	−	0.690982i	−0.951056	+	0.309018i	$0.900000\pi$
$234$	38.2696	+	8.13446i	2.50176	+	0.531767i
$235$	−0.258409	+	2.45859i	−0.0168567	+	0.160381i
$236$	−0.144455	−	1.37440i	−0.00940321	−	0.0894655i
$237$	−37.0606	+	7.87747i	−2.40734	+	0.511697i
$238$	0.266569	+	0.118684i	0.0172791	+	0.00769315i
$239$	−7.83432	+	8.70089i	−0.506760	+	0.562814i	−0.941184	−	0.337895i	$-0.890285\pi$
$239$	−7.83432	+	8.70089i	−0.506760	+	0.562814i	0.434424	+	0.900708i	$0.356952\pi$
$240$	4.85410	+	14.9394i	0.313331	+	0.964333i
$241$	9.60917	+	10.6721i	0.618981	+	0.687448i	0.968367	−	0.249531i	$-0.0802764\pi$
$241$	9.60917	+	10.6721i	0.618981	+	0.687448i	−0.349386	+	0.936979i	$0.613610\pi$
$242$	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
$245$	−6.34391	+	2.82449i	−0.405297	+	0.180450i
$246$	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
$251$	−1.66234	+	0.740122i	−0.104926	+	0.0467161i	−0.458528	−	0.888680i	$-0.651623\pi$
$251$	−1.66234	+	0.740122i	−0.104926	+	0.0467161i	0.353602	+	0.935396i	$0.384957\pi$
$252$	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
$255$	−1.65418	−	1.83716i	−0.103589	−	0.115047i
$256$	4.19098	+	12.8985i	0.261936	+	0.806157i
$257$	1.30097	−	1.44488i	0.0811524	−	0.0901289i	−0.701201	−	0.712964i	$-0.747352\pi$
$257$	1.30097	−	1.44488i	0.0811524	−	0.0901289i	0.782353	+	0.622835i	$0.214019\pi$
$258$	−5.91259	−	2.63245i	−0.368102	−	0.163889i
$259$	0.461819	−	0.0981626i	0.0286960	−	0.00609953i
$260$	0.209057	+	1.98904i	0.0129652	+	0.123355i
$261$	−2.15877	+	20.5393i	−0.133625	+	1.27135i
$262$	−18.9921	−	4.03690i	−1.17334	−	0.249400i
$263$	18.7984	+	13.6578i	1.15916	+	0.842177i	0.989671	−	0.143355i	$-0.0457892\pi$
$263$	18.7984	+	13.6578i	1.15916	+	0.842177i	0.169486	+	0.985533i	$0.445789\pi$
$264$	−11.7082	−	8.50651i	−0.720590	−	0.523539i
$265$	10.2433	+	2.17728i	0.629241	+	0.133749i
$266$	0.0892780	−	0.849423i	0.00547398	−	0.0520815i
$267$	3.96043	+	37.6810i	0.242374	+	2.30604i
$268$	−4.83623	+	1.02797i	−0.295420	+	0.0627934i
$269$	−10.0999	−	4.49677i	−0.615802	−	0.274173i	0.0750374	−	0.997181i	$-0.476092\pi$
$269$	−10.0999	−	4.49677i	−0.615802	−	0.274173i	−0.690840	+	0.723008i	$0.742759\pi$
$270$	−15.6686	+	17.4018i	−0.953563	+	1.05904i
$271$	−4.38197	−	13.4863i	−0.266185	−	0.819235i	−0.991418	−	0.130731i	$-0.958268\pi$
$271$	−4.38197	−	13.4863i	−0.266185	−	0.819235i	0.725232	−	0.688504i	$-0.241732\pi$
$272$	−2.48127	−	2.75573i	−0.150449	−	0.167091i
$273$	−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
$276$	−10.4294	+	4.64347i	−0.627777	+	0.279504i
$277$	10.2361	−	7.43694i	0.615026	−	0.446842i	−0.236155	−	0.971715i	$-0.575887\pi$
$277$	10.2361	−	7.43694i	0.615026	−	0.446842i	0.851180	+	0.524873i	$0.175887\pi$
$278$	21.7082			1.30197
$279$		0			0
$280$	−0.527864			−0.0315459
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	−0.916842	−	0.399250i	$-0.869271\pi$
$281$	−13.7533	+	9.99235i	−0.820452	+	0.596094i	0.0963896	+	0.995344i	$0.469271\pi$
$282$	−11.8252	+	5.26491i	−0.704179	+	0.313521i
$283$	−4.29180	+	13.2088i	−0.255121	+	0.785181i	0.738685	+	0.674051i	$0.235447\pi$
$283$	−4.29180	+	13.2088i	−0.255121	+	0.785181i	−0.993806	+	0.111130i	$0.964553\pi$
$284$	2.83688	+	4.91362i	0.168338	+	0.291570i
$285$	−3.61803	+	6.26662i	−0.214314	+	0.371202i
$286$	−7.00723	−	7.78231i	−0.414346	−	0.460178i
$287$	0.510643	+	1.57160i	0.0301423	+	0.0927685i
$288$	−16.9093	+	18.7796i	−0.996388	+	1.10660i
$289$	−14.9971	−	6.67715i	−0.882184	−	0.392774i
$290$	−4.37441	+	0.929809i	−0.256874	+	0.0546003i
$291$	−5.39333	−	51.3141i	−0.316163	−	3.00809i
$292$	−0.547318	+	5.20738i	−0.0320294	+	0.304739i
$293$	0.461819	+	0.0981626i	0.0269797	+	0.00573472i	0.221382	−	0.975187i	$-0.428943\pi$
$293$	0.461819	+	0.0981626i	0.0269797	+	0.00573472i	−0.194402	+	0.980922i	$0.562277\pi$
$294$	−29.4164	−	21.3723i	−1.71560	−	1.24646i
$295$	−1.80902	−	1.31433i	−0.105325	−	0.0765231i
$296$	−4.37441	−	0.929809i	−0.254257	−	0.0540441i
