LMFDB - Embedded newform 961.2.d.j.628.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [961,2,Mod(374,961)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(961, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("961.374");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.64000000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 4x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 4x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.1
Root			$1.14412 - 0.831254i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.j.531.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 2.48990i) q^{2} +(-0.270091 - 0.831254i) q^{3} +(-3.92705 - 2.85317i) q^{4} +2.23607 q^{5} -2.28825 q^{6} +(0.809017 + 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(1.80902 - 1.31433i) q^{9} +(1.80902 - 5.56758i) q^{10} +(-3.43237 - 2.49376i) q^{11} +(-1.31105 + 4.03499i) q^{12} +(-0.810272 - 2.49376i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.603941 - 1.85874i) q^{15} +(3.04508 + 9.37181i) q^{16} +(-2.99535 + 2.17625i) q^{17} +(-1.80902 - 5.56758i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-8.78115 - 6.37988i) q^{20} +(0.270091 - 0.831254i) q^{21} +(-8.98606 + 6.52875i) q^{22} +(2.12132 - 1.54123i) q^{23} +(5.28360 + 3.83876i) q^{24} -6.86474 q^{26} +(-3.70246 - 2.68999i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-0.166925 + 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 + 3.52671i) q^{33} +(2.99535 + 9.21875i) q^{34} +(1.80902 + 1.31433i) q^{35} -10.8541 q^{36} +4.24264 q^{37} +(-2.11803 - 1.53884i) q^{38} +(-1.85410 + 1.34708i) q^{39} +(-13.5172 + 9.82084i) q^{40} +(-0.454915 + 1.40008i) q^{41} +(-1.85123 - 1.34500i) q^{42} +(-2.99535 + 9.21875i) q^{43} +(6.36396 + 19.5863i) q^{44} +(4.04508 - 2.93893i) q^{45} +(-2.12132 - 6.52875i) q^{46} +(-3.00000 - 9.23305i) q^{47} +(6.96790 - 5.06248i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(2.61803 + 1.90211i) q^{51} +(-3.93314 + 12.1050i) q^{52} +(11.1074 - 8.06998i) q^{53} +(-9.69316 + 7.04250i) q^{54} +(-7.67501 - 5.57622i) q^{55} -7.47214 q^{56} -0.874032 q^{57} +(1.14412 + 0.831254i) q^{58} +(3.69098 + 11.3597i) q^{59} +(-2.93159 + 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 - 8.28199i) q^{64} +(-1.81182 - 5.57622i) q^{65} +(7.85410 + 5.70634i) q^{66} +6.00000 q^{67} +17.9721 q^{68} +(-1.85410 - 1.34708i) q^{69} +(4.73607 - 3.44095i) q^{70} +(1.19098 - 0.865300i) q^{71} +(-5.16312 + 15.8904i) q^{72} +(-3.43237 - 2.49376i) q^{73} +(3.43237 - 10.5637i) q^{74} +(-3.92705 + 2.85317i) q^{76} +(-1.31105 - 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(1.31105 - 0.952532i) q^{79} +(6.80902 + 20.9560i) q^{80} +(0.836881 - 2.57565i) q^{81} +(3.11803 + 2.26538i) q^{82} +(-0.977198 + 3.00750i) q^{83} +(-3.43237 + 2.49376i) q^{84} +(-6.69781 + 4.86624i) q^{85} +(20.5305 + 14.9162i) q^{86} +0.472136 q^{87} +31.7016 q^{88} +(12.4184 + 9.02251i) q^{89} +(-4.04508 - 12.4495i) q^{90} +(0.810272 - 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 - 2.12663i) q^{95} +(-2.93159 - 9.02251i) q^{96} +(5.66312 + 4.11450i) q^{97} -15.7082 q^{98} -9.48683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 18 q^{4} + 2 q^{7} - 26 q^{8} + 10 q^{9} + 10 q^{10} + 8 q^{14} + 2 q^{16} - 10 q^{18} - 2 q^{19} - 30 q^{20} - 12 q^{28} + 60 q^{32} - 36 q^{33} + 10 q^{35} - 60 q^{36} - 8 q^{38} + 12 q^{39}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 18 * q^4 + 2 * q^7 - 26 * q^8 + 10 * q^9 + 10 * q^10 + 8 * q^14 + 2 * q^16 - 10 * q^18 - 2 * q^19 - 30 * q^20 - 12 * q^28 + 60 * q^32 - 36 * q^33 + 10 * q^35 - 60 * q^36 - 8 * q^38 + 12 * q^39 - 50 * q^40 - 26 * q^41 + 10 * q^45 - 24 * q^47 + 12 * q^49 + 12 * q^51 - 24 * q^56 + 34 * q^59 + 26 * q^64 + 36 * q^66 + 48 * q^67 + 12 * q^69 + 20 * q^70 + 14 * q^71 - 10 * q^72 - 18 * q^76 - 12 * q^78 + 50 * q^80 + 38 * q^81 + 16 * q^82 - 32 * q^87 - 10 * q^90 - 96 * q^94 + 10 * q^95 + 14 * q^97 - 72 * q^98

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.809017	−	2.48990i	0.572061	−	1.76062i	−0.0739128	−	0.997265i	$-0.523549\pi$
$2$	0.809017	−	2.48990i	0.572061	−	1.76062i	0.645974	−	0.763359i	$-0.276451\pi$
$3$	−0.270091	−	0.831254i	−0.155937	−	0.479925i	0.842318	−	0.538981i	$-0.181191\pi$
$3$	−0.270091	−	0.831254i	−0.155937	−	0.479925i	−0.998255	+	0.0590568i	$0.981191\pi$
$4$	−3.92705	−	2.85317i	−1.96353	−	1.42658i
$5$	2.23607			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$5$	2.23607			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$6$	−2.28825			−0.934172
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	0.730084	−	0.683358i	$-0.239481\pi$
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	−0.424304	+	0.905520i	$0.639481\pi$
$8$	−6.04508	+	4.39201i	−2.13726	+	1.55281i
$9$	1.80902	−	1.31433i	0.603006	−	0.438109i
