LMFDB - Embedded newform 325.2.x.b.7.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [325,2,Mod(7,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("325.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$325 = 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	325.x (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1$ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.3
Root			$0.493902i$ of defining polynomial
Character	$\chi$	$=$	325.7
Dual form			325.2.x.b.93.3

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.427732 + 0.246951i) q^{2} +(0.243392 + 0.908353i) q^{3} +(-0.878030 - 1.52079i) q^{4} +(-0.120212 + 0.448637i) q^{6} +(-1.83775 - 3.18307i) q^{7} -1.85513i q^{8} +(1.83221 - 1.05783i) q^{9} +(-0.177987 - 0.664257i) q^{11} +(1.16771 - 1.16771i) q^{12} +(2.92331 - 2.11051i) q^{13} -1.81533i q^{14} +(-1.29794 + 2.24809i) q^{16} +(-2.29359 - 0.614565i) q^{17} +1.04493 q^{18} +(5.29067 + 1.41763i) q^{19} +(2.44406 - 2.44406i) q^{21} +(0.0879082 - 0.328078i) q^{22} +(-1.30811 + 0.350507i) q^{23} +(1.68511 - 0.451523i) q^{24} +(1.77158 - 0.180816i) q^{26} +(3.40171 + 3.40171i) q^{27} +(-3.22719 + 5.58966i) q^{28} +(-8.24134 - 4.75814i) q^{29} +(4.81595 + 4.81595i) q^{31} +(-4.32351 + 2.49618i) q^{32} +(0.560059 - 0.323350i) q^{33} +(-0.829273 - 0.829273i) q^{34} +(-3.21748 - 1.85761i) q^{36} +(0.917615 - 1.58936i) q^{37} +(1.91290 + 1.91290i) q^{38} +(2.62860 + 2.14172i) q^{39} +(-0.534988 + 0.143350i) q^{41} +(1.64896 - 0.441838i) q^{42} +(0.560778 - 2.09285i) q^{43} +(-0.853919 + 0.853919i) q^{44} +(-0.646078 - 0.173116i) q^{46} +3.80918 q^{47} +(-2.35797 - 0.631815i) q^{48} +(-3.25462 + 5.63717i) q^{49} -2.23297i q^{51} +(-5.77640 - 2.59266i) q^{52} +(2.47293 - 2.47293i) q^{53} +(0.614963 + 2.29507i) q^{54} +(-5.90499 + 3.40925i) q^{56} +5.15084i q^{57} +(-2.35005 - 4.07041i) q^{58} +(-2.69310 + 10.0508i) q^{59} +(-3.09904 - 5.36770i) q^{61} +(0.870630 + 3.24924i) q^{62} +(-6.73428 - 3.88804i) q^{63} +2.72601 q^{64} +0.319406 q^{66} +(10.6066 + 6.12371i) q^{67} +(1.07921 + 4.02768i) q^{68} +(-0.636768 - 1.10291i) q^{69} +(-1.73500 + 6.47512i) q^{71} +(-1.96240 - 3.39898i) q^{72} +3.37642i q^{73} +(0.784986 - 0.453212i) q^{74} +(-2.48945 - 9.29074i) q^{76} +(-1.78728 + 1.78728i) q^{77} +(0.595435 + 1.56521i) q^{78} +3.12149i q^{79} +(0.911483 - 1.57873i) q^{81} +(-0.264231 - 0.0708006i) q^{82} -2.13918 q^{83} +(-5.86286 - 1.57095i) q^{84} +(0.756694 - 0.756694i) q^{86} +(2.31619 - 8.64414i) q^{87} +(-1.23228 + 0.330188i) q^{88} +(3.26255 - 0.874198i) q^{89} +(-12.0902 - 5.42653i) q^{91} +(1.68161 + 1.68161i) q^{92} +(-3.20242 + 5.54675i) q^{93} +(1.62931 + 0.940681i) q^{94} +(-3.31972 - 3.31972i) q^{96} +(-6.12606 + 3.53688i) q^{97} +(-2.78421 + 1.60746i) q^{98} +(-1.02878 - 1.02878i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 6 q^{2} + 2 q^{3} + 6 q^{4} - 8 q^{6} + 2 q^{7} + 12 q^{9} - 16 q^{11} + 24 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 20 q^{19} + 4 q^{21} - 16 q^{22} + 10 q^{23} + 32 q^{24} - 24 q^{26} - 4 q^{27}+ \cdots + 60 q^{99}+O(q^{100})$ 20 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 - 8 * q^6 + 2 * q^7 + 12 * q^9 - 16 * q^11 + 24 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 20 * q^19 + 4 * q^21 - 16 * q^22 + 10 * q^23 + 32 * q^24 - 24 * q^26 - 4 * q^27 - 18 * q^28 - 48 * q^32 - 18 * q^33 + 2 * q^34 + 36 * q^36 + 4 * q^37 + 8 * q^38 + 4 * q^39 + 10 * q^41 - 40 * q^42 - 10 * q^43 - 36 * q^44 + 4 * q^46 + 40 * q^47 + 56 * q^48 + 18 * q^49 + 30 * q^52 + 10 * q^53 - 48 * q^54 - 16 * q^59 - 16 * q^61 + 44 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 - 22 * q^68 - 16 * q^69 - 16 * q^71 - 4 * q^72 + 18 * q^74 - 64 * q^76 + 28 * q^77 - 68 * q^78 - 14 * q^81 - 56 * q^82 - 48 * q^83 - 40 * q^84 + 60 * q^86 + 34 * q^87 - 82 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 48 * q^94 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$ .

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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

)

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

$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	0.643544	−	0.765409i	$-0.277463\pi$
$2$	0.427732	+	0.246951i	0.302452	+	0.174621i	−0.341092	+	0.940030i	$0.610797\pi$
$3$	0.243392	+	0.908353i	0.140523	+	0.524438i	0.999914	+	0.0131191i	$0.00417607\pi$
$3$	0.243392	+	0.908353i	0.140523	+	0.524438i	−0.859391	+	0.511318i	$0.829157\pi$
$4$	−0.878030	−	1.52079i	−0.439015	−	0.760397i
$5$		0			0
$5$		0			0
$6$	−0.120212	+	0.448637i	−0.0490763	+	0.183155i
$7$	−1.83775	−	3.18307i	−0.694603	−	1.20309i	−0.970314	−	0.241847i	$-0.922247\pi$
$7$	−1.83775	−	3.18307i	−0.694603	−	1.20309i	0.275712	−	0.961240i	$-0.411086\pi$
$8$		−	1.85513i		−	0.655886i
$9$	1.83221	−	1.05783i	0.610737	−	0.352609i
$10$		0			0
$11$	−0.177987	−	0.664257i	−0.0536651	−	0.200281i	0.933888	−	0.357565i	$-0.116393\pi$
$11$	−0.177987	−	0.664257i	−0.0536651	−	0.200281i	−0.987553	+	0.157284i	$0.949726\pi$
$12$	1.16771	−	1.16771i	0.337089	−	0.337089i
$13$	2.92331	−	2.11051i	0.810781	−	0.585350i
$13$	2.92331	−	2.11051i	0.810781	−	0.585350i
$14$		−	1.81533i		−	0.485168i
$15$		0			0
$16$	−1.29794	+	2.24809i	−0.324484	+	0.562023i
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.0302815	−	0.999541i	$-0.509640\pi$
$17$	−2.29359	−	0.614565i	−0.556277	−	0.149054i	−0.525995	+	0.850487i	$0.676307\pi$
$18$	1.04493			0.246291
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.808238	−	0.588857i	$-0.200422\pi$
$19$	5.29067	+	1.41763i	1.21376	+	0.325227i	0.405526	+	0.914084i	$0.367088\pi$
$20$		0			0
$21$	2.44406	−	2.44406i	0.533337	−	0.533337i
$22$	0.0879082	−	0.328078i	0.0187421	−	0.0699464i
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	−0.392606	−	0.919707i	$-0.628426\pi$
$23$	−1.30811	+	0.350507i	−0.272760	+	0.0730858i	0.119846	+	0.992792i	$0.461760\pi$
$24$	1.68511	−	0.451523i	0.343971	−	0.0921668i
$25$		0			0
$26$	1.77158	−	0.180816i	0.347436	−	0.0354610i
$27$	3.40171	+	3.40171i	0.654659	+	0.654659i
$28$	−3.22719	+	5.58966i	−0.609882	+	1.05635i
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.999344	−	0.0362142i	$-0.988470\pi$
$29$	−8.24134	−	4.75814i	−1.53038	−	0.883564i	−0.531034	−	0.847350i	$-0.678197\pi$
$30$		0			0
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	0.991910	−	0.126940i	$-0.0405157\pi$
$31$	4.81595	+	4.81595i	0.864970	+	0.864970i	−0.126940	+	0.991910i	$0.540516\pi$
$32$	−4.32351	+	2.49618i	−0.764295	+	0.441266i
$33$	0.560059	−	0.323350i	0.0974937	−	0.0562880i
$34$	−0.829273	−	0.829273i	−0.142219	−	0.142219i
$35$		0			0
$36$	−3.21748	−	1.85761i	−0.536246	−	0.309602i
$37$	0.917615	−	1.58936i	0.150855	−	0.261289i	−0.780687	−	0.624922i	$-0.785131\pi$
$37$	0.917615	−	1.58936i	0.150855	−	0.261289i	0.931542	+	0.363634i	$0.118464\pi$
$38$	1.91290	+	1.91290i	0.310314	+	0.310314i
$39$	2.62860	+	2.14172i	0.420912	+	0.342949i
$40$		0			0
$41$	−0.534988	+	0.143350i	−0.0835510	+	0.0223874i	−0.300352	−	0.953828i	$-0.597104\pi$
$41$	−0.534988	+	0.143350i	−0.0835510	+	0.0223874i	0.216801	+	0.976216i	$0.430438\pi$
$42$	1.64896	−	0.441838i	0.254440	−	0.0681771i
$43$	0.560778	−	2.09285i	0.0855178	−	0.319157i	−0.909894	−	0.414841i	$-0.863837\pi$
$43$	0.560778	−	2.09285i	0.0855178	−	0.319157i	0.995412	+	0.0956841i	$0.0305039\pi$
$44$	−0.853919	+	0.853919i	−0.128733	+	0.128733i
$45$		0			0
$46$	−0.646078	−	0.173116i	−0.0952590	−	0.0255246i
$47$	3.80918			0.555626			0.277813	−	0.960635i	$-0.410390\pi$
$47$	3.80918			0.555626			0.277813	+	0.960635i	$0.410390\pi$
$48$	−2.35797	−	0.631815i	−0.340343	−	0.0911947i
$49$	−3.25462	+	5.63717i	−0.464946	+	0.805310i
$50$		0			0
$51$		−	2.23297i		−	0.312678i
$52$	−5.77640	−	2.59266i	−0.801043	−	0.359538i
$53$	2.47293	−	2.47293i	0.339683	−	0.339683i	−0.516565	−	0.856248i	$-0.672789\pi$
$53$	2.47293	−	2.47293i	0.339683	−	0.339683i	0.856248	+	0.516565i	$0.172789\pi$
$54$	0.614963	+	2.29507i	0.0836858	+	0.312320i
$55$		0			0
$56$	−5.90499	+	3.40925i	−0.789088	+	0.455580i
$57$			5.15084i			0.682245i
$58$	−2.35005	−	4.07041i	−0.308577	−	0.534471i
$59$	−2.69310	+	10.0508i	−0.350612	+	1.30850i	0.535305	+	0.844659i	$0.320197\pi$