$297$	3.02550	−	28.7857i	0.175557	−	1.67032i
$298$	−1.69131	−	16.0917i	−0.0979747	−	0.932167i
$299$	18.0685	−	3.84057i	1.04493	−	0.222106i
$300$	7.30836	+	3.25389i	0.421949	+	0.187864i
$301$	0.195250	−	0.216847i	0.0112540	−	0.0124988i
$302$	−7.09017	−	21.8213i	−0.407993	−	1.25567i
$303$	6.49606	+	7.21460i	0.373189	+	0.414468i
$304$	−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
$307$	−26.2262	+	11.6767i	−1.49681	+	0.666423i	−0.981654	−	0.190672i	$-0.938933\pi$
$307$	−26.2262	+	11.6767i	−1.49681	+	0.666423i	−0.515157	+	0.857096i	$0.672267\pi$
$308$	−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
$313$	15.3146	−	6.81851i	0.865633	−	0.385405i	0.0746260	−	0.997212i	$-0.476224\pi$
$313$	15.3146	−	6.81851i	0.865633	−	0.385405i	0.791007	+	0.611807i	$0.209557\pi$
$314$	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
$317$	2.71381	+	3.01399i	0.152423	+	0.169283i	0.814520	−	0.580135i	$-0.197000\pi$
$317$	2.71381	+	3.01399i	0.152423	+	0.169283i	−0.662097	+	0.749418i	$0.730334\pi$
$318$	16.9443	+	52.1491i	0.950188	+	2.92438i
$319$	3.69886	−	4.10800i	0.207097	−	0.230004i
$320$	3.86984	+	1.72296i	0.216331	+	0.0963166i
$321$	18.2449	−	3.87807i	1.01833	−	0.216453i
$322$	−0.227908	−	2.16840i	−0.0127008	−	0.120840i
$323$	0.178556	−	1.69885i	0.00993512	−	0.0945263i
$324$	−14.7604	−	3.13742i	−0.820023	−	0.174301i
$325$	−10.4721	−	7.60845i	−0.580890	−	0.422041i
$326$	−14.0172	−	10.1841i	−0.776342	−	0.564046i
$327$	−44.1385	−	9.38193i	−2.44087	−	0.518822i
$328$	1.63613	−	15.5667i	0.0903401	−	0.859529i
$329$	−0.0610020	−	0.580395i	−0.00336315	−	0.0319982i
$330$	10.2433	−	2.17728i	0.563875	−	0.119855i
$331$	1.82709	+	0.813473i	0.100426	+	0.0447125i	0.456335	−	0.889808i	$-0.349162\pi$
$331$	1.82709	+	0.813473i	0.100426	+	0.0447125i	−0.355909	+	0.934521i	$0.615829\pi$
$332$	−6.18014	+	6.86374i	−0.339179	+	0.376696i
$333$	−4.61803	−	14.2128i	−0.253067	−	0.778859i
$334$	−7.00723	−	7.78231i	−0.383418	−	0.425829i
$335$	−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	0.746512	+	0.665372i	$0.231727\pi$
$337$	−4.56231	+	14.0413i	−0.248525	+	0.764880i	−0.995037	+	0.0995083i	$0.968273\pi$
$338$	−3.73656	+	1.66362i	−0.203242	+	0.0904891i
$339$	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
$344$	−2.52498	+	1.12419i	−0.136138	+	0.0606124i
$345$	−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	$0.941840\pi$
$348$	−3.69886	−	4.10800i	−0.198280	−	0.220212i
$349$	−2.43769	−	7.50245i	−0.130487	−	0.401597i	0.864374	−	0.502849i	$-0.167715\pi$
$349$	−2.43769	−	7.50245i	−0.130487	−	0.401597i	−0.994861	+	0.101252i	$0.967715\pi$
$350$	−1.02234	+	1.13542i	−0.0546464	+	0.0606910i
$351$	42.7839	+	19.0486i	2.28364	+	1.01674i
$352$	6.61612	−	1.40630i	0.352641	−	0.0749561i
$353$	−0.775226	−	7.37578i	−0.0412611	−	0.392573i	−0.995590	−	0.0938142i	$-0.970094\pi$
$353$	−0.775226	−	7.37578i	−0.0412611	−	0.392573i	0.954329	−	0.298759i	$-0.0965726\pi$
$354$	1.22384	−	11.6441i	0.0650464	−	0.618875i
$355$	8.97973	+	1.90870i	0.476594	+	0.101303i
$356$	−5.85410	−	4.25325i	−0.310267	−	0.225422i
$357$	0.472136	+	0.343027i	0.0249881	+	0.0181549i
$358$	−2.70353	−	0.574654i	−0.142886	−	0.0303714i
$359$	−2.32430	+	22.1143i	−0.122672	+	1.16715i	0.743969	+	0.668214i	$0.232941\pi$
$359$	−2.32430	+	22.1143i	−0.122672	+	1.16715i	−0.866641	+	0.498932i	$0.833726\pi$
$360$	1.74648	+	16.6167i	0.0920477	+	0.875776i
$361$	13.6941	−	2.91076i	0.720740	−	0.153198i
$362$	−6.17916	−	2.75114i	−0.324769	−	0.144597i
$363$	15.1575	−	16.8341i	0.795561	−	0.883560i
$364$	−0.145898	−	0.449028i	−0.00764713	−	0.0235355i
$365$	5.66897	+	6.29602i	0.296727	+	0.329549i
$366$	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
$369$	47.7830	−	21.2743i	2.48748	−	1.10750i
$370$	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
$375$	26.6067	−	11.8460i	1.37396	−	0.611727i
$376$	−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
$379$	−1.41284	−	1.56912i	−0.0725727	−	0.0806002i	0.705765	−	0.708446i	$-0.250603\pi$