$10$	1.80902	−	5.56758i	0.572061	−	1.76062i
$11$	−3.43237	−	2.49376i	−1.03490	−	0.751897i	−0.0656149	−	0.997845i	$-0.520901\pi$
$11$	−3.43237	−	2.49376i	−1.03490	−	0.751897i	−0.969283	+	0.245948i	$0.920901\pi$
$12$	−1.31105	+	4.03499i	−0.378467	+	1.16480i
$13$	−0.810272	−	2.49376i	−0.224729	−	0.691645i	−0.998319	−	0.0579585i	$-0.981541\pi$
$13$	−0.810272	−	2.49376i	−0.224729	−	0.691645i	0.773590	−	0.633687i	$-0.218459\pi$
$14$	2.11803	−	1.53884i	0.566068	−	0.411273i
$15$	−0.603941	−	1.85874i	−0.155937	−	0.479925i
$16$	3.04508	+	9.37181i	0.761271	+	2.34295i
$17$	−2.99535	+	2.17625i	−0.726480	+	0.527818i	−0.888448	−	0.458978i	$-0.848216\pi$
$17$	−2.99535	+	2.17625i	−0.726480	+	0.527818i	0.161968	+	0.986796i	$0.448216\pi$
$18$	−1.80902	−	5.56758i	−0.426389	−	1.31229i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	−0.909332	−	0.416071i	$-0.863407\pi$
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	0.980226	+	0.197884i	$0.0634068\pi$
$20$	−8.78115	−	6.37988i	−1.96353	−	1.42658i
$21$	0.270091	−	0.831254i	0.0589386	−	0.181394i
$22$	−8.98606	+	6.52875i	−1.91583	+	1.39193i
$23$	2.12132	−	1.54123i	0.442326	−	0.321369i	−0.344233	−	0.938884i	$-0.611861\pi$
$23$	2.12132	−	1.54123i	0.442326	−	0.321369i	0.786558	+	0.617516i	$0.211861\pi$
$24$	5.28360	+	3.83876i	1.07851	+	0.783583i
$25$		0			0
$26$	−6.86474			−1.34629
$27$	−3.70246	−	2.68999i	−0.712539	−	0.517690i
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	−0.166925	+	0.513743i	−0.0309972	+	0.0953997i	−0.965358	−	0.260928i	$-0.915971\pi$
$29$	−0.166925	+	0.513743i	−0.0309972	+	0.0953997i	0.934361	+	0.356328i	$0.115971\pi$
$30$	−5.11667			−0.934172
$31$		0			0
$31$		0			0
$32$	10.8541			1.91875
$33$	−1.14590	+	3.52671i	−0.199475	+	0.613922i
$34$	2.99535	+	9.21875i	0.513699	+	1.58100i
$35$	1.80902	+	1.31433i	0.305780	+	0.222162i
$36$	−10.8541			−1.80902
$37$	4.24264			0.697486			0.348743	−	0.937218i	$-0.386609\pi$
$37$	4.24264			0.697486			0.348743	+	0.937218i	$0.386609\pi$
$38$	−2.11803	−	1.53884i	−0.343590	−	0.249633i
$39$	−1.85410	+	1.34708i	−0.296894	+	0.215706i
$40$	−13.5172	+	9.82084i	−2.13726	+	1.55281i
$41$	−0.454915	+	1.40008i	−0.0710458	+	0.218656i	−0.980275	−	0.197640i	$-0.936672\pi$
$41$	−0.454915	+	1.40008i	−0.0710458	+	0.218656i	0.909229	+	0.416297i	$0.136672\pi$
$42$	−1.85123	−	1.34500i	−0.285651	−	0.207538i
$43$	−2.99535	+	9.21875i	−0.456787	+	1.40585i	0.412237	+	0.911076i	$0.364747\pi$
$43$	−2.99535	+	9.21875i	−0.456787	+	1.40585i	−0.869024	+	0.494769i	$0.835253\pi$
$44$	6.36396	+	19.5863i	0.959403	+	2.95274i
$45$	4.04508	−	2.93893i	0.603006	−	0.438109i
$46$	−2.12132	−	6.52875i	−0.312772	−	0.962612i
$47$	−3.00000	−	9.23305i	−0.437595	−	1.34678i	−0.890404	−	0.455171i	$-0.849578\pi$
$47$	−3.00000	−	9.23305i	−0.437595	−	1.34678i	0.452809	−	0.891608i	$-0.350422\pi$
$48$	6.96790	−	5.06248i	1.00573	−	0.730706i
$49$	−1.85410	−	5.70634i	−0.264872	−	0.815191i
$50$		0			0
$51$	2.61803	+	1.90211i	0.366598	+	0.266349i
$52$	−3.93314	+	12.1050i	−0.545429	+	1.67866i
$53$	11.1074	−	8.06998i	1.52572	−	1.10850i	0.567154	−	0.823612i	$-0.308044\pi$
$53$	11.1074	−	8.06998i	1.52572	−	1.10850i	0.958562	−	0.284886i	$-0.0919556\pi$
$54$	−9.69316	+	7.04250i	−1.31907	+	0.958362i
$55$	−7.67501	−	5.57622i	−1.03490	−	0.751897i
$56$	−7.47214			−0.998506
$57$	−0.874032			−0.115768
$58$	1.14412	+	0.831254i	0.150231	+	0.109149i
$59$	3.69098	+	11.3597i	0.480525	+	1.47890i	0.838359	+	0.545119i	$0.183515\pi$
$59$	3.69098	+	11.3597i	0.480525	+	1.47890i	−0.357834	+	0.933785i	$0.616485\pi$
$60$	−2.93159	+	9.02251i	−0.378467	+	1.16480i
$61$	13.9358			1.78430			0.892148	−	0.451742i	$-0.149197\pi$
$61$	13.9358			1.78430			0.892148	+	0.451742i	$0.149197\pi$
$62$		0			0
$63$	2.23607			0.281718
$64$	2.69098	−	8.28199i	0.336373	−	1.03525i
$65$	−1.81182	−	5.57622i	−0.224729	−	0.691645i
$66$	7.85410	+	5.70634i	0.966773	+	0.702402i
$67$	6.00000			0.733017			0.366508	−	0.930415i	$-0.380553\pi$
$67$	6.00000			0.733017			0.366508	+	0.930415i	$0.380553\pi$
$68$	17.9721			2.17944
$69$	−1.85410	−	1.34708i	−0.223208	−	0.162170i
$70$	4.73607	−	3.44095i	0.566068	−	0.411273i
$71$	1.19098	−	0.865300i	0.141344	−	0.102692i	−0.514866	−	0.857270i	$-0.672158\pi$
$71$	1.19098	−	0.865300i	0.141344	−	0.102692i	0.656210	+	0.754578i	$0.272158\pi$
$72$	−5.16312	+	15.8904i	−0.608479	+	1.87271i
$73$	−3.43237	−	2.49376i	−0.401728	−	0.291873i	0.368516	−	0.929621i	$-0.379866\pi$
$73$	−3.43237	−	2.49376i	−0.401728	−	0.291873i	−0.770245	+	0.637749i	$0.779866\pi$
$74$	3.43237	−	10.5637i	0.399005	−	1.22801i
$75$		0			0
$76$	−3.92705	+	2.85317i	−0.450464	+	0.327281i
$77$	−1.31105	−	4.03499i	−0.149408	−	0.459830i
$78$	1.85410	+	5.70634i	0.209936	+	0.646116i
$79$	1.31105	−	0.952532i	0.147504	−	0.107168i	−0.511586	−	0.859232i	$-0.670942\pi$
