LMFDB - Embedded newform 961.2.g.v.846.12

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:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			846.12
Character	$\chi$	$=$	961.846
Dual form			961.2.g.v.844.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.771380 - 2.37406i) q^{2} +(2.41901 + 0.514177i) q^{3} +(-3.42311 - 2.48704i) q^{4} +(0.574589 + 0.995217i) q^{5} +(3.08667 - 5.34626i) q^{6} +(0.242122 - 0.107800i) q^{7} +(-4.50591 + 3.27373i) q^{8} +(2.84661 + 1.26739i) q^{9} +(2.80593 - 0.596420i) q^{10} +(0.0304838 - 0.290034i) q^{11} +(-7.00178 - 7.77626i) q^{12} +(3.02692 - 3.36174i) q^{13} +(-0.0691552 - 0.657968i) q^{14} +(0.878220 + 2.70288i) q^{15} +(1.68126 + 5.17438i) q^{16} +(-0.574567 - 5.46664i) q^{17} +(5.20468 - 5.78038i) q^{18} +(4.65089 + 5.16534i) q^{19} +(0.508259 - 4.83577i) q^{20} +(0.641125 - 0.136275i) q^{21} +(-0.665045 - 0.296097i) q^{22} +(-2.40079 + 1.74427i) q^{23} +(-12.5831 + 5.60237i) q^{24} +(1.83970 - 3.18645i) q^{25} +(-5.64607 - 9.77928i) q^{26} +(0.232085 + 0.168620i) q^{27} +(-1.09691 - 0.233156i) q^{28} +(-1.02816 + 3.16436i) q^{29} +7.09426 q^{30} +2.44197 q^{32} +(0.222870 - 0.685922i) q^{33} +(-13.4213 - 2.85279i) q^{34} +(0.246405 + 0.179024i) q^{35} +(-6.59221 - 11.4180i) q^{36} +(2.03890 - 3.53147i) q^{37} +(15.8504 - 7.05707i) q^{38} +(9.05069 - 6.57571i) q^{39} +(-5.84712 - 2.60331i) q^{40} +(-7.33515 + 1.55913i) q^{41} +(0.171025 - 1.62719i) q^{42} +(5.39184 + 5.98824i) q^{43} +(-0.825675 + 0.917006i) q^{44} +(0.374299 + 3.56122i) q^{45} +(2.28910 + 7.04512i) q^{46} +(1.70515 + 5.24791i) q^{47} +(1.40644 + 13.3814i) q^{48} +(-4.63691 + 5.14981i) q^{49} +(-6.14572 - 6.82551i) q^{50} +(1.42093 - 13.5193i) q^{51} +(-18.7223 + 3.97954i) q^{52} +(-4.34164 - 1.93302i) q^{53} +(0.579339 - 0.420915i) q^{54} +(0.306163 - 0.136312i) q^{55} +(-0.738073 + 1.27838i) q^{56} +(8.59466 + 14.8864i) q^{57} +(6.71928 + 4.88184i) q^{58} +(2.30121 + 0.489138i) q^{59} +(3.71593 - 11.4364i) q^{60} -10.0530 q^{61} +0.825852 q^{63} +(-1.47883 + 4.55136i) q^{64} +(5.08489 + 1.08083i) q^{65} +(-1.45651 - 1.05821i) q^{66} +(1.79343 + 3.10631i) q^{67} +(-11.6289 + 20.1419i) q^{68} +(-6.70440 + 2.98499i) q^{69} +(0.615085 - 0.446886i) q^{70} +(9.93851 + 4.42491i) q^{71} +(-16.9757 + 3.60829i) q^{72} +(0.237735 - 2.26189i) q^{73} +(-6.81118 - 7.56458i) q^{74} +(6.08864 - 6.76212i) q^{75} +(-3.07414 - 29.2485i) q^{76} +(-0.0238848 - 0.0735099i) q^{77} +(-8.62963 - 26.5593i) q^{78} +(0.396603 + 3.77342i) q^{79} +(-4.18360 + 4.64636i) q^{80} +(-5.78032 - 6.41969i) q^{81} +(-1.95670 + 18.6168i) q^{82} +(-2.73232 + 0.580773i) q^{83} +(-2.53357 - 1.12802i) q^{84} +(5.11035 - 3.71289i) q^{85} +(18.3756 - 8.18135i) q^{86} +(-4.11418 + 7.12597i) q^{87} +(0.812137 + 1.40666i) q^{88} +(2.59031 + 1.88197i) q^{89} +(8.74329 + 1.85844i) q^{90} +(0.370491 - 1.14025i) q^{91} +12.5562 q^{92} +13.7742 q^{94} +(-2.46828 + 7.59659i) q^{95} +(5.90716 + 1.25561i) q^{96} +(-1.63167 - 1.18548i) q^{97} +(8.64916 + 14.9808i) q^{98} +(0.454362 - 0.786978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) $ 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	0.771380	−	2.37406i	0.545448	−	1.67872i	−0.174475	−	0.984662i	$-0.555823\pi$
$2$	0.771380	−	2.37406i	0.545448	−	1.67872i	0.719923	−	0.694054i	$-0.244177\pi$
$3$	2.41901	+	0.514177i	1.39662	+	0.296860i	0.843896	−	0.536506i	$-0.180256\pi$
$3$	2.41901	+	0.514177i	1.39662	+	0.296860i	0.552721	+	0.833366i	$0.313589\pi$
$4$	−3.42311	−	2.48704i	−1.71156	−	1.24352i
$5$	0.574589	+	0.995217i	0.256964	+	0.445075i	0.965427	−	0.260673i	$-0.0839445\pi$
$5$	0.574589	+	0.995217i	0.256964	+	0.445075i	−0.708463	+	0.705748i	$0.750611\pi$
$6$	3.08667	−	5.34626i	1.26013	−	2.18260i
$7$	0.242122	−	0.107800i	0.0915136	−	0.0407445i	−0.360469	−	0.932771i	$-0.617383\pi$
$7$	0.242122	−	0.107800i	0.0915136	−	0.0407445i	0.451983	+	0.892027i	$0.350717\pi$
$8$	−4.50591	+	3.27373i	−1.59308	+	1.15744i
$9$	2.84661	+	1.26739i	0.948869	+	0.422464i
$10$	2.80593	−	0.596420i	0.887314	−	0.188604i
$11$	0.0304838	−	0.290034i	0.00919122	−	0.0874486i	−0.988965	−	0.148152i	$-0.952668\pi$
$11$	0.0304838	−	0.290034i	0.00919122	−	0.0874486i	0.998156	+	0.0607031i	$0.0193343\pi$
$12$	−7.00178	−	7.77626i	−2.02124	−	2.24481i
$13$	3.02692	−	3.36174i	0.839517	−	0.932378i	−0.158975	−	0.987283i	$-0.550819\pi$
$13$	3.02692	−	3.36174i	0.839517	−	0.932378i	0.998492	+	0.0549046i	$0.0174855\pi$
$14$	−0.0691552	−	0.657968i	−0.0184825	−	0.175849i
$15$	0.878220	+	2.70288i	0.226755	+	0.697881i
$16$	1.68126	+	5.17438i	0.420314	+	1.29359i
$17$	−0.574567	−	5.46664i	−0.139353	−	1.32585i	−0.811028	−	0.585008i	$-0.801091\pi$
$17$	−0.574567	−	5.46664i	−0.139353	−	1.32585i	0.671675	−	0.740846i	$-0.265575\pi$
$18$	5.20468	−	5.78038i	1.22676	−	1.36245i
$19$	4.65089	+	5.16534i	1.06699	+	1.18501i	0.982050	+	0.188623i	$0.0604024\pi$
$19$	4.65089	+	5.16534i	1.06699	+	1.18501i	0.0849375	+	0.996386i	$0.472931\pi$
$20$	0.508259	−	4.83577i	0.113650	−	1.08131i
$21$	0.641125	−	0.136275i	0.139905	−	0.0297377i
$22$	−0.665045	−	0.296097i	−0.141788	−	0.0631281i
$23$	−2.40079	+	1.74427i	−0.500599	+	0.363706i	−0.809246	−	0.587470i	$-0.800124\pi$
$23$	−2.40079	+	1.74427i	−0.500599	+	0.363706i	0.308647	+	0.951177i	$0.400124\pi$
$24$	−12.5831	+	5.60237i	−2.56852	+	1.14358i
$25$	1.83970	−	3.18645i	0.367939	−	0.637289i
$26$	−5.64607	−	9.77928i	−1.10729	−	1.91787i
$27$	0.232085	+	0.168620i	0.0446648	+	0.0324509i
$28$	−1.09691	−	0.233156i	−0.207297	−	0.0440624i
$29$	−1.02816	+	3.16436i	−0.190925	+	0.587607i	−1.00000		9.87269e-5i	$-0.999969\pi$
$29$	−1.02816	+	3.16436i	−0.190925	+	0.587607i	0.809075	+	0.587705i	$0.199969\pi$
$30$	7.09426			1.29523
$31$		0			0
$31$		0			0
$32$	2.44197			0.431684
$33$	0.222870	−	0.685922i	0.0387966	−	0.119404i
$34$	−13.4213	−	2.85279i	−2.30174	−	0.489250i
$35$	0.246405	+	0.179024i	0.0416500	+	0.0302605i
$36$	−6.59221	−	11.4180i	−1.09870	−	1.90301i
$37$	2.03890	−	3.53147i	0.335193	−	0.580571i	−0.648329	−	0.761360i	$-0.724532\pi$
$37$	2.03890	−	3.53147i	0.335193	−	0.580571i	0.983522	+	0.180789i	$0.0578652\pi$
$38$	15.8504	−	7.05707i	2.57128	−	1.14481i
$39$	9.05069	−	6.57571i	1.44927	−	1.05296i
$40$	−5.84712	−	2.60331i	−0.924511	−	0.411619i
$41$	−7.33515	+	1.55913i	−1.14556	+	0.243496i	−0.741316	−	0.671156i	$-0.765798\pi$
$41$	−7.33515	+	1.55913i	−1.14556	+	0.243496i	−0.404242	+	0.914652i	$0.632465\pi$
$42$	0.171025	−	1.62719i	0.0263897	−	0.251081i
$43$	5.39184	+	5.98824i	0.822247	+	0.913198i	0.997453	−	0.0713337i	$-0.0227255\pi$
$43$	5.39184	+	5.98824i	0.822247	+	0.913198i	−0.175205	+	0.984532i	$0.556059\pi$
$44$	−0.825675	+	0.917006i	−0.124475	+	0.138244i
$45$	0.374299	+	3.56122i	0.0557973	+	0.530875i
$46$	2.28910	+	7.04512i	0.337509	+	1.03875i
$47$	1.70515	+	5.24791i	0.248721	+	0.765486i	0.995002	+	0.0998545i	$0.0318377\pi$
$47$	1.70515	+	5.24791i	0.248721	+	0.765486i	−0.746281	+	0.665632i	$0.768162\pi$
$48$	1.40644	+	13.3814i	0.203002	+	1.93143i
$49$	−4.63691	+	5.14981i	−0.662416	+	0.735687i
$50$	−6.14572	−	6.82551i	−0.869136	−	0.965273i
$51$	1.42093	−	13.5193i	0.198971	−	1.89308i
$52$	−18.7223	+	3.97954i	−2.59631	+	0.551863i
$53$	−4.34164	−	1.93302i	−0.596370	−	0.265521i	0.0862747	−	0.996271i	$-0.472504\pi$
$53$	−4.34164	−	1.93302i	−0.596370	−	0.265521i	−0.682645	+	0.730750i	$0.739170\pi$
$54$	0.579339	−	0.420915i	0.0788381	−	0.0572792i
$55$	0.306163	−	0.136312i	0.0412830	−	0.0183804i
$56$	−0.738073	+	1.27838i	−0.0986292	+	0.170831i
$57$	8.59466	+	14.8864i	1.13839	+	1.97175i
$58$	6.71928	+	4.88184i	0.882285	+	0.641018i
$59$	2.30121	+	0.489138i	0.299592	+	0.0636803i	0.355255	−	0.934769i	$-0.384394\pi$
$59$	2.30121	+	0.489138i	0.299592	+	0.0636803i	−0.0556631	+	0.998450i	$0.517727\pi$
$60$	3.71593	−	11.4364i	0.479724	−	1.47644i
$61$	−10.0530			−1.28716			−0.643580	−	0.765379i	$-0.722551\pi$
$61$	−10.0530			−1.28716			−0.643580	+	0.765379i	$0.722551\pi$
$62$		0			0
$63$	0.825852			0.104048
$64$	−1.47883	+	4.55136i	−0.184854	+	0.568921i
$65$	5.08489	+	1.08083i	0.630703	+	0.134060i
$66$	−1.45651	−	1.05821i	−0.179283	−	0.130257i
$67$	1.79343	+	3.10631i	0.219102	+	0.379496i	0.954534	−	0.298103i	$-0.0963539\pi$
$67$	1.79343	+	3.10631i	0.219102	+	0.379496i	−0.735432	+	0.677599i	$0.763021\pi$
$68$	−11.6289	+	20.1419i	−1.41021	+	2.44256i
$69$	−6.70440	+	2.98499i	−0.807115	+	0.359351i
$70$	0.615085	−	0.446886i	0.0735168	−	0.0534131i
$71$	9.93851	+	4.42491i	1.17948	+	0.525140i	0.900373	−	0.435119i	$-0.143294\pi$
$71$	9.93851	+	4.42491i	1.17948	+	0.525140i	0.279111	+	0.960259i	$0.409960\pi$
$72$	−16.9757	+	3.60829i	−2.00060	+	0.425241i
$73$	0.237735	−	2.26189i	0.0278247	−	0.264735i	−0.971761	−	0.235966i	$-0.924175\pi$
$73$	0.237735	−	2.26189i	0.0278247	−	0.264735i	0.999586	−	0.0287689i	$-0.00915869\pi$
$74$	−6.81118	−	7.56458i	−0.791783	−	0.879364i
$75$	6.08864	−	6.76212i	0.703056	−	0.780823i
$76$	−3.07414	−	29.2485i	−0.352628	−	3.35503i
$77$	−0.0238848	−	0.0735099i	−0.00272193	−	0.00837723i
$78$	−8.62963	−	26.5593i	−0.977113	−	3.00725i
$79$	0.396603	+	3.77342i	0.0446213	+	0.424543i	0.993915	+	0.110152i	$0.0351337\pi$
$79$	0.396603	+	3.77342i	0.0446213	+	0.424543i	−0.949293	+	0.314391i	$0.898200\pi$
$80$	−4.18360	+	4.64636i	−0.467741	+	0.519478i
$81$	−5.78032	−	6.41969i	−0.642257	−	0.713299i
$82$	−1.95670	+	18.6168i	−0.216082	+	2.05588i