$379$	−1.41284	−	1.56912i	−0.0725727	−	0.0806002i	−0.778338	+	0.627846i	$0.783937\pi$
$380$	−0.427051	−	1.31433i	−0.0219073	−	0.0674236i
$381$	−27.0066	+	29.9938i	−1.38359	+	1.53663i
$382$	−28.3514	−	12.6228i	−1.45058	−	0.645841i
$383$	23.3665	−	4.96671i	1.19397	−	0.253787i	0.432289	−	0.901735i	$-0.357706\pi$
$383$	23.3665	−	4.96671i	1.19397	−	0.253787i	0.761684	+	0.647948i	$0.224373\pi$
$384$	4.60645	+	43.8275i	0.235072	+	2.23656i
$385$	−0.0493516	+	0.469550i	−0.00251519	+	0.0239305i
$386$	−5.49527	−	1.16805i	−0.279702	−	0.0594524i
$387$	−7.47214	−	5.42882i	−0.379830	−	0.275963i
$388$	7.97214	+	5.79210i	0.404724	+	0.294049i
$389$	17.4976	+	3.71924i	0.887165	+	0.188573i	0.628886	−	0.777497i	$-0.283511\pi$
$389$	17.4976	+	3.71924i	0.887165	+	0.188573i	0.258279	+	0.966070i	$0.416845\pi$
$390$	−1.77116	+	16.8514i	−0.0896861	+	0.853306i
$391$	−0.455815	−	4.33679i	−0.0230516	−	0.219321i
$392$	−15.1885	+	3.22842i	−0.767137	+	0.163060i
$393$	−35.4755	−	15.7947i	−1.78950	−	0.796739i
$394$	12.3603	−	13.7275i	0.622701	−	0.691580i
$395$	−3.61803	−	11.1352i	−0.182043	−	0.560271i
$396$	6.18014	+	6.86374i	0.310564	+	0.344916i
$397$	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
$400$	17.7378	−	7.89736i	0.886889	−	0.394868i
$401$	−30.8885	+	22.4418i	−1.54250	+	1.12069i	−0.593757	+	0.804644i	$0.702356\pi$
$401$	−30.8885	+	22.4418i	−1.54250	+	1.12069i	−0.948743	+	0.316048i	$0.897644\pi$
$402$	−41.8885			−2.08921
$403$		0			0
$404$	−1.85410			−0.0922450
$405$	−19.7533	+	14.3516i	−0.981549	+	0.713137i
$406$	0.964456	−	0.429403i	0.0478651	−	0.0213109i
$407$	−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	$0.136562\pi$
$410$	7.57873	+	8.41704i	0.374287	+	0.415688i
$411$	−6.29180	−	19.3642i	−0.310351	−	0.955163i
$412$	2.57890	−	2.86416i	0.127053	−	0.141107i
$413$	0.482228	+	0.214702i	0.0237289	+	0.0105648i
$414$	−67.5051	+	14.3486i	−3.31769	+	0.705197i
$415$	1.56210	+	14.8624i	0.0766806	+	0.729567i
$416$	−1.14399	+	10.8843i	−0.0560886	+	0.533648i
$417$	42.4677	+	9.02678i	2.07965	+	0.442043i
$418$	5.85410	+	4.25325i	0.286333	+	0.208033i
$419$	8.19098	+	5.95110i	0.400156	+	0.290730i	0.769604	−	0.638521i	$-0.220453\pi$
$419$	8.19098	+	5.95110i	0.400156	+	0.290730i	−0.369449	+	0.929251i	$0.620453\pi$
$420$	0.461819	+	0.0981626i	0.0225344	+	0.00478984i
$421$	−3.06903	+	29.1998i	−0.149575	+	1.42311i	0.620023	+	0.784584i	$0.287123\pi$
$421$	−3.06903	+	29.1998i	−0.149575	+	1.42311i	−0.769598	+	0.638529i	$0.779543\pi$
$422$	−3.92050	−	37.3011i	−0.190847	−	1.81579i
$423$	−18.0685	+	3.84057i	−0.878519	+	0.186735i
$424$	21.3920	+	9.52431i	1.03889	+	0.462541i
$425$	−2.04468	+	2.27085i	−0.0991816	+	0.110152i
$426$	14.8541	+	45.7162i	0.719684	+	2.21496i
$427$	1.29217	+	1.43510i	0.0625324	+	0.0694493i
$428$	−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
$431$	10.9625	−	4.88084i	0.528047	−	0.235102i	−0.125356	−	0.992112i	$-0.540007\pi$
$431$	10.9625	−	4.88084i	0.528047	−	0.235102i	0.653403	+	0.757010i	$0.273341\pi$
$432$	−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
$437$	−11.6604	+	5.19156i	−0.557794	+	0.248346i
$438$	−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
$441$	−34.7202	−	38.5607i	−1.65334	−	1.83622i
$442$	−1.23607	−	3.80423i	−0.0587938	−	0.180949i
$443$	20.5478	−	22.8206i	0.976255	−	1.08424i	−0.0201727	−	0.999797i	$-0.506422\pi$
$443$	20.5478	−	22.8206i	0.976255	−	1.08424i	0.996428	−	0.0844450i	$-0.0269117\pi$
$444$	3.65418	+	1.62695i	0.173420	+	0.0772115i
$445$	−11.4524	+	2.43427i	−0.542894	+	0.115396i
$446$	−0.676522	−	6.43668i	−0.0320343	−	0.304786i
$447$	3.38261	−	32.1834i	0.159992	−	1.52222i
$448$	−0.978148	−	0.207912i	−0.0462131	−	0.00982290i
$449$	25.3262	+	18.4006i	1.19522	+	0.868377i	0.993806	−	0.111129i	$-0.0354466\pi$
$449$	25.3262	+	18.4006i	1.19522	+	0.868377i	0.201413	+	0.979506i	$0.435447\pi$
$450$	39.1246	+	28.4257i	1.84435	+	1.34000i
$451$	−13.6941	−	2.91076i	−0.644828	−	0.137063i
$452$	−0.224307	+	2.13414i	−0.0105505	+	0.100382i