$59$	−2.69310	+	10.0508i	−0.350612	+	1.30850i	−0.885917	+	0.463844i	$0.846470\pi$
$60$		0			0
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	0.596536	−	0.802586i	$-0.296543\pi$
$61$	−3.09904	−	5.36770i	−0.396792	−	0.687263i	−0.993328	+	0.115323i	$0.963210\pi$
$62$	0.870630	+	3.24924i	0.110570	+	0.412653i
$63$	−6.73428	−	3.88804i	−0.848439	−	0.489847i
$64$	2.72601			0.340751
$65$		0			0
$66$	0.319406			0.0393162
$67$	10.6066	+	6.12371i	1.29580	+	0.748130i	0.979676	−	0.200588i	$-0.0642852\pi$
$67$	10.6066	+	6.12371i	1.29580	+	0.748130i	0.316124	+	0.948718i	$0.397619\pi$
$68$	1.07921	+	4.02768i	0.130874	+	0.488428i
$69$	−0.636768	−	1.10291i	−0.0766579	−	0.132775i
$70$		0			0
$71$	−1.73500	+	6.47512i	−0.205907	+	0.768456i	0.783264	+	0.621689i	$0.213553\pi$
$71$	−1.73500	+	6.47512i	−0.205907	+	0.768456i	−0.989171	+	0.146767i	$0.953113\pi$
$72$	−1.96240	−	3.39898i	−0.231271	−	0.400574i
$73$			3.37642i			0.395180i	0.980285	+	0.197590i	$0.0633115\pi$
$73$			3.37642i			0.395180i	−0.980285	+	0.197590i	$0.936688\pi$
$74$	0.784986	−	0.453212i	0.0912528	−	0.0526848i
$75$		0			0
$76$	−2.48945	−	9.29074i	−0.285559	−	1.06572i
$77$	−1.78728	+	1.78728i	−0.203680	+	0.203680i
$78$	0.595435	+	1.56521i	0.0674198	+	0.177226i
$79$			3.12149i			0.351195i	0.984462	+	0.175598i	$0.0561857\pi$
$79$			3.12149i			0.351195i	−0.984462	+	0.175598i	$0.943814\pi$
$80$		0			0
$81$	0.911483	−	1.57873i	0.101276	−	0.175415i
$82$	−0.264231	−	0.0708006i	−0.0291795	−	0.00781862i
$83$	−2.13918			−0.234805			−0.117403	−	0.993084i	$-0.537457\pi$
$83$	−2.13918			−0.234805			−0.117403	+	0.993084i	$0.537457\pi$
$84$	−5.86286	−	1.57095i	−0.639691	−	0.171405i
$85$		0			0
$86$	0.756694	−	0.756694i	0.0815964	−	0.0815964i
$87$	2.31619	−	8.64414i	0.248322	−	0.926749i
$88$	−1.23228	+	0.330188i	−0.131361	+	0.0351982i
$89$	3.26255	−	0.874198i	0.345830	−	0.0926648i	−0.0817233	−	0.996655i	$-0.526042\pi$
$89$	3.26255	−	0.874198i	0.345830	−	0.0926648i	0.427553	+	0.903990i	$0.359376\pi$
$90$		0			0
$91$	−12.0902	−	5.42653i	−1.26740	−	0.568855i
$92$	1.68161	+	1.68161i	0.175320	+	0.175320i
$93$	−3.20242	+	5.54675i	−0.332075	+	0.575171i
$94$	1.62931	+	0.940681i	0.168050	+	0.0970238i
$95$		0			0
$96$	−3.31972	−	3.31972i	−0.338817	−	0.338817i
$97$	−6.12606	+	3.53688i	−0.622007	+	0.359116i	−0.777650	−	0.628697i	$-0.783588\pi$
$97$	−6.12606	+	3.53688i	−0.622007	+	0.359116i	0.155643	+	0.987813i	$0.450255\pi$
$98$	−2.78421	+	1.60746i	−0.281248	+	0.162378i
$99$	−1.02878	−	1.02878i	−0.103396	−	0.103396i
$100$		0			0
$101$	12.9641	+	7.48483i	1.28998	+	0.744769i	0.978650	−	0.205534i	$-0.0658932\pi$
$101$	12.9641	+	7.48483i	1.28998	+	0.744769i	0.311327	+	0.950303i	$0.399226\pi$
$102$	0.551433	−	0.955111i	0.0546000	−	0.0945700i
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	0.846143	−	0.532956i	$-0.178919\pi$
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	−0.532956	+	0.846143i	$0.678919\pi$
$104$	−3.91526	−	5.42311i	−0.383923	−	0.531780i
$105$		0			0
$106$	1.66844	−	0.447058i	0.162054	−	0.0434221i
$107$	−14.7329	+	3.94767i	−1.42428	+	0.381635i	−0.887001	−	0.461767i	$-0.847216\pi$
$107$	−14.7329	+	3.94767i	−1.42428	+	0.381635i	−0.537282	+	0.843403i	$0.680549\pi$
$108$	2.18649	−	8.16010i	0.210395	−	0.785206i
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	−0.590594	−	0.806969i	$-0.701107\pi$
$109$	2.25902	−	2.25902i	0.216375	−	0.216375i	0.806969	+	0.590594i	$0.201107\pi$
$110$		0			0
$111$	1.66704	+	0.446681i	0.158228	+	0.0423971i
$112$	9.54111			0.901550
$113$	16.0061	+	4.28882i	1.50573	+	0.403458i	0.915014	−	0.403423i	$-0.132180\pi$
$113$	16.0061	+	4.28882i	1.50573	+	0.403458i	0.590713	+	0.806881i	$0.298846\pi$
$114$	−1.27200	+	2.20318i	−0.119134	+	0.206346i
$115$		0			0
$116$			16.7112i			1.55159i
$117$	3.12357	−	6.95926i	0.288774	−	0.643384i
$118$	−3.63398	+	3.63398i	−0.334535	+	0.334535i
$119$	2.25883	+	8.43007i	0.207067	+	0.772783i
$120$		0			0
$121$	9.11672	−	5.26354i	0.828793	−	0.478504i
$122$		−	3.06124i		−	0.277152i
$123$	−0.260424	−	0.451067i	−0.0234816	−	0.0406714i
$124$	3.09551	−	11.5526i	0.277985	−	1.03746i
$125$		0			0
$126$	−1.92031	−	3.32607i	−0.171075	−	0.296310i
$127$	2.14812	+	8.01688i	0.190614	+	0.711383i	0.993359	+	0.115059i	$0.0367058\pi$
$127$	2.14812	+	8.01688i	0.190614	+	0.711383i	−0.802744	+	0.596324i	$0.796628\pi$
$128$	9.81302	+	5.66555i	0.867356	+	0.500768i
$129$	2.03754			0.179395
$130$		0			0
$131$	1.37409			0.120054			0.0600272	−	0.998197i	$-0.480881\pi$
$131$	1.37409			0.120054			0.0600272	+	0.998197i	$0.480881\pi$
$132$	−0.983497	−	0.567822i	−0.0856025	−	0.0494226i
$133$	−5.21049	−	19.4458i	−0.451807	−	1.68617i
$134$	3.02451	+	5.23861i	0.261278	+	0.452547i
$135$		0			0
$136$	−1.14010	+	4.25489i	−0.0977624	+	0.364854i
$137$	6.16380	+	10.6760i	0.526609	+	0.912114i	0.999519	+	0.0310029i	$0.00987013\pi$
$137$	6.16380	+	10.6760i	0.526609	+	0.912114i	−0.472910	+	0.881111i	$0.656797\pi$
$138$		−	0.629002i		−	0.0535442i
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	−0.246107	−	0.969243i	$-0.579151\pi$
$139$	5.54392	−	3.20078i	0.470229	−	0.271487i	0.716336	+	0.697756i	$0.245818\pi$
$140$		0			0
$141$	0.927126	+	3.46008i	0.0780781	+	0.291391i
$142$	−2.34115	+	2.34115i	−0.196465	+	0.196465i
$143$	−1.92223	−	1.56619i	−0.160745	−	0.130971i
$144$			5.49197i			0.457664i
$145$		0			0
$146$	−0.833811	+	1.44420i	−0.0690067	+	0.119523i
$147$	−5.91269	−	1.58430i	−0.487670	−	0.130671i
$148$	−3.22278			−0.264911
$149$	−16.2300	−	4.34882i	−1.32961	−	0.356269i	−0.477043	−	0.878880i	$-0.658291\pi$
$149$	−16.2300	−	4.34882i	−1.32961	−	0.356269i	−0.852571	+	0.522611i	$0.824958\pi$
$150$		0			0
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	−0.829022	−	0.559217i	$-0.811102\pi$
$151$	−3.31542	+	3.31542i	−0.269805	+	0.269805i	0.559217	+	0.829022i	$0.311102\pi$
$152$	2.62988	−	9.81486i	0.213312	−	0.796090i
$153$	−4.85244	+	1.30021i	−0.392297	+	0.105116i
$154$	−1.20585	+	0.323106i	−0.0971699	+	0.0260366i
$155$		0			0
$156$	0.949120	−	5.87805i	0.0759904	−	0.470620i
$157$	−9.87941	−	9.87941i	−0.788463	−	0.788463i	0.192779	−	0.981242i	$-0.438250\pi$
$157$	−9.87941	−	9.87941i	−0.788463	−	0.788463i	−0.981242	+	0.192779i	$0.938250\pi$
$158$	−0.770855	+	1.33516i	−0.0613259	+	0.106220i
$159$	2.84819	+	1.64440i	0.225876	+	0.130410i
$160$		0			0
$161$	3.51966	+	3.51966i	0.277388	+	0.277388i
$162$	0.779740	−	0.450183i	0.0612622	−	0.0353697i
$163$	0.114289	−	0.0659848i	0.00895180	−	0.00516833i	−0.495517	−	0.868598i	$-0.665022\pi$
$163$	0.114289	−	0.0659848i	0.00895180	−	0.00516833i	0.504469	+	0.863430i	$0.331688\pi$
$164$	0.687741	+	0.687741i	0.0537035	+	0.0537035i
$165$		0			0
$166$	−0.914995	−	0.528272i	−0.0710174	−	0.0410019i
$167$	10.8184	−	18.7380i	0.837152	−	1.44999i	−0.0551149	−	0.998480i	$-0.517553\pi$
$167$	10.8184	−	18.7380i	0.837152	−	1.44999i	0.892267	−	0.451509i	$-0.149114\pi$
$168$	−4.53403	−	4.53403i	−0.349808	−	0.349808i
$169$	4.09151	−	12.3393i	0.314731	−	0.949181i
$170$		0			0
$171$	11.1932	−	2.99922i	0.855969	−	0.229356i
$172$	−3.67518	+	0.984760i	−0.280230	+	0.0750873i
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	−0.847150	−	0.531353i	$-0.821684\pi$
$173$	2.00162	−	7.47013i	0.152180	−	0.567943i	0.999330	−	0.0365902i	$-0.0116496\pi$
$174$	3.12539	−	3.12539i	0.236935	−	0.236935i
$175$		0			0
$176$	1.72433	+	0.462032i	0.129976	+	0.0348270i
$177$	−9.78515			−0.735497
$178$	1.61138	+	0.431768i	0.120778	+	0.0323624i
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	−0.379881	−	0.925035i	$-0.624035\pi$
$179$	8.17681	−	14.1627i	0.611164	−	1.05857i	0.991045	−	0.133531i	$-0.0426317\pi$
$180$		0			0
$181$		−	18.0387i		−	1.34081i	−0.741997	−	0.670403i	$-0.766121\pi$
$181$		−	18.0387i		−	1.34081i	0.741997	−	0.670403i	$-0.233879\pi$
$182$	−3.83127	−	5.30678i	−0.283993	−	0.393365i
$183$	4.12148	−	4.12148i	0.304668	−	0.304668i
$184$	0.650235	+	2.42671i	0.0479359	+	0.178899i
$185$		0			0
$186$	−2.73955	+	1.58168i	−0.200873	+	0.115974i
$187$			1.63292i			0.119411i
$188$	−3.34458	−	5.79298i	−0.243928	−	0.422496i
$189$	4.57640	−	17.0793i	0.332884	−	1.24234i
$190$		0			0