$83$	−2.73232	+	0.580773i	−0.299912	+	0.0637482i	−0.355410	−	0.934711i	$-0.615659\pi$
$83$	−2.73232	+	0.580773i	−0.299912	+	0.0637482i	0.0554981	+	0.998459i	$0.482325\pi$
$84$	−2.53357	−	1.12802i	−0.276435	−	0.123077i
$85$	5.11035	−	3.71289i	0.554295	−	0.402719i
$86$	18.3756	−	8.18135i	1.98149	−	0.882218i
$87$	−4.11418	+	7.12597i	−0.441086	+	0.763984i
$88$	0.812137	+	1.40666i	0.0865741	+	0.149951i
$89$	2.59031	+	1.88197i	0.274572	+	0.199488i	0.716547	−	0.697539i	$-0.245722\pi$
$89$	2.59031	+	1.88197i	0.274572	+	0.199488i	−0.441974	+	0.897028i	$0.645722\pi$
$90$	8.74329	+	1.85844i	0.921624	+	0.195897i
$91$	0.370491	−	1.14025i	0.0388380	−	0.119531i
$92$	12.5562			1.30908
$93$		0			0
$94$	13.7742			1.42070
$95$	−2.46828	+	7.59659i	−0.253240	+	0.779394i
$96$	5.90716	+	1.25561i	0.602897	+	0.128150i
$97$	−1.63167	−	1.18548i	−0.165671	−	0.120367i	0.501860	−	0.864949i	$-0.332649\pi$
$97$	−1.63167	−	1.18548i	−0.165671	−	0.120367i	−0.667532	+	0.744581i	$0.732649\pi$
$98$	8.64916	+	14.9808i	0.873697	+	1.51329i
$99$	0.454362	−	0.786978i	0.0456651	−	0.0790943i
$100$	−14.2223	+	6.33218i	−1.42223	+	0.633218i
$101$	−8.78750	+	6.38449i	−0.874389	+	0.635281i	−0.931761	−	0.363072i	$-0.881728\pi$
$101$	−8.78750	+	6.38449i	−0.874389	+	0.635281i	0.0573722	+	0.998353i	$0.481728\pi$
$102$	−30.9996	−	13.8019i	−3.06941	−	1.36659i
$103$	3.92571	−	0.834436i	0.386812	−	0.0822195i	−0.0104009	−	0.999946i	$-0.503311\pi$
$103$	3.92571	−	0.834436i	0.386812	−	0.0822195i	0.397213	+	0.917726i	$0.369977\pi$
$104$	−2.63360	+	25.0570i	−0.258246	+	2.45704i
$105$	0.504007	+	0.559756i	0.0491860	+	0.0546266i
$106$	−7.93817	+	8.81623i	−0.771023	+	0.856308i
$107$	1.88711	+	17.9547i	0.182434	+	1.73574i	0.576883	+	0.816827i	$0.304269\pi$
$107$	1.88711	+	17.9547i	0.182434	+	1.73574i	−0.394449	+	0.918918i	$0.629064\pi$
$108$	−0.375090	−	1.15441i	−0.0360930	−	0.111083i
$109$	0.0807750	+	0.248600i	0.00773684	+	0.0238116i	0.954850	−	0.297087i	$-0.0960151\pi$
$109$	0.0807750	+	0.248600i	0.00773684	+	0.0238116i	−0.947114	+	0.320899i	$0.896015\pi$
$110$	−0.0874465	−	0.831998i	−0.00833770	−	0.0793279i
$111$	6.74792	−	7.49433i	0.640484	−	0.711330i
$112$	0.964867	+	1.07159i	0.0911714	+	0.101256i
$113$	0.292728	−	2.78512i	0.0275375	−	0.262002i	−0.972088	−	0.234619i	$-0.924616\pi$
$113$	0.292728	−	2.78512i	0.0275375	−	0.262002i	0.999625	−	0.0273832i	$-0.00871744\pi$
$114$	41.9710	−	8.92121i	3.93094	−	0.835548i
$115$	−3.11540	−	1.38706i	−0.290512	−	0.129344i
$116$	11.3894	−	8.27488i	1.05748	−	0.768303i
$117$	12.8771	−	5.73325i	1.19049	−	0.530039i
$118$	2.93635	−	5.08591i	0.270313	−	0.468196i
$119$	−0.728418	−	1.26166i	−0.0667739	−	0.115656i
$120$	−12.8057	−	9.30388i	−1.16899	−	0.849325i
$121$	10.6764	+	2.26935i	0.970585	+	0.206304i
$122$	−7.75471	+	23.8665i	−0.702078	+	2.16078i
$123$	−18.5455			−1.67219
$124$		0			0
$125$	9.97416			0.892116
$126$	0.637045	−	1.96062i	0.0567525	−	0.174666i
$127$	−5.52964	−	1.17536i	−0.490676	−	0.104296i	−0.0440725	−	0.999028i	$-0.514033\pi$
$127$	−5.52964	−	1.17536i	−0.490676	−	0.104296i	−0.446604	+	0.894732i	$0.647367\pi$
$128$	13.6157	+	9.89237i	1.20347	+	0.874370i
$129$	9.96390	+	17.2580i	0.877273	+	1.51948i
$130$	6.48834	−	11.2381i	0.569065	−	0.985649i
$131$	5.81591	−	2.58941i	0.508138	−	0.226238i	−0.136621	−	0.990623i	$-0.543624\pi$
$131$	5.81591	−	2.58941i	0.508138	−	0.226238i	0.644759	+	0.764386i	$0.276958\pi$
$132$	−2.46882	+	1.79370i	−0.214883	+	0.156122i
$133$	1.68291	+	0.749278i	0.145926	+	0.0649706i
$134$	8.75798	−	1.86157i	0.756575	−	0.160815i
$135$	−0.0344597	+	0.327862i	−0.00296582	+	0.0282179i
$136$	20.4853	+	22.7512i	1.75660	+	1.95090i
$137$	1.98256	−	2.20185i	0.169381	−	0.188117i	−0.652478	−	0.757808i	$-0.726270\pi$
$137$	1.98256	−	2.20185i	0.169381	−	0.188117i	0.821859	+	0.569691i	$0.192937\pi$
$138$	1.91492	+	18.2192i	0.163009	+	1.55092i
$139$	−3.95738	−	12.1796i	−0.335660	−	1.03306i	−0.966396	−	0.257058i	$-0.917247\pi$
$139$	−3.95738	−	12.1796i	−0.335660	−	1.03306i	0.630736	−	0.775998i	$-0.282753\pi$
$140$	−0.398234	−	1.22564i	−0.0336569	−	0.103585i
$141$	1.42642	+	13.5715i	0.120126	+	1.14293i
$142$	18.1714	−	20.1814i	1.52491	−	1.69358i
$143$	−0.882746	−	0.980389i	−0.0738190	−	0.0819843i
$144$	−1.77208	+	16.8602i	−0.147674	+	1.40502i
$145$	−3.73999	+	0.794960i	−0.310590	+	0.0660179i
$146$	−5.18650	−	2.30918i	−0.429238	−	0.191109i
$147$	−13.8647	+	10.0733i	−1.14354	+	0.830829i
$148$	−15.7623	+	7.01782i	−1.29565	+	0.576862i
$149$	−8.72673	+	15.1151i	−0.714921	+	1.23828i	0.248069	+	0.968742i	$0.420204\pi$
$149$	−8.72673	+	15.1151i	−0.714921	+	1.23828i	−0.962990	+	0.269537i	$0.913129\pi$
$150$	−11.3570	−	19.6710i	−0.927299	−	1.60613i
$151$	−17.5484	−	12.7496i	−1.42807	−	1.03755i	−0.990373	−	0.138427i	$-0.955795\pi$
$151$	−17.5484	−	12.7496i	−1.42807	−	1.03755i	−0.437694	−	0.899124i	$-0.644205\pi$
$152$	−37.8664	−	8.04875i	−3.07137	−	0.652840i
$153$	5.29280	−	16.2896i	0.427898	−	1.31693i
$154$	−0.192941			−0.0155477
$155$		0			0
$156$	−47.3356			−3.78988
$157$	−4.49074	+	13.8211i	−0.358400	+	1.10304i	0.595611	+	0.803273i	$0.296910\pi$
$157$	−4.49074	+	13.8211i	−0.358400	+	1.10304i	−0.954012	+	0.299770i	$0.903090\pi$
$158$	9.26428	+	1.96918i	0.737026	+	0.156660i
$159$	−9.50857	−	6.90838i	−0.754078	−	0.547870i
$160$	1.40313	+	2.43029i	0.110927	+	0.192131i
$161$	−0.393252	+	0.681132i	−0.0309926	+	0.0536807i
$162$	−19.6996	+	8.77081i	−1.54774	+	0.689100i
$163$	−0.0555256	+	0.0403417i	−0.00434910	+	0.00315981i	−0.589958	−	0.807434i	$-0.700856\pi$
$163$	−0.0555256	+	0.0403417i	−0.00434910	+	0.00315981i	0.585609	+	0.810594i	$0.300856\pi$
$164$	28.9867	+	12.9057i	2.26348	+	1.00777i
$165$	0.810700	−	0.172320i	0.0631129	−	0.0134151i
$166$	−0.728867	+	6.93471i	−0.0565711	+	0.538238i
$167$	3.24971	+	3.60917i	0.251470	+	0.279286i	0.855642	−	0.517568i	$-0.173163\pi$
$167$	3.24971	+	3.60917i	0.251470	+	0.279286i	−0.604172	+	0.796854i	$0.706496\pi$
$168$	−2.44272	+	2.71292i	−0.188460	+	0.209306i
$169$	−0.780151	−	7.42264i	−0.0600116	−	0.570973i
$170$	−4.87260	−	14.9963i	−0.373712	−	1.15017i
$171$	6.69275	+	20.5982i	0.511808	+	1.57518i
$172$	−3.56389	−	33.9081i	−0.271744	−	2.58547i
$173$	−7.55830	+	8.39434i	−0.574647	+	0.638210i	−0.958469	−	0.285197i	$-0.907941\pi$
$173$	−7.55830	+	8.39434i	−0.574647	+	0.638210i	0.383822	+	0.923407i	$0.374608\pi$
$174$	13.7439	+	15.2641i	1.04192	+	1.15717i
$175$	0.101933	−	0.969828i	0.00770542	−	0.0733121i
$176$	1.55200	−	0.329887i	0.116986	−	0.0248662i
$177$	5.31516	+	2.36646i	0.399512	+	0.177874i
$178$	6.46603	−	4.69785i	0.484649	−	0.352118i
$179$	−13.1827	+	5.86932i	−0.985322	+	0.438693i	−0.835183	−	0.549972i	$-0.814639\pi$
$179$	−13.1827	+	5.86932i	−0.985322	+	0.438693i	−0.150138	+	0.988665i	$0.547972\pi$
$180$	7.57562	−	13.1214i	0.564653	−	0.978009i
$181$	11.0002	+	19.0529i	0.817639	+	1.41619i	0.907417	+	0.420231i	$0.138051\pi$
$181$	11.0002	+	19.0529i	0.817639	+	1.41619i	−0.0897781	+	0.995962i	$0.528616\pi$
$182$	−2.42124	−	1.75914i	−0.179475	−	0.130396i
$183$	−24.3184	−	5.16904i	−1.79767	−	0.382106i
$184$	5.10744	−	15.7191i	0.376525	−	1.15883i
$185$	4.68611			0.344530
$186$		0			0
$187$	−1.60303			−0.117225
$188$	7.21483	−	22.2050i	0.526195	−	1.61946i
$189$	0.0743701	+	0.0158079i	0.00540963	+	0.00114985i
$190$	16.1308	+	11.7197i	1.17025	+	0.850237i
$191$	−10.8832	−	18.8502i	−0.787478	−	1.36395i	−0.927507	−	0.373805i	$-0.878053\pi$
$191$	−10.8832	−	18.8502i	−0.787478	−	1.36395i	0.140029	−	0.990147i	$-0.455280\pi$
$192$	−5.91751	+	10.2494i	−0.427060	+	0.739689i
$193$	2.02006	−	0.899388i	0.145407	−	0.0647394i	−0.332743	−	0.943018i	$-0.607974\pi$
$193$	2.02006	−	0.899388i	0.145407	−	0.0647394i	0.478150	+	0.878278i	$0.341308\pi$
$194$	−4.07305	+	2.95924i	−0.292428	+	0.212461i
$195$	11.7447	+	5.22907i	0.841054	+	0.374462i
$196$	28.6805	−	6.09622i	2.04860	−	0.435444i
$197$	1.81808	−	17.2979i	0.129533	−	1.23242i	−0.715847	−	0.698257i	$-0.753959\pi$
$197$	1.81808	−	17.2979i	0.129533	−	1.23242i	0.845380	−	0.534165i	$-0.179374\pi$
$198$	−1.51785	−	1.68574i	−0.107869	−	0.119801i
$199$	−7.86888	+	8.73928i	−0.557810	+	0.619511i	−0.954417	−	0.298478i	$-0.903521\pi$
$199$	−7.86888	+	8.73928i	−0.557810	+	0.619511i	0.396606	+	0.917989i	$0.370188\pi$
$200$	2.14208	+	20.3805i	0.151468	+	1.44112i
$201$	2.74113	+	8.43634i	0.193345	+	0.595053i
$202$	8.37869	+	25.7869i	0.589522	+	1.81436i
$203$	0.0921762	+	0.876998i	0.00646950	+	0.0615532i
$204$	−38.4870	+	42.7441i	−2.69463	+	2.99269i
$205$	−5.76637	−	6.40421i	−0.402741	−	0.447289i
$206$	1.04721	−	9.96356i	0.0729627	−	0.694194i
$207$	−9.04477	+	1.92253i	−0.628655	+	0.133625i
$208$	22.4839	+	10.0105i	1.55898	+	0.694103i
$209$	1.63990	−	1.19146i	0.113434	−	0.0824148i
$210$	1.71768	−	0.764759i	0.118531	−	0.0527734i
$211$	3.73250	−	6.46488i	0.256956	−	0.445061i	−0.708469	−	0.705742i	$-0.750614\pi$
$211$	3.73250	−	6.46488i	0.256956	−	0.445061i	0.965425	+	0.260681i	$0.0839471\pi$
$212$	10.0544	+	17.4148i	0.690541	+	1.19605i
$213$	21.7662	+	15.8141i	1.49139	+	1.08356i
$214$	44.0812	+	9.36975i	3.01333	+	0.640503i
$215$	−2.86151	+	8.80682i	−0.195153	+	0.600620i
$216$	−1.59777			−0.108714
$217$		0			0
$218$	0.652500			0.0441929
$219$	1.73810	−	5.34931i	0.117450	−	0.361473i
$220$	−1.38704	−	0.294825i	−0.0935145	−	0.0198771i
$221$	−20.1166	−	14.6155i	−1.35319	−	0.983147i
$222$	−12.5868	−	21.8010i	−0.844770	−	1.46318i