$453$	−4.79666	−	45.6372i	−0.225367	−	2.14422i
$454$	10.2433	−	2.17728i	0.480742	−	0.102185i
$455$	−0.697887	−	0.310719i	−0.0327174	−	0.0145667i
$456$	−10.8268	+	12.0243i	−0.507010	+	0.563091i
$457$	−0.944272	−	2.90617i	−0.0441712	−	0.135945i	0.926539	−	0.376199i	$-0.122769\pi$
$457$	−0.944272	−	2.90617i	−0.0441712	−	0.135945i	−0.970710	+	0.240254i	$0.922769\pi$
$458$	−14.5256	−	16.1323i	−0.678738	−	0.753815i
$459$	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	−0.323155	−	0.946346i	$-0.604744\pi$
$461$	10.6180	−	32.6789i	0.494531	−	1.52201i	0.817686	−	0.575664i	$-0.195256\pi$
$462$	−2.25841	+	1.00551i	−0.105071	+	0.0467805i
$463$	2.09017	−	1.51860i	0.0971384	−	0.0705752i	−0.538156	−	0.842845i	$-0.680879\pi$
$463$	2.09017	−	1.51860i	0.0971384	−	0.0705752i	0.635294	+	0.772270i	$0.280879\pi$
$464$	−13.4164			−0.622841
$465$		0			0
$466$	29.0344			1.34499
$467$	−3.80902	+	2.76741i	−0.176260	+	0.128061i	−0.672417	−	0.740172i	$-0.734744\pi$
$467$	−3.80902	+	2.76741i	−0.176260	+	0.128061i	0.496157	+	0.868233i	$0.334744\pi$
$468$	−13.6523	+	6.07838i	−0.631076	+	0.280973i
$469$	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
$472$	−3.34565	−	3.71572i	−0.153996	−	0.171030i
$473$	0.763932	+	2.35114i	0.0351256	+	0.108106i
$474$	41.0210	−	45.5585i	1.88416	−	2.09257i
$475$	8.17100	+	3.63796i	0.374911	+	0.166921i
$476$	−0.109021	+	0.0231730i	−0.00499695	+	0.00106213i
$477$	8.17927	+	77.8206i	0.374503	+	3.56316i
$478$	1.98022	−	18.8405i	0.0905730	−	0.861744i
$479$	−22.7828	−	4.84264i	−1.04097	−	0.221266i	−0.344454	−	0.938803i	$-0.611936\pi$
$479$	−22.7828	−	4.84264i	−1.04097	−	0.221266i	−0.696520	+	0.717538i	$0.745269\pi$
$480$	−8.85410	−	6.43288i	−0.404133	−	0.293620i
$481$	−5.23607	−	3.80423i	−0.238744	−	0.173458i
$482$	−22.7283	−	4.83105i	−1.03525	−	0.220048i
$483$	0.455815	−	4.33679i	0.0207403	−	0.197331i
$484$	0.452215	+	4.30254i	0.0205552	+	0.195570i
$485$	15.5959	−	3.31500i	0.708171	−	0.150526i
$486$	−52.6172	−	23.4267i	−2.38677	−	1.06266i
$487$	−12.8714	+	14.2952i	−0.583261	+	0.647777i	−0.960481	−	0.278347i	$-0.910213\pi$
$487$	−12.8714	+	14.2952i	−0.583261	+	0.647777i	0.377220	+	0.926124i	$0.376880\pi$
$488$	−5.65248	−	17.3965i	−0.255876	−	0.787504i
$489$	−23.1870	−	25.7518i	−1.04855	−	1.16454i
$490$	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
$493$	1.92891	−	0.858807i	0.0868738	−	0.0386787i
$494$	−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
$499$	−6.01441	+	2.67779i	−0.269242	+	0.119874i	−0.536917	−	0.843635i	$-0.680411\pi$
$499$	−6.01441	+	2.67779i	−0.269242	+	0.119874i	0.267675	+	0.963509i	$0.413745\pi$
$500$	−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
$503$	19.8414	+	22.0361i	0.884683	+	0.982540i	0.999942	−	0.0107951i	$-0.00343626\pi$
$503$	19.8414	+	22.0361i	0.884683	+	0.982540i	−0.115258	+	0.993336i	$0.536770\pi$
$504$	−1.21885	−	3.75123i	−0.0542918	−	0.167093i
$505$	−2.00739	+	2.22943i	−0.0893278	+	0.0992085i
$506$	16.8751	+	7.51329i	0.750191	+	0.334007i
$507$	−8.00158	+	1.70079i	−0.355363	+	0.0755347i
$508$	−0.805727	−	7.66598i	−0.0357483	−	0.340123i
$509$	−3.09370	+	29.4346i	−0.137126	+	1.30467i	0.682127	+	0.731234i	$0.261055\pi$
$509$	−3.09370	+	29.4346i	−0.137126	+	1.30467i	−0.819253	+	0.573432i	$0.805611\pi$
$510$	3.91259	+	0.831647i	0.173252	+	0.0368259i
$511$	−1.61803	−	1.17557i	−0.0715776	−	0.0520042i
$512$	4.28115	+	3.11044i	0.189202	+	0.137463i
$513$	−31.6535	−	6.72816i	−1.39754	−	0.297056i
$514$	−0.328836	+	3.12866i	−0.0145043	+	0.137999i
$515$	−0.651847	−	6.20191i	−0.0287238	−	0.273289i
$516$	2.41811	−	0.513986i	0.106452	−	0.0226270i
$517$	4.51682	+	2.01102i	0.198649	+	0.0884444i
$518$	−0.511170	+	0.567712i	−0.0224595	+	0.0249438i
$519$	−2.94427	−	9.06154i	−0.129239	−	0.397757i
$520$	4.84187	+	5.37745i	0.212330	+	0.235817i
$521$	−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	0.757245	+	0.653131i	$0.226545\pi$
$523$	−5.47214	+	16.8415i	−0.239280	+	0.736427i	−0.996525	+	0.0832966i	$0.973455\pi$