$79$	1.31105	−	0.952532i	0.147504	−	0.107168i	0.659090	+	0.752064i	$0.270942\pi$
$80$	6.80902	+	20.9560i	0.761271	+	2.34295i
$81$	0.836881	−	2.57565i	0.0929868	−	0.286184i
$82$	3.11803	+	2.26538i	0.344329	+	0.250170i
$83$	−0.977198	+	3.00750i	−0.107261	+	0.330117i	−0.990255	−	0.139269i	$-0.955525\pi$
$83$	−0.977198	+	3.00750i	−0.107261	+	0.330117i	0.882993	+	0.469386i	$0.155525\pi$
$84$	−3.43237	+	2.49376i	−0.374502	+	0.272092i
$85$	−6.69781	+	4.86624i	−0.726480	+	0.527818i
$86$	20.5305	+	14.9162i	2.21386	+	1.60846i
$87$	0.472136			0.0506183
$88$	31.7016			3.37940
$89$	12.4184	+	9.02251i	1.31635	+	0.956385i	0.999970	+	0.00775224i	$0.00246764\pi$
$89$	12.4184	+	9.02251i	1.31635	+	0.956385i	0.316381	+	0.948632i	$0.397532\pi$
$90$	−4.04508	−	12.4495i	−0.426389	−	1.31229i
$91$	0.810272	−	2.49376i	0.0849396	−	0.261417i
$92$	−12.7279			−1.32698
$93$		0			0
$94$	−25.4164			−2.62150
$95$	0.690983	−	2.12663i	0.0708934	−	0.218187i
$96$	−2.93159	−	9.02251i	−0.299204	−	0.920857i
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	0.836919	−	0.547327i	$-0.184354\pi$
$97$	5.66312	+	4.11450i	0.575003	+	0.417764i	−0.261916	+	0.965091i	$0.584354\pi$
$98$	−15.7082			−1.58677
$99$	−9.48683			−0.953463
$100$		0			0
$101$	−1.80902	+	1.31433i	−0.180004	+	0.130781i	−0.674139	−	0.738605i	$-0.735485\pi$
$101$	−1.80902	+	1.31433i	−0.180004	+	0.130781i	0.494135	+	0.869385i	$0.335485\pi$
$102$	6.85410	−	4.97980i	0.678657	−	0.493073i
$103$	3.30902	−	10.1841i	0.326047	−	1.00347i	−0.644919	−	0.764251i	$-0.723109\pi$
$103$	3.30902	−	10.1841i	0.326047	−	1.00347i	0.970966	−	0.239219i	$-0.0768913\pi$
$104$	15.8508	+	11.5163i	1.55430	+	1.12926i
$105$	0.603941	−	1.85874i	0.0589386	−	0.181394i
$106$	−11.1074	−	34.1850i	−1.07884	−	3.32034i
$107$	−1.19098	+	0.865300i	−0.115137	+	0.0836517i	−0.643864	−	0.765140i	$-0.722670\pi$
$107$	−1.19098	+	0.865300i	−0.115137	+	0.0836517i	0.528727	+	0.848792i	$0.322670\pi$
$108$	6.86474	+	21.1275i	0.660560	+	2.03299i
$109$	−0.399187	−	1.22857i	−0.0382352	−	0.117676i	0.930117	−	0.367263i	$-0.119705\pi$
$109$	−0.399187	−	1.22857i	−0.0382352	−	0.117676i	−0.968352	+	0.249587i	$0.919705\pi$
$110$	−20.0934	+	14.5987i	−1.91583	+	1.39193i
$111$	−1.14590	−	3.52671i	−0.108764	−	0.334741i
$112$	−3.04508	+	9.37181i	−0.287733	+	0.885553i
$113$	7.89919	+	5.73910i	0.743093	+	0.539889i	0.893678	−	0.448708i	$-0.148116\pi$
$113$	7.89919	+	5.73910i	0.743093	+	0.539889i	−0.150585	+	0.988597i	$0.548116\pi$
$114$	−0.707107	+	2.17625i	−0.0662266	+	0.203825i
$115$	4.74342	−	3.44629i	0.442326	−	0.321369i
$116$	2.12132	−	1.54123i	0.196960	−	0.143100i
$117$	−4.74342	−	3.44629i	−0.438529	−	0.318610i
$118$	31.2705			2.87868
$119$	−3.70246			−0.339404
$120$	11.8145	+	8.58373i	1.07851	+	0.783583i
$121$	2.16312	+	6.65740i	0.196647	+	0.605218i
$122$	11.2743	−	34.6987i	1.02073	−	3.14148i
$123$	1.28669			0.116017
$124$		0			0
$125$	−11.1803			−1.00000
$126$	1.80902	−	5.56758i	0.161160	−	0.496000i
$127$	−2.93159	−	9.02251i	−0.260137	−	0.800619i	−0.992774	−	0.119999i	$-0.961711\pi$
$127$	−2.93159	−	9.02251i	−0.260137	−	0.800619i	0.732637	−	0.680619i	$-0.238289\pi$
$128$	−0.881966	−	0.640786i	−0.0779555	−	0.0566380i
$129$	8.47214			0.745930
$130$	−15.3500			−1.34629
$131$	−6.00000	−	4.35926i	−0.524222	−	0.380870i	0.293970	−	0.955815i	$-0.405024\pi$
$131$	−6.00000	−	4.35926i	−0.524222	−	0.380870i	−0.818192	+	0.574945i	$0.805024\pi$
$132$	14.5623	−	10.5801i	1.26749	−	0.920883i
$133$	0.809017	−	0.587785i	0.0701507	−	0.0509674i
$134$	4.85410	−	14.9394i	0.419331	−	1.29057i
$135$	−8.27895	−	6.01501i	−0.712539	−	0.517690i
$136$	8.54904	−	26.3112i	0.733074	−	2.25617i
$137$	−0.810272	−	2.49376i	−0.0692262	−	0.213056i	0.910458	−	0.413601i	$-0.135729\pi$
$137$	−0.810272	−	2.49376i	−0.0692262	−	0.213056i	−0.979685	+	0.200544i	$0.935729\pi$
$138$	−4.85410	+	3.52671i	−0.413209	+	0.300214i
$139$	−5.55369	−	17.0925i	−0.471058	−	1.44977i	−0.851201	−	0.524839i	$-0.824125\pi$
$139$	−5.55369	−	17.0925i	−0.471058	−	1.44977i	0.380144	−	0.924927i	$-0.375875\pi$
$140$	−3.35410	−	10.3229i	−0.283473	−	0.872441i
$141$	−6.86474	+	4.98752i	−0.578115	+	0.420025i
$142$	−1.19098	−	3.66547i	−0.0999451	−	0.307599i
$143$	−3.43769	+	10.5801i	−0.287474	+	0.884755i
$144$	17.8262	+	12.9515i	1.48552	+	1.07929i
$145$	−0.373256	+	1.14876i	−0.0309972	+	0.0953997i
$146$	−8.98606	+	6.52875i	−0.743691	+	0.540323i
$147$	−4.24264	+	3.08246i	−0.349927	+	0.254237i
$148$	−16.6611	−	12.1050i	−1.36953	−	0.995023i
$149$	−13.4164			−1.09911			−0.549557	−	0.835456i	$-0.685204\pi$
$149$	−13.4164			−1.09911			−0.549557	+	0.835456i	$0.685204\pi$
$150$		0			0
$151$	−10.1302	−	7.36001i	−0.824382	−	0.598949i	0.0935821	−	0.995612i	$-0.470168\pi$
$151$	−10.1302	−	7.36001i	−0.824382	−	0.598949i	−0.917964	+	0.396663i	$0.870168\pi$
$152$	2.30902	+	7.10642i	0.187286	+	0.576407i