$223$	14.5733	−	25.2418i	0.975903	−	1.69031i	0.298979	−	0.954260i	$-0.403354\pi$
$223$	14.5733	−	25.2418i	0.975903	−	1.69031i	0.676924	−	0.736053i	$-0.263313\pi$
$224$	0.591256	−	0.263244i	0.0395049	−	0.0175887i
$225$	9.27536	−	6.73895i	0.618358	−	0.449263i
$226$	−6.38624	−	2.84334i	−0.424806	−	0.189136i
$227$	−5.81777	+	1.23661i	−0.386139	+	0.0820764i	−0.396891	−	0.917866i	$-0.629911\pi$
$227$	−5.81777	+	1.23661i	−0.386139	+	0.0820764i	0.0107518	+	0.999942i	$0.496578\pi$
$228$	7.60251	−	72.3331i	0.503489	−	4.79037i
$229$	−3.74122	−	4.15504i	−0.247226	−	0.274573i	0.606741	−	0.794900i	$-0.292477\pi$
$229$	−3.74122	−	4.15504i	−0.247226	−	0.274573i	−0.853967	+	0.520327i	$0.825810\pi$
$230$	−5.69613	+	6.32619i	−0.375592	+	0.417137i
$231$	−0.0199806	−	0.190102i	−0.00131462	−	0.0125078i
$232$	−5.72646	−	17.6242i	−0.375961	−	1.15709i
$233$	−8.15163	−	25.0881i	−0.534031	−	1.64358i	−0.745733	−	0.666245i	$-0.767901\pi$
$233$	−8.15163	−	25.0881i	−0.534031	−	1.64358i	0.211702	−	0.977334i	$-0.432099\pi$
$234$	−3.67797	−	34.9935i	−0.240436	−	2.28760i
$235$	−4.24305	+	4.71238i	−0.276786	+	0.307402i
$236$	−6.66081	−	7.39757i	−0.433581	−	0.481541i
$237$	−0.980820	+	9.33188i	−0.0637111	+	0.606171i
$238$	−3.55714	+	0.756093i	−0.230575	+	0.0490102i
$239$	19.0230	+	8.46959i	1.23050	+	0.547852i	0.915913	−	0.401378i	$-0.131468\pi$
$239$	19.0230	+	8.46959i	1.23050	+	0.547852i	0.314583	+	0.949230i	$0.398135\pi$
$240$	−12.5092	+	9.08848i	−0.807467	+	0.586659i
$241$	13.0277	−	5.80031i	0.839188	−	0.373631i	0.0582981	−	0.998299i	$-0.481433\pi$
$241$	13.0277	−	5.80031i	0.839188	−	0.373631i	0.780890	+	0.624669i	$0.214766\pi$
$242$	13.6232	−	23.5960i	0.875730	−	1.51681i
$243$	−11.1121	−	19.2467i	−0.712842	−	1.23468i
$244$	34.4127	+	25.0023i	2.20305	+	1.60061i
$245$	−7.78950	−	1.65571i	−0.497653	−	0.105779i
$246$	−14.3056	+	44.0282i	−0.912093	+	2.80713i
$247$	31.4424			2.00063
$248$		0			0
$249$	−6.90815			−0.437786
$250$	7.69387	−	23.6793i	0.486603	−	1.49761i
$251$	−8.60831	−	1.82975i	−0.543352	−	0.115493i	−0.0719444	−	0.997409i	$-0.522920\pi$
$251$	−8.60831	−	1.82975i	−0.543352	−	0.115493i	−0.471407	+	0.881916i	$0.656254\pi$
$252$	−2.82698	−	2.05392i	−0.178083	−	0.129385i
$253$	0.432714	+	0.749482i	0.0272045	+	0.0471196i
$254$	−7.05583	+	12.2211i	−0.442722	+	0.766818i
$255$	14.2711	−	6.35389i	0.893690	−	0.397896i
$256$	26.2447	−	19.0679i	1.64030	−	1.19174i
$257$	3.66301	+	1.63088i	0.228492	+	0.101731i	0.517790	−	0.855508i	$-0.326755\pi$
$257$	3.66301	+	1.63088i	0.228492	+	0.101731i	−0.289297	+	0.957239i	$0.593422\pi$
$258$	48.6575	−	10.3425i	3.02928	−	0.643894i
$259$	0.112970	−	1.07484i	0.00701964	−	0.0667874i
$260$	−14.7181	−	16.3461i	−0.912779	−	1.01374i
$261$	−6.93725	+	7.70460i	−0.429405	+	0.476903i
$262$	−1.66115	−	15.8048i	−0.102626	−	0.976421i
$263$	0.189150	+	0.582143i	0.0116635	+	0.0358965i	0.956719	−	0.291014i	$-0.0939925\pi$
$263$	0.189150	+	0.582143i	0.0116635	+	0.0358965i	−0.945055	+	0.326910i	$0.893993\pi$
$264$	1.24130	+	3.82032i	0.0763965	+	0.235124i
$265$	−0.570881	−	5.43157i	−0.0350689	−	0.333659i
$266$	3.07699	−	3.41735i	0.188663	−	0.209531i
$267$	5.29833	+	5.88439i	0.324252	+	0.360119i
$268$	1.58640	−	15.0936i	0.0969047	−	0.921986i
$269$	1.10169	−	0.234171i	0.0671711	−	0.0142777i	−0.174204	−	0.984710i	$-0.555735\pi$
$269$	1.10169	−	0.234171i	0.0671711	−	0.0142777i	0.241375	+	0.970432i	$0.422402\pi$
$270$	0.751783	+	0.334715i	0.0457521	+	0.0203701i
$271$	0.168217	−	0.122217i	0.0102185	−	0.00742416i	−0.582664	−	0.812713i	$-0.697990\pi$
$271$	0.168217	−	0.122217i	0.0102185	−	0.00742416i	0.592883	+	0.805289i	$0.297990\pi$
$272$	27.3204	−	12.1638i	1.65655	−	0.737542i
$273$	1.48251	−	2.56779i	0.0897258	−	0.155410i
$274$	−3.69803	−	6.40518i	−0.223406	−	0.386951i
$275$	−0.868097	−	0.630709i	−0.0523482	−	0.0380332i
$276$	30.3737	+	6.45613i	1.82828	+	0.388613i
$277$	7.68682	−	23.6576i	0.461856	−	1.42145i	−0.401037	−	0.916062i	$-0.631350\pi$
$277$	7.68682	−	23.6576i	0.461856	−	1.42145i	0.862894	−	0.505386i	$-0.168650\pi$
$278$	−31.9677			−1.91729
$279$		0			0
$280$	−1.69635			−0.101377
$281$	7.96124	−	24.5022i	0.474928	−	1.46168i	−0.371128	−	0.928582i	$-0.621029\pi$
$281$	7.96124	−	24.5022i	0.474928	−	1.46168i	0.846055	−	0.533095i	$-0.178971\pi$
$282$	33.3199	+	7.08237i	1.98417	+	0.421749i
$283$	21.6665	+	15.7417i	1.28794	+	0.935744i	0.999762	−	0.0218320i	$-0.00694988\pi$
$283$	21.6665	+	15.7417i	1.28794	+	0.935744i	0.288180	+	0.957576i	$0.406950\pi$
$284$	−23.0157	−	39.8644i	−1.36573	−	2.36552i
$285$	−9.87679	+	17.1071i	−0.585051	+	1.01334i
$286$	−3.00844	+	1.33944i	−0.177893	+	0.0792029i
$287$	−1.60793	+	1.16823i	−0.0949131	+	0.0689584i
$288$	6.95133	+	3.09493i	0.409611	+	0.182371i
$289$	−12.9255	+	2.74739i	−0.760321	+	0.161611i
$290$	−0.997670	+	9.49220i	−0.0585852	+	0.557401i
$291$	−3.33749	−	3.70666i	−0.195647	−	0.217288i
$292$	−6.43921	+	7.15147i	−0.376826	+	0.418508i
$293$	−2.33755	−	22.2403i	−0.136561	−	1.29929i	−0.821298	−	0.570500i	$-0.806750\pi$
$293$	−2.33755	−	22.2403i	−0.136561	−	1.29929i	0.684737	−	0.728790i	$-0.259917\pi$
$294$	13.2196	+	40.6859i	0.770986	+	2.37285i
$295$	0.835452	+	2.57126i	0.0486419	+	0.149704i
$296$	2.37402	+	22.5873i	0.137987	+	1.31286i
$297$	0.0559803	−	0.0621724i	0.00324830	−	0.00360761i
$298$	29.1527	+	32.3773i	1.68877	+	1.87557i
$299$	−1.40320	+	13.3506i	−0.0811494	+	0.772085i
$300$	−37.6598	+	8.00483i	−2.17429	+	0.462159i
$301$	1.95102	+	0.868648i	0.112455	+	0.0500680i
$302$	−43.8049	+	31.8261i	−2.52069	+	1.83139i
$303$	−24.5398	+	10.9258i	−1.40978	+	0.627673i
$304$	−18.9081	+	32.7497i	−1.08445	+	1.87833i
$305$	−5.77636	−	10.0050i	−0.330754	−	0.572882i
$306$	−34.5897	−	25.1309i	−1.97736	−	1.43664i
$307$	−7.12858	−	1.51523i	−0.406849	−	0.0864785i	−5.88765e−5	−	1.00000i	$-0.500019\pi$
$307$	−7.12858	−	1.51523i	−0.406849	−	0.0864785i	−0.406790	+	0.913522i	$0.633352\pi$
$308$	−0.101061	+	0.311035i	−0.00575851	+	0.0177229i
$309$	9.92540			0.564636
$310$		0			0
$311$	−25.6025			−1.45179			−0.725893	−	0.687808i	$-0.758573\pi$
$311$	−25.6025			−1.45179			−0.725893	+	0.687808i	$0.758573\pi$
$312$	−19.2544	+	59.2591i	−1.09007	+	3.35489i
$313$	24.9202	+	5.29696i	1.40857	+	0.299402i	0.848568	−	0.529086i	$-0.177465\pi$
$313$	24.9202	+	5.29696i	1.40857	+	0.299402i	0.560007	+	0.828488i	$0.310799\pi$
$314$	29.3481	+	21.3226i	1.65621	+	1.20330i
$315$	0.474525	+	0.821902i	0.0267365	+	0.0463089i
$316$	8.02703	−	13.9032i	0.451556	−	0.782118i
$317$	−13.0062	+	5.79075i	−0.730503	+	0.325241i	−0.738064	−	0.674731i	$-0.764260\pi$
$317$	−13.0062	+	5.79075i	−0.730503	+	0.325241i	0.00756143	+	0.999971i	$0.497593\pi$
$318$	−23.7356	+	17.2450i	−1.33103	+	0.967049i
$319$	0.886430	+	0.394664i	0.0496305	+	0.0220969i
$320$	−5.37931	+	1.14341i	−0.300713	+	0.0639185i
$321$	−4.66693	+	44.4029i	−0.260483	+	2.47833i
$322$	1.31370	+	1.45902i	0.0732098	+	0.0813078i
$323$	25.5648	−	28.3925i	1.42246	−	1.57980i
$324$	3.82066	+	36.3512i	0.212259	+	2.01951i
$325$	−5.14338	−	15.8297i	−0.285303	−	0.878073i
$326$	0.0529425	+	0.162940i	0.00293221	+	0.00902442i
$327$	0.0675714	+	0.642899i	0.00373671	+	0.0355524i
$328$	27.9473	−	31.0387i	1.54313	−	1.71382i
$329$	0.978578	+	1.08682i	0.0539507	+	0.0599184i
$330$	0.216260	−	2.05758i	0.0119047	−	0.113266i
$331$	−17.1093	+	3.63669i	−0.940412	+	0.199891i	−0.652520	−	0.757772i	$-0.726288\pi$
$331$	−17.1093	+	3.63669i	−0.940412	+	0.199891i	−0.287893	+	0.957663i	$0.592955\pi$
$332$	10.7975	+	4.80734i	0.592588	+	0.263837i
$333$	10.2797	−	7.46864i	0.563324	−	0.409279i
$334$	11.0752	−	4.93098i	0.606006	−	0.269811i
$335$	−2.06097	+	3.56970i	−0.112603	+	0.195034i
$336$	1.78304	+	3.08831i	0.0972726	+	0.168481i
$337$	−13.2867	−	9.65334i	−0.723772	−	0.525851i	0.163815	−	0.986491i	$-0.447620\pi$
$337$	−13.2867	−	9.65334i	−0.723772	−	0.525851i	−0.887587	+	0.460640i	$0.847620\pi$
$338$	−18.2236	−	3.87355i	−0.991234	−	0.210693i
$339$	2.14015	−	6.58672i	0.116237	−	0.357741i
$340$	−26.7274			−1.44950
$341$		0			0
$342$	54.0640			2.92345
$343$	−1.14086	+	3.51119i	−0.0616004	+	0.189587i
$344$	−43.8990	−	9.33103i	−2.36688	−	0.503095i
$345$	−6.82299	−	4.95719i	−0.367337	−	0.266886i
$346$	14.0984	+	24.4191i	0.757933	+	1.31278i
$347$	13.0438	−	22.5925i	0.700228	−	1.21283i	−0.268158	−	0.963375i	$-0.586415\pi$
$347$	13.0438	−	22.5925i	0.700228	−	1.21283i	0.968386	−	0.249456i	$-0.0802519\pi$
$348$	31.8058	−	14.1609i	1.70497	−	0.759103i
$349$	−8.65311	+	6.28685i	−0.463190	+	0.336527i	−0.794781	−	0.606896i	$-0.792415\pi$
$349$	−8.65311	+	6.28685i	−0.463190	+	0.336527i	0.331591	+	0.943423i	$0.392415\pi$
$350$	−2.22380	−	0.990102i	−0.118867	−	0.0529232i
$351$	1.26936	−	0.269810i	0.0677533	−	0.0144014i
$352$	0.0744406	−	0.708255i	0.00396770	−	0.0377501i
$353$	9.12786	+	10.1375i	0.485827	+	0.539566i	0.935360	−	0.353698i	$-0.115076\pi$
$353$	9.12786	+	10.1375i	0.485827	+	0.539566i	−0.449532	+	0.893264i	$0.648409\pi$
$354$	9.71813	−	10.7931i	0.516513	−	0.573645i
$355$	1.30681	+	12.4335i	0.0693583	+	0.659900i
$356$	−4.18640	−	12.8844i	−0.221879	−	0.682872i
$357$	−1.11334	−	3.42650i	−0.0589240	−	0.181349i
$358$	3.76526	+	35.8240i	0.199000	+	1.89336i
$359$	1.39840	−	1.55308i	0.0738048	−	0.0819686i	−0.705111	−	0.709097i	$-0.749103\pi$
$359$	1.39840	−	1.55308i	0.0738048	−	0.0819686i	0.778916	+	0.627128i	$0.215770\pi$
$360$	−13.3450	−	14.8212i	−0.703346	−	0.781145i