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	0.756713	−	0.653747i	$-0.226804\pi$
$191$	−2.59552	−	4.49557i	−0.187805	−	0.325288i	−0.944518	+	0.328459i	$0.893471\pi$
$192$	0.663490	+	2.47618i	0.0478833	+	0.178703i
$193$	8.74813	+	5.05073i	0.629704	+	0.363560i	0.780637	−	0.624984i	$-0.214895\pi$
$193$	8.74813	+	5.05073i	0.629704	+	0.363560i	−0.150934	+	0.988544i	$0.548228\pi$
$194$	−3.49375			−0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	0.845589	−	0.533835i	$-0.179250\pi$
$197$	11.3137	+	6.53197i	0.806068	+	0.465384i	−0.0395205	+	0.999219i	$0.512583\pi$
$198$	−0.185983	−	0.694099i	−0.0132173	−	0.0493275i
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	0.692707	−	0.721219i	$-0.256418\pi$
$199$	−3.92506	−	6.79840i	−0.278240	−	0.481926i	−0.970947	+	0.239293i	$0.923084\pi$
$200$		0			0
$201$	−2.98093	+	11.1250i	−0.210258	+	0.784695i
$202$	3.69677	+	6.40300i	0.260104	+	0.450513i
$203$			34.9770i			2.45491i
$204$	−3.39588	+	1.96061i	−0.237759	+	0.137270i
$205$		0			0
$206$	0.574613	+	2.14448i	0.0400352	+	0.149413i
$207$	−2.02596	+	2.02596i	−0.140814	+	0.140814i
$208$	0.950343	+	9.31118i	0.0658944	+	0.645614i
$209$		−	3.76669i		−	0.260547i
$210$		0			0
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	−0.996664	−	0.0816108i	$-0.973994\pi$
$211$	−6.21205	+	10.7596i	−0.427655	+	0.740720i	0.569009	+	0.822331i	$0.307327\pi$
$212$	−5.93213	−	1.58951i	−0.407420	−	0.109168i
$213$	−6.30398			−0.431942
$214$	−7.27661	−	1.94976i	−0.497419	−	0.133283i
$215$		0			0
$216$	6.31059	−	6.31059i	0.429382	−	0.429382i
$217$	6.47901	−	24.1800i	0.439824	−	1.64145i
$218$	1.52412	−	0.408387i	0.103226	−	0.0276594i
$219$	−3.06698	+	0.821796i	−0.207248	+	0.0555318i
$220$		0			0
$221$	−8.00192	+	3.04407i	−0.538267	+	0.204766i
$222$	0.602736	+	0.602736i	0.0404530	+	0.0404530i
$223$	4.97247	−	8.61258i	0.332981	−	0.576741i	−0.650114	−	0.759837i	$-0.725279\pi$
$223$	4.97247	−	8.61258i	0.332981	−	0.576741i	0.983095	+	0.183096i	$0.0586120\pi$
$224$	15.8910	+	9.17468i	1.06176	+	0.613009i
$225$		0			0
$226$	5.78718	+	5.78718i	0.384958	+	0.384958i
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	−0.857109	−	0.515135i	$-0.827742\pi$
$227$	−12.6490	+	7.30290i	−0.839543	+	0.484710i	0.0175659	+	0.999846i	$0.494408\pi$
$228$	7.83336	−	4.52259i	0.518777	−	0.299516i
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.999468	+	0.0326207i	$0.0103853\pi$
$229$	15.6183	+	15.6183i	1.03209	+	1.03209i	0.0326207	+	0.999468i	$0.489615\pi$
$230$		0			0
$231$	−2.05849	−	1.18847i	−0.135439	−	0.0781956i
$232$	−8.82695	+	15.2887i	−0.579517	+	1.00375i
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.996030	−	0.0890148i	$-0.971628\pi$
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.0890148	−	0.996030i	$-0.528372\pi$
$234$	3.05465	−	2.20533i	0.199688	−	0.144167i
$235$		0			0
$236$	17.6498	−	4.72926i	1.14891	−	0.307848i
$237$	−2.83541	+	0.759747i	−0.184180	+	0.0493509i
$238$	−1.11564	+	4.16362i	−0.0723162	+	0.269888i
$239$	−14.6022	+	14.6022i	−0.944535	+	0.944535i	−0.998541	−	0.0540053i	$-0.982801\pi$
$239$	−14.6022	+	14.6022i	−0.944535	+	0.944535i	0.0540053	+	0.998541i	$0.482801\pi$
$240$		0			0
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	0.353936	−	0.935270i	$-0.384843\pi$
$241$	2.99335	+	0.802065i	0.192818	+	0.0516656i	−0.161117	+	0.986935i	$0.551510\pi$
$242$	5.19935			0.334227
$243$	15.5964	+	4.17903i	1.00051	+	0.268085i
$244$	−5.44211	+	9.42600i	−0.348395	+	0.603438i
$245$		0			0
$246$		−	0.257248i		−	0.0164015i
$247$	18.4582	−	7.02183i	1.17447	−	0.446788i
$248$	8.93419	−	8.93419i	0.567322	−	0.567322i
$249$	−0.520660	−	1.94313i	−0.0329955	−	0.123141i
$250$		0			0
$251$	−25.5728	+	14.7645i	−1.61414	+	0.931925i	−0.625745	+	0.780028i	$0.715205\pi$
$251$	−25.5728	+	14.7645i	−1.61414	+	0.931925i	−0.988396	+	0.151897i	$0.951462\pi$
$252$			13.6553i			0.860201i
$253$	0.465654	+	0.806536i	0.0292754	+	0.0507065i
$254$	−1.06096	+	3.95955i	−0.0665704	+	0.248444i
$255$		0			0
$256$	0.0722145	+	0.125079i	0.00451341	+	0.00781745i
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	0.999337	−	0.0364143i	$-0.0115936\pi$
$257$	1.85447	+	6.92097i	0.115679	+	0.431718i	−0.883658	+	0.468133i	$0.844927\pi$
$258$	0.871519	+	0.503172i	0.0542584	+	0.0313261i
$259$	−6.74538			−0.419137
$260$		0			0
$261$	−20.1332			−1.24621
$262$	0.587740	+	0.339332i	0.0363107	+	0.0209640i
$263$	3.48511	+	13.0066i	0.214901	+	0.802023i	0.986201	+	0.165551i	$0.0529402\pi$
$263$	3.48511	+	13.0066i	0.214901	+	0.802023i	−0.771300	+	0.636472i	$0.780393\pi$
$264$	−0.599855	−	1.03898i	−0.0369185	−	0.0639448i
$265$		0			0
$266$	2.57347	−	9.60433i	0.157790	−	0.588879i
$267$	1.58816	+	2.75077i	0.0971938	+	0.168345i
$268$		−	21.5072i		−	1.31376i
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	−0.698451	−	0.715658i	$-0.746127\pi$
$269$	−7.01806	+	4.05188i	−0.427899	+	0.247047i	0.270552	+	0.962705i	$0.412794\pi$
$270$		0			0
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	−0.999773	−	0.0212923i	$-0.993222\pi$
$271$	−2.38026	−	8.88325i	−0.144590	−	0.539619i	0.855183	−	0.518326i	$-0.173445\pi$
$272$	4.35853	−	4.35853i	0.264275	−	0.264275i
$273$	1.98654	−	12.3029i	0.120231	−	0.744608i
$274$			6.08862i			0.367827i
$275$		0			0
$276$	−1.11820	+	1.93679i	−0.0673080	+	0.116581i
$277$	−24.9641	−	6.68911i	−1.49995	−	0.401910i	−0.586865	−	0.809685i	$-0.699638\pi$
$277$	−24.9641	−	6.68911i	−1.49995	−	0.401910i	−0.913082	+	0.407775i	$0.866305\pi$
$278$	3.16174			0.189629
$279$	13.9183	+	3.72939i	0.833266	+	0.223273i
$280$		0			0
$281$	5.41928	−	5.41928i	0.323287	−	0.323287i	−0.526740	−	0.850027i	$-0.676586\pi$
$281$	5.41928	−	5.41928i	0.323287	−	0.323287i	0.850027	+	0.526740i	$0.176586\pi$
$282$	−0.457909	+	1.70894i	−0.0272681	+	0.101766i
$283$	−8.48623	+	2.27388i	−0.504454	+	0.135168i	−0.502066	−	0.864829i	$-0.667427\pi$
$283$	−8.48623	+	2.27388i	−0.504454	+	0.135168i	−0.00238762	+	0.999997i	$0.500760\pi$
$284$	11.3707	−	3.04677i	0.674728	−	0.180793i
$285$		0			0
$286$	−0.435428	−	1.14460i	−0.0257474	−	0.0676819i
$287$	1.43946	+	1.43946i	0.0849688	+	0.0849688i
$288$	−5.28105	+	9.14705i	−0.311189	+	0.538995i
$289$	−9.83958	−	5.68088i	−0.578799	−	0.334170i
$290$		0			0
$291$	−4.70377	−	4.70377i	−0.275740	−	0.275740i
$292$	5.13484	−	2.96460i	0.300494	−	0.173490i
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	−0.795947	−	0.605367i	$-0.793026\pi$
$293$	−11.4627	+	6.61798i	−0.669657	+	0.386626i	0.126290	+	0.991993i	$0.459693\pi$
$294$	−2.13780	−	2.13780i	−0.124679	−	0.124679i
$295$		0			0
$296$	−2.94846	−	1.70229i	−0.171375	−	0.0989437i
$297$	1.65415	−	2.86507i	0.0959834	−	0.166248i
$298$	−5.86814	−	5.86814i	−0.339932	−	0.339932i
$299$	−3.08427	+	3.78542i	−0.178368	+	0.218916i
$300$		0			0
$301$	−7.69226	+	2.06114i	−0.443375	+	0.118802i
$302$	−2.23685	+	0.599363i	−0.128716	+	0.0344895i
$303$	−3.64350	+	13.5977i	−0.209314	+	0.781169i
$304$	−10.0539	+	10.0539i	−0.576632	+	0.576632i
$305$		0			0
$306$	−2.39663	−	0.642175i	−0.137006	−	0.0367107i
$307$	15.4782			0.883389			0.441695	−	0.897165i	$-0.354377\pi$
$307$	15.4782			0.883389			0.441695	+	0.897165i	$0.354377\pi$
$308$	4.28737	+	1.14880i	0.244296	+	0.0654588i
$309$	−2.11358	+	3.66083i	−0.120237	+	0.208257i
$310$		0			0
$311$		−	5.34922i		−	0.303326i	−0.988432	−	0.151663i	$-0.951537\pi$
$311$		−	5.34922i		−	0.303326i	0.988432	−	0.151663i	$-0.0484629\pi$
$312$	3.97315	−	4.87638i	0.224936	−	0.276071i
$313$	−24.3923	+	24.3923i	−1.37873	+	1.37873i	−0.531967	+	0.846765i	$0.678547\pi$
$313$	−24.3923	+	24.3923i	−1.37873	+	1.37873i	−0.846765	+	0.531967i	$0.821453\pi$
$314$	−1.78601	−	6.66547i	−0.100790	−	0.376154i
$315$		0			0
$316$	4.74714	−	2.74076i	0.267048	−	0.154180i
$317$			18.9851i			1.06631i	0.846017	+	0.533156i	$0.178994\pi$
$317$			18.9851i			1.06631i	−0.846017	+	0.533156i	$0.821006\pi$
$318$	0.812173	+	1.40673i	0.0455444	+	0.0788852i
$319$	−1.69378	+	6.32125i	−0.0948332	+	0.353922i
$320$		0			0
$321$	−7.17175	−	12.4218i	−0.400288	−	0.693319i
$322$	0.636287	+	2.37466i	0.0354589	+	0.132334i
$323$	−11.2634	−	6.50293i	−0.626712	−	0.361832i
$324$	−3.20124			−0.177847
$325$		0			0
$326$	0.0651800			0.00360999
$327$	2.60181	+	1.50216i	0.143881	+	0.0830695i