$153$	−2.55834	+	7.87375i	−0.206829	+	0.636555i
$154$	−11.1074			−0.895058
$155$		0			0
$156$	11.1246			0.890682
$157$	2.69098	−	8.28199i	0.214764	−	0.660975i	−0.784406	−	0.620247i	$-0.787032\pi$
$157$	2.69098	−	8.28199i	0.214764	−	0.660975i	0.999170	−	0.0407279i	$-0.0129677\pi$
$158$	−1.31105	−	4.03499i	−0.104301	−	0.321007i
$159$	−9.70820	−	7.05342i	−0.769911	−	0.559373i
$160$	24.2705			1.91875
$161$	2.62210			0.206650
$162$	−5.73607	−	4.16750i	−0.450668	−	0.327430i
$163$	−11.6631	+	8.47375i	−0.913526	+	0.663715i	−0.941904	−	0.335882i	$-0.890966\pi$
$163$	−11.6631	+	8.47375i	−0.913526	+	0.663715i	0.0283782	+	0.999597i	$0.490966\pi$
$164$	5.78115	−	4.20025i	0.451432	−	0.327985i
$165$	−2.56231	+	7.88597i	−0.199475	+	0.613922i
$166$	6.69781	+	4.86624i	0.519851	+	0.377694i
$167$	−0.333851	+	1.02749i	−0.0258341	+	0.0795093i	−0.963142	−	0.268992i	$-0.913309\pi$
$167$	−0.333851	+	1.02749i	−0.0258341	+	0.0795093i	0.937308	+	0.348502i	$0.113309\pi$
$168$	2.01815	+	6.21124i	0.155704	+	0.479208i
$169$	4.95492	−	3.59996i	0.381147	−	0.276920i
$170$	6.69781	+	20.6137i	0.513699	+	1.58100i
$171$	−0.690983	−	2.12663i	−0.0528408	−	0.162627i
$172$	38.0655	−	27.6562i	2.90247	−	2.10877i
$173$	5.56231	+	17.1190i	0.422894	+	1.30153i	0.904996	+	0.425420i	$0.139873\pi$
$173$	5.56231	+	17.1190i	0.422894	+	1.30153i	−0.482102	+	0.876115i	$0.660127\pi$
$174$	0.381966	−	1.17557i	0.0289568	−	0.0891198i
$175$		0			0
$176$	12.9192	−	39.7612i	0.973821	−	2.99711i
$177$	8.44588	−	6.13629i	0.634831	−	0.461232i
$178$	32.5119	−	23.6212i	2.43687	−	1.77049i
$179$	−10.7341	−	7.79880i	−0.802306	−	0.582909i	0.109284	−	0.994011i	$-0.465144\pi$
$179$	−10.7341	−	7.79880i	−0.802306	−	0.582909i	−0.911590	+	0.411101i	$0.865144\pi$
$180$	−24.2705			−1.80902
$181$	8.69161			0.646042			0.323021	−	0.946392i	$-0.395301\pi$
$181$	8.69161			0.646042			0.323021	+	0.946392i	$0.395301\pi$
$182$	−5.55369	−	4.03499i	−0.411667	−	0.299093i
$183$	−3.76393	−	11.5842i	−0.278238	−	0.856328i
$184$	−6.05446	+	18.6337i	−0.446341	+	1.37370i
$185$	9.48683			0.697486
$186$		0			0
$187$	15.7082			1.14870
$188$	−14.5623	+	44.8182i	−1.06207	+	3.26870i
$189$	−1.41421	−	4.35250i	−0.102869	−	0.316598i
$190$	−4.73607	−	3.44095i	−0.343590	−	0.249633i
$191$	9.76393			0.706493			0.353247	−	0.935530i	$-0.385078\pi$
$191$	9.76393			0.706493			0.353247	+	0.935530i	$0.385078\pi$
$192$	−7.61125			−0.549295
$193$	16.7533	+	12.1720i	1.20593	+	0.876158i	0.994855	−	0.101312i	$-0.0323041\pi$
$193$	16.7533	+	12.1720i	1.20593	+	0.876158i	0.211073	+	0.977470i	$0.432304\pi$
$194$	14.8262	−	10.7719i	1.06446	−	0.773377i
$195$	−4.14590	+	3.01217i	−0.296894	+	0.215706i
$196$	−9.00000	+	27.6992i	−0.642857	+	1.97851i
$197$	0.874032	+	0.635021i	0.0622722	+	0.0452434i	0.618486	−	0.785796i	$-0.287746\pi$
$197$	0.874032	+	0.635021i	0.0622722	+	0.0452434i	−0.556214	+	0.831039i	$0.687746\pi$
$198$	−7.67501	+	23.6212i	−0.545439	+	1.67869i
$199$	7.17423	+	22.0800i	0.508568	+	1.56521i	0.794688	+	0.607017i	$0.207634\pi$
$199$	7.17423	+	22.0800i	0.508568	+	1.56521i	−0.286121	+	0.958194i	$0.592366\pi$
$200$		0			0
$201$	−1.62054	−	4.98752i	−0.114304	−	0.351793i
$202$	1.80902	+	5.56758i	0.127282	+	0.391734i
$203$	−0.437016	+	0.317511i	−0.0306725	+	0.0222849i
$204$	−4.85410	−	14.9394i	−0.339855	−	1.04597i
$205$	−1.01722	+	3.13068i	−0.0710458	+	0.218656i
$206$	−22.6803	−	16.4782i	−1.58021	−	1.14809i
$207$	1.81182	−	5.57622i	0.125930	−	0.387574i
$208$	20.9037	−	15.1874i	1.44941	−	1.05306i
$209$	−3.43237	+	2.49376i	−0.237422	+	0.172497i
$210$	−4.13948	−	3.00750i	−0.285651	−	0.207538i
$211$	−5.00000			−0.344214			−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000			−0.344214			−0.172107	+	0.985078i	$0.555058\pi$
$212$	−66.6443			−4.57715
$213$	−1.04096	−	0.756300i	−0.0713252	−	0.0518208i
$214$	1.19098	+	3.66547i	0.0814139	+	0.250566i
$215$	−6.69781	+	20.6137i	−0.456787	+	1.40585i
$216$	34.1962			2.32675
$217$		0			0
$218$	−3.38197			−0.229056
$219$	−1.14590	+	3.52671i	−0.0774326	+	0.238313i
$220$	14.2302	+	43.7962i	0.959403	+	2.95274i
$221$	7.85410	+	5.70634i	0.528324	+	0.383850i
$222$	−9.70820			−0.651572
$223$	16.1452			1.08117			0.540583	−	0.841291i	$-0.318204\pi$
$223$	16.1452			1.08117			0.540583	+	0.841291i	$0.318204\pi$
$224$	8.78115	+	6.37988i	0.586715	+	0.426274i
$225$		0			0
$226$	20.6803	−	15.0251i	1.37564	−	0.999458i
$227$	0.708204	−	2.17963i	0.0470051	−	0.144667i	−0.924799	−	0.380455i	$-0.875767\pi$
$227$	0.708204	−	2.17963i	0.0470051	−	0.144667i	0.971804	+	0.235788i	$0.0757672\pi$
$228$	3.43237	+	2.49376i	0.227314	+	0.165153i
$229$	1.31105	−	4.03499i	0.0866365	−	0.266640i	−0.898347	−	0.439286i	$-0.855232\pi$
$229$	1.31105	−	4.03499i	0.0866365	−	0.266640i	0.984984	+	0.172646i	$0.0552316\pi$
$230$	−4.74342	−	14.5987i	−0.312772	−	0.962612i
$231$	−3.00000	+	2.17963i	−0.197386	+	0.143409i