$361$	−3.06388	+	29.1509i	−0.161257	+	1.53426i
$362$	53.7182	−	11.4182i	2.82336	−	0.600125i
$363$	24.6596	+	10.9792i	1.29429	+	0.576256i
$364$	−4.10408	+	2.98179i	−0.215112	+	0.156288i
$365$	2.38768	−	1.06306i	0.124977	−	0.0556432i
$366$	−31.0304	+	53.7462i	−1.62198	+	2.80936i
$367$	−9.96005	−	17.2513i	−0.519910	−	0.900511i	−0.999732	−	0.0231450i	$-0.992632\pi$
$367$	−9.96005	−	17.2513i	−0.519910	−	0.900511i	0.479822	−	0.877366i	$-0.340701\pi$
$368$	−13.0619	−	9.49001i	−0.680897	−	0.494701i
$369$	−22.8563	−	4.85826i	−1.18985	−	0.252911i
$370$	3.61477	−	11.1251i	0.187923	−	0.578368i
$371$	−1.25959			−0.0653945
$372$		0			0
$373$	10.7238			0.555257			0.277629	−	0.960688i	$-0.410452\pi$
$373$	10.7238			0.555257			0.277629	+	0.960688i	$0.410452\pi$
$374$	−1.23654	+	3.80568i	−0.0639401	+	0.196787i
$375$	24.1276	+	5.12848i	1.24595	+	0.264834i
$376$	−24.8635	−	18.0644i	−1.28224	−	0.931600i
$377$	7.52557	+	13.0347i	0.387587	+	0.671320i
$378$	0.0948964	−	0.164365i	0.00488095	−	0.00845405i
$379$	12.9300	−	5.75680i	0.664169	−	0.295707i	−0.0468274	−	0.998903i	$-0.514911\pi$
$379$	12.9300	−	5.75680i	0.664169	−	0.295707i	0.710996	+	0.703196i	$0.248244\pi$
$380$	27.3422	−	19.8653i	1.40263	−	1.01907i
$381$	−12.7719	−	5.68643i	−0.654325	−	0.291324i
$382$	−53.1466	+	11.2967i	−2.71922	+	0.577988i
$383$	−1.86648	+	17.7584i	−0.0953727	+	0.907410i	0.837314	+	0.546723i	$0.184125\pi$
$383$	−1.86648	+	17.7584i	−0.0953727	+	0.907410i	−0.932687	+	0.360688i	$0.882542\pi$
$384$	27.8501	+	30.9306i	1.42122	+	1.57842i
$385$	0.0594343	−	0.0660085i	0.00302905	−	0.00336411i
$386$	−0.576971	−	5.48952i	−0.0293671	−	0.279409i
$387$	7.75900	+	23.8797i	0.394412	+	1.21388i
$388$	2.63707	+	8.11607i	0.133877	+	0.412031i
$389$	2.45444	+	23.3524i	0.124445	+	1.18402i	0.861347	+	0.508016i	$0.169621\pi$
$389$	2.45444	+	23.3524i	0.124445	+	1.18402i	−0.736902	+	0.675999i	$0.763712\pi$
$390$	21.4738	−	23.8490i	1.08737	−	1.20764i
$391$	10.9147	+	12.1220i	0.551981	+	0.613037i
$392$	4.03438	−	38.3846i	0.203767	−	1.93872i
$393$	15.4002	−	3.27341i	0.776836	−	0.165122i
$394$	−39.6638	−	17.6595i	−1.99823	−	0.889671i
$395$	−3.52749	+	2.56287i	−0.177487	+	0.128952i
$396$	−3.51258	+	1.56390i	−0.176514	+	0.0785890i
$397$	5.05313	−	8.75228i	0.253609	−	0.439264i	−0.710907	−	0.703286i	$-0.751716\pi$
$397$	5.05313	−	8.75228i	0.253609	−	0.439264i	0.964517	+	0.264021i	$0.0850489\pi$
$398$	14.6777	+	25.4225i	0.735727	+	1.27432i
$399$	3.68571	+	2.67782i	0.184516	+	0.134059i
$400$	19.5809	+	4.16204i	0.979044	+	0.208102i
$401$	−7.06820	+	21.7537i	−0.352969	+	1.08633i	0.604209	+	0.796826i	$0.293489\pi$
$401$	−7.06820	+	21.7537i	−0.352969	+	1.08633i	−0.957178	+	0.289501i	$0.906511\pi$
$402$	22.1428			1.10438
$403$		0			0
$404$	45.9591			2.28655
$405$	3.06768	−	9.44135i	0.152434	−	0.469145i
$406$	2.15315	+	0.457666i	0.106859	+	0.0227136i
$407$	−0.962095	−	0.699003i	−0.0476893	−	0.0346483i
$408$	37.8560	+	65.5684i	1.87415	+	3.24612i
$409$	−6.59713	+	11.4266i	−0.326207	+	0.565007i	−0.981756	−	0.190146i	$-0.939104\pi$
$409$	−6.59713	+	11.4266i	−0.326207	+	0.565007i	0.655549	+	0.755153i	$0.272437\pi$
$410$	−19.6521	+	8.74966i	−0.970546	+	0.432115i
$411$	5.92797	−	4.30692i	0.292405	−	0.212445i
$412$	−15.5134	−	6.90703i	−0.764292	−	0.340285i
$413$	0.609904	−	0.129639i	0.0300114	−	0.00637912i
$414$	−2.41276	+	22.9559i	−0.118581	+	1.12822i
$415$	−2.14796	−	2.38555i	−0.105439	−	0.117102i
$416$	7.39166	−	8.20926i	0.362406	−	0.402492i
$417$	−3.31050	−	31.4973i	−0.162116	−	1.54243i
$418$	−1.56361	−	4.81229i	−0.0764786	−	0.235377i
$419$	−1.37802	−	4.24112i	−0.0673208	−	0.207192i	0.911737	−	0.410774i	$-0.134742\pi$
$419$	−1.37802	−	4.24112i	−0.0673208	−	0.207192i	−0.979058	+	0.203582i	$0.934742\pi$
$420$	−0.333138	−	3.16959i	−0.0162555	−	0.154660i
$421$	−12.9298	+	14.3600i	−0.630162	+	0.699866i	−0.970681	−	0.240372i	$-0.922731\pi$
$421$	−12.9298	+	14.3600i	−0.630162	+	0.699866i	0.340519	+	0.940238i	$0.389397\pi$
$422$	−12.4689	−	13.8481i	−0.606975	−	0.674114i
$423$	−1.79726	+	17.0998i	−0.0873859	+	0.831422i
$424$	25.8912	−	5.50335i	1.25739	−	0.267266i
$425$	−18.4762	−	8.22612i	−0.896226	−	0.399025i
$426$	54.3336	−	39.4757i	2.63247	−	1.91260i
$427$	−2.43406	+	1.08372i	−0.117793	+	0.0524447i
$428$	38.1942	−	66.1543i	1.84619	−	3.19769i
$429$	−1.63128	−	2.82546i	−0.0787590	−	0.136415i
$430$	18.7006	+	13.5868i	0.901825	+	0.655214i
$431$	10.2171	+	2.17170i	0.492138	+	0.104607i	0.447294	−	0.894387i	$-0.352388\pi$
$431$	10.2171	+	2.17170i	0.492138	+	0.104607i	0.0448437	+	0.998994i	$0.485721\pi$
$432$	−0.482307	+	1.48439i	−0.0232050	+	0.0714177i
$433$	20.7300			0.996220			0.498110	−	0.867114i	$-0.334028\pi$
$433$	20.7300			0.996220			0.498110	+	0.867114i	$0.334028\pi$
$434$		0			0
$435$	−9.45584			−0.453373
$436$	0.341775	−	1.05188i	0.0163681	−	0.0503758i
$437$	−20.1756	−	4.28845i	−0.965128	−	0.205144i
$438$	−11.3589	−	8.25271i	−0.542748	−	0.394330i
$439$	−14.1778	−	24.5567i	−0.676669	−	1.17203i	−0.975978	−	0.217869i	$-0.930089\pi$
$439$	−14.1778	−	24.5567i	−0.676669	−	1.17203i	0.299309	−	0.954156i	$-0.403244\pi$
$440$	−0.933290	+	1.61651i	−0.0444929	+	0.0770639i
$441$	−19.7263	+	8.78271i	−0.939347	+	0.418224i
$442$	−50.2157	+	36.4838i	−2.38852	+	1.73536i
$443$	−26.6907	−	11.8835i	−1.26811	−	0.564600i	−0.341240	−	0.939976i	$-0.610847\pi$
$443$	−26.6907	−	11.8835i	−1.26811	−	0.564600i	−0.926873	+	0.375376i	$0.877514\pi$
$444$	−41.7376	+	8.87160i	−1.98078	+	0.421027i
$445$	−0.384606	+	3.65928i	−0.0182321	+	0.173467i
$446$	−48.6839	−	54.0690i	−2.30525	−	2.56024i
$447$	−28.8819	+	32.0766i	−1.36607	+	1.51717i
$448$	0.132579	+	1.26140i	0.00626377	+	0.0595958i
$449$	−0.360510	−	1.10954i	−0.0170135	−	0.0523622i	0.942189	−	0.335081i	$-0.108764\pi$
$449$	−0.360510	−	1.10954i	−0.0170135	−	0.0523622i	−0.959203	+	0.282719i	$0.908764\pi$
$450$	−8.84385	−	27.2186i	−0.416903	−	1.28310i
$451$	0.228599	+	2.17497i	0.0107643	+	0.102415i
$452$	−7.92873	+	8.80575i	−0.372936	+	0.414188i
$453$	−35.8942	−	39.8645i	−1.68646	−	1.87300i
$454$	−1.55193	+	14.7656i	−0.0728358	+	0.692986i
$455$	1.34768	−	0.286458i	0.0631802	−	0.0134294i
$456$	−87.4608	−	38.9401i	−4.09573	−	1.82354i
$457$	32.5888	−	23.6772i	1.52444	−	1.10757i	0.565211	−	0.824946i	$-0.308795\pi$
$457$	32.5888	−	23.6772i	1.52444	−	1.10757i	0.959230	−	0.282626i	$-0.0912054\pi$
$458$	−12.7502	+	5.67677i	−0.595779	+	0.265258i
$459$	0.788433	−	1.36561i	0.0368009	−	0.0637411i
$460$	7.21468	+	12.4962i	0.336386	+	0.582638i
$461$	−23.7360	−	17.2452i	−1.10550	−	0.803191i	−0.123549	−	0.992338i	$-0.539428\pi$
$461$	−23.7360	−	17.2452i	−1.10550	−	0.803191i	−0.981949	+	0.189148i	$0.939428\pi$
$462$	−0.466728	−	0.0992060i	−0.0217141	−	0.00461548i
$463$	0.197619	−	0.608208i	0.00918413	−	0.0282658i	−0.946359	−	0.323116i	$-0.895270\pi$
$463$	0.197619	−	0.608208i	0.00918413	−	0.0282658i	0.955544	+	0.294850i	$0.0952697\pi$
$464$	−18.1022			−0.840373
$465$		0			0
$466$	−65.8488			−3.05039
$467$	0.894736	−	2.75372i	0.0414035	−	0.127427i	−0.928218	−	0.372036i	$-0.878660\pi$
$467$	0.894736	−	2.75372i	0.0414035	−	0.127427i	0.969622	+	0.244609i	$0.0786597\pi$
$468$	−58.3386	−	12.4002i	−2.69670	−	0.573202i
$469$	0.769088	+	0.558775i	0.0355132	+	0.0258018i
$470$	7.91449	+	13.7083i	0.365068	+	0.632317i
$471$	−17.9696	+	31.1243i	−0.827998	+	1.43413i
$472$	−11.9704	+	5.32955i	−0.550980	+	0.245312i
$473$	1.90116	−	1.38127i	0.0874153	−	0.0635110i
$474$	21.3979	+	9.52695i	0.982838	+	0.437588i
$475$	25.0153	−	5.31716i	1.14778	−	0.243968i
$476$	−0.644330	+	6.13040i	−0.0295328	+	0.280986i
$477$	−9.90905	−	11.0051i	−0.453704	−	0.503889i
$478$	34.7813	−	38.6285i	1.59086	−	1.76683i
$479$	−3.02547	−	28.7854i	−0.138237	−	1.31524i	−0.815182	−	0.579206i	$-0.803363\pi$
$479$	−3.02547	−	28.7854i	−0.138237	−	1.31524i	0.676944	−	0.736034i	$-0.263304\pi$
$480$	2.14459	+	6.60036i	0.0978866	+	0.301264i
$481$	−5.70030	−	17.5437i	−0.259912	−	0.799925i
$482$	−3.72099	−	35.4028i	−0.169486	−	1.61255i
$483$	−1.30150	+	1.44547i	−0.0592204	+	0.0657710i
$484$	−30.9027	−	34.3209i	−1.40467	−	1.56004i
$485$	0.242269	−	2.30503i	0.0110009	−	0.104666i
$486$	−54.2646	+	11.5343i	−2.46149	+	0.523206i
$487$	2.49692	+	1.11170i	0.113146	+	0.0503760i	0.462529	−	0.886604i	$-0.346942\pi$
$487$	2.49692	+	1.11170i	0.113146	+	0.0503760i	−0.349383	+	0.936980i	$0.613609\pi$
$488$	45.2981	−	32.9110i	2.05055	−	1.48981i
$489$	−0.155060	+	0.0690372i	−0.00701206	+	0.00312197i
$490$	−9.93942	+	17.2156i	−0.449017	+	0.777721i
$491$	5.71487	+	9.89845i	0.257908	+	0.446711i	0.965681	−	0.259729i	$-0.0836334\pi$
$491$	5.71487	+	9.89845i	0.257908	+	0.446711i	−0.707773	+	0.706440i	$0.750300\pi$
$492$	63.4834	+	46.1234i	2.86205	+	2.07940i
$493$	17.8891	+	3.80245i	0.805686	+	0.171254i
$494$	24.2540	−	74.6462i	1.09124	−	3.35849i
$495$	1.04429			0.0469372
$496$		0			0
$497$	2.88334			0.129335
$498$	−5.32881	+	16.4004i	−0.238789	+	0.734918i
$499$	−6.28152	−	1.33518i	−0.281199	−	0.0597708i	0.0651530	−	0.997875i	$-0.479246\pi$
$499$	−6.28152	−	1.33518i	−0.281199	−	0.0597708i	−0.346352	+	0.938105i	$0.612580\pi$
$500$	−34.1427	−	24.8061i	−1.52691	−	1.10936i
$501$	6.00534	+	10.4016i	0.268299	+	0.464707i
$502$	−10.9842	+	19.0252i	−0.490250	+	0.849138i
$503$	−11.4593	+	5.10200i	−0.510945	+	0.227487i	−0.645981	−	0.763353i	$-0.723551\pi$
$503$	−11.4593	+	5.10200i	−0.510945	+	0.227487i	0.135037	+	0.990841i	$0.456885\pi$