$328$	0.265931	+	0.992469i	0.0146836	+	0.0548000i
$329$	−7.00031	−	12.1249i	−0.385940	−	0.668467i
$330$		0			0
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	−0.997706	−	0.0676941i	$-0.978436\pi$
$331$	−1.81607	+	6.77766i	−0.0998202	+	0.372534i	0.897886	+	0.440228i	$0.145102\pi$
$332$	1.87826	+	3.25325i	0.103083	+	0.178545i
$333$		−	3.88272i		−	0.212772i
$334$	9.25473	−	5.34322i	0.506396	−	0.292368i
$335$		0			0
$336$	2.32223	+	8.66669i	0.126688	+	0.472807i
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	−0.676456	−	0.736483i	$-0.736485\pi$
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	0.736483	+	0.676456i	$0.236485\pi$
$338$	4.79728	−	4.26753i	0.260938	−	0.232123i
$339$			15.5830i			0.846355i
$340$		0			0
$341$	2.34185	−	4.05620i	0.126818	−	0.219656i
$342$	5.52836	+	1.48132i	0.298940	+	0.0801006i
$343$	−1.80378			−0.0973947
$344$	−3.88250	−	1.04031i	−0.209331	−	0.0560899i
$345$		0			0
$346$	2.70091	−	2.70091i	0.145202	−	0.145202i
$347$	−6.68561	+	24.9510i	−0.358902	+	1.33944i	0.516600	+	0.856227i	$0.327197\pi$
$347$	−6.68561	+	24.9510i	−0.358902	+	1.33944i	−0.875502	+	0.483214i	$0.839469\pi$
$348$	−15.1796	+	4.06737i	−0.813714	+	0.218034i
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	−0.493504	−	0.869744i	$-0.664284\pi$
$349$	−9.07958	+	2.43287i	−0.486019	+	0.130228i	0.00748510	+	0.999972i	$0.497617\pi$
$350$		0			0
$351$	17.1236	+	2.76492i	0.913989	+	0.147581i
$352$	2.42763	+	2.42763i	0.129393	+	0.129393i
$353$	−1.63274	+	2.82798i	−0.0869017	+	0.150518i	−0.906200	−	0.422849i	$-0.861030\pi$
$353$	−1.63274	+	2.82798i	−0.0869017	+	0.150518i	0.819298	+	0.573368i	$0.194363\pi$
$354$	−4.18542	−	2.41645i	−0.222452	−	0.128433i
$355$		0			0
$356$	−4.19410	−	4.19410i	−0.222287	−	0.222287i
$357$	−7.10769	+	4.10363i	−0.376179	+	0.217187i
$358$	6.99496	−	4.03854i	0.369695	−	0.213444i
$359$	3.12090	+	3.12090i	0.164715	+	0.164715i	0.784652	−	0.619937i	$-0.212842\pi$
$359$	3.12090	+	3.12090i	0.164715	+	0.164715i	−0.619937	+	0.784652i	$0.712842\pi$
$360$		0			0
$361$	9.52706	+	5.50045i	0.501424	+	0.289497i
$362$	4.45468	−	7.71573i	0.234133	−	0.405530i
$363$	7.00009	+	7.00009i	0.367410	+	0.367410i
$364$	2.36294	+	23.1514i	0.123852	+	1.21346i
$365$		0			0
$366$	2.78069	−	0.745084i	0.145349	−	0.0389461i
$367$	24.2349	−	6.49371i	1.26505	−	0.338969i	0.436917	−	0.899502i	$-0.356070\pi$
$367$	24.2349	−	6.49371i	1.26505	−	0.338969i	0.828132	+	0.560533i	$0.189404\pi$
$368$	0.909872	−	3.39569i	0.0474303	−	0.177012i
$369$	−0.828572	+	0.828572i	−0.0431337	+	0.0431337i
$370$		0			0
$371$	−12.4161	−	3.32690i	−0.644614	−	0.172724i
$372$	11.2473			0.583144
$373$	−11.0372	−	2.95740i	−0.571483	−	0.153128i	−0.0385061	−	0.999258i	$-0.512260\pi$
$373$	−11.0372	−	2.95740i	−0.571483	−	0.153128i	−0.532976	+	0.846130i	$0.678927\pi$
$374$	−0.403250	+	0.698450i	−0.0208516	+	0.0361160i
$375$		0			0
$376$		−	7.06651i		−	0.364427i
$377$	−34.1341	+	3.48389i	−1.75800	+	0.179429i
$378$	6.17523	−	6.17523i	0.317620	−	0.317620i
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	0.977997	−	0.208621i	$-0.0668975\pi$
$379$	0.520109	+	1.94107i	0.0267162	+	0.0997062i	−0.951280	+	0.308327i	$0.900231\pi$
$380$		0			0
$381$	−6.75932	+	3.90249i	−0.346290	+	0.199931i
$382$		−	2.56386i		−	0.131179i
$383$	−13.2258	−	22.9077i	−0.675806	−	1.17053i	−0.976233	−	0.216725i	$-0.930462\pi$
$383$	−13.2258	−	22.9077i	−0.675806	−	1.17053i	0.300427	−	0.953805i	$-0.402871\pi$
$384$	−2.75790	+	10.2926i	−0.140739	+	0.525244i
$385$		0			0
$386$	2.49457	+	4.32072i	0.126970	+	0.219919i
$387$	−1.18641	−	4.42775i	−0.0603088	−	0.225075i
$388$	10.7577	+	6.21098i	0.546141	+	0.315315i
$389$	−0.650094			−0.0329611			−0.0164805	−	0.999864i	$-0.505246\pi$
$389$	−0.650094			−0.0329611			−0.0164805	+	0.999864i	$0.505246\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$	10.4577	+	6.03773i	0.528191	+	0.304951i
$393$	0.334442	+	1.24815i	0.0168704	+	0.0629610i
$394$	3.22615	+	5.58786i	0.162531	+	0.281512i
$395$		0			0
$396$	−0.661261	+	2.46786i	−0.0332296	+	0.124015i
$397$	−13.5041	−	23.3897i	−0.677750	−	1.17390i	−0.975657	−	0.219303i	$-0.929622\pi$
$397$	−13.5041	−	23.3897i	−0.677750	−	1.17390i	0.297907	−	0.954595i	$-0.403712\pi$
$398$		−	3.87719i		−	0.194346i
$399$	16.3955	−	9.46593i	0.820800	−	0.473889i
$400$		0			0
$401$	−1.28339	−	4.78969i	−0.0640896	−	0.239186i	0.926449	−	0.376421i	$-0.122845\pi$
$401$	−1.28339	−	4.78969i	−0.0640896	−	0.239186i	−0.990539	+	0.137235i	$0.956179\pi$
$402$	−4.02236	+	4.02236i	−0.200617	+	0.200617i
$403$	24.2426	+	3.91442i	1.20761	+	0.194991i
$404$		−	26.2876i		−	1.30786i
$405$		0			0
$406$	−8.63761	+	14.9608i	−0.428677	+	0.742491i
$407$	−1.21906	−	0.326647i	−0.0604268	−	0.0161913i
$408$	−4.14243			−0.205081
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	0.400288	−	0.916390i	$-0.368910\pi$
$409$	5.83965	+	1.56473i	0.288752	+	0.0773708i	−0.111536	+	0.993760i	$0.535577\pi$
$410$		0			0
$411$	−8.19736	+	8.19736i	−0.404346	+	0.404346i
$412$	2.04303	−	7.62468i	0.100653	−	0.375641i
$413$	36.9416	−	9.89848i	1.81778	−	0.487073i
$414$	−1.36688	+	0.366254i	−0.0671784	+	0.0180004i
$415$		0			0
$416$	−7.37076	+	16.4219i	−0.361381	+	0.805150i
$417$	4.25679	+	4.25679i	0.208456	+	0.208456i
$418$	0.930187	−	1.61113i	0.0454969	−	0.0788030i
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	0.609290	−	0.792947i	$-0.291454\pi$
$419$	4.65114	+	2.68534i	0.227223	+	0.131187i	−0.382067	+	0.924135i	$0.624788\pi$
$420$		0			0
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	0.962017	−	0.272988i	$-0.0880119\pi$
$421$	14.1377	+	14.1377i	0.689029	+	0.689029i	−0.272988	+	0.962017i	$0.588012\pi$
$422$	−5.31418	+	3.06814i	−0.258690	+	0.149355i
$423$	6.97923	−	4.02946i	0.339342	−	0.195919i
$424$	−4.58760	−	4.58760i	−0.222794	−	0.222794i
$425$		0			0
$426$	−2.69641	−	1.55677i	−0.130642	−	0.0754260i
$427$	−11.3905	+	19.7289i	−0.551225	+	0.954750i
$428$	18.9395	+	18.9395i	0.915476	+	0.915476i
$429$	0.954794	−	2.12726i	0.0460979	−	0.102705i
$430$		0			0
$431$	16.1219	−	4.31985i	0.776564	−	0.208080i	0.151295	−	0.988489i	$-0.451656\pi$
$431$	16.1219	−	4.31985i	0.776564	−	0.208080i	0.625269	+	0.780409i	$0.284989\pi$
$432$	−12.0625	+	3.23215i	−0.580360	+	0.155507i
$433$	1.96538	−	7.33490i	0.0944502	−	0.352493i	−0.902485	−	0.430721i	$-0.858259\pi$
$433$	1.96538	−	7.33490i	0.0944502	−	0.352493i	0.996936	+	0.0782277i	$0.0249261\pi$
$434$	8.74255	−	8.74255i	0.419656	−	0.419656i
$435$		0			0
$436$	−5.41899	−	1.45201i	−0.259522	−	0.0695388i
$437$	−7.41767			−0.354835
$438$	−1.51479	−	0.405886i	−0.0723794	−	0.0193940i
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	−0.655146	−	0.755502i	$-0.727393\pi$
$439$	6.84536	−	11.8565i	0.326711	−	0.565880i	0.981857	+	0.189622i	$0.0607262\pi$
$440$		0			0
$441$			13.7713i			0.655777i
$442$	−4.17441	−	0.674036i	−0.198556	−	0.0320606i
$443$	−6.46290	+	6.46290i	−0.307062	+	0.307062i	−0.843769	−	0.536707i	$-0.819668\pi$
$443$	−6.46290	+	6.46290i	−0.307062	+	0.307062i	0.536707	+	0.843769i	$0.319668\pi$
$444$	−0.784399	−	2.92742i	−0.0372259	−	0.138929i
$445$		0			0
$446$	4.25377	−	2.45591i	0.201422	−	0.116291i
$447$		−	15.8010i		−	0.747364i
$448$	−5.00971	−	8.67708i	−0.236687	−	0.409953i
$449$	−6.65458	+	24.8352i	−0.314049	+	1.17205i	0.610822	+	0.791768i	$0.290839\pi$
$449$	−6.65458	+	24.8352i	−0.314049	+	1.17205i	−0.924872	+	0.380280i	$0.875828\pi$
$450$		0			0
$451$	0.190442	+	0.329855i	0.00896755	+	0.0155323i
$452$	−7.53143	−	28.1077i	−0.354249	−	1.32207i
$453$	−3.81852	−	2.20462i	−0.179409	−	0.103582i
$454$	−7.21383			−0.338562
$455$		0			0
$456$	9.55545			0.447475
$457$	0.716665	+	0.413767i	0.0335242	+	0.0193552i	0.516668	−	0.856186i	$-0.327172\pi$
$457$	0.716665	+	0.413767i	0.0335242	+	0.0193552i	−0.483144	+	0.875541i	$0.660505\pi$
$458$	2.82349	+	10.5374i	0.131933	+	0.492381i
$459$	−5.71155	−	9.89269i	−0.266592	−	0.461751i
$460$		0			0
$461$	6.23219	−	23.2589i	0.290262	−	1.08327i	−0.654646	−	0.755936i	$-0.727182\pi$
$461$	6.23219	−	23.2589i	0.290262	−	1.08327i	0.944908	−	0.327337i	$-0.106151\pi$
$462$	−0.586988	−	1.01669i	−0.0273091	−	0.0473008i
$463$			6.35566i			0.295373i	0.989034	+	0.147686i	$0.0471826\pi$