$524$	6.77523	−	3.01652i	0.295977	−	0.131777i
$525$	−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
$530$	−15.4794	+	6.89186i	−0.672381	+	0.299363i
$531$	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
$534$	−41.0210	−	45.5585i	−1.77515	−	1.97151i
$535$	1.78115	+	5.48183i	0.0770060	+	0.237000i
$536$	−11.9698	+	13.2938i	−0.517015	+	0.574204i
$537$	−5.04996	−	2.24838i	−0.217922	−	0.0970250i
$538$	17.4976	−	3.71924i	0.754377	−	0.160348i
$539$	1.45175	+	13.8125i	0.0625312	+	0.594945i
$540$	0.934931	−	8.89527i	0.0402330	−	0.382792i
$541$	24.8065	+	5.27278i	1.06651	+	0.226695i	0.707555	−	0.706659i	$-0.249798\pi$
$541$	24.8065	+	5.27278i	1.06651	+	0.226695i	0.358959	+	0.933353i	$0.383132\pi$
$542$	18.5623	+	13.4863i	0.797319	+	0.579286i
$543$	−10.9443	−	7.95148i	−0.469664	−	0.341231i
$544$	2.52713	+	0.537159i	0.108350	+	0.0230305i
$545$	1.45757	−	13.8679i	0.0624356	−	0.594035i
$546$	−0.418114	−	3.97809i	−0.0178936	−	0.170246i
$547$	11.8597	−	2.52085i	0.507082	−	0.107784i	0.0527355	−	0.998609i	$-0.483206\pi$
$547$	11.8597	−	2.52085i	0.507082	−	0.107784i	0.454347	+	0.890825i	$0.349873\pi$
$548$	3.55236	+	1.58161i	0.151749	+	0.0675632i
$549$	40.9003	−	45.4244i	1.74558	−	1.93867i
$550$	−4.00000	−	12.3107i	−0.170561	−	0.524931i
$551$	−4.13545	−	4.59289i	−0.176176	−	0.195664i
$552$	−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
$555$	5.91259	−	2.63245i	0.250975	−	0.111741i
$556$	−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
$561$	−4.51682	+	2.01102i	−0.190700	+	0.0849052i
$562$	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
$565$	2.32331	+	2.58030i	0.0977425	+	0.108554i
$566$	−6.94427	−	21.3723i	−0.291890	−	0.898344i
$567$	3.85682	−	4.28344i	0.161971	−	0.179887i
$568$	18.7531	+	8.34943i	0.786864	+	0.350334i
$569$	−5.40707	+	1.14931i	−0.226676	+	0.0481815i	−0.319849	−	0.947468i	$-0.603632\pi$
$569$	−5.40707	+	1.14931i	−0.226676	+	0.0481815i	0.0931733	+	0.995650i	$0.470299\pi$
$570$	−1.22384	−	11.6441i	−0.0512610	−	0.487716i
$571$	−2.94565	+	28.0260i	−0.123272	+	1.17285i	0.741595	+	0.670848i	$0.234070\pi$
$571$	−2.94565	+	28.0260i	−0.123272	+	1.17285i	−0.864866	+	0.502002i	$0.832597\pi$
$572$	3.91259	+	0.831647i	0.163594	+	0.0347729i
$573$	−50.2148	−	36.4832i	−2.09775	−	1.52411i
$574$	−2.16312	−	1.57160i	−0.0902868	−	0.0655972i
$575$	22.3339	+	4.74721i	0.931387	+	0.197972i
$576$	−3.30858	+	31.4791i	−0.137858	+	1.31163i
$577$	3.01385	+	28.6749i	0.125468	+	1.19375i	0.858230	+	0.513265i	$0.171564\pi$
$577$	3.01385	+	28.6749i	0.125468	+	1.19375i	−0.732762	+	0.680485i	$0.761769\pi$
$578$	25.9819	−	5.52261i	1.08070	−	0.229710i
$579$	−10.2647	−	4.57012i	−0.426585	−	0.189928i
$580$	1.14301	−	1.26944i	0.0474610	−	0.0527107i
$581$	−1.09017	−	3.35520i	−0.0452279	−	0.139197i
$582$	55.8626	+	62.0417i	2.31558	+	2.57171i
$583$	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
$586$	−0.697887	+	0.310719i	−0.0288294	+	0.0128357i
$587$	5.23607	−	3.80423i	0.216116	−	0.157017i	−0.474461	−	0.880277i	$-0.657357\pi$
$587$	5.23607	−	3.80423i	0.216116	−	0.157017i	0.690576	+	0.723259i	$0.257357\pi$
$588$	13.8885			0.572754
$589$		0			0
$590$	3.61803			0.148952
$591$	29.8885	−	21.7153i	1.22945	−	0.893248i
$592$	8.86889	−	3.94868i	0.364509	−	0.162290i
$593$	−2.01722	+	6.20837i	−0.0828373	+	0.254947i	−0.983894	−	0.178755i	$-0.942793\pi$
$593$	−2.01722	+	6.20837i	−0.0828373	+	0.254947i	0.901056	+	0.433702i	$0.142793\pi$
$594$	23.4164	+	40.5584i	0.960787	+	1.66413i
$595$	−0.0901699	+	0.156179i	−0.00369661	+	0.00640271i
$596$	4.13545	+	4.59289i	0.169395	+	0.188132i
$597$	18.9443	+	58.3045i	0.775337	+	2.38624i
$598$	−19.9993	+	22.2115i	−0.817834	+	0.908296i
$599$	−13.3348	−	5.93703i	−0.544845	−	0.242581i	0.115809	−	0.993272i	$-0.463054\pi$
$599$	−13.3348	−	5.93703i	−0.544845	−	0.242581i	−0.660653	+	0.750691i	$0.729721\pi$
$600$	28.3118	−	6.01785i	1.15582	−	0.245678i
$601$	−3.19241	−	30.3737i	−0.130221	−	1.23897i	−0.843129	−	0.537712i	$-0.819289\pi$