$504$	−3.72121	+	2.70362i	−0.165756	+	0.120429i
$505$	−11.4032	−	5.07701i	−0.507434	−	0.225924i
$506$	2.11311	−	0.449154i	0.0939390	−	0.0199673i
$507$	1.92936	−	18.3566i	0.0856858	−	0.815245i
$508$	16.0054	+	17.7758i	0.710126	+	0.788674i
$509$	−19.3894	+	21.5341i	−0.859419	+	0.954481i	−0.999363	−	0.0356779i	$-0.988641\pi$
$509$	−19.3894	+	21.5341i	−0.859419	+	0.954481i	0.139944	+	0.990159i	$0.455308\pi$
$510$	−4.07612	−	38.7817i	−0.180494	−	1.71728i
$511$	−0.186271	−	0.573283i	−0.00824014	−	0.0253605i
$512$	−14.6223	−	45.0029i	−0.646221	−	1.98886i
$513$	0.208425	+	1.98303i	0.00920217	+	0.0875528i
$514$	6.69737	−	7.43818i	0.295408	−	0.328084i
$515$	3.08612	+	3.42748i	0.135991	+	0.151033i
$516$	8.81369	−	83.8567i	0.388001	−	3.69158i
$517$	1.57405	−	0.334575i	0.0692267	−	0.0147146i
$518$	−2.46460	−	1.09731i	−0.108288	−	0.0482130i
$519$	−22.5998	+	16.4197i	−0.992021	+	0.720745i
$520$	−26.4504	+	11.7765i	−1.15993	+	0.516433i
$521$	6.40611	−	11.0957i	0.280657	−	0.486112i	−0.690890	−	0.722960i	$-0.742781\pi$
$521$	6.40611	−	11.0957i	0.280657	−	0.486112i	0.971547	+	0.236848i	$0.0761144\pi$
$522$	12.9400	+	22.4127i	0.566366	+	0.980975i
$523$	15.5195	+	11.2756i	0.678619	+	0.493045i	0.872899	−	0.487901i	$-0.162237\pi$
$523$	15.5195	+	11.2756i	0.678619	+	0.493045i	−0.194280	+	0.980946i	$0.562237\pi$
$524$	−26.3485	−	5.60054i	−1.15104	−	0.244661i
$525$	0.745241	−	2.29362i	0.0325250	−	0.100102i
$526$	1.52795			0.0666218
$527$		0			0
$528$	3.92392			0.170767
$529$	−4.38610	+	13.4990i	−0.190700	+	0.586915i
$530$	−13.3352	−	2.83449i	−0.579246	−	0.123123i
$531$	5.93072	+	4.30892i	0.257371	+	0.186991i
$532$	−3.89730	−	6.75032i	−0.168969	−	0.292663i
$533$	−16.9615	+	29.3782i	−0.734685	+	1.27251i
$534$	18.0569	−	8.03946i	0.781400	−	0.347902i
$535$	−16.7845	+	12.1946i	−0.725657	+	0.527221i
$536$	−18.2502	−	8.12553i	−0.788291	−	0.350970i
$537$	−34.9070	+	7.41971i	−1.50635	+	0.320184i
$538$	0.293883	−	2.79611i	0.0126702	−	0.120549i
$539$	1.35227	+	1.50185i	0.0582464	+	0.0646892i
$540$	0.933364	−	1.03661i	0.0401656	−	0.0446084i
$541$	3.86440	+	36.7673i	0.166144	+	1.58075i	0.686711	+	0.726930i	$0.259054\pi$
$541$	3.86440	+	36.7673i	0.166144	+	1.58075i	−0.520568	+	0.853820i	$0.674280\pi$
$542$	−0.160392	−	0.493635i	−0.00688941	−	0.0212034i
$543$	16.8131	+	51.7453i	0.721518	+	2.22060i
$544$	−1.40307	−	13.3494i	−0.0601563	−	0.572349i
$545$	−0.200999	+	0.223231i	−0.00860983	+	0.00956219i
$546$	−4.95251	−	5.50032i	−0.211948	−	0.235392i
$547$	3.41790	−	32.5191i	0.146139	−	1.39042i	−0.638098	−	0.769955i	$-0.720279\pi$
$547$	3.41790	−	32.5191i	0.146139	−	1.39042i	0.784237	−	0.620462i	$-0.213055\pi$
$548$	−12.2626	+	2.60650i	−0.523833	+	0.111344i
$549$	−28.6170	−	12.7411i	−1.22135	−	0.543778i
$550$	−2.16698	+	1.57440i	−0.0924002	+	0.0671327i
$551$	−21.1268	+	9.40628i	−0.900034	+	0.400721i
$552$	20.4373	−	35.3985i	0.869871	−	1.50666i
$553$	0.502801	+	0.870876i	0.0213813	+	0.0370334i
$554$	−50.2352	−	36.4980i	−2.13429	−	1.55065i
$555$	11.3358	+	2.40949i	0.481176	+	0.102277i
$556$	−16.7445	+	51.5342i	−0.710123	+	2.18553i
$557$	−28.6262			−1.21293			−0.606466	−	0.795109i	$-0.707413\pi$
$557$	−28.6262			−1.21293			−0.606466	+	0.795109i	$0.707413\pi$
$558$		0			0
$559$	36.4516			1.54174
$560$	−0.512066	+	1.57598i	−0.0216387	+	0.0665972i
$561$	−3.87774	−	0.824239i	−0.163718	−	0.0347994i
$562$	−52.0285	−	37.8010i	−2.19469	−	1.59454i
$563$	−12.8550	−	22.2656i	−0.541775	−	0.938382i	−0.998802	−	0.0489294i	$-0.984419\pi$
$563$	−12.8550	−	22.2656i	−0.541775	−	0.938382i	0.457027	−	0.889453i	$-0.348914\pi$
$564$	28.8700	−	50.0044i	1.21565	−	2.10556i
$565$	2.93999	−	1.30897i	0.123686	−	0.0550688i
$566$	54.0848	−	39.2949i	2.27335	−	1.65169i
$567$	−2.09158	−	0.931234i	−0.0878383	−	0.0391081i
$568$	−59.2680	+	12.5978i	−2.48683	+	0.528592i
$569$	2.53803	−	24.1477i	0.106400	−	1.01233i	−0.802880	−	0.596141i	$-0.796700\pi$
$569$	2.53803	−	24.1477i	0.106400	−	1.01233i	0.909280	−	0.416185i	$-0.136633\pi$
$570$	32.9946	+	36.6442i	1.38199	+	1.53486i
$571$	−8.99115	+	9.98568i	−0.376268	+	0.417888i	−0.901301	−	0.433194i	$-0.857386\pi$
$571$	−8.99115	+	9.98568i	−0.376268	+	0.417888i	0.525033	+	0.851082i	$0.324053\pi$
$572$	0.583476	+	5.55141i	0.0243964	+	0.232116i
$573$	−16.6342	−	51.1947i	−0.694903	−	2.13869i
$574$	1.53313	+	4.71847i	0.0639914	+	0.196945i
$575$	1.14132	+	10.8589i	0.0475962	+	0.452848i
$576$	−9.97800	+	11.0817i	−0.415750	+	0.461737i
$577$	18.2154	+	20.2303i	0.758319	+	0.842198i	0.991483	−	0.130239i	$-0.0415746\pi$
$577$	18.2154	+	20.2303i	0.758319	+	0.842198i	−0.233164	+	0.972437i	$0.574908\pi$
$578$	−3.44796	+	32.8051i	−0.143416	+	1.36451i
$579$	5.34899	−	1.13696i	0.222296	−	0.0472506i
$580$	14.7795	+	6.58027i	0.613686	+	0.273231i
$581$	−0.598949	+	0.435162i	−0.0248486	+	0.0180536i
$582$	−11.3743	+	5.06417i	−0.471481	+	0.209917i
$583$	−0.692992	+	1.20030i	−0.0287008	+	0.0497113i
$584$	6.33363	+	10.9702i	0.262088	+	0.453949i
$585$	13.1049	+	9.52124i	0.541819	+	0.393655i
$586$	−54.6029	−	11.6062i	−2.25563	−	0.479448i
$587$	−1.30923	+	4.02941i	−0.0540378	+	0.166311i	−0.974433	−	0.224678i	$-0.927867\pi$
$587$	−1.30923	+	4.02941i	−0.0540378	+	0.166311i	0.920395	+	0.390989i	$0.127867\pi$
$588$	72.5129			2.99038
$589$		0			0
$590$	6.74878			0.277843
$591$	13.2921	−	40.9090i	0.546765	−	1.68277i
$592$	21.7011	+	4.61271i	0.891910	+	0.189581i
$593$	15.0621	+	10.9433i	0.618527	+	0.449386i	0.852407	−	0.522879i	$-0.175142\pi$
$593$	15.0621	+	10.9433i	0.618527	+	0.449386i	−0.233880	+	0.972266i	$0.575142\pi$
$594$	−0.104419	−	0.180859i	−0.00428437	−	0.00742074i
$595$	0.837081	−	1.44987i	0.0343170	−	0.0594388i
$596$	67.4645	−	30.0371i	2.76345	−	1.23037i
$597$	−23.5285	+	17.0944i	−0.962956	+	0.699628i
$598$	30.6128	+	13.6297i	1.25185	+	0.557359i
$599$	10.5256	−	2.23729i	0.430065	−	0.0914131i	0.0122069	−	0.999925i	$-0.496114\pi$
$599$	10.5256	−	2.23729i	0.430065	−	0.0914131i	0.417858	+	0.908512i	$0.362781\pi$
$600$	−5.29747	+	50.4021i	−0.216269	+	2.05766i
$601$	14.1919	+	15.7617i	0.578901	+	0.642935i	0.959468	−	0.281819i	$-0.0909377\pi$
$601$	14.1919	+	15.7617i	0.578901	+	0.642935i	−0.380567	+	0.924754i	$0.624271\pi$
$602$	3.56720	−	3.96178i	0.145388	−	0.161470i
$603$	1.16828	+	11.1154i	0.0475759	+	0.452655i
$604$	28.3613	+	87.2870i	1.15400	+	3.55166i
$605$	3.87607	+	11.9293i	0.157585	+	0.484995i
$606$	7.00909	+	66.6871i	0.284725	+	2.70898i
$607$	−7.15138	+	7.94241i	−0.290265	+	0.322372i	−0.870587	−	0.492015i	$-0.836260\pi$
$607$	−7.15138	+	7.94241i	−0.290265	+	0.322372i	0.580321	+	0.814388i	$0.302927\pi$
$608$	11.3573	+	12.6136i	0.460601	+	0.511549i
$609$	−0.227957	+	2.16886i	−0.00923727	+	0.0878868i
$610$	−28.2082	+	5.99583i	−1.14211	+	0.242764i
$611$	22.8034	+	10.1527i	0.922528	+	0.410736i
$612$	−58.6306	+	42.5976i	−2.37000	+	1.72191i
$613$	−6.79587	+	3.02572i	−0.274483	+	0.122208i	−0.539362	−	0.842074i	$-0.681335\pi$
$613$	−6.79587	+	3.02572i	−0.274483	+	0.122208i	0.264879	+	0.964282i	$0.414668\pi$
$614$	−9.09608	+	15.7549i	−0.367088	+	0.635815i
$615$	−10.6560	−	18.4568i	−0.429693	−	0.744250i
$616$	0.348275	+	0.253036i	0.0140324	+	0.0101951i
$617$	−13.1691	−	2.79919i	−0.530170	−	0.112691i	−0.0649538	−	0.997888i	$-0.520690\pi$
$617$	−13.1691	−	2.79919i	−0.530170	−	0.112691i	−0.465216	+	0.885197i	$0.654023\pi$
$618$	7.65625	−	23.5635i	0.307980	−	0.947864i
$619$	6.91762			0.278043			0.139021	−	0.990289i	$-0.455604\pi$
$619$	6.91762			0.278043			0.139021	+	0.990289i	$0.455604\pi$
$620$		0			0
$621$	−0.851305			−0.0341617
$622$	−19.7493	+	60.7820i	−0.791873	+	2.43714i
$623$	0.830048	+	0.176432i	0.0332552	+	0.00706860i
$624$	49.2418	+	35.7762i	1.97125	+	1.43220i
$625$	−3.46743	−	6.00577i	−0.138697	−	0.240231i
$626$	31.7983	−	55.0762i	1.27091	−	2.20129i
$627$	4.57956	−	2.03895i	0.182890	−	0.0814279i
$628$	49.7459	−	36.1425i	1.98508	−	1.44224i
$629$	−20.4768	−	9.11684i	−0.816462	−	0.363512i
$630$	2.31729	−	0.492554i	0.0923229	−	0.0196238i
$631$	1.42122	−	13.5220i	0.0565779	−	0.538303i	−0.929120	−	0.369779i	$-0.879433\pi$
$631$	1.42122	−	13.5220i	0.0565779	−	0.538303i	0.985698	−	0.168524i	$-0.0539000\pi$
$632$	−14.1402	−	15.7043i	−0.562469	−	0.624685i
$633$	12.3531	−	13.7195i	0.490990	−	0.545300i
$634$	3.71485	+	35.3445i	0.147536	+	1.40371i
$635$	−2.00753	−	6.17854i	−0.0796664	−	0.245188i
$636$	15.3675	+	47.2963i	0.609361	+	1.87542i
$637$	3.27675	+	31.1762i	0.129829	+	1.23524i
$638$	1.62073	−	1.80000i	0.0641654	−	0.0712628i
$639$	22.6829	+	25.1920i	0.897323	+	0.996578i
$640$	−2.02164	+	19.2346i	−0.0799123	+	0.760314i
$641$	−3.74942	+	0.796963i	−0.148093	+	0.0314782i	−0.281362	−	0.959602i	$-0.590786\pi$
$641$	−3.74942	+	0.796963i	−0.148093	+	0.0314782i	0.133269	+	0.991080i	$0.457453\pi$
$642$	101.815	+	45.3311i	4.01833	+	1.78908i
$643$	−6.25343	+	4.54339i	−0.246611	+	0.179174i	−0.704224	−	0.709978i	$-0.748705\pi$
$643$	−6.25343	+	4.54339i	−0.246611	+	0.179174i	0.457612	+	0.889152i	$0.348705\pi$
$644$	3.04015	−	1.35356i	0.119799	−	0.0533378i
$645$	−11.4503	+	19.8325i	−0.450855	+	0.780904i
$646$	−47.6855	−	82.5938i	−1.87616	−	3.24961i
$647$	15.0438	+	10.9299i	0.591431	+	0.429700i	0.842827	−	0.538184i	$-0.180890\pi$
$647$	15.0438	+	10.9299i	0.591431	+	0.429700i	−0.251396	+	0.967884i	$0.580890\pi$
$648$	47.0619	+	10.0033i	1.84877	+	0.392968i
$649$	0.212016	−	0.652519i	0.00832237	−	0.0256136i
$650$	−41.5482			−1.62965