$463$			6.35566i			0.295373i	−0.989034	+	0.147686i	$0.952817\pi$
$464$	21.3935	−	12.3515i	0.993167	−	0.573405i
$465$		0			0
$466$	−2.99418	−	11.1744i	−0.138703	−	0.517645i
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	−0.246390	−	0.969171i	$-0.579244\pi$
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	0.969171	+	0.246390i	$0.0792443\pi$
$468$	−13.3262	+	1.36013i	−0.616003	+	0.0628722i
$469$		−	45.0153i		−	2.07861i
$470$		0			0
$471$	6.56942	−	11.3786i	0.302703	−	0.524297i
$472$	18.6455	+	4.99605i	0.858229	+	0.229962i
$473$	−1.49000			−0.0685104
$474$	−1.40042	−	0.375240i	−0.0643232	−	0.0172354i
$475$		0			0
$476$	10.8371	−	10.8371i	0.496716	−	0.496716i
$477$	1.91500	−	7.14687i	0.0876818	−	0.327233i
$478$	−9.85182	+	2.63979i	−0.450612	+	0.120741i
$479$	9.14111	−	2.44935i	0.417668	−	0.111914i	−0.0438638	−	0.999038i	$-0.513967\pi$
$479$	9.14111	−	2.44935i	0.417668	−	0.111914i	0.461532	+	0.887124i	$0.347300\pi$
$480$		0			0
$481$	−0.671874	−	6.58282i	−0.0306348	−	0.300151i
$482$	1.08228	+	1.08228i	0.0492964	+	0.0492964i
$483$	−2.34044	+	4.05375i	−0.106494	+	0.184452i
$484$	−16.0095	−	9.24310i	−0.727705	−	0.420141i
$485$		0			0
$486$	5.63904	+	5.63904i	0.255792	+	0.255792i
$487$	−5.33382	+	3.07948i	−0.241698	+	0.139545i	−0.615957	−	0.787780i	$-0.711231\pi$
$487$	−5.33382	+	3.07948i	−0.241698	+	0.139545i	0.374259	+	0.927324i	$0.377897\pi$
$488$	−9.95775	+	5.74911i	−0.450766	+	0.260250i
$489$	0.0877545	+	0.0877545i	0.00396840	+	0.00396840i
$490$		0			0
$491$	12.8290	+	7.40681i	0.578964	+	0.334265i	0.760721	−	0.649078i	$-0.224845\pi$
$491$	12.8290	+	7.40681i	0.578964	+	0.334265i	−0.181758	+	0.983343i	$0.558179\pi$
$492$	−0.457320	+	0.792102i	−0.0206176	+	0.0357107i
$493$	15.9781	+	15.9781i	0.719615	+	0.719615i
$494$	9.62921	+	1.55481i	0.433238	+	0.0699544i
$495$		0			0
$496$	−17.0775	+	4.57590i	−0.766802	+	0.205464i
$497$	23.7993	−	6.37699i	1.06754	−	0.286047i
$498$	0.257155	−	0.959715i	0.0115234	−	0.0430059i
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	−0.0559733	−	0.998432i	$-0.517826\pi$
$499$	21.0529	−	21.0529i	0.942459	−	0.942459i	0.998432	+	0.0559733i	$0.0178262\pi$
$500$		0			0
$501$	19.6538	+	5.26622i	0.878068	+	0.235278i
$502$	−14.5844			−0.650933
$503$	−37.4393	−	10.0318i	−1.66934	−	0.447297i	−0.704404	−	0.709799i	$-0.748786\pi$
$503$	−37.4393	−	10.0318i	−1.66934	−	0.447297i	−0.964932	+	0.262502i	$0.915452\pi$
$504$	−7.21280	+	12.4929i	−0.321284	+	0.556479i
$505$		0			0
$506$			0.459974i			0.0204484i
$507$	12.2043	+	0.713230i	0.542013	+	0.0316756i
$508$	10.3059	−	10.3059i	0.457250	−	0.457250i
$509$	−1.43699	−	5.36291i	−0.0636933	−	0.237707i	0.926739	−	0.375706i	$-0.122600\pi$
$509$	−1.43699	−	5.36291i	−0.0636933	−	0.237707i	−0.990432	+	0.137999i	$0.955933\pi$
$510$		0			0
$511$	10.7474	−	6.20501i	0.475437	−	0.274493i
$512$		−	22.5909i		−	0.998384i
$513$	13.1750	+	22.8197i	0.581688	+	1.00751i
$514$	−0.915926	+	3.41828i	−0.0403997	+	0.150774i
$515$		0			0
$516$	−1.78902	−	3.09867i	−0.0787572	−	0.136411i
$517$	−0.677985	−	2.53028i	−0.0298178	−	0.111281i
$518$	−2.88521	−	1.66578i	−0.126769	−	0.0731900i
$519$	7.27269			0.319236
$520$		0			0
$521$	−13.8692			−0.607619			−0.303809	−	0.952733i	$-0.598259\pi$
$521$	−13.8692			−0.607619			−0.303809	+	0.952733i	$0.598259\pi$
$522$	−8.61159	−	4.97191i	−0.376919	−	0.217614i
$523$	−8.10818	−	30.2601i	−0.354546	−	1.32318i	−0.881055	−	0.473014i	$-0.843166\pi$
$523$	−8.10818	−	30.2601i	−0.354546	−	1.32318i	0.526509	−	0.850170i	$-0.323501\pi$
$524$	−1.20649	−	2.08970i	−0.0527057	−	0.0912890i
$525$		0			0
$526$	−1.72130	+	6.42400i	−0.0750524	+	0.280100i
$527$	−8.08609	−	14.0055i	−0.352236	−	0.610090i
$528$			1.67875i			0.0730583i
$529$	−18.3303	+	10.5830i	−0.796969	+	0.460130i
$530$		0			0
$531$	5.69768	+	21.2640i	0.247258	+	0.922781i
$532$	−24.9981	+	24.9981i	−1.08381	+	1.08381i
$533$	−1.26140	+	1.54815i	−0.0546371	+	0.0670579i
$534$			1.56879i			0.0678882i
$535$		0			0
$536$	11.3602	−	19.6765i	0.490688	−	0.849897i
$537$	14.8549	+	3.98035i	0.641035	+	0.171765i
$538$	−4.00246			−0.172558
$539$	4.32381	+	1.15856i	0.186240	+	0.0499028i
$540$		0			0
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	−0.899695	−	0.436520i	$-0.856211\pi$
$541$	−10.7732	+	10.7732i	−0.463175	+	0.463175i	0.436520	+	0.899695i	$0.356211\pi$
$542$	1.17561	−	4.38745i	0.0504969	−	0.188457i
$543$	16.3855	−	4.39048i	0.703170	−	0.188414i
$544$	11.4504	−	3.06813i	0.490932	−	0.131545i
$545$		0			0
$546$	3.88793	−	4.77178i	0.166388	−	0.204213i
$547$	−14.2704	−	14.2704i	−0.610159	−	0.610159i	0.332828	−	0.942987i	$-0.391997\pi$
$547$	−14.2704	−	14.2704i	−0.610159	−	0.610159i	−0.942987	+	0.332828i	$0.891997\pi$
$548$	10.8240	−	18.7477i	0.462379	−	0.800863i
$549$	−11.3562	−	6.55650i	−0.484671	−	0.279825i
$550$		0			0
$551$	−36.8569	−	36.8569i	−1.57016	−	1.57016i
$552$	−2.04605	+	1.18128i	−0.0870855	+	0.0502788i
$553$	9.93592	−	5.73651i	0.422518	−	0.243941i
$554$	−9.02605	−	9.02605i	−0.383480	−	0.383480i
$555$		0			0
$556$	−9.73546	−	5.62077i	−0.412875	−	0.238374i
$557$	8.35584	−	14.4727i	0.354048	−	0.613229i	−0.632906	−	0.774228i	$-0.718138\pi$
$557$	8.35584	−	14.4727i	0.354048	−	0.613229i	0.986955	+	0.160999i	$0.0514716\pi$
$558$	5.03231	+	5.03231i	0.213035	+	0.213035i
$559$	−2.77765	−	7.30159i	−0.117482	−	0.308824i
$560$		0			0
$561$	−1.48326	+	0.397439i	−0.0626234	+	0.0167799i
$562$	3.65629	−	0.979701i	0.154231	−	0.0413262i
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	−0.726573	−	0.687089i	$-0.758888\pi$
$563$	5.84179	−	21.8019i	0.246202	−	0.918839i	0.972775	−	0.231750i	$-0.0744452\pi$
$564$	4.44802	−	4.44802i	0.187296	−	0.187296i
$565$		0			0
$566$	−4.19136	−	1.12307i	−0.176176	−	0.0472063i
$567$	−6.70030			−0.281386
$568$	12.0122	+	3.21865i	0.504019	+	0.135052i
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	−0.799616	−	0.600512i	$-0.794963\pi$
$569$	2.86843	−	4.96826i	0.120251	−	0.208280i	0.919866	+	0.392232i	$0.128297\pi$
$570$		0			0
$571$			46.5634i			1.94862i	0.225214	+	0.974309i	$0.427692\pi$
$571$			46.5634i			1.94862i	−0.225214	+	0.974309i	$0.572308\pi$
$572$	−0.694069	+	4.29848i	−0.0290205	+	0.179728i
$573$	3.45183	−	3.45183i	0.144202	−	0.144202i
$574$	0.260227	+	0.971181i	0.0108617	+	0.0405363i
$575$		0			0
$576$	4.99463	−	2.88365i	0.208109	−	0.120152i
$577$			28.9429i			1.20491i	0.798153	+	0.602455i	$0.205811\pi$
$577$			28.9429i			1.20491i	−0.798153	+	0.602455i	$0.794189\pi$
$578$	−2.80580	−	4.85978i	−0.116706	−	0.202140i
$579$	−2.45862	+	9.17569i	−0.102177	+	0.381329i
$580$		0			0
$581$	3.93127	+	6.80916i	0.163097	+	0.282491i
$582$	−0.850351	−	3.17355i	−0.0352482	−	0.131548i
$583$	−2.08281	−	1.20251i	−0.0862613	−	0.0498030i
$584$	6.26369			0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	0.104918	−	0.994481i	$-0.466542\pi$
$587$	−17.0534	−	9.84577i	−0.703868	−	0.406379i	−0.808787	+	0.588102i	$0.799875\pi$
$588$	2.78213	+	10.3830i	0.114733	+	0.428189i
$589$	18.6524	+	32.3069i	0.768558	+	1.33118i
$590$		0			0
$591$	−3.17966	+	11.8667i	−0.130794	+	0.488129i
$592$	2.38201	+	4.12577i	0.0979001	+	0.169568i
$593$		−	21.8216i		−	0.896106i	−0.894007	−	0.448053i	$-0.852118\pi$
$593$		−	21.8216i		−	0.896106i	0.894007	−	0.448053i	$-0.147882\pi$
$594$	1.41506	−	0.816987i	0.0580607	−	0.0335214i
$595$		0			0
$596$	7.63679	+	28.5009i	0.312815	+	1.16744i
$597$	5.22002	−	5.22002i	0.213641	−	0.213641i
$598$	−2.25405	+	0.857481i	−0.0921750	+	0.0350650i
$599$			37.6041i			1.53646i	0.640172	+	0.768232i	$0.278863\pi$
$599$			37.6041i			1.53646i	−0.640172	+	0.768232i	$0.721137\pi$
$600$		0			0
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	−0.581344	−	0.813658i	$-0.697473\pi$
$601$	10.1487	−	17.5781i	0.413976	−	0.717027i	0.995320	+	0.0966302i	$0.0308064\pi$
$602$	−3.79922	−	1.01800i	−0.154845	−	0.0414905i
$603$	25.9113			1.05519
$604$	7.95310	+	2.13103i	0.323607	+	0.0867103i
$605$		0			0
$606$	−4.91641	+	4.91641i	−0.199716	+	0.199716i
$607$	−8.91757	+	33.2808i	−0.361953	+	1.35083i	0.509552	+	0.860440i	$0.329811\pi$
$607$	−8.91757	+	33.2808i	−0.361953	+	1.35083i	−0.871505	+	0.490387i	$0.836856\pi$
$608$	−26.4129	+	7.07732i	−1.07119	+	0.287023i