$601$	−3.19241	−	30.3737i	−0.130221	−	1.23897i	0.712908	−	0.701258i	$-0.247378\pi$
$602$	−0.0493516	+	0.469550i	−0.00201142	+	0.0191374i
$603$	−58.4708	−	12.4284i	−2.38112	−	0.506122i
$604$	7.09017	+	5.15131i	0.288495	+	0.209604i
$605$	5.66312	+	4.11450i	0.230239	+	0.167278i
$606$	−15.3649	−	3.26592i	−0.624158	−	0.132669i
$607$	−2.34898	+	22.3490i	−0.0953421	+	0.907119i	0.837404	+	0.546585i	$0.184072\pi$
$607$	−2.34898	+	22.3490i	−0.0953421	+	0.907119i	−0.932746	+	0.360534i	$0.882594\pi$
$608$	−0.790476	−	7.52088i	−0.0320580	−	0.305012i
$609$	2.06532	−	0.438996i	0.0836908	−	0.0177890i
$610$	12.0917	+	5.38359i	0.489581	+	0.217975i
$611$	−5.35304	+	5.94516i	−0.216561	+	0.240515i
$612$	1.09017	+	3.35520i	0.0440675	+	0.135626i
$613$	−29.3672	−	32.6155i	−1.18613	−	1.31733i	−0.937194	−	0.348809i	$-0.886586\pi$
$613$	−29.3672	−	32.6155i	−1.18613	−	1.31733i	−0.248935	−	0.968520i	$-0.580081\pi$
$614$	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
$617$	29.6648	−	13.2076i	1.19426	−	0.531718i	0.289309	−	0.957236i	$-0.406575\pi$
$617$	29.6648	−	13.2076i	1.19426	−	0.531718i	0.904950	+	0.425518i	$0.139908\pi$
$618$	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
$623$	2.52498	−	1.12419i	0.101161	−	0.0450398i
$624$	−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
$627$	9.68375	+	10.7549i	0.386732	+	0.429509i
$628$	3.98936	+	12.2780i	0.159193	+	0.489945i
$629$	−1.02234	+	1.13542i	−0.0407634	+	0.0452723i
$630$	2.60735	+	1.16087i	0.103879	+	0.0462501i
$631$	−33.6098	+	7.14399i	−1.33799	+	0.284398i	−0.820673	−	0.571399i	$-0.806401\pi$
$631$	−33.6098	+	7.14399i	−1.33799	+	0.284398i	−0.517313	+	0.855796i	$0.673068\pi$
$632$	−2.73659	−	26.0369i	−0.108856	−	1.03569i
$633$	7.84101	−	74.6022i	0.311652	−	2.96517i
$634$	−6.41890	−	1.36438i	−0.254927	−	0.0541865i
$635$	−10.0902	−	7.33094i	−0.400416	−	0.290919i
$636$	−16.9443	−	12.3107i	−0.671884	−	0.488152i
$637$	−21.9811	−	4.67222i	−0.870922	−	0.185120i
$638$	−0.934931	+	8.89527i	−0.0370143	+	0.352167i
$639$	7.17031	+	68.2210i	0.283653	+	2.69878i
$640$	−13.3204	+	2.83135i	−0.526537	+	0.111919i
$641$	10.9625	+	4.88084i	0.432995	+	0.192782i	0.611647	−	0.791131i	$-0.290507\pi$
$641$	10.9625	+	4.88084i	0.432995	+	0.192782i	−0.178653	+	0.983912i	$0.557174\pi$
$642$	−20.1946	+	22.4284i	−0.797017	+	0.885177i
$643$	6.03444	+	18.5721i	0.237975	+	0.732412i	0.996713	+	0.0810159i	$0.0258165\pi$
$643$	6.03444	+	18.5721i	0.237975	+	0.732412i	−0.758738	+	0.651396i	$0.774184\pi$
$644$	0.557262	+	0.618903i	0.0219592	+	0.0243882i
$645$	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	−0.956629	−	0.291311i	$-0.905909\pi$
$647$	−0.291796	+	0.898056i	−0.0114717	+	0.0353062i	0.945157	+	0.326617i	$0.105909\pi$
$648$	−49.8766	+	22.2065i	−1.95934	+	0.872354i
$649$	−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	0.526332	−	0.850279i	$-0.323567\pi$
$653$	38.2705	−	27.8052i	1.49764	−	1.08810i	0.971309	−	0.237820i	$-0.0764329\pi$
$654$	66.7008	−	29.6971i	2.60821	−	1.16125i
$655$	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
$658$	0.631841	+	0.701731i	0.0246317	+	0.0273563i
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	0.978234	+	0.207504i	$0.0665341\pi$
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	−0.669440	+	0.742866i	$0.733466\pi$
$660$	−2.67652	+	2.97258i	−0.104183	+	0.115707i
$661$	−0.584048	−	0.260035i	−0.0227168	−	0.0101142i	0.395347	−	0.918532i	$-0.370624\pi$
$661$	−0.584048	−	0.260035i	−0.0227168	−	0.0101142i	−0.418064	+	0.908418i	$0.637291\pi$
$662$	−3.16535	+	0.672816i	−0.123025	+	0.0261498i
$663$	−0.836228	−	7.95618i	−0.0324764	−	0.308992i
$664$	−3.49297	+	33.2333i	−0.135553	+	1.28970i
$665$	0.516329	+	0.109749i	0.0200224	+	0.00425589i
$666$	19.5623	+	14.2128i	0.758024	+	0.550737i
$667$	−12.7639	−	9.27354i	−0.494221	−	0.359073i
$668$	3.91259	+	0.831647i	0.151383	+	0.0321774i
$669$	1.35304	−	12.8734i	0.0523117	−	0.497713i
$670$	−1.35304	−	12.8734i	−0.0522727	−	0.497341i