$651$		0			0
$652$	0.290402			0.0113730
$653$	−12.1295	+	37.3309i	−0.474665	+	1.46087i	0.371743	+	0.928336i	$0.378760\pi$
$653$	−12.1295	+	37.3309i	−0.474665	+	1.46087i	−0.846408	+	0.532534i	$0.821240\pi$
$654$	1.57841	+	0.335501i	0.0617206	+	0.0131191i
$655$	5.91878	+	4.30025i	0.231266	+	0.168025i
$656$	−20.3998	−	35.3336i	−0.796480	−	1.37954i
$657$	3.54344	−	6.13742i	0.138243	−	0.239444i
$658$	3.33504	−	1.48485i	0.130013	−	0.0578856i
$659$	−11.0680	+	8.04140i	−0.431150	+	0.313249i	−0.782108	−	0.623142i	$-0.785856\pi$
$659$	−11.0680	+	8.04140i	−0.431150	+	0.313249i	0.350959	+	0.936391i	$0.385856\pi$
$660$	−3.20368	−	1.42637i	−0.124703	−	0.0555214i
$661$	38.8409	−	8.25588i	1.51074	−	0.321117i	0.623276	−	0.782002i	$-0.285801\pi$
$661$	38.8409	−	8.25588i	1.51074	−	0.321117i	0.887460	+	0.460886i	$0.152468\pi$
$662$	−4.56403	+	43.4238i	−0.177386	+	1.68772i
$663$	−41.1472	−	45.6986i	−1.59803	−	1.77479i
$664$	10.4103	−	11.5618i	0.403998	−	0.448685i
$665$	0.221285	+	2.10538i	0.00858105	+	0.0816433i
$666$	−9.80147	−	30.1658i	−0.379799	−	1.16890i
$667$	−3.05111	−	9.39035i	−0.118139	−	0.363596i
$668$	−2.14799	−	20.4368i	−0.0831082	−	0.790722i
$669$	48.2318	−	53.5668i	1.86475	−	2.07101i
$670$	6.88490	+	7.64646i	0.265987	+	0.295409i
$671$	−0.306455	+	2.91572i	−0.0118306	+	0.112560i
$672$	1.56561	−	0.332780i	0.0603947	−	0.0128373i
$673$	−23.4864	−	10.4568i	−0.905334	−	0.403081i	−0.0993739	−	0.995050i	$-0.531684\pi$
$673$	−23.4864	−	10.4568i	−0.905334	−	0.403081i	−0.805960	+	0.591969i	$0.798351\pi$
$674$	−33.1667	+	24.0970i	−1.27753	+	0.928183i
$675$	0.964263	−	0.429317i	0.0371145	−	0.0165244i
$676$	−15.7899	+	27.3488i	−0.607302	+	1.05188i
$677$	3.47357	+	6.01639i	0.133500	+	0.231229i	0.925023	−	0.379910i	$-0.124045\pi$
$677$	3.47357	+	6.01639i	0.133500	+	0.231229i	−0.791523	+	0.611139i	$0.790712\pi$
$678$	−13.9864	−	10.1617i	−0.537145	−	0.390259i
$679$	−0.522859	−	0.111137i	−0.0200655	−	0.00426505i
$680$	−10.8718	+	33.4598i	−0.416913	+	1.28313i
$681$	−14.7091			−0.563654
$682$		0			0
$683$	28.4558			1.08883			0.544415	−	0.838816i	$-0.316752\pi$
$683$	28.4558			1.08883			0.544415	+	0.838816i	$0.316752\pi$
$684$	28.3184	−	87.1550i	1.08278	−	3.33246i
$685$	3.33048	+	0.707915i	0.127251	+	0.0270480i
$686$	7.45576	+	5.41692i	0.284662	+	0.206819i
$687$	−6.91362	−	11.9747i	−0.263771	−	0.456865i
$688$	−21.9204	+	37.9672i	−0.835706	+	1.44749i
$689$	−19.6401	+	8.74434i	−0.748229	+	0.333133i
$690$	−17.0318	+	12.3743i	−0.648389	+	0.471082i
$691$	26.7288	+	11.9004i	1.01681	+	0.452713i	0.846336	−	0.532649i	$-0.178804\pi$
$691$	26.7288	+	11.9004i	1.01681	+	0.452713i	0.170474	+	0.985362i	$0.445470\pi$
$692$	46.7500	−	9.93701i	1.77717	−	0.377748i
$693$	0.0251751	−	0.239525i	0.000956323	−	0.00909881i
$694$	−43.5744	−	48.3943i	−1.65406	−	1.83702i
$695$	9.84744	−	10.9367i	0.373535	−	0.414852i
$696$	−4.79041	−	45.5777i	−0.181580	−	1.72762i
$697$	12.7378	+	39.2028i	0.482477	+	1.48491i
$698$	8.25055	+	25.3926i	0.312288	+	0.961123i
$699$	−6.81916	−	64.8799i	−0.257924	−	2.45398i
$700$	−2.76093	+	3.06632i	−0.104353	+	0.115896i
$701$	−5.67468	−	6.30237i	−0.214330	−	0.238037i	0.626387	−	0.779512i	$-0.284533\pi$
$701$	−5.67468	−	6.30237i	−0.214330	−	0.238037i	−0.840717	+	0.541475i	$0.817866\pi$
$702$	0.338610	−	3.22166i	0.0127800	−	0.121594i
$703$	27.7239	−	5.89290i	1.04563	−	0.222255i
$704$	1.27497	+	0.567654i	0.0480523	+	0.0213943i
$705$	−12.6870	+	9.21763i	−0.477819	+	0.347156i
$706$	31.1082	−	13.8502i	1.17077	−	0.521261i
$707$	−1.43940	+	2.49312i	−0.0541343	+	0.0937634i
$708$	−12.3089	−	21.3197i	−0.462597	−	0.801242i
$709$	−38.4289	−	27.9203i	−1.44323	−	1.04857i	−0.987355	−	0.158523i	$-0.949327\pi$
$709$	−38.4289	−	27.9203i	−1.44323	−	1.04857i	−0.455874	−	0.890044i	$-0.650673\pi$
$710$	30.5259	+	6.48848i	1.14562	+	0.243508i
$711$	−3.65343	+	11.2441i	−0.137014	+	0.421687i
$712$	−17.8328			−0.668311
$713$		0			0
$714$	−8.99353			−0.336574
$715$	0.468484	−	1.44184i	0.0175203	−	0.0539219i
$716$	59.7231	+	12.6945i	2.23196	+	0.474417i
$717$	41.6620	+	30.2692i	1.55590	+	1.13043i
$718$	−2.60842	−	4.51791i	−0.0973453	−	0.168607i
$719$	−8.81254	+	15.2638i	−0.328652	+	0.569243i	−0.982245	−	0.187604i	$-0.939928\pi$
$719$	−8.81254	+	15.2638i	−0.328652	+	0.569243i	0.653592	+	0.756847i	$0.273261\pi$
$720$	−17.7978	+	7.92410i	−0.663285	+	0.295314i
$721$	0.860551	−	0.625227i	0.0320486	−	0.0232847i
$722$	66.8426	+	29.7603i	2.48762	+	1.10756i
$723$	34.4966	−	7.33247i	1.28294	−	0.272697i
$724$	9.73037	−	92.5783i	0.361626	−	3.44064i
$725$	8.19155	+	9.09764i	0.304227	+	0.337878i
$726$	45.0871	−	50.0743i	1.67334	−	1.85843i
$727$	0.416291	+	3.96075i	0.0154394	+	0.146896i	0.999526	−	0.0307950i	$-0.00980390\pi$
$727$	0.416291	+	3.96075i	0.0154394	+	0.146896i	−0.984086	+	0.177691i	$0.943137\pi$
$728$	2.06349	+	6.35076i	0.0764780	+	0.235375i
$729$	−8.97573	−	27.6244i	−0.332434	−	1.02313i
$730$	−0.681971	−	6.48852i	−0.0252409	−	0.240151i
$731$	29.6376	−	32.9158i	1.09618	−	1.21744i
$732$	70.3891	+	78.1750i	2.60166	+	2.88943i
$733$	2.87325	−	27.3372i	0.106126	−	1.00972i	−0.803785	−	0.594919i	$-0.797184\pi$
$733$	2.87325	−	27.3372i	0.106126	−	1.00972i	0.909911	−	0.414803i	$-0.136149\pi$
$734$	−48.6387	+	10.3385i	−1.79529	+	0.381600i
$735$	−17.9916	−	8.01036i	−0.663629	−	0.295467i
$736$	−5.86265	+	4.25947i	−0.216100	+	0.157006i
$737$	0.955606	−	0.425463i	0.0352002	−	0.0156721i
$738$	−29.1647	+	50.5148i	−1.07357	+	1.85948i
$739$	10.2855	+	17.8150i	0.378358	+	0.655335i	0.990823	−	0.135162i	$-0.0431555\pi$
$739$	10.2855	+	17.8150i	0.378358	+	0.655335i	−0.612466	+	0.790497i	$0.709822\pi$
$740$	−16.0411	−	11.6545i	−0.589682	−	0.428429i
$741$	76.0595	+	16.1669i	2.79412	+	0.593908i
$742$	−0.971620	+	2.99034i	−0.0356693	+	0.109779i
$743$	−9.45031			−0.346698			−0.173349	−	0.984860i	$-0.555459\pi$
$743$	−9.45031			−0.346698			−0.173349	+	0.984860i	$0.555459\pi$
$744$		0			0
$745$	−20.0571			−0.734836
$746$	8.27212	−	25.4590i	0.302864	−	0.932119i
$747$	−8.51392	−	1.80969i	−0.311508	−	0.0662131i
$748$	5.48734	+	3.98679i	0.200637	+	0.145771i
$749$	2.39242	+	4.14380i	0.0874173	+	0.151411i
$750$	30.7869	−	53.3245i	1.12418	−	1.94713i
$751$	10.6180	−	4.72746i	0.387458	−	0.172507i	−0.203757	−	0.979021i	$-0.565315\pi$
$751$	10.6180	−	4.72746i	0.387458	−	0.172507i	0.591215	+	0.806514i	$0.298649\pi$
$752$	−24.2879	+	17.6462i	−0.885687	+	0.643490i
$753$	−19.8828	−	8.85239i	−0.724569	−	0.322599i
$754$	36.7502	−	7.81150i	1.33836	−	0.284478i
$755$	2.60556	−	24.7902i	0.0948260	−	0.902209i
$756$	−0.215263	−	0.239073i	−0.00782902	−	0.00869501i
$757$	−16.3198	+	18.1249i	−0.593152	+	0.658762i	−0.962738	−	0.270434i	$-0.912833\pi$
$757$	−16.3198	+	18.1249i	−0.593152	+	0.658762i	0.369586	+	0.929196i	$0.379499\pi$
$758$	−3.69308	−	35.1373i	−0.134139	−	1.27624i
$759$	0.661374	+	2.03550i	0.0240063	+	0.0738839i
$760$	−13.7474	−	42.3100i	−0.498669	−	1.53475i
$761$	−2.38825	−	22.7227i	−0.0865741	−	0.823698i	−0.948524	−	0.316705i	$-0.897424\pi$
$761$	−2.38825	−	22.7227i	−0.0865741	−	0.823698i	0.861950	−	0.506993i	$-0.169243\pi$
$762$	−23.3519	+	25.9350i	−0.845951	+	0.939524i
$763$	0.0463565	+	0.0514841i	0.00167822	+	0.00186385i
$764$	−9.62684	+	91.5932i	−0.348287	+	3.31373i
$765$	19.2528	−	4.09232i	0.696088	−	0.147958i
$766$	40.7197	+	18.1296i	1.47126	+	0.655049i
$767$	8.60994	−	6.25549i	0.310887	−	0.225873i
$768$	73.2906	−	32.6311i	2.64465	−	1.17747i
$769$	11.4715	−	19.8693i	0.413674	−	0.716505i	−0.581614	−	0.813465i	$-0.697579\pi$
$769$	11.4715	−	19.8693i	0.413674	−	0.716505i	0.995288	+	0.0969600i	$0.0309119\pi$
$770$	−0.110862	−	0.192019i	−0.00399519	−	0.00691987i
$771$	8.02230	+	5.82854i	0.288916	+	0.209910i
$772$	−9.15170	−	1.94525i	−0.329377	−	0.0700112i
$773$	−11.4012	+	35.0892i	−0.410071	+	1.26207i	0.506515	+	0.862231i	$0.330934\pi$
$773$	−11.4012	+	35.0892i	−0.410071	+	1.26207i	−0.916586	+	0.399838i	$0.869066\pi$
$774$	62.6771			2.25288
$775$		0			0
$776$	11.2331			0.403246
$777$	0.825935	−	2.54197i	0.0296303	−	0.0911926i
$778$	57.3335	+	12.1866i	2.05550	+	0.436911i
$779$	−42.1684	−	30.6372i	−1.51084	−	1.09769i
$780$	−27.1985	−	47.1092i	−0.973862	−	1.68678i
$781$	1.58634	−	2.74762i	0.0567636	−	0.0983175i
$782$	37.1978	−	16.5615i	1.33019	−	0.592240i
$783$	−0.772194	+	0.561032i	−0.0275960	+	0.0200496i
$784$	−34.4429	−	15.3350i	−1.23010	−	0.547678i
$785$	−16.3353	+	3.47218i	−0.583032	+	0.123927i
$786$	4.10811	−	39.0860i	0.146531	−	1.39415i
$787$	−35.5581	−	39.4913i	−1.26751	−	1.40771i	−0.872189	−	0.489168i	$-0.837300\pi$
$787$	−35.5581	−	39.4913i	−1.26751	−	1.40771i	−0.395320	−	0.918543i	$-0.629366\pi$
$788$	−49.2440	+	54.6910i	−1.75424	+	1.94828i
$789$	0.158231	+	1.50547i	0.00563317	+	0.0535960i
$790$	3.36339	+	10.3514i	0.119664	+	0.368288i
$791$	−0.229359	−	0.705895i	−0.00815507	−	0.0250987i
$792$	0.529044	+	5.03351i	0.0187987	+	0.178858i
$793$	−30.4298	+	33.7957i	−1.08059	+	1.20012i
$794$	−16.8806	−	18.7478i	−0.599069	−	0.665334i
$795$	1.41182	−	13.4326i	0.0500721	−	0.476404i
$796$	48.6710	−	10.3453i	1.72510	−	0.366681i
$797$	15.4186	+	6.86479i	0.546153	+	0.243163i	0.661217	−	0.750195i	$-0.270040\pi$
$797$	15.4186	+	6.86479i	0.546153	+	0.243163i	−0.115063	+	0.993358i	$0.536707\pi$
$798$	9.20041	−	6.68449i	0.325691	−	0.236628i
$799$	27.7087	−	12.3367i	0.980262	−	0.436441i
$800$	4.49248	−	7.78121i	0.158833	−	0.275107i