$609$	−31.7715	+	8.51314i	−1.28744	+	0.344970i
$610$		0			0
$611$	11.1354	−	8.03931i	0.450491	−	0.325236i
$612$	6.23794	+	6.23794i	0.252154	+	0.252154i
$613$	−12.4332	+	21.5350i	−0.502173	+	0.869790i	0.497824	+	0.867278i	$0.334133\pi$
$613$	−12.4332	+	21.5350i	−0.502173	+	0.869790i	−0.999997	+	0.00251133i	$0.999201\pi$
$614$	6.62053	+	3.82236i	0.267183	+	0.154258i
$615$		0			0
$616$	3.31563	+	3.31563i	0.133591	+	0.133591i
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.0706286	−	0.997503i	$-0.477499\pi$
$617$	24.0895	−	13.9081i	0.969805	−	0.559917i	0.899177	+	0.437585i	$0.144166\pi$
$618$	−1.80809	+	1.04390i	−0.0727321	+	0.0419919i
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	0.194705	−	0.980862i	$-0.437625\pi$
$619$	−19.5593	−	19.5593i	−0.786156	−	0.786156i	−0.980862	+	0.194705i	$0.937625\pi$
$620$		0			0
$621$	−5.64213	−	3.25749i	−0.226411	−	0.130718i
$622$	1.32099	−	2.28803i	0.0529671	−	0.0917416i
$623$	−8.77838	−	8.77838i	−0.351698	−	0.351698i
$624$	−8.22653	+	3.12952i	−0.329325	+	0.125281i
$625$		0			0
$626$	−16.4570	+	4.40965i	−0.657755	+	0.176245i
$627$	3.42148	−	0.916783i	0.136641	−	0.0366128i
$628$	−6.35012	+	23.6990i	−0.253397	+	0.945692i
$629$	−3.08139	+	3.08139i	−0.122863	+	0.122863i
$630$		0			0
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.501086	−	0.865397i	$-0.332934\pi$
$631$	12.6187	+	3.38116i	0.502341	+	0.134602i	0.00125496	+	0.999999i	$0.499601\pi$
$632$	5.79076			0.230344
$633$	−11.2855	−	3.02393i	−0.448557	−	0.120190i
$634$	−4.68840	+	8.12054i	−0.186200	+	0.322508i
$635$		0			0
$636$		−	5.77534i		−	0.229007i
$637$	2.38302	+	23.3481i	0.0944186	+	0.925086i
$638$	−2.28552	+	2.28552i	−0.0904846	+	0.0904846i
$639$	3.67067	+	13.6991i	0.145210	+	0.541929i
$640$		0			0
$641$	23.7092	−	13.6885i	0.936456	−	0.540663i	0.0476083	−	0.998866i	$-0.484840\pi$
$641$	23.7092	−	13.6885i	0.936456	−	0.540663i	0.888848	+	0.458203i	$0.151507\pi$
$642$		−	7.08428i		−	0.279594i
$643$	15.7510	+	27.2816i	0.621161	+	1.07588i	0.989270	+	0.146099i	$0.0466719\pi$
$643$	15.7510	+	27.2816i	0.621161	+	1.07588i	−0.368109	+	0.929783i	$0.619995\pi$
$644$	2.26231	−	8.44305i	0.0891475	−	0.332703i
$645$		0			0
$646$	−3.21181	−	5.56301i	−0.126367	−	0.218874i
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	0.763905	+	0.645329i	$0.223280\pi$
$647$	10.8106	+	40.3457i	0.425008	+	1.58615i	−0.338896	+	0.940824i	$0.610054\pi$
$648$	−2.92875	−	1.69092i	−0.115052	−	0.0664254i
$649$	7.15565			0.280884
$650$		0			0
$651$	23.5409			0.922641
$652$	−0.200698	−	0.115873i	−0.00785996	−	0.00453795i
$653$	3.93069	+	14.6695i	0.153820	+	0.574064i	0.999204	+	0.0399041i	$0.0127052\pi$
$653$	3.93069	+	14.6695i	0.153820	+	0.574064i	−0.845384	+	0.534160i	$0.820628\pi$
$654$	0.741918	+	1.28504i	0.0290113	+	0.0502490i
$655$		0			0
$656$	0.372117	−	1.38876i	0.0145287	−	0.0542220i
$657$	3.57167	+	6.18632i	0.139344	+	0.241351i
$658$		−	6.91493i		−	0.269572i
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.896739	−	0.442560i	$-0.854070\pi$
$659$	−24.6914	+	14.2556i	−0.961840	+	0.555319i	−0.0651015	+	0.997879i	$0.520737\pi$
$660$		0			0
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	0.926928	−	0.375240i	$-0.122440\pi$
$661$	−1.63091	−	6.08664i	−0.0634351	−	0.236743i	−0.990363	+	0.138497i	$0.955773\pi$
$662$	−2.45054	+	2.45054i	−0.0952430	+	0.0952430i
$663$	−4.71270	−	6.52766i	−0.183026	−	0.253513i
$664$			3.96845i			0.154006i
$665$		0			0
$666$	0.958840	−	1.66076i	0.0371543	−	0.0643531i
$667$	12.4483	+	3.33552i	0.482002	+	0.129152i
$668$	−37.9955			−1.47009
$669$	9.03352	+	2.42052i	0.349256	+	0.0935829i
$670$		0			0
$671$	−3.01394	+	3.01394i	−0.116352	+	0.116352i
$672$	−4.46610	+	16.6677i	−0.172283	+	0.642970i
$673$	22.1285	−	5.92931i	0.852991	−	0.228558i	0.194272	−	0.980948i	$-0.437765\pi$
$673$	22.1285	−	5.92931i	0.852991	−	0.228558i	0.658719	+	0.752389i	$0.271099\pi$
$674$	0.743468	−	0.199212i	0.0286373	−	0.00767334i
$675$		0			0
$676$	−22.3581	+	4.61199i	−0.859926	+	0.177384i
$677$	16.1247	+	16.1247i	0.619724	+	0.619724i	0.945461	−	0.325736i	$-0.105612\pi$
$677$	16.1247	+	16.1247i	0.619724	+	0.619724i	−0.325736	+	0.945461i	$0.605612\pi$
$678$	−3.84825	+	6.66536i	−0.147791	+	0.255982i
$679$	22.5163	+	12.9998i	0.864096	+	0.498886i
$680$		0			0
$681$	−9.71227	−	9.71227i	−0.372175	−	0.372175i
$682$	2.00337	−	1.15664i	0.0767129	−	0.0442902i
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.925983	−	0.377565i	$-0.876761\pi$
$683$	−27.7544	+	16.0240i	−1.06199	+	0.613142i	−0.136010	+	0.990707i	$0.543428\pi$
$684$	−14.3892	−	14.3892i	−0.550185	−	0.550185i
$685$		0			0
$686$	−0.771532	−	0.445444i	−0.0294572	−	0.0170071i
$687$	−10.3856	+	17.9883i	−0.396234	+	0.686298i
$688$	3.97707	+	3.97707i	0.151624	+	0.151624i
$689$	2.01001	−	12.4483i	0.0765753	−	0.474243i
$690$		0			0
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	−0.268929	−	0.963160i	$-0.586670\pi$
$691$	−0.532264	+	0.142620i	−0.0202483	+	0.00542551i	0.248681	+	0.968586i	$0.420003\pi$
$692$	−13.1180	+	3.51496i	−0.498672	+	0.133619i
$693$	−1.38404	+	5.16531i	−0.0525754	+	0.196214i
$694$	−9.02132	+	9.02132i	−0.342445	+	0.342445i
$695$		0			0
$696$	−16.0360	−	4.29682i	−0.607842	−	0.162871i
$697$	1.31514			0.0498144
$698$	−4.48442	−	1.20160i	−0.169738	−	0.0454811i
$699$	11.0134	−	19.0758i	0.416565	−	0.721512i
$700$		0			0
$701$		−	9.52279i		−	0.359671i	−0.983697	−	0.179835i	$-0.942443\pi$
$701$		−	9.52279i		−	0.359671i	0.983697	−	0.179835i	$-0.0575565\pi$
$702$	6.64150	+	5.41133i	0.250667	+	0.204237i
$703$	7.10792	−	7.10792i	0.268080	−	0.268080i
$704$	−0.485195	−	1.81077i	−0.0182865	−	0.0682460i
$705$		0			0
$706$	−1.39674	+	0.806411i	−0.0525672	+	0.0303497i
$707$		−	55.0209i		−	2.06927i
$708$	8.59166	+	14.8812i	0.322894	+	0.559270i
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	−0.608124	−	0.793842i	$-0.708078\pi$
$709$	8.39944	−	31.3471i	0.315448	−	1.17727i	0.923572	−	0.383425i	$-0.125255\pi$
$710$		0			0
$711$	3.30200	+	5.71923i	0.123835	+	0.214488i
$712$	−1.62175	−	6.05244i	−0.0607776	−	0.226825i
$713$	−7.98782	−	4.61177i	−0.299146	−	0.172712i
$714$	−4.05358			−0.151701
$715$		0			0
$716$	−28.7180			−1.07324
$717$	−16.8180	−	9.70986i	−0.628079	−	0.362621i
$718$	0.564197	+	2.10561i	0.0210557	+	0.0785808i
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	0.933820	−	0.357743i	$-0.116454\pi$
$719$	4.21240	+	7.29608i	0.157096	+	0.272098i	−0.776724	+	0.629841i	$0.783120\pi$
$720$		0			0
$721$	4.27612	−	15.9587i	0.159251	−	0.594333i
$722$	2.71668	+	4.70543i	0.101104	+	0.175118i
$723$			2.91423i			0.108381i
$724$	−27.4332	+	15.8385i	−1.01955	+	0.588635i
$725$		0			0
$726$	1.26548	+	4.72284i	0.0469664	+	0.175281i
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	−0.535402	−	0.844597i	$-0.679840\pi$
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	0.844597	+	0.535402i	$0.179840\pi$
$728$	−10.0669	+	22.4288i	−0.373104	+	0.831268i
$729$			9.71523i			0.359824i
$730$		0			0
$731$	−2.57239	+	4.45551i	−0.0951432	+	0.164793i
$732$	−9.88670	−	2.64913i	−0.365423	−	0.0979148i
$733$	18.6238			0.687887			0.343944	−	0.938990i	$-0.388237\pi$
$733$	18.6238			0.687887			0.343944	+	0.938990i	$0.388237\pi$
$734$	11.9696	+	3.20725i	0.441807	+	0.118382i
$735$		0			0
$736$	4.78070	−	4.78070i	0.176219	−	0.176219i
$737$	2.17988	−	8.13543i	0.0802970	−	0.299672i
$738$	−0.559023	+	0.149790i	−0.0205779	+	0.00551383i
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.791949	−	0.610587i	$-0.790934\pi$
$739$	−31.8740	+	8.54061i	−1.17250	+	0.314171i	−0.380555	+	0.924758i	$0.624267\pi$
$740$		0			0
$741$	10.8709	+	15.0575i	0.399352	+	0.553151i
$742$	−4.48920	−	4.48920i	−0.164804	−	0.164804i
$743$	18.7850	−	32.5366i	0.689155	−	1.19365i	−0.282957	−	0.959133i	$-0.591315\pi$
$743$	18.7850	−	32.5366i	0.689155	−	1.19365i	0.972112	−	0.234518i	$-0.0753512\pi$
$744$	10.2899	+	5.94088i	0.377246	+	0.217803i
$745$		0			0
$746$	−3.99061	−	3.99061i	−0.146107	−	0.146107i
$747$	−3.91943	+	2.26288i	−0.143404	+	0.0827946i
$748$	2.48333	−	1.43375i	0.0907995	−	0.0524231i
$749$	39.6410	+	39.6410i	1.44845	+	1.44845i
$750$		0			0
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.136059	−	0.990701i	$-0.543444\pi$