$671$	−16.0032	+	3.40158i	−0.617795	+	0.131316i
$672$	2.36023	+	1.05084i	0.0910478	+	0.0405371i
$673$	−19.4136	+	21.5610i	−0.748339	+	0.831115i	−0.990267	−	0.139180i	$-0.955553\pi$
$673$	−19.4136	+	21.5610i	−0.748339	+	0.831115i	0.241928	+	0.970294i	$0.422220\pi$
$674$	−7.38197	−	22.7194i	−0.284343	−	0.875117i
$675$	38.7350	+	43.0196i	1.49091	+	1.65582i
$676$	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
$679$	−3.43852	+	1.53093i	−0.131958	+	0.0587517i
$680$	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
$685$	5.74784	−	2.55910i	0.219614	−	0.0977783i
$686$	−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
$689$	22.6759	+	25.1841i	0.863882	+	0.959438i
$690$	−9.23607	−	28.4257i	−0.351611	−	1.08215i
$691$	2.12806	−	2.36345i	0.0809553	−	0.0899100i	−0.701306	−	0.712860i	$-0.747399\pi$
$691$	2.12806	−	2.36345i	0.0809553	−	0.0899100i	0.782262	+	0.622950i	$0.214066\pi$
$692$	1.66234	+	0.740122i	0.0631928	+	0.0281352i
$693$	−3.45077	+	0.733484i	−0.131084	+	0.0278628i
$694$	−4.08964	−	38.9103i	−0.155240	−	1.47701i
$695$	−1.40240	+	13.3429i	−0.0531959	+	0.506125i
$696$	−19.5630	−	4.15823i	−0.741532	−	0.157617i
$697$	−4.32624	−	3.14320i	−0.163868	−	0.119057i
$698$	10.3262	+	7.50245i	0.390854	+	0.283972i
$699$	56.7999	+	12.0732i	2.14837	+	0.456650i
$700$	0.0610020	−	0.580395i	0.00230566	−	0.0219369i
$701$	−0.731699	−	6.96165i	−0.0276359	−	0.262938i	−0.999612	−	0.0278579i	$-0.991131\pi$
$701$	−0.731699	−	6.96165i	−0.0276359	−	0.262938i	0.971976	−	0.235080i	$-0.0755353\pi$
$702$	−74.1212	+	15.7549i	−2.79752	+	0.594632i
$703$	4.08550	+	1.81898i	0.154088	+	0.0686042i
$704$	5.66897	−	6.29602i	0.213657	−	0.237290i
$705$	−2.47214	−	7.60845i	−0.0931060	−	0.286551i
$706$	8.02957	+	8.91774i	0.302197	+	0.335623i
$707$	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	−0.686535	−	0.727097i	$-0.740869\pi$
$709$	7.88854	−	24.2784i	0.296260	−	0.911796i	0.982795	−	0.184699i	$-0.0591310\pi$
$710$	−13.5699	+	6.04171i	−0.509269	+	0.226741i
$711$	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
$716$	0.964456	−	0.429403i	0.0360434	−	0.0160476i
$717$	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	$0.0837043\pi$
$720$	−24.2697	−	26.9542i	−0.904479	−	1.00453i
$721$	0.454915	+	1.40008i	0.0169419	+	0.0521419i
$722$	−15.1575	+	16.8341i	−0.564102	+	0.626499i
$723$	−42.4544	−	18.9019i	−1.57890	−	0.702970i
$724$	2.52713	−	0.537159i	0.0939202	−	0.0199634i
$725$	1.15564	+	10.9952i	0.0429193	+	0.408350i
$726$	−3.83123	+	36.4517i	−0.142190	+	1.35285i
$727$	43.2694	+	9.19720i	1.60477	+	0.341105i	0.921295	−	0.388865i	$-0.127133\pi$
$727$	43.2694	+	9.19720i	1.60477	+	0.341105i	0.683479	+	0.729970i	$0.260466\pi$
$728$	−1.38197	−	1.00406i	−0.0512191	−	0.0372128i
$729$	−33.9336	−	24.6542i	−1.25680	−	0.913119i
$730$	−13.4086	−	2.85010i	−0.496276	−	0.105487i
$731$	−0.0987033	+	0.939099i	−0.00365067	+	0.0347338i
$732$	1.71016	+	16.2711i	0.0632092	+	0.601395i
$733$	−3.39626	+	0.721898i	−0.125444	+	0.0266639i	−0.270206	−	0.962803i	$-0.587092\pi$
$733$	−3.39626	+	0.721898i	−0.125444	+	0.0266639i	0.144762	+	0.989467i	$0.453758\pi$
$734$	26.6067	+	11.8460i	0.982070	+	0.437246i
$735$	15.0368	−	16.7001i	0.554641	−	0.615991i
$736$	−5.96556	−	18.3601i	−0.219893	−	0.676762i
$737$	10.7061	+	11.8903i	0.394364	+	0.437985i
$738$	−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
$741$	−21.3920	+	9.52431i	−0.785853	+	0.349884i
$742$	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
$747$	−102.012	+	45.4185i	−3.73241	+	1.66178i
$748$	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
$751$	−14.4138	−	16.0081i	−0.525965	−	0.584144i	0.420361	−	0.907357i	$-0.361904\pi$
$751$	−14.4138	−	16.0081i	−0.525965	−	0.584144i	−0.946326	+	0.323213i	$0.895237\pi$
$752$	−3.70820	−	11.4127i	−0.135224	−	0.416178i
$753$	3.94020	−	4.37604i	0.143589	−	0.159472i
$754$	−13.2210	−	5.88635i	−0.481479	−	0.214368i
$755$	13.8705	−	2.94826i	0.504798	−	0.107298i