$232$	−1.24729	−	3.83876i	−0.0818885	−	0.252027i
$233$	−4.16312	−	12.8128i	−0.272735	−	0.839392i	−0.989810	−	0.142396i	$-0.954519\pi$
$233$	−4.16312	−	12.8128i	−0.272735	−	0.839392i	0.717075	−	0.696996i	$-0.245481\pi$
$234$	−12.4184	+	9.02251i	−0.811818	+	0.589820i
$235$	−6.70820	−	20.6457i	−0.437595	−	1.34678i
$236$	17.9164	−	55.1410i	1.16626	−	3.58938i
$237$	−1.14590	−	0.832544i	−0.0744341	−	0.0540795i
$238$	−2.99535	+	9.21875i	−0.194160	+	0.597563i
$239$	−9.79633	+	7.11745i	−0.633672	+	0.460390i	−0.857670	−	0.514200i	$-0.828089\pi$
$239$	−9.79633	+	7.11745i	−0.633672	+	0.460390i	0.223998	+	0.974589i	$0.428089\pi$
$240$	15.5807	−	11.3200i	1.00573	−	0.730706i
$241$	18.7824	+	13.6462i	1.20988	+	0.879029i	0.995220	−	0.0976596i	$-0.0311357\pi$
$241$	18.7824	+	13.6462i	1.20988	+	0.879029i	0.214660	+	0.976689i	$0.431136\pi$
$242$	18.3262			1.17806
$243$	−16.0965			−1.03259
$244$	−54.7266	−	39.7612i	−3.50351	−	2.54545i
$245$	−4.14590	−	12.7598i	−0.264872	−	0.815191i
$246$	1.04096	−	3.20374i	0.0663690	−	0.204263i
$247$	−2.62210			−0.166840
$248$		0			0
$249$	2.76393			0.175157
$250$	−9.04508	+	27.8379i	−0.572061	+	1.76062i
$251$	3.40801	+	10.4888i	0.215112	+	0.662047i	0.999146	+	0.0413282i	$0.0131589\pi$
$251$	3.40801	+	10.4888i	0.215112	+	0.662047i	−0.784034	+	0.620718i	$0.786841\pi$
$252$	−8.78115	−	6.37988i	−0.553161	−	0.401895i
$253$	−11.1246			−0.699398
$254$	−24.8369			−1.55840
$255$	5.85410	+	4.25325i	0.366598	+	0.266349i
$256$	11.7812	−	8.55951i	0.736322	−	0.534969i
$257$	−4.89919	+	3.55947i	−0.305603	+	0.222033i	−0.730007	−	0.683439i	$-0.760483\pi$
$257$	−4.89919	+	3.55947i	−0.305603	+	0.222033i	0.424405	+	0.905473i	$0.360483\pi$
$258$	6.85410	−	21.0948i	0.426718	−	1.31330i
$259$	3.43237	+	2.49376i	0.213277	+	0.154955i
$260$	−8.79478	+	27.0675i	−0.545429	+	1.67866i
$261$	0.373256	+	1.14876i	0.0231040	+	0.0711067i
$262$	−15.7082	+	11.4127i	−0.970456	+	0.705078i
$263$	5.72061	+	17.6062i	0.352748	+	1.08565i	0.957304	+	0.289084i	$0.0933508\pi$
$263$	5.72061	+	17.6062i	0.352748	+	1.08565i	−0.604555	+	0.796563i	$0.706649\pi$
$264$	−8.56231	−	26.3521i	−0.526973	−	1.62186i
$265$	24.8369	−	18.0450i	1.52572	−	1.10850i
$266$	−0.809017	−	2.48990i	−0.0496040	−	0.152665i
$267$	4.14590	−	12.7598i	0.253725	−	0.780885i
$268$	−23.5623	−	17.1190i	−1.43930	−	1.04571i
$269$	0.667701	−	2.05497i	0.0407105	−	0.125294i	−0.928636	−	0.370993i	$-0.879017\pi$
$269$	0.667701	−	2.05497i	0.0407105	−	0.125294i	0.969346	+	0.245699i	$0.0790175\pi$
$270$	−21.6746	+	15.7475i	−1.31907	+	0.958362i
$271$	15.0405	−	10.9276i	0.913647	−	0.663803i	−0.0282879	−	0.999600i	$-0.509006\pi$
$271$	15.0405	−	10.9276i	0.913647	−	0.663803i	0.941934	+	0.335797i	$0.109006\pi$
$272$	−29.5165	−	21.4450i	−1.78970	−	1.30029i
$273$	−2.29180			−0.138706
$274$	−6.86474			−0.414714
$275$		0			0
$276$	3.43769	+	10.5801i	0.206925	+	0.636849i
$277$	3.12287	−	9.61121i	0.187635	−	0.577482i	−0.812349	−	0.583172i	$-0.801811\pi$
$277$	3.12287	−	9.61121i	0.187635	−	0.577482i	0.999984	+	0.00569038i	$0.00181131\pi$
$278$	−47.0516			−2.82197
$279$		0			0
$280$	−16.7082			−0.998506
$281$	4.12868	−	12.7068i	0.246296	−	0.758022i	−0.749124	−	0.662429i	$-0.769525\pi$
$281$	4.12868	−	12.7068i	0.246296	−	0.758022i	0.995421	−	0.0955924i	$-0.0304745\pi$
$282$	6.86474	+	21.1275i	0.408789	+	1.25812i
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.165154	−	0.986268i	$-0.552812\pi$
$283$	−19.4164	−	14.1068i	−1.15419	−	0.838565i	−0.989032	+	0.147703i	$0.952812\pi$
$284$	−7.14590			−0.424031
$285$	−1.95440			−0.115768
$286$	23.5623	+	17.1190i	1.39327	+	1.01227i
$287$	−1.19098	+	0.865300i	−0.0703015	+	0.0510770i
$288$	19.6353	−	14.2658i	1.15702	−	0.840623i
$289$	−1.01722	+	3.13068i	−0.0598365	+	0.184158i
$290$	2.55834	+	1.85874i	0.150231	+	0.109149i
$291$	1.89064	−	5.81878i	0.110831	−	0.341103i
$292$	6.36396	+	19.5863i	0.372423	+	1.14620i
$293$	1.85410	−	1.34708i	0.108318	−	0.0786975i	−0.532308	−	0.846551i	$-0.678675\pi$
$293$	1.85410	−	1.34708i	0.108318	−	0.0786975i	0.640626	+	0.767853i	$0.278675\pi$
$294$	4.24264	+	13.0575i	0.247436	+	0.761529i
$295$	8.25329	+	25.4010i	0.480525	+	1.47890i
$296$	−25.6471	+	18.6337i	−1.49071	+	1.08306i
$297$	6.00000	+	18.4661i	0.348155	+	1.07151i
$298$	−10.8541	+	33.4055i	−0.628761	+	1.93513i
$299$	−5.56231	−	4.04125i	−0.321676	−	0.233712i
$300$		0			0
$301$	−7.84193	+	5.69750i	−0.452002	+	0.328398i
$302$	−26.5212	+	19.2687i	−1.52612	+	1.10879i
$303$	1.58114	+	1.14876i	0.0908341	+	0.0659948i
$304$	9.85410			0.565172
$305$	31.1614			1.78430
$306$	17.5351	+	12.7400i	1.00241	+	0.728297i
$307$	7.45492	+	22.9439i	0.425474	+	1.30948i	0.902539	+	0.430608i	$0.141701\pi$
$307$	7.45492	+	22.9439i	0.425474	+	1.30948i	−0.477065	+	0.878868i	$0.658299\pi$
$308$	−6.36396	+	19.5863i	−0.362620	+	1.11603i
$309$	−9.35931			−0.532433