$751$	−29.1051	−	16.8038i	−1.06206	−	0.613181i	−0.926001	+	0.377520i	$0.876777\pi$
$752$	−4.94407	+	8.56339i	−0.180292	+	0.312275i
$753$	−19.6356	−	19.6356i	−0.715560	−	0.715560i
$754$	−15.4606	−	6.93928i	−0.563041	−	0.252714i
$755$		0			0
$756$	−29.9924	+	8.03643i	−1.09081	+	0.292282i
$757$	−15.5871	+	4.17654i	−0.566521	+	0.151799i	−0.530701	−	0.847559i	$-0.678071\pi$
$757$	−15.5871	+	4.17654i	−0.566521	+	0.151799i	−0.0358205	+	0.999358i	$0.511404\pi$
$758$	−0.256883	+	0.958699i	−0.00933040	+	0.0348215i
$759$	−0.619282	+	0.619282i	−0.0224785	+	0.0224785i
$760$		0			0
$761$	−15.1340	−	4.05514i	−0.548606	−	0.146999i	−0.0261397	−	0.999658i	$-0.508321\pi$
$761$	−15.1340	−	4.05514i	−0.548606	−	0.146999i	−0.522467	+	0.852660i	$0.674988\pi$
$762$	−3.85490			−0.139648
$763$	−11.3421	−	3.03911i	−0.410612	−	0.110023i
$764$	−4.55789	+	7.89449i	−0.164899	+	0.285613i
$765$		0			0
$766$		−	13.0645i		−	0.472039i
$767$	13.3395	+	35.0655i	0.481662	+	1.26614i
$768$	−0.0960396	+	0.0960396i	−0.00346553	+	0.00346553i
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	0.933522	+	0.358521i	$0.116719\pi$
$769$	8.43930	+	31.4959i	0.304329	+	1.13577i	−0.629193	+	0.777249i	$0.716614\pi$
$770$		0			0
$771$	−5.83532	+	3.36902i	−0.210154	+	0.121332i
$772$		−	17.7388i		−	0.638433i
$773$	11.9531	+	20.7033i	0.429921	+	0.744646i	0.996866	−	0.0791103i	$-0.0252079\pi$
$773$	11.9531	+	20.7033i	0.429921	+	0.744646i	−0.566944	+	0.823756i	$0.691875\pi$
$774$	0.585972	−	2.18688i	0.0210623	−	0.0786056i
$775$		0			0
$776$	6.56136	+	11.3646i	0.235539	+	0.407966i
$777$	−1.64177	−	6.12718i	−0.0588983	−	0.219811i
$778$	−0.278066	−	0.160541i	−0.00996914	−	0.00575569i
$779$	−3.03366			−0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$	1.37545	+	0.794114i	0.0491858	+	0.0283975i
$783$	−11.8488	−	44.2204i	−0.423443	−	1.58031i
$784$	−8.44858	−	14.6334i	−0.301735	−	0.522620i
$785$		0			0
$786$	−0.165181	+	0.616466i	−0.00589183	+	0.0219886i
$787$	7.85572	+	13.6065i	0.280026	+	0.485020i	0.971391	−	0.237486i	$-0.0763235\pi$
$787$	7.85572	+	13.6065i	0.280026	+	0.485020i	−0.691365	+	0.722506i	$0.742990\pi$
$788$		−	22.9411i		−	0.817242i
$789$	−10.9664	+	6.33143i	−0.390412	+	0.225405i
$790$		0			0
$791$	−15.7635	−	58.8303i	−0.560487	−	2.09176i
$792$	−1.90851	+	1.90851i	−0.0678161	+	0.0678161i
$793$	−20.3880	−	9.15090i	−0.724000	−	0.324958i
$794$		−	13.3394i		−	0.473397i
$795$		0			0
$796$	−6.89264	+	11.9384i	−0.244303	+	0.423146i
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.749900	−	0.661552i	$-0.230102\pi$
$797$	30.1666	+	8.08312i	1.06856	+	0.286319i	0.318656	+	0.947870i	$0.396768\pi$
$798$	9.35048			0.331003
$799$	−8.73669	−	2.34099i	−0.309082	−	0.0828183i
$800$		0			0
$801$	5.05293	−	5.05293i	0.178537	−	0.178537i
$802$	0.633871	−	2.36564i	0.0223827	−	0.0835336i
$803$	2.24281	−	0.600960i	0.0791471	−	0.0212074i
$804$	19.5361	−	5.23469i	0.688986	−	0.184613i
$805$		0			0
$806$	9.40267	+	7.66106i	0.331195	+	0.269849i
$807$	−5.38868	−	5.38868i	−0.189690	−	0.189690i
$808$	13.8853	−	24.0500i	0.488483	−	0.846078i
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	0.687658	−	0.726035i	$-0.258639\pi$
$809$	11.4546	+	6.61331i	0.402722	+	0.232512i	−0.284936	+	0.958547i	$0.591972\pi$
$810$		0			0
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	0.978995	−	0.203886i	$-0.0653572\pi$
$811$	22.0736	+	22.0736i	0.775109	+	0.775109i	−0.203886	+	0.978995i	$0.565357\pi$
$812$	53.1928	−	30.7109i	1.86670	−	1.07774i
$813$	7.48978	−	4.32423i	0.262678	−	0.151657i
$814$	−0.440767	−	0.440767i	−0.0154489	−	0.0154489i
$815$		0			0
$816$	5.01991	+	2.89825i	0.175732	+	0.101459i
$817$	5.93379	−	10.2776i	0.207597	−	0.359568i
$818$	2.11139	+	2.11139i	0.0738230	+	0.0738230i
$819$	−27.8921	+	2.84680i	−0.974630	+	0.0994754i
$820$		0			0
$821$	−8.74860	+	2.34418i	−0.305328	+	0.0818124i	−0.408230	−	0.912879i	$-0.633854\pi$
$821$	−8.74860	+	2.34418i	−0.305328	+	0.0818124i	0.102902	+	0.994692i	$0.467187\pi$
$822$	−5.53062	+	1.48192i	−0.192902	+	0.0516881i
$823$	−10.8551	+	40.5117i	−0.378384	+	1.41215i	0.469953	+	0.882691i	$0.344271\pi$
$823$	−10.8551	+	40.5117i	−0.378384	+	1.41215i	−0.848337	+	0.529457i	$0.822396\pi$
$824$	5.89653	−	5.89653i	0.205415	−	0.205415i
$825$		0			0
$826$	18.2455	+	4.88888i	0.634844	+	0.170106i
$827$	−38.2009			−1.32838			−0.664188	−	0.747566i	$-0.731222\pi$
$827$	−38.2009			−1.32838			−0.664188	+	0.747566i	$0.731222\pi$
$828$	4.85992	+	1.30221i	0.168894	+	0.0452550i
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	0.490255	+	0.871579i	$0.336904\pi$
$829$	−14.6750	+	25.4178i	−0.509682	+	0.882796i	−0.999937	+	0.0112165i	$0.996430\pi$
$830$		0			0
$831$		−	24.3043i		−	0.843106i
$832$	7.96898	−	5.75327i	0.276275	−	0.199459i
$833$	10.9292	−	10.9292i	0.378673	−	0.378673i
$834$	0.769545	+	2.87198i	0.0266471	+	0.0994485i
$835$		0			0
$836$	−5.72835	+	3.30726i	−0.198119	+	0.114384i
$837$			32.7649i			1.13252i
$838$	1.32629	+	2.29721i	0.0458161	+	0.0793557i
$839$	9.11914	−	34.0331i	0.314828	−	1.17495i	−0.609322	−	0.792923i	$-0.708558\pi$
$839$	9.11914	−	34.0331i	0.314828	−	1.17495i	0.924150	−	0.382030i	$-0.124775\pi$
$840$		0			0
$841$	30.7798	+	53.3122i	1.06137	+	1.83835i
$842$	2.55582	+	9.53846i	0.0880795	+	0.328717i
$843$	6.24163	+	3.60361i	0.214973	+	0.124115i
$844$	21.8175			0.750988
$845$		0			0
$846$	3.98031			0.136846
$847$	−33.5084	−	19.3461i	−1.15136	−	0.664740i
$848$	2.34967	+	8.76909i	0.0806880	+	0.301132i
$849$	−4.13097	−	7.15504i	−0.141774	−	0.245560i
$850$		0			0
$851$	−0.643261	+	2.40068i	−0.0220507	+	0.0822944i
$852$	5.53509	+	9.58705i	0.189629	+	0.328447i
$853$			17.6392i			0.603954i	0.953315	+	0.301977i	$0.0976465\pi$
$853$			17.6392i			0.603954i	−0.953315	+	0.301977i	$0.902353\pi$
$854$	−9.74415	+	5.62579i	−0.333438	+	0.192511i
$855$		0			0
$856$	7.32342	+	27.3314i	0.250309	+	0.934167i
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	−0.806535	−	0.591186i	$-0.798660\pi$
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	0.591186	+	0.806535i	$0.298660\pi$
$858$	0.933725	−	0.674110i	0.0318768	−	0.0230137i
$859$			29.2307i			0.997338i	0.866793	+	0.498669i	$0.166178\pi$
$859$			29.2307i			0.997338i	−0.866793	+	0.498669i	$0.833822\pi$
$860$		0			0
$861$	−0.957186	+	1.65789i	−0.0326208	+	0.0565009i
$862$	7.96263	+	2.13358i	0.271208	+	0.0726701i
$863$	15.7688			0.536775			0.268387	−	0.963311i	$-0.413509\pi$
$863$	15.7688			0.536775			0.268387	+	0.963311i	$0.413509\pi$
$864$	−23.1986	−	6.21604i	−0.789232	−	0.211474i
$865$		0			0
$866$	2.65202	−	2.65202i	0.0901192	−	0.0901192i
$867$	2.76537	−	10.3205i	0.0939168	−	0.350502i
$868$	−42.4615	+	11.3775i	−1.44124	+	0.386179i
$869$	2.07347	−	0.555585i	0.0703377	−	0.0188469i
$870$		0			0
$871$	43.9305	−	4.48375i	1.48853	−	0.151926i
$872$	−4.19076	−	4.19076i	−0.141917	−	0.141917i
$873$	−7.48283	+	12.9606i	−0.253255	+	0.438651i
$874$	−3.17277	−	1.83180i	−0.107321	−	0.0619616i
$875$		0			0
$876$	3.94269	+	3.94269i	0.133211	+	0.133211i
$877$	38.7309	−	22.3613i	1.30785	−	0.755088i	0.326114	−	0.945331i	$-0.394261\pi$
$877$	38.7309	−	22.3613i	1.30785	−	0.755088i	0.981737	+	0.190242i	$0.0609274\pi$
$878$	5.85595	−	3.38094i	0.197629	−	0.114101i
$879$	−8.80139	−	8.80139i	−0.296863	−	0.296863i
$880$		0			0
$881$	−18.0323	−	10.4110i	−0.607525	−	0.350755i	0.164471	−	0.986382i	$-0.447408\pi$
$881$	−18.0323	−	10.4110i	−0.607525	−	0.350755i	−0.771996	+	0.635627i	$0.780742\pi$
$882$	−3.40084	+	5.89043i	−0.114512	+	0.198341i
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	0.611570	−	0.791190i	$-0.290538\pi$
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	−0.791190	+	0.611570i	$0.790538\pi$
$884$	11.6553	+	9.49648i	0.392011	+	0.319401i
$885$		0			0
$886$	−4.36041	+	1.16837i	−0.146491	+	0.0392521i
$887$	−25.8911	+	6.93749i	−0.869337	+	0.232938i	−0.665801	−	0.746129i	$-0.731910\pi$
$887$	−25.8911	+	6.93749i	−0.869337	+	0.232938i	−0.203536	+	0.979067i	$0.565243\pi$
$888$	0.828649	−	3.09256i	0.0278077	−	0.103780i
$889$	21.5706	−	21.5706i	0.723454	−	0.723454i
$890$		0			0
$891$	−1.21092	−	0.324464i	−0.0405673	−	0.0108700i
$892$	−17.4639			−0.584736
$893$	20.1531	+	5.40002i	0.674399	+	0.180705i