$756$	0.220707	+	2.09989i	0.00802705	+	0.0763722i
$757$	−0.904430	+	8.60508i	−0.0328721	+	0.312757i	0.965714	+	0.259607i	$0.0835929\pi$
$757$	−0.904430	+	8.60508i	−0.0328721	+	0.312757i	−0.998587	+	0.0531502i	$0.983074\pi$
$758$	3.34175	+	0.710311i	0.121378	+	0.0257997i
$759$	29.8885	+	21.7153i	1.08489	+	0.788215i
$760$	−4.04508	−	2.93893i	−0.146731	−	0.106606i
$761$	−1.95630	−	0.415823i	−0.0709156	−	0.0150736i	0.172317	−	0.985042i	$-0.444875\pi$
$761$	−1.95630	−	0.415823i	−0.0709156	−	0.0150736i	−0.243233	+	0.969968i	$0.578208\pi$
$762$	6.82623	−	64.9472i	0.247288	−	2.35279i
$763$	0.344086	+	3.27376i	0.0124568	+	0.118518i
$764$	11.5951	−	2.46461i	0.419495	−	0.0891663i
$765$	5.21470	+	2.32174i	0.188538	+	0.0839425i
$766$	−25.8636	+	28.7244i	−0.934488	+	1.03785i

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} +(-2.95630 + 1.31623i) q^{3} +(0.190983 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.61803 - 4.53457i) q^{6} +(0.157960 + 0.175433i) q^{7} +(-0.690983 - 2.12663i) q^{8} +(4.99983 - 5.55288i) q^{9} +(1.47815 + 0.658114i) q^{10} +(-1.95630 + 0.415823i) q^{11} +(0.209057 + 1.98904i) q^{12} +(0.338261 - 3.21834i) q^{13} +(-0.373619 - 0.0794152i) q^{14} +(2.61803 + 1.90211i) q^{15} +(3.92705 + 2.85317i) q^{16} +(-0.747238 - 0.158830i) q^{17} +(-1.26377 + 12.0239i) q^{18} +(0.233733 + 2.22382i) q^{19} +(-0.604528 + 0.128496i) q^{20} +(-0.697887 - 0.310719i) q^{21} +(2.16535 - 2.40487i) q^{22} +(1.76393 + 5.42882i) q^{23} +(4.84187 + 5.37745i) q^{24} +(2.00000 - 3.46410i) q^{25} +(2.61803 + 4.53457i) q^{26} +(-4.47214 + 13.7638i) q^{27} +(0.133284 - 0.0593421i) q^{28} +(-2.23607 + 1.62460i) q^{29} -5.23607 q^{30} -3.38197 q^{32} +(5.23607 - 3.80423i) q^{33} +(1.12920 - 0.502754i) q^{34} +(0.0729490 - 0.224514i) q^{35} +(-2.30902 - 3.99933i) q^{36} +(1.00000 - 1.73205i) q^{37} +(-2.42094 - 2.68872i) q^{38} +(3.23607 + 9.95959i) q^{39} +(-1.49622 + 1.66172i) q^{40} +(6.39482 + 2.84716i) q^{41} +(1.20906 - 0.256993i) q^{42} +(-0.129204 - 1.22930i) q^{43} +(-0.129204 + 1.22930i) q^{44} +(-7.30885 - 1.55354i) q^{45} +(-7.47214 - 5.42882i) q^{46} +(-2.00000 - 1.45309i) q^{47} +(-15.3649 - 3.26592i) q^{48} +(0.725874 - 6.90623i) q^{49} +(0.676522 + 6.43668i) q^{50} +(2.41811 - 0.513986i) q^{51} +(-1.82709 - 0.813473i) q^{52} +(-7.00723 + 7.78231i) q^{53} +(-7.23607 - 22.2703i) q^{54} +(1.33826 + 1.48629i) q^{55} +(0.263932 - 0.457144i) q^{56} +(-3.61803 - 6.26662i) q^{57} +(1.38197 - 4.25325i) q^{58} +(2.04275 - 0.909491i) q^{59} +(1.61803 - 1.17557i) q^{60} +8.18034 q^{61} +1.76393 q^{63} +(-3.42705 + 2.48990i) q^{64} +(-2.95630 + 1.31623i) q^{65} +(-3.23607 + 9.95959i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(-12.3603 - 13.7275i) q^{69} +(0.118034 + 0.363271i) q^{70} +(-6.14285 + 6.82232i) q^{71} +(-15.2637 - 6.79584i) q^{72} +(-8.28700 + 1.76146i) q^{73} +(0.338261 + 3.21834i) q^{74} +(-1.35304 + 12.8734i) q^{75} +(1.35177 + 0.287327i) q^{76} +(-0.381966 - 0.277515i) q^{77} +(-13.7082 - 9.95959i) q^{78} +(11.4524 + 2.43427i) q^{79} +(0.507392 - 4.82751i) q^{80} +(-2.55221 - 24.2827i) q^{81} +(-11.0787 + 2.35486i) q^{82} +(-13.6523 - 6.07838i) q^{83} +(-0.315921 + 0.350865i) q^{84} +(0.236068 + 0.726543i) q^{85} +(1.33826 + 1.48629i) q^{86} +(4.47214 - 7.74597i) q^{87} +(2.23607 + 3.87298i) q^{88} +(3.61803 - 11.1352i) q^{89} +(11.0449 - 4.91752i) q^{90} +(0.618034 - 0.449028i) q^{91} +3.52786 q^{92} +4.00000 q^{94} +(1.80902 - 1.31433i) q^{95} +(9.99809 - 4.45144i) q^{96} +(-4.92705 + 15.1639i) q^{97} +(5.61803 + 9.73072i) q^{98} +(-7.47214 + 12.9421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - 4 q^{5} + 12 q^{6} - 7 q^{7} - 10 q^{8} - 7 q^{9} + 3 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 4 q^{14} + 12 q^{15} + 18 q^{16} + 8 q^{17} + 19 q^{18} - 5 q^{19} - 3 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 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

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