$310$		0			0
$311$	25.4721			1.44439			0.722196	−	0.691688i	$-0.243133\pi$
$311$	25.4721			1.44439			0.722196	+	0.691688i	$0.243133\pi$
$312$	5.29180	−	16.2865i	0.299589	−	0.922040i
$313$	−3.55989	−	10.9562i	−0.201217	−	0.619282i	−0.999848	−	0.0174602i	$-0.994442\pi$
$313$	−3.55989	−	10.9562i	−0.201217	−	0.619282i	0.798631	−	0.601821i	$-0.205558\pi$
$314$	−18.4443	−	13.4005i	−1.04087	−	0.756237i
$315$	5.00000			0.281718
$316$	−7.86629			−0.442513
$317$	−21.2254	−	15.4212i	−1.19214	−	0.866139i	−0.198650	−	0.980071i	$-0.563656\pi$
$317$	−21.2254	−	15.4212i	−1.19214	−	0.866139i	−0.993489	+	0.113931i	$0.963656\pi$
$318$	−25.4164	+	18.4661i	−1.42528	+	1.03553i
$319$	1.85410	−	1.34708i	0.103810	−	0.0754222i
$320$	6.01722	−	18.5191i	0.336373	−	1.03525i
$321$	1.04096	+	0.756300i	0.0581006	+	0.0422125i
$322$	2.12132	−	6.52875i	0.118217	−	0.363833i
$323$	1.14412	+	3.52125i	0.0636607	+	0.195927i
$324$	−10.6353	+	7.72696i	−0.590847	+	0.429276i
$325$		0			0
$326$	11.6631	+	35.8954i	0.645960	+	1.98806i
$327$	−0.913438	+	0.663651i	−0.0505132	+	0.0367000i
$328$	−3.39919	−	10.4616i	−0.187689	−	0.577646i
$329$	3.00000	−	9.23305i	0.165395	−	0.509035i
$330$	17.5623	+	12.7598i	0.966773	+	0.702402i
$331$	9.66881	−	29.7575i	0.531446	−	1.63562i	−0.219760	−	0.975554i	$-0.570527\pi$
$331$	9.66881	−	29.7575i	0.531446	−	1.63562i	0.751206	−	0.660068i	$-0.229473\pi$
$332$	12.4184	−	9.02251i	0.681550	−	0.495175i
$333$	7.67501	−	5.57622i	0.420588	−	0.305575i
$334$	2.28825	+	1.66251i	0.125207	+	0.0909684i
$335$	13.4164			0.733017
$336$	8.61280			0.469867
$337$	12.4184	+	9.02251i	0.676475	+	0.491488i	0.872186	−	0.489174i	$-0.162702\pi$
$337$	12.4184	+	9.02251i	0.676475	+	0.491488i	−0.195712	+	0.980662i	$0.562702\pi$
$338$	−4.95492	−	15.2497i	−0.269512	−	0.829472i
$339$	2.63715	−	8.11631i	0.143230	−	0.440817i
$340$	40.1869			2.17944
$341$		0			0
$342$	−5.85410			−0.316554
$343$	4.01722	−	12.3637i	0.216910	−	0.667579i
$344$	−22.3817	−	68.8837i	−1.20674	−	3.71396i
$345$	−4.14590	−	3.01217i	−0.223208	−	0.162170i
$346$	47.1246			2.53343
$347$	−21.5958			−1.15932			−0.579661	−	0.814858i	$-0.696815\pi$
$347$	−21.5958			−1.15932			−0.579661	+	0.814858i	$0.696815\pi$
$348$	−1.85410	−	1.34708i	−0.0993903	−	0.0722113i
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	−0.710074	−	0.704127i	$-0.751338\pi$
$349$	−4.85410	+	3.52671i	−0.259834	+	0.188781i	0.450240	+	0.892908i	$0.351338\pi$
$350$		0			0
$351$	−3.70820	+	11.4127i	−0.197929	+	0.609164i
$352$	−37.2553	−	27.0675i	−1.98571	−	1.44270i
$353$	2.95595	−	9.09747i	0.157329	−	0.484209i	−0.841060	−	0.540941i	$-0.818068\pi$
$353$	2.95595	−	9.09747i	0.157329	−	0.484209i	0.998389	+	0.0567320i	$0.0180681\pi$
$354$	−8.44588	−	25.9937i	−0.448893	−	1.38155i
$355$	2.66312	−	1.93487i	0.141344	−	0.102692i
$356$	−23.0250	−	70.8637i	−1.22032	−	3.75577i
$357$	1.00000	+	3.07768i	0.0529256	+	0.162888i
$358$	−28.1023	+	20.4175i	−1.48525	+	1.07910i
$359$	4.39919	+	13.5393i	0.232180	+	0.714577i	0.997483	+	0.0709067i	$0.0225893\pi$
$359$	4.39919	+	13.5393i	0.232180	+	0.714577i	−0.765303	+	0.643670i	$0.777411\pi$
$360$	−11.5451	+	35.5321i	−0.608479	+	1.87271i
$361$	14.5623	+	10.5801i	0.766437	+	0.556849i
$362$	7.03166	−	21.6412i	0.369576	−	1.13744i
$363$	4.94975	−	3.59620i	0.259794	−	0.188752i
$364$	−10.2971	+	7.48128i	−0.539715	+	0.392126i
$365$	−7.67501	−	5.57622i	−0.401728	−	0.291873i
$366$	−31.8885			−1.66684
$367$	6.65841			0.347566			0.173783	−	0.984784i	$-0.444401\pi$
$367$	6.65841			0.347566			0.173783	+	0.984784i	$0.444401\pi$
$368$	20.9037	+	15.1874i	1.08968	+	0.791700i
$369$	1.01722	+	3.13068i	0.0529544	+	0.162977i
$370$	7.67501	−	23.6212i	0.399005	−	1.22801i
$371$	13.7295			0.712799
$372$		0			0
$373$	−9.29180			−0.481111			−0.240555	−	0.970635i	$-0.577330\pi$
$373$	−9.29180			−0.481111			−0.240555	+	0.970635i	$0.577330\pi$
$374$	12.7082	−	39.1118i	0.657126	−	2.02242i
$375$	3.01971	+	9.29370i	0.155937	+	0.479925i
$376$	58.6869	+	42.6385i	3.02655	+	2.19891i
$377$	1.41641			0.0729487
$378$	−11.9814			−0.616257
$379$	−6.00000	−	4.35926i	−0.308199	−	0.223920i	0.422924	−	0.906165i	$-0.361004\pi$
$379$	−6.00000	−	4.35926i	−0.308199	−	0.223920i	−0.731123	+	0.682245i	$0.761004\pi$
$380$	−8.78115	+	6.37988i	−0.450464	+	0.327281i
$381$	−6.70820	+	4.87380i	−0.343672	+	0.249692i
$382$	7.89919	−	24.3112i	0.404158	−	1.24387i
$383$	5.18043	+	3.76380i	0.264708	+	0.192321i	0.712220	−	0.701956i	$-0.247690\pi$
$383$	5.18043	+	3.76380i	0.264708	+	0.192321i	−0.447512	+	0.894278i	$0.647690\pi$
$384$	−0.294445	+	0.906208i	−0.0150258	+	0.0462447i
$385$	−2.93159	−	9.02251i	−0.149408	−	0.459830i
$386$	43.8607	−	31.8666i	2.23245	−	1.62197i
$387$	6.69781	+	20.6137i	0.340469	+	1.04786i
$388$	−10.5000	−	32.3157i	−0.533057	−	1.64058i
$389$	13.6020	−	9.88240i	0.689646	−	0.501057i	−0.186897	−	0.982379i	$-0.559843\pi$