$801$	4.98840	+	8.64017i	0.176257	+	0.305285i
$802$	46.1923	+	33.5607i	1.63111	+	1.18507i
$803$	−0.648780	−	0.137902i	−0.0228949	−	0.00486647i
$804$	11.5983	−	35.6958i	0.409040	−	1.25890i
$805$	−0.903832			−0.0318559
$806$		0			0
$807$	2.78540			0.0980508
$808$	18.6945	−	57.5359i	0.657672	−	2.02410i
$809$	−3.46017	−	0.735481i	−0.121653	−	0.0258581i	0.146683	−	0.989184i	$-0.453140\pi$
$809$	−3.46017	−	0.735481i	−0.121653	−	0.0258581i	−0.268336	+	0.963325i	$0.586474\pi$
$810$	−20.0480	−	14.5657i	−0.704415	−	0.511788i
$811$	5.92283	+	10.2586i	0.207979	+	0.360230i	0.951078	−	0.308952i	$-0.0999782\pi$
$811$	5.92283	+	10.2586i	0.207979	+	0.360230i	−0.743099	+	0.669181i	$0.766645\pi$
$812$	1.86560	−	3.23131i	0.0654696	−	0.113397i
$813$	0.469761	−	0.209151i	0.0164753	−	0.00733525i
$814$	−2.40162	+	1.74488i	−0.0841766	+	0.0611579i
$815$	−0.0720532	−	0.0320802i	−0.00252391	−	0.00112372i
$816$	72.3429	−	15.3770i	2.53251	−	0.538301i
$817$	−5.85444	+	55.7013i	−0.204821	+	1.94874i
$818$	22.0385	+	24.4762i	0.770558	+	0.855791i
$819$	2.49979	−	2.77630i	0.0873497	−	0.0970116i
$820$	3.81145	+	36.2635i	0.133102	+	1.26638i
$821$	13.3556	+	41.1044i	0.466115	+	1.43455i	0.857575	+	0.514359i	$0.171970\pi$
$821$	13.3556	+	41.1044i	0.466115	+	1.43455i	−0.391460	+	0.920195i	$0.628030\pi$
$822$	−5.65219	−	17.3957i	−0.197143	−	0.606743i
$823$	−2.82986	−	26.9243i	−0.0986426	−	0.938522i	−0.926173	−	0.377100i	$-0.876921\pi$
$823$	−2.82986	−	26.9243i	−0.0986426	−	0.938522i	0.827530	−	0.561422i	$-0.189745\pi$
$824$	−14.9572	+	16.6116i	−0.521058	+	0.578694i
$825$	−1.77564	−	1.97205i	−0.0618199	−	0.0686580i
$826$	0.162696	−	1.54795i	0.00566092	−	0.0538601i
$827$	−4.29552	+	0.913041i	−0.149370	+	0.0317495i	−0.281990	−	0.959417i	$-0.590994\pi$
$827$	−4.29552	+	0.913041i	−0.149370	+	0.0317495i	0.132620	+	0.991167i	$0.457661\pi$
$828$	35.7427	+	15.9137i	1.24214	+	0.553038i
$829$	−13.0749	+	9.49945i	−0.454109	+	0.329929i	−0.791216	−	0.611537i	$-0.790552\pi$
$829$	−13.0749	+	9.49945i	−0.454109	+	0.329929i	0.337107	+	0.941466i	$0.390552\pi$
$830$	−7.32034	+	3.25922i	−0.254093	+	0.113129i
$831$	30.7587	−	53.2756i	1.06701	−	1.84811i
$832$	10.8242	+	18.7481i	0.375261	+	0.649972i
$833$	30.8164	+	22.3894i	1.06772	+	0.775747i
$834$	−77.3302	−	16.4370i	−2.67773	−	0.569168i
$835$	−1.72466	+	5.30796i	−0.0596843	+	0.183689i
$836$	−8.57677			−0.296634
$837$		0			0
$838$	−11.1317			−0.384537
$839$	14.8175	−	45.6037i	0.511558	−	1.57441i	−0.277899	−	0.960610i	$-0.589638\pi$
$839$	14.8175	−	45.6037i	0.511558	−	1.57441i	0.789458	−	0.613805i	$-0.210362\pi$
$840$	−4.10350	−	0.872226i	−0.141584	−	0.0300947i
$841$	14.5054	+	10.5388i	0.500188	+	0.363408i
$842$	24.1178	+	41.7733i	0.831155	+	1.43960i
$843$	31.8568	−	55.1776i	1.09721	−	1.90042i
$844$	−28.8552	+	12.8472i	−0.993237	+	0.442218i
$845$	6.93888	−	5.04139i	0.238705	−	0.173429i
$846$	39.2097	+	17.4573i	1.34806	+	0.600193i
$847$	2.82964	−	0.601458i	0.0972275	−	0.0206663i
$848$	2.70278	−	25.7152i	0.0928137	−	0.883064i
$849$	44.3176	+	49.2197i	1.52098	+	1.68922i
$850$	−33.7815	+	37.5181i	−1.15869	+	1.28686i
$851$	1.26490	+	12.0347i	0.0433602	+	0.412545i
$852$	−35.1780	−	108.267i	−1.20518	−	3.70916i
$853$	10.0254	+	30.8551i	0.343265	+	1.05646i	0.962506	+	0.271259i	$0.0874401\pi$
$853$	10.0254	+	30.8551i	0.343265	+	1.05646i	−0.619242	+	0.785200i	$0.712560\pi$
$854$	0.695220	+	6.61458i	0.0237899	+	0.226346i
$855$	−16.6541	+	18.4962i	−0.569557	+	0.632558i
$856$	−67.2820	−	74.7243i	−2.29965	−	2.55402i
$857$	−0.567276	+	5.39727i	−0.0193778	+	0.184367i	−0.999929	−	0.0118949i	$-0.996214\pi$
$857$	−0.567276	+	5.39727i	−0.0193778	+	0.184367i	0.980551	+	0.196262i	$0.0628803\pi$
$858$	−7.96616	+	1.69326i	−0.271960	+	0.0578069i
$859$	−36.9636	−	16.4573i	−1.26118	−	0.561515i	−0.336296	−	0.941756i	$-0.609174\pi$
$859$	−36.9636	−	16.4573i	−1.26118	−	0.561515i	−0.924887	+	0.380242i	$0.875841\pi$
$860$	31.6982	−	23.0301i	1.08090	−	0.785319i
$861$	−4.49028	+	1.99920i	−0.153028	+	0.0681326i
$862$	13.0370	−	22.5807i	0.444041	−	0.769102i
$863$	−1.18137	−	2.04620i	−0.0402144	−	0.0696533i	0.845218	−	0.534422i	$-0.179471\pi$
$863$	−1.18137	−	2.04620i	−0.0402144	−	0.0696533i	−0.885432	+	0.464769i	$0.846137\pi$
$864$	0.566745	+	0.411764i	0.0192810	+	0.0140085i
$865$	−12.6971	−	2.69885i	−0.431715	−	0.0917638i
$866$	15.9907	−	49.2143i	0.543386	−	1.67237i
$867$	−32.6795			−1.10985
$868$		0			0
$869$	1.10651			0.0375358
$870$	−7.29405	+	22.4488i	−0.247291	+	0.761085i
$871$	15.8712	+	3.37352i	0.537774	+	0.114307i
$872$	−1.17782	−	0.855733i	−0.0398859	−	0.0289788i
$873$	−3.14227	−	5.44257i	−0.106350	−	0.184203i
$874$	−25.7441	+	44.5900i	−0.870806	+	1.50828i
$875$	2.41497	−	1.07521i	0.0816408	−	0.0363488i
$876$	−19.2537	+	13.9886i	−0.650521	+	0.472631i
$877$	−30.5197	−	13.5882i	−1.03058	−	0.458843i	−0.179431	−	0.983771i	$-0.557426\pi$
$877$	−30.5197	−	13.5882i	−1.03058	−	0.458843i	−0.851147	+	0.524928i	$0.824092\pi$
$878$	−69.2355	+	14.7165i	−2.33659	+	0.496656i
$879$	5.78088	−	55.0014i	0.194984	−	1.85515i
$880$	1.22007	+	1.35503i	0.0411286	+	0.0456779i
$881$	31.3706	−	34.8405i	1.05690	−	1.17381i	0.0725910	−	0.997362i	$-0.476873\pi$
$881$	31.3706	−	34.8405i	1.05690	−	1.17381i	0.984310	−	0.176446i	$-0.0564601\pi$
$882$	5.63425	+	53.6063i	0.189715	+	1.80502i
$883$	9.55440	+	29.4054i	0.321531	+	0.989571i	0.972982	+	0.230881i	$0.0741606\pi$
$883$	9.55440	+	29.4054i	0.321531	+	0.989571i	−0.651451	+	0.758691i	$0.725839\pi$
$884$	32.5119	+	100.061i	1.09349	+	3.36543i
$885$	0.698888	+	6.64948i	0.0234929	+	0.223520i
$886$	−48.8007	+	54.1987i	−1.63949	+	1.82084i
$887$	23.3385	+	25.9201i	0.783632	+	0.870311i	0.994231	−	0.107261i	$-0.0342082\pi$
$887$	23.3385	+	25.9201i	0.783632	+	0.870311i	−0.210599	+	0.977572i	$0.567542\pi$
$888$	−5.87109	+	55.8596i	−0.197021	+	1.87453i
$889$	−1.46555	+	0.311513i	−0.0491531	+	0.0104478i
$890$	8.39068	+	3.73577i	0.281256	+	0.125223i
$891$	−2.03814	+	1.48079i	−0.0682801	+	0.0496084i
$892$	−112.663	+	50.1610i	−3.77225	+	1.67951i
$893$	−19.1767	+	33.2151i	−0.641725	+	1.11150i
$894$	53.8730	+	93.3107i	1.80178	+	3.12078i
$895$	−13.4159	−	9.74721i	−0.448443	−	0.325813i
$896$	4.36306	+	0.927396i	0.145759	+	0.0309821i
$897$	−10.2589	+	31.5738i	−0.342536	+	1.05422i
$898$	−2.91220			−0.0971813
$899$		0			0
$900$	−48.5106			−1.61702
$901$	−8.07257	+	24.8448i	−0.268936	+	0.827701i
$902$	5.33986	+	1.13502i	0.177798	+	0.0377921i
$903$	4.27289	+	3.10444i	0.142193	+	0.103309i
$904$	7.79873	+	13.5078i	0.259382	+	0.449263i
$905$	−12.6412	+	21.8952i	−0.420208	+	0.727821i
$906$	−122.329	+	54.4643i	−4.06411	+	1.80946i
$907$	35.4950	−	25.7886i	1.17859	−	0.856297i	0.186580	−	0.982440i	$-0.440260\pi$
$907$	35.4950	−	25.7886i	1.17859	−	0.856297i	0.992012	+	0.126143i	$0.0402598\pi$
$908$	22.9904	+	10.2360i	0.762962	+	0.339693i
$909$	−33.1062	+	7.03694i	−1.09806	+	0.233401i
$910$	0.359503	−	3.42044i	0.0119174	−	0.113387i
$911$	29.2477	+	32.4828i	0.969019	+	1.07620i	0.997062	+	0.0765975i	$0.0244057\pi$
$911$	29.2477	+	32.4828i	0.969019	+	1.07620i	−0.0280434	+	0.999607i	$0.508928\pi$
$912$	−62.5780	+	69.4999i	−2.07216	+	2.30137i
$913$	0.0851525	+	0.810172i	0.00281814	+	0.0268128i
$914$	−31.0727	−	95.6321i	−1.02779	−	3.16323i
$915$	−8.82878	−	27.1722i	−0.291870	−	0.898285i
$916$	2.47286	+	23.5277i	0.0817057	+	0.777378i
$917$	1.12902	−	1.25391i	0.0372836	−	0.0414077i
$918$	−2.63385	−	2.92519i	−0.0869302	−	0.0965457i
$919$	3.76033	−	35.7771i	0.124042	−	1.18018i	−0.738522	−	0.674230i	$-0.764476\pi$
$919$	3.76033	−	35.7771i	0.124042	−	1.18018i	0.862563	−	0.505949i	$-0.168858\pi$
$920$	18.5786	−	3.94900i	0.612517	−	0.130195i
$921$	−16.4650	−	7.33070i	−0.542541	−	0.241555i
$922$	−59.2508	+	43.0482i	−1.95132	+	1.41772i
$923$	44.9585	−	20.0168i	1.47983	−	0.658861i
$924$	−0.404396	+	0.700434i	−0.0133037	+	0.0230426i
$925$	−7.50190	−	12.9937i	−0.246661	−	0.427229i
$926$	−1.29149	−	0.938319i	−0.0424408	−	0.0308351i
$927$	12.2325	+	2.60010i	0.401769	+	0.0853986i
$928$	−2.51074	+	7.72727i	−0.0824192	+	0.253660i
$929$	−7.67225			−0.251719			−0.125859	−	0.992048i	$-0.540169\pi$
$929$	−7.67225			−0.251719			−0.125859	+	0.992048i	$0.540169\pi$
$930$		0			0
$931$	−48.1663			−1.57859
$932$	−34.4912	+	106.153i	−1.12980	+	3.47716i
$933$	−61.9328	−	13.1642i	−2.02759	−	0.430977i
$934$	−5.84731	−	4.24832i	−0.191330	−	0.139009i
$935$	−0.921081	−	1.59536i	−0.0301226	−	0.0521738i
$936$	−39.2539	+	67.9897i	−1.28305	+	2.22231i
$937$	39.3762	−	17.5314i	1.28636	−	0.572726i	0.354337	−	0.935118i	$-0.384707\pi$
$937$	39.3762	−	17.5314i	1.28636	−	0.572726i	0.932026	+	0.362392i	$0.118040\pi$
$938$	1.91983	−	1.39484i	0.0626846	−	0.0455430i
$939$	57.5588	+	25.6268i	1.87836	+	0.836300i
$940$	26.2443	−	5.57840i	0.855995	−	0.181947i
$941$	−3.86481	+	36.7712i	−0.125989	+	1.19871i	0.730636	+	0.682767i	$0.239224\pi$
$941$	−3.86481	+	36.7712i	−0.125989	+	1.19871i	−0.856625	+	0.515939i	$0.827443\pi$
$942$	60.0297	+	66.6698i	1.95587	+	2.17222i
$943$	14.8906	−	16.5377i	0.484904	−	0.538541i
$944$	1.33795	+	12.7297i	0.0435464	+	0.414317i
$945$	0.0270000	+	0.0830974i	0.000878310	+	0.00270316i
$946$	−1.81271	−	5.57895i	−0.0589364	−	0.181387i
$947$	−6.11516	−	58.1818i	−0.198716	−	1.89066i	−0.408274	−	0.912859i	$-0.633869\pi$
$947$	−6.11516	−	58.1818i	−0.198716	−	1.89066i	0.209559	−	0.977796i	$-0.432797\pi$
$948$	26.5662	−	29.5048i	0.862830	−	0.958270i