$894$	3.90208	−	6.75861i	0.130505	−	0.226042i
$895$		0			0
$896$		−	41.6474i		−	1.39134i
$897$	−4.18918	−	1.88026i	−0.139873	−	0.0627800i
$898$	−8.97946	+	8.97946i	−0.299648	+	0.299648i
$899$	−16.7749	−	62.6048i	−0.559475	−	2.08799i
$900$		0			0
$901$	−7.19167	+	4.15211i	−0.239589	+	0.138327i
$902$			0.188119i			0.00626368i
$903$	−3.74447	−	6.48562i	−0.124608	−	0.215828i
$904$	7.95630	−	29.6933i	0.264623	−	0.987585i
$905$		0			0
$906$	−1.08887	−	1.88597i	−0.0361752	−	0.0626572i
$907$	−10.4931	−	39.1608i	−0.348418	−	1.30031i	−0.888568	−	0.458744i	$-0.848299\pi$
$907$	−10.4931	−	39.1608i	−0.348418	−	1.30031i	0.540151	−	0.841568i	$-0.318367\pi$
$908$	22.2124	+	12.8243i	0.737144	+	0.425590i
$909$	31.6707			1.05045
$910$		0			0
$911$	8.00072			0.265076			0.132538	−	0.991178i	$-0.457687\pi$
$911$	8.00072			0.265076			0.132538	+	0.991178i	$0.457687\pi$
$912$	−11.5796	−	6.68546i	−0.383437	−	0.221378i
$913$	0.380746	+	1.42096i	0.0126009	+	0.0470271i
$914$	0.204360	+	0.353962i	0.00675963	+	0.0117080i
$915$		0			0
$916$	10.0389	−	37.4656i	0.331694	−	1.23790i
$917$	−2.52522	−	4.37381i	−0.0833901	−	0.144436i
$918$		−	5.64189i		−	0.186210i
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	−0.530079	−	0.847948i	$-0.677838\pi$
$919$	−1.84237	+	1.06369i	−0.0607741	+	0.0350879i	0.469305	+	0.883036i	$0.344504\pi$
$920$		0			0
$921$	3.76728	+	14.0597i	0.124136	+	0.463283i
$922$	8.40950	−	8.40950i	0.276952	−	0.276952i
$923$	8.59384	+	22.5905i	0.282870	+	0.743577i
$924$			4.17405i			0.137316i
$925$		0			0
$926$	−1.56954	+	2.71852i	−0.0515782	+	0.0893360i
$927$	9.18601	+	2.46138i	0.301708	+	0.0808425i
$928$	47.5087			1.55955
$929$	19.2515	+	5.15841i	0.631620	+	0.169242i	0.560405	−	0.828219i	$-0.310646\pi$
$929$	19.2515	+	5.15841i	0.631620	+	0.169242i	0.0712153	+	0.997461i	$0.477312\pi$
$930$		0			0
$931$	−25.2106	+	25.2106i	−0.826243	+	0.826243i
$932$	−10.6458	+	39.7305i	−0.348713	+	1.30142i
$933$	4.85898	−	1.30196i	0.159076	−	0.0426242i
$934$	10.5382	−	2.82369i	0.344819	−	0.0923940i
$935$		0			0
$936$	−12.9103	−	5.79462i	−0.421986	−	0.189403i
$937$	−17.2774	−	17.2774i	−0.564427	−	0.564427i	0.366135	−	0.930562i	$-0.380681\pi$
$937$	−17.2774	−	17.2774i	−0.564427	−	0.564427i	−0.930562	+	0.366135i	$0.880681\pi$
$938$	11.1166	−	19.2545i	0.362969	−	0.628680i
$939$	−28.0937	−	16.2199i	−0.916802	−	0.529316i
$940$		0			0
$941$	24.2129	+	24.2129i	0.789319	+	0.789319i	0.981383	−	0.192063i	$-0.0615179\pi$
$941$	24.2129	+	24.2129i	0.789319	+	0.789319i	−0.192063	+	0.981383i	$0.561518\pi$
$942$	5.61989	−	3.24465i	0.183106	−	0.105716i
$943$	0.649578	−	0.375034i	0.0211532	−	0.0122128i
$944$	−19.0996	−	19.0996i	−0.621640	−	0.621640i
$945$		0			0
$946$	−0.637321	−	0.367957i	−0.0207211	−	0.0119633i
$947$	−4.15045	+	7.18880i	−0.134872	+	0.233605i	−0.925548	−	0.378629i	$-0.876396\pi$
$947$	−4.15045	+	7.18880i	−0.134872	+	0.233605i	0.790677	+	0.612234i	$0.209729\pi$
$948$	3.64500	+	3.64500i	0.118384	+	0.118384i
$949$	7.12597	+	9.87034i	0.231319	+	0.320405i
$950$		0			0
$951$	−17.2452	+	4.62084i	−0.559214	+	0.149841i
$952$	15.6388	−	4.19041i	0.506857	−	0.135812i
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	−0.983081	−	0.183173i	$-0.941363\pi$
$953$	−1.23858	+	4.62244i	−0.0401215	+	0.149736i	0.942959	+	0.332908i	$0.108030\pi$
$954$	2.58403	−	2.58403i	0.0836611	−	0.0836611i
$955$		0			0
$956$	35.0280	+	9.38573i	1.13289	+	0.303556i
$957$	−6.15418			−0.198936
$958$	4.51481	+	1.20974i	0.145867	+	0.0390849i
$959$	22.6550	−	39.2396i	0.731568	−	1.26711i
$960$		0			0
$961$			15.3867i			0.496346i
$962$	1.33825	−	2.98160i	0.0431470	−	0.0961306i
$963$	−22.8178	+	22.8178i	−0.735294	+	0.735294i
$964$	−1.40848	−	5.25650i	−0.0453639	−	0.169301i
$965$		0			0
$966$	−2.00216	+	1.15595i	−0.0644183	+	0.0371919i
$967$		−	8.78782i		−	0.282597i	−0.989967	−	0.141299i	$-0.954872\pi$
$967$		−	8.78782i		−	0.282597i	0.989967	−	0.141299i	$-0.0451278\pi$
$968$	−9.76453	−	16.9127i	−0.313844	−	0.543594i
$969$	3.16552	−	11.8139i	0.101691	−	0.379517i
$970$		0			0
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	0.906323	−	0.422587i	$-0.138878\pi$
$971$	2.71693	+	4.70586i	0.0871905	+	0.151018i	−0.819132	+	0.573605i	$0.805544\pi$
$972$	−7.33863	−	27.3881i	−0.235387	−	0.878475i
$973$	−20.3766	−	11.7645i	−0.653245	−	0.377151i
$974$	−3.04192			−0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	0.218499	−	0.975837i	$-0.429884\pi$
$977$	−16.1709	−	9.33626i	−0.517352	−	0.298693i	−0.735851	+	0.677144i	$0.763217\pi$
$978$	0.0158643	+	0.0592064i	0.000507285	+	0.00189321i
$979$	−1.16138	−	2.01158i	−0.0371180	−	0.0642903i
$980$		0			0
$981$	1.74935	−	6.52865i	0.0558524	−	0.208444i
$982$	3.65824	+	6.33626i	0.116739	+	0.202198i
$983$			6.62470i			0.211295i	0.994404	+	0.105648i	$0.0336915\pi$
$983$			6.62470i			0.211295i	−0.994404	+	0.105648i	$0.966308\pi$
$984$	−0.836786	+	0.483119i	−0.0266758	+	0.0154013i
$985$		0			0
$986$	2.88852	+	10.7801i	0.0919893	+	0.343309i
$987$	9.30986	−	9.30986i	0.296336	−	0.296336i
$988$	−26.8856	−	21.9057i	−0.855346	−	0.696915i
$989$			2.93424i			0.0933033i
$990$		0			0
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	−0.286362	−	0.958121i	$-0.592446\pi$
$991$	21.6135	−	37.4357i	0.686576	−	1.18919i	0.972939	−	0.231064i	$-0.0742206\pi$
$992$	−32.8433	−	8.80033i	−1.04277	−	0.279411i
$993$	−6.59853			−0.209398
$994$	11.7545	+	3.14961i	0.372830	+	0.0998995i
$995$		0			0
$996$	−2.49794	+	2.49794i	−0.0791504	+	0.0791504i
$997$	−11.7001	+	43.6654i	−0.370547	+	1.38290i	0.489197	+	0.872173i	$0.337290\pi$
$997$	−11.7001	+	43.6654i	−0.370547	+	1.38290i	−0.859744	+	0.510725i	$0.829377\pi$
$998$	14.2040	−	3.80596i	0.449621	−	0.120476i
$999$	8.52799	−	2.28507i	0.269814	−	0.0722963i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.x.b.7.3		20
5.2	odd	4		65.2.o.a.33.3	yes	20
5.3	odd	4		325.2.s.b.293.3		20
5.4	even	2		65.2.t.a.7.3	yes	20
13.2	odd	12		325.2.s.b.132.3		20
15.2	even	4		585.2.cf.a.163.3		20
15.14	odd	2		585.2.dp.a.397.3		20
65.2	even	12		65.2.t.a.28.3	yes	20
65.4	even	6		845.2.f.d.437.5		20
65.7	even	12		845.2.f.d.408.6		20
65.9	even	6		845.2.f.e.437.6		20
65.12	odd	4		845.2.o.g.488.3		20
65.17	odd	12		845.2.k.d.268.5		20
65.19	odd	12		845.2.k.e.577.6		20
65.22	odd	12		845.2.k.e.268.6		20
65.24	odd	12		845.2.o.g.587.3		20
65.28	even	12	inner	325.2.x.b.93.3		20
65.29	even	6		845.2.t.f.427.3		20
65.32	even	12		845.2.f.e.408.5		20
65.34	odd	4		845.2.o.f.357.3		20
65.37	even	12		845.2.t.g.418.3		20
65.42	odd	12		845.2.o.e.258.3		20
65.44	odd	4		845.2.o.e.357.3		20
65.47	even	4		845.2.t.e.188.3		20
65.49	even	6		845.2.t.e.427.3		20
65.54	odd	12		65.2.o.a.2.3	✓	20
65.57	even	4		845.2.t.f.188.3		20
65.59	odd	12		845.2.k.d.577.5		20
65.62	odd	12		845.2.o.f.258.3		20
65.64	even	2		845.2.t.g.657.3		20
195.2	odd	12		585.2.dp.a.28.3		20
195.119	even	12		585.2.cf.a.262.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	65.54	odd	12
65.2.o.a.33.3	yes	20	5.2	odd	4
65.2.t.a.7.3	yes	20	5.4	even	2
65.2.t.a.28.3	yes	20	65.2	even	12
325.2.s.b.132.3		20	13.2	odd	12
325.2.s.b.293.3		20	5.3	odd	4
325.2.x.b.7.3		20	1.1	even	1	trivial
325.2.x.b.93.3		20	65.28	even	12	inner
585.2.cf.a.163.3		20	15.2	even	4
585.2.cf.a.262.3		20	195.119	even	12
585.2.dp.a.28.3		20	195.2	odd	12
585.2.dp.a.397.3		20	15.14	odd	2
845.2.f.d.408.6		20	65.7	even	12
845.2.f.d.437.5		20	65.4	even	6
845.2.f.e.408.5		20	65.32	even	12
845.2.f.e.437.6		20	65.9	even	6
845.2.k.d.268.5		20	65.17	odd	12
845.2.k.d.577.5		20	65.59	odd	12
845.2.k.e.268.6		20	65.22	odd	12
845.2.k.e.577.6		20	65.19	odd	12
845.2.o.e.258.3		20	65.42	odd	12
845.2.o.e.357.3		20	65.44	odd	4
845.2.o.f.258.3		20	65.62	odd	12
845.2.o.f.357.3		20	65.34	odd	4
845.2.o.g.488.3		20	65.12	odd	4
845.2.o.g.587.3		20	65.24	odd	12
845.2.t.e.188.3		20	65.47	even	4
845.2.t.e.427.3		20	65.49	even	6
845.2.t.f.188.3		20	65.57	even	4
845.2.t.f.427.3		20	65.29	even	6
845.2.t.g.418.3		20	65.37	even	12
845.2.t.g.657.3		20	65.64	even	2

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	325.2.x.b.7.3

Level	$325$
Weight	$2$
Character	325.7
Analytic conductor	$2.595$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$