$389$	13.6020	−	9.88240i	0.689646	−	0.501057i	0.876544	+	0.481322i	$0.159843\pi$
$390$	4.14590	+	12.7598i	0.209936	+	0.646116i
$391$	−3.00000	+	9.23305i	−0.151717	+	0.466935i
$392$	36.2705	+	26.3521i	1.83194	+	1.33098i
$393$	−2.00310	+	6.16492i	−0.101043	+	0.310979i
$394$	2.28825	−	1.66251i	0.115280	−	0.0837559i
$395$	2.93159	−	2.12993i	0.147504	−	0.107168i
$396$	37.2553	+	27.0675i	1.87215	+	1.36020i
$397$	14.7082			0.738184			0.369092	−	0.929393i	$-0.379669\pi$
$397$	14.7082			0.738184			0.369092	+	0.929393i	$0.379669\pi$
$398$	60.7811			3.04668
$399$	−0.707107	−	0.513743i	−0.0353996	−	0.0257193i
$400$		0			0
$401$	−0.166925	+	0.513743i	−0.00833585	+	0.0256551i	−0.955138	−	0.296161i	$-0.904293\pi$
$401$	−0.166925	+	0.513743i	−0.00833585	+	0.0256551i	0.946802	+	0.321816i	$0.104293\pi$
$402$	−13.7295			−0.684764
$403$		0			0
$404$	10.8541			0.540012
$405$	1.87132	−	5.75934i	0.0929868	−	0.286184i
$406$	0.437016	+	1.34500i	0.0216887	+	0.0667511i
$407$	−14.5623	−	10.5801i	−0.721827	−	0.524438i
$408$	−24.1803			−1.19711
$409$	30.0810			1.48741			0.743706	−	0.668507i	$-0.233066\pi$
$409$	30.0810			1.48741			0.743706	+	0.668507i	$0.233066\pi$
$410$	6.97214	+	5.06555i	0.344329	+	0.250170i
$411$	−1.85410	+	1.34708i	−0.0914561	+	0.0664468i
$412$	−42.0517	+	30.5523i	−2.07174	+	1.50520i
$413$	−3.69098	+	11.3597i	−0.181621	+	0.558973i
$414$	−12.4184	−	9.02251i	−0.610332	−	0.443432i
$415$	−2.18508	+	6.72499i	−0.107261	+	0.330117i
$416$	−8.79478	−	27.0675i	−0.431199	−	1.32710i
$417$	−12.7082	+	9.23305i	−0.622323	+	0.452144i
$418$	3.43237	+	10.5637i	0.167883	+	0.516690i
$419$	9.45492	+	29.0992i	0.461903	+	1.42159i	0.862836	+	0.505484i	$0.168686\pi$
$419$	9.45492	+	29.0992i	0.461903	+	1.42159i	−0.400933	+	0.916107i	$0.631314\pi$
$420$	−7.67501	+	5.57622i	−0.374502	+	0.272092i
$421$	8.16312	+	25.1235i	0.397846	+	1.22444i	0.926723	+	0.375746i	$0.122613\pi$
$421$	8.16312	+	25.1235i	0.397846	+	1.22444i	−0.528877	+	0.848699i	$0.677387\pi$
$422$	−4.04508	+	12.4495i	−0.196912	+	0.606032i
$423$	−17.5623	−	12.7598i	−0.853909	−	0.620401i
$424$	−31.7016	+	97.5675i	−1.53957	+	4.73829i
$425$		0			0
$426$	−2.72526	+	1.98002i	−0.132039	+	0.0959322i
$427$	11.2743	+	8.19126i	0.545602	+	0.396403i
$428$	7.14590			0.345410
$429$	9.72327			0.469444
$430$	45.9075	+	33.3537i	2.21386	+	1.60846i
$431$	−11.0902	−	34.1320i	−0.534195	−	1.64408i	−0.745383	−	0.666637i	$-0.767733\pi$
$431$	−11.0902	−	34.1320i	−0.534195	−	1.64408i	0.211188	−	0.977445i	$-0.432267\pi$
$432$	13.9358	−	42.8900i	0.670487	−	2.06355i
$433$	−25.8384			−1.24171			−0.620857	−	0.783924i	$-0.713215\pi$
$433$	−25.8384			−1.24171			−0.620857	+	0.783924i	$0.713215\pi$
$434$		0			0
$435$	1.05573			0.0506183
$436$	−1.93769	+	5.96361i	−0.0927987	+	0.285605i
$437$	−0.810272	−	2.49376i	−0.0387606	−	0.119293i
$438$	7.85410	+	5.70634i	0.375284	+	0.272659i
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	70.8869			3.37940
$441$	−10.8541	−	7.88597i	−0.516862	−	0.375522i
$442$	20.5623	−	14.9394i	0.978049	−	0.710594i
$443$	−4.89919	+	3.55947i	−0.232767	+	0.169115i	−0.698055	−	0.716044i	$-0.745951\pi$
$443$	−4.89919	+	3.55947i	−0.232767	+	0.169115i	0.465288	+	0.885160i	$0.345951\pi$
$444$	−5.56231	+	17.1190i	−0.263975	+	0.812433i
$445$	27.7684	+	20.1750i	1.31635	+	0.956385i
$446$	13.0618	−	40.2000i	0.618493	−	1.90353i
$447$	3.62365	+	11.1524i	0.171393	+	0.527492i
$448$	7.04508	−	5.11855i	0.332849	−	0.241829i
$449$	10.4153	+	32.0551i	0.491529	+	1.51277i	0.822296	+	0.569060i	$0.192693\pi$
$449$	10.4153	+	32.0551i	0.491529	+	1.51277i	−0.330767	+	0.943713i	$0.607307\pi$
$450$		0			0
$451$	5.05291	−	3.67116i	0.237932	−	0.172868i
$452$	−14.6459	−	45.0754i	−0.688885	−	2.12017i
$453$	−3.38197	+	10.4086i	−0.158899	+	0.489040i
$454$	−4.85410	−	3.52671i	−0.227814	−	0.165517i
$455$	1.81182	−	5.57622i	0.0849396	−	0.261417i
$456$	5.28360	−	3.83876i	0.247427	−	0.179766i
$457$	−9.15298	+	6.65003i	−0.428158	+	0.311075i	−0.780912	−	0.624641i	$-0.785245\pi$
$457$	−9.15298	+	6.65003i	−0.428158	+	0.311075i	0.352754	+	0.935716i	$0.385245\pi$
$458$	−8.98606	−	6.52875i	−0.419891	−	0.305069i
$459$	16.9443			0.790891
$460$	−28.4605			−1.32698
$461$	−4.17888	−	3.03613i	−0.194630	−	0.141407i	0.486202	−	0.873846i	$-0.338382\pi$
$461$	−4.17888	−	3.03613i	−0.194630	−	0.141407i	−0.680832	+	0.732439i	$0.738382\pi$
$462$	3.00000	+	9.23305i	0.139573	+	0.429560i
$463$	−1.18353	+	3.64253i	−0.0550032	+	0.169283i	−0.974784	−	0.223150i	$-0.928366\pi$
$463$	−1.18353	+	3.64253i	−0.0550032	+	0.169283i	0.919781	+	0.392432i	$0.128366\pi$
$464$	−5.32300			−0.247114
$465$		0			0
$466$	−35.2705			−1.63387
$467$	−4.83688	+	14.8864i	−0.223824	+	0.688860i	0.774585	+	0.632470i	$0.217959\pi$
$467$	−4.83688	+	14.8864i	−0.223824	+	0.688860i	−0.998409	+	0.0563897i	$0.982041\pi$