$949$	−6.88429	−	7.64578i	−0.223474	−	0.248193i
$950$	6.67300	−	63.4894i	0.216501	−	2.05987i
$951$	−34.4397	+	7.32038i	−1.11678	+	0.237380i
$952$	7.41251	+	3.30026i	0.240241	+	0.106962i
$953$	43.0699	−	31.2921i	1.39517	−	1.01365i	0.399897	−	0.916560i	$-0.369046\pi$
$953$	43.0699	−	31.2921i	1.39517	−	1.01365i	0.995275	−	0.0970918i	$-0.0309540\pi$
$954$	−33.7705	+	15.0356i	−1.09336	+	0.486795i
$955$	12.5067	−	21.6622i	0.404707	−	0.700973i
$956$	−44.0537	−	76.3033i	−1.42480	−	2.46783i
$957$	1.94136	+	1.41048i	0.0627552	+	0.0455943i
$958$	−70.6722	−	15.0218i	−2.28332	−	0.485334i
$959$	0.242662	−	0.746837i	0.00783597	−	0.0241166i
$960$	−13.6005			−0.438956
$961$		0			0
$962$	−46.0470			−1.48462
$963$	−17.3837	+	53.5016i	−0.560183	+	1.72407i
$964$	−59.0209	−	12.5453i	−1.90093	−	0.404056i
$965$	2.05579	+	1.49362i	0.0661782	+	0.0480813i
$966$	2.42767	+	4.20485i	0.0781091	+	0.135289i
$967$	−6.05038	+	10.4796i	−0.194567	+	0.337000i	−0.946759	−	0.321945i	$-0.895664\pi$
$967$	−6.05038	+	10.4796i	−0.194567	+	0.337000i	0.752191	+	0.658945i	$0.228997\pi$
$968$	−55.5363	+	24.7263i	−1.78500	+	0.794735i
$969$	76.4403	−	55.5371i	2.45562	−	1.78411i
$970$	−5.28541	−	2.35322i	−0.169704	−	0.0755573i
$971$	−10.4354	+	2.21811i	−0.334887	+	0.0711825i	−0.372286	−	0.928118i	$-0.621426\pi$
$971$	−10.4354	+	2.21811i	−0.334887	+	0.0711825i	0.0373991	+	0.999300i	$0.488093\pi$
$972$	−9.82935	+	93.5200i	−0.315276	+	2.99966i
$973$	−2.27112	−	2.52234i	−0.0728089	−	0.0808624i
$974$	4.56533	−	5.07031i	0.146282	−	0.162463i
$975$	−4.30263	−	40.9368i	−0.137795	−	1.31103i
$976$	−16.9017	−	52.0182i	−0.541012	−	1.66506i
$977$	−14.5231	−	44.6974i	−0.464634	−	1.43000i	−0.859443	−	0.511232i	$-0.829189\pi$
$977$	−14.5231	−	44.6974i	−0.464634	−	1.43000i	0.394809	−	0.918763i	$-0.370811\pi$
$978$	0.0442884	+	0.421376i	0.00141619	+	0.0134741i
$979$	0.624798	−	0.693909i	0.0199686	−	0.0221774i
$980$	22.5465	+	25.0405i	0.720223	+	0.799888i
$981$	−0.0851386	+	0.810040i	−0.00271827	+	0.0258626i
$982$	27.9079	−	5.93200i	0.890576	−	0.189298i
$983$	−10.5185	−	4.68314i	−0.335488	−	0.149369i	0.232077	−	0.972697i	$-0.425448\pi$
$983$	−10.5185	−	4.68314i	−0.335488	−	0.149369i	−0.567565	+	0.823328i	$0.692115\pi$
$984$	83.5643	−	60.7130i	2.66393	−	1.93546i
$985$	18.2598	−	8.12978i	0.581805	−	0.259036i
$986$	22.8266	−	39.5368i	0.726947	−	1.25911i
$987$	1.80837	+	3.13220i	0.0575612	+	0.0996989i
$988$	−107.631	−	78.1984i	−3.42419	−	2.48782i
$989$	−23.3898	−	4.97165i	−0.743752	−	0.158089i
$990$	0.805541	−	2.47920i	0.0256018	−	0.0787941i
$991$	56.6493			1.79952			0.899762	−	0.436381i	$-0.143740\pi$
$991$	56.6493			1.79952			0.899762	+	0.436381i	$0.143740\pi$
$992$		0			0
$993$	−43.2575			−1.37274
$994$	2.22415	−	6.84523i	0.0705457	−	0.217117i
$995$	−13.2189	−	2.80975i	−0.419066	−	0.0890752i
$996$	23.6474	+	17.1808i	0.749296	+	0.544395i
$997$	23.5058	+	40.7133i	0.744436	+	1.28940i	0.950458	+	0.310854i	$0.100615\pi$
$997$	23.5058	+	40.7133i	0.744436	+	1.28940i	−0.206021	+	0.978548i	$0.566052\pi$
$998$	−8.01523	+	13.8828i	−0.253718	+	0.439452i
$999$	1.06867	−	0.475804i	0.0338113	−	0.0150538i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.g.v.846.12		96
31.2	even	5		961.2.c.k.439.12		24
31.3	odd	30	inner	961.2.g.v.732.2		96
31.4	even	5	inner	961.2.g.v.547.11		96
31.5	even	3		961.2.d.r.628.11		48
31.6	odd	6	inner	961.2.g.v.448.12		96
31.7	even	15	inner	961.2.g.v.844.12		96
31.8	even	5	inner	961.2.g.v.235.1		96
31.9	even	15		961.2.d.r.388.2		48
31.10	even	15		961.2.a.k.1.11	✓	12
31.11	odd	30		961.2.d.r.531.12		48
31.12	odd	30		961.2.c.k.521.11		24
31.13	odd	30		961.2.d.r.374.1		48
31.14	even	15	inner	961.2.g.v.338.2		96
31.15	odd	10	inner	961.2.g.v.816.1		96
31.16	even	5	inner	961.2.g.v.816.2		96
31.17	odd	30	inner	961.2.g.v.338.1		96
31.18	even	15		961.2.d.r.374.2		48
31.19	even	15		961.2.c.k.521.12		24
31.20	even	15		961.2.d.r.531.11		48
31.21	odd	30		961.2.a.k.1.12	yes	12
31.22	odd	30		961.2.d.r.388.1		48
31.23	odd	10	inner	961.2.g.v.235.2		96
31.24	odd	30	inner	961.2.g.v.844.11		96
31.25	even	3	inner	961.2.g.v.448.11		96
31.26	odd	6		961.2.d.r.628.12		48
31.27	odd	10	inner	961.2.g.v.547.12		96
31.28	even	15	inner	961.2.g.v.732.1		96
31.29	odd	10		961.2.c.k.439.11		24
31.30	odd	2	inner	961.2.g.v.846.11		96
93.41	odd	30		8649.2.a.bp.1.2		12
93.83	even	30		8649.2.a.bp.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.k.1.11	✓	12	31.10	even	15
961.2.a.k.1.12	yes	12	31.21	odd	30
961.2.c.k.439.11		24	31.29	odd	10
961.2.c.k.439.12		24	31.2	even	5
961.2.c.k.521.11		24	31.12	odd	30
961.2.c.k.521.12		24	31.19	even	15
961.2.d.r.374.1		48	31.13	odd	30
961.2.d.r.374.2		48	31.18	even	15
961.2.d.r.388.1		48	31.22	odd	30
961.2.d.r.388.2		48	31.9	even	15
961.2.d.r.531.11		48	31.20	even	15
961.2.d.r.531.12		48	31.11	odd	30
961.2.d.r.628.11		48	31.5	even	3
961.2.d.r.628.12		48	31.26	odd	6
961.2.g.v.235.1		96	31.8	even	5	inner
961.2.g.v.235.2		96	31.23	odd	10	inner
961.2.g.v.338.1		96	31.17	odd	30	inner
961.2.g.v.338.2		96	31.14	even	15	inner
961.2.g.v.448.11		96	31.25	even	3	inner
961.2.g.v.448.12		96	31.6	odd	6	inner
961.2.g.v.547.11		96	31.4	even	5	inner
961.2.g.v.547.12		96	31.27	odd	10	inner
961.2.g.v.732.1		96	31.28	even	15	inner
961.2.g.v.732.2		96	31.3	odd	30	inner
961.2.g.v.816.1		96	31.15	odd	10	inner
961.2.g.v.816.2		96	31.16	even	5	inner
961.2.g.v.844.11		96	31.24	odd	30	inner
961.2.g.v.844.12		96	31.7	even	15	inner
961.2.g.v.846.11		96	31.30	odd	2	inner
961.2.g.v.846.12		96	1.1	even	1	trivial
8649.2.a.bp.1.1		12	93.83	even	30
8649.2.a.bp.1.2		12	93.41	odd	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+(0.771380 - 2.37406i) q^{2} +(2.41901 + 0.514177i) q^{3} +(-3.42311 - 2.48704i) q^{4} +(0.574589 + 0.995217i) q^{5} +(3.08667 - 5.34626i) q^{6} +(0.242122 - 0.107800i) q^{7} +(-4.50591 + 3.27373i) q^{8} +(2.84661 + 1.26739i) q^{9} +(2.80593 - 0.596420i) q^{10} +(0.0304838 - 0.290034i) q^{11} +(-7.00178 - 7.77626i) q^{12} +(3.02692 - 3.36174i) q^{13} +(-0.0691552 - 0.657968i) q^{14} +(0.878220 + 2.70288i) q^{15} +(1.68126 + 5.17438i) q^{16} +(-0.574567 - 5.46664i) q^{17} +(5.20468 - 5.78038i) q^{18} +(4.65089 + 5.16534i) q^{19} +(0.508259 - 4.83577i) q^{20} +(0.641125 - 0.136275i) q^{21} +(-0.665045 - 0.296097i) q^{22} +(-2.40079 + 1.74427i) q^{23} +(-12.5831 + 5.60237i) q^{24} +(1.83970 - 3.18645i) q^{25} +(-5.64607 - 9.77928i) q^{26} +(0.232085 + 0.168620i) q^{27} +(-1.09691 - 0.233156i) q^{28} +(-1.02816 + 3.16436i) q^{29} +7.09426 q^{30} +2.44197 q^{32} +(0.222870 - 0.685922i) q^{33} +(-13.4213 - 2.85279i) q^{34} +(0.246405 + 0.179024i) q^{35} +(-6.59221 - 11.4180i) q^{36} +(2.03890 - 3.53147i) q^{37} +(15.8504 - 7.05707i) q^{38} +(9.05069 - 6.57571i) q^{39} +(-5.84712 - 2.60331i) q^{40} +(-7.33515 + 1.55913i) q^{41} +(0.171025 - 1.62719i) q^{42} +(5.39184 + 5.98824i) q^{43} +(-0.825675 + 0.917006i) q^{44} +(0.374299 + 3.56122i) q^{45} +(2.28910 + 7.04512i) q^{46} +(1.70515 + 5.24791i) q^{47} +(1.40644 + 13.3814i) q^{48} +(-4.63691 + 5.14981i) q^{49} +(-6.14572 - 6.82551i) q^{50} +(1.42093 - 13.5193i) q^{51} +(-18.7223 + 3.97954i) q^{52} +(-4.34164 - 1.93302i) q^{53} +(0.579339 - 0.420915i) q^{54} +(0.306163 - 0.136312i) q^{55} +(-0.738073 + 1.27838i) q^{56} +(8.59466 + 14.8864i) q^{57} +(6.71928 + 4.88184i) q^{58} +(2.30121 + 0.489138i) q^{59} +(3.71593 - 11.4364i) q^{60} -10.0530 q^{61} +0.825852 q^{63} +(-1.47883 + 4.55136i) q^{64} +(5.08489 + 1.08083i) q^{65} +(-1.45651 - 1.05821i) q^{66} +(1.79343 + 3.10631i) q^{67} +(-11.6289 + 20.1419i) q^{68} +(-6.70440 + 2.98499i) q^{69} +(0.615085 - 0.446886i) q^{70} +(9.93851 + 4.42491i) q^{71} +(-16.9757 + 3.60829i) q^{72} +(0.237735 - 2.26189i) q^{73} +(-6.81118 - 7.56458i) q^{74} +(6.08864 - 6.76212i) q^{75} +(-3.07414 - 29.2485i) q^{76} +(-0.0238848 - 0.0735099i) q^{77} +(-8.62963 - 26.5593i) q^{78} +(0.396603 + 3.77342i) q^{79} +(-4.18360 + 4.64636i) q^{80} +(-5.78032 - 6.41969i) q^{81} +(-1.95670 + 18.6168i) q^{82} +(-2.73232 + 0.580773i) q^{83} +(-2.53357 - 1.12802i) q^{84} +(5.11035 - 3.71289i) q^{85} +(18.3756 - 8.18135i) q^{86} +(-4.11418 + 7.12597i) q^{87} +(0.812137 + 1.40666i) q^{88} +(2.59031 + 1.88197i) q^{89} +(8.74329 + 1.85844i) q^{90} +(0.370491 - 1.14025i) q^{91} +12.5562 q^{92} +13.7742 q^{94} +(-2.46828 + 7.59659i) q^{95} +(5.90716 + 1.25561i) q^{96} +(-1.63167 - 1.18548i) q^{97} +(8.64916 + 14.9808i) q^{98} +(0.454362 - 0.786978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 32 q^{4} - 32 q^{5} + 8 q^{7} - 24 q^{8} + 20 q^{9} + 20 q^{10} + 28 q^{14} + 32 q^{16} - 8 q^{18} + 16 q^{19} - 20 q^{20} - 48 q^{25} - 20 q^{28} + 192 q^{32} + 80 q^{33} - 112 q^{35} - 160 q^{36}+ \cdots - 16 q^{98}+O(q^{100}) \) 96 * q - 32 * q^4 - 32 * q^5 + 8 * q^7 - 24 * q^8 + 20 * q^9 + 20 * q^10 + 28 * q^14 + 32 * q^16 - 8 * q^18 + 16 * q^19 - 20 * q^20 - 48 * q^25 - 20 * q^28 + 192 * q^32 + 80 * q^33 - 112 * q^35 - 160 * q^36 + 36 * q^38 + 32 * q^39 - 16 * q^40 + 32 * q^41 + 16 * q^45 - 96 * q^47 - 20 * q^49 + 20 * q^50 + 16 * q^51 + 32 * q^56 + 40 * q^59 - 64 * q^63 + 56 * q^64 - 48 * q^66 - 64 * q^67 + 24 * q^69 - 24 * q^70 + 72 * q^71 + 36 * q^72 + 36 * q^76 + 208 * q^78 - 20 * q^80 - 36 * q^81 - 4 * q^82 - 256 * q^87 - 44 * q^90 + 128 * q^94 - 80 * q^95 + 16 * q^97 - 16 * q^98

Introduction

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