$468$	8.79478	+	27.0675i	0.406539	+	1.25120i
$469$	4.85410	+	3.52671i	0.224142	+	0.162848i
$470$	−56.8328			−2.62150
$471$	−7.61125			−0.350708
$472$	−72.2041	−	52.4594i	−3.32346	−	2.41464i
$473$	33.2705	−	24.1724i	1.52978	−	1.11145i
$474$	−3.00000	+	2.17963i	−0.137795	+	0.100114i
$475$		0			0
$476$	14.5397	+	10.5637i	0.666428	+	0.484188i
$477$	9.48683	−	29.1975i	0.434372	−	1.33686i
$478$	9.79633	+	30.1500i	0.448074	+	1.37903i
$479$	−13.3713	+	9.71483i	−0.610951	+	0.443882i	−0.849749	−	0.527187i	$-0.823247\pi$
$479$	−13.3713	+	9.71483i	−0.610951	+	0.443882i	0.238798	+	0.971069i	$0.423247\pi$
$480$	−6.55524	−	20.1750i	−0.299204	−	0.920857i
$481$	−3.43769	−	10.5801i	−0.156745	−	0.482413i
$482$	49.1729	−	35.7262i	2.23977	−	1.62728i
$483$	−0.708204	−	2.17963i	−0.0322244	−	0.0991765i
$484$	10.5000	−	32.3157i	0.477273	−	1.46889i
$485$	12.6631	+	9.20029i	0.575003	+	0.417764i
$486$	−13.0224	+	40.0787i	−0.590707	+	1.81801i
$487$	−22.7155	+	16.5038i	−1.02934	+	0.747859i	−0.968176	−	0.250269i	$-0.919481\pi$
$487$	−22.7155	+	16.5038i	−1.02934	+	0.747859i	−0.0611627	+	0.998128i	$0.519481\pi$
$488$	−84.2431	+	61.2062i	−3.81351	+	2.77068i
$489$	10.1939	+	7.40633i	0.460986	+	0.334926i
$490$	−35.1246			−1.58677
$491$	−15.8902			−0.717115			−0.358557	−	0.933508i	$-0.616731\pi$
$491$	−15.8902			−0.717115			−0.358557	+	0.933508i	$0.616731\pi$
$492$	−5.05291	−	3.67116i	−0.227803	−	0.165509i
$493$	−0.618034	−	1.90211i	−0.0278349	−	0.0856669i
$494$	−2.12132	+	6.52875i	−0.0954427	+	0.293742i
$495$	−21.2132			−0.953463
$496$		0			0
$497$	1.47214			0.0660343
$498$	2.23607	−	6.88191i	0.100201	−	0.308386i
$499$	5.68121	+	17.4850i	0.254326	+	0.782734i	0.993962	+	0.109727i	$0.0349977\pi$
$499$	5.68121	+	17.4850i	0.254326	+	0.782734i	−0.739636	+	0.673007i	$0.765002\pi$
$500$	43.9058	+	31.8994i	1.96353	+	1.42658i
$501$	0.944272			0.0421870
$502$	28.8732			1.28867
$503$	26.6074	+	19.3314i	1.18636	+	0.861945i	0.992875	−	0.119158i	$-0.0380194\pi$
$503$	26.6074	+	19.3314i	1.18636	+	0.861945i	0.193490	+	0.981102i	$0.438019\pi$
$504$	−13.5172	+	9.82084i	−0.602105	+	0.437455i
$505$	−4.04508	+	2.93893i	−0.180004	+	0.130781i
$506$	−9.00000	+	27.6992i	−0.400099	+	1.23138i
$507$	−4.33075	−	3.14648i	−0.192336	−	0.139740i
$508$	−14.2302	+	43.7962i	−0.631365	+	1.94314i
$509$	−2.45517	−	7.55624i	−0.108824	−	0.334924i	0.881785	−	0.471651i	$-0.156342\pi$
$509$	−2.45517	−	7.55624i	−0.108824	−	0.334924i	−0.990609	+	0.136727i	$0.956342\pi$
$510$	15.3262	−	11.1352i	0.678657	−	0.493073i
$511$	−1.31105	−	4.03499i	−0.0579974	−	0.178497i
$512$	−12.4549	−	38.3323i	−0.550435	−	1.69406i
$513$	−3.70246	+	2.68999i	−0.163468	+	0.118766i
$514$	4.89919	+	15.0781i	0.216094	+	0.665069i
$515$	7.39919	−	22.7724i	0.326047	−	1.00347i
$516$	−33.2705	−	24.1724i	−1.46465	−	1.06413i
$517$	−12.7279	+	39.1725i	−0.559773	+	1.72281i
$518$	8.98606	−	6.52875i	0.394825	−	0.286857i
$519$	12.7279	−	9.24738i	0.558694	−	0.405915i
$520$	35.4435	+	25.7512i	1.55430	+	1.12926i
$521$	−13.4164			−0.587784			−0.293892	−	0.955839i	$-0.594951\pi$
$521$	−13.4164			−0.587784			−0.293892	+	0.955839i	$0.594951\pi$
$522$	3.16228			0.138409
$523$	−0.500776	−	0.363835i	−0.0218974	−	0.0159094i	0.576783	−	0.816898i	$-0.304308\pi$
$523$	−0.500776	−	0.363835i	−0.0218974	−	0.0159094i	−0.598680	+	0.800988i	$0.704308\pi$
$524$	11.1246	+	34.2380i	0.485981	+	1.49570i
$525$		0			0
$526$	48.4658			2.11321
$527$		0			0
$528$	−36.5410			−1.59024
$529$	−4.98278	+	15.3354i	−0.216643	+	0.666757i
$530$	−24.8369	−	76.4400i	−1.07884	−	3.32034i
$531$	21.6074	+	15.6987i	0.937681	+	0.681265i
$532$	−4.85410			−0.210452
$533$	3.86008			0.167199
$534$	−28.4164	−	20.6457i	−1.22970	−	0.893428i
$535$	−2.66312	+	1.93487i	−0.115137	+	0.0836517i
$536$	−36.2705	+	26.3521i	−1.56665	+	1.13824i
$537$	−3.58359	+	11.0292i	−0.154643	+	0.475943i
$538$	−4.57649	−	3.32502i	−0.197307	−	0.143352i
$539$	−7.86629	+	24.2099i	−0.338825	+	1.04280i
$540$	15.3500	+	47.2425i	0.660560	+	2.03299i
$541$	−20.8992	+	15.1841i	−0.898526	+	0.652818i	−0.938087	−	0.346400i	$-0.887404\pi$
$541$	−20.8992	+	15.1841i	−0.898526	+	0.652818i	0.0395608	+	0.999217i	$0.487404\pi$
$542$	−15.0405	−	46.2900i	−0.646046	−	1.98832i
$543$	−2.34752	−	7.22494i	−0.100742	−	0.310052i
$544$	−32.5119	+	23.6212i	−1.39393	+	1.01275i
$545$	−0.892609	−	2.74717i	−0.0382352	−	0.117676i
$546$	−1.85410	+	5.70634i	−0.0793482	+	0.244209i
$547$	−1.95492	−	1.42033i	−0.0835861	−	0.0607289i	0.545207	−	0.838301i	$-0.316451\pi$
$547$	−1.95492	−	1.42033i	−0.0835861	−	0.0607289i	−0.628793	+	0.777572i	$0.716451\pi$
$548$	−3.93314	+	12.1050i	−0.168016	+	0.517099i
$549$	25.2101	−	18.3162i	1.07594	−	0.781717i
$550$		0			0
$551$	0.437016	+	0.317511i	0.0186175	+	0.0135264i
$552$	17.1246			0.728872
$553$	1.62054			0.0689126
$554$	−21.4045	−	15.5513i	−0.909389	−	0.660710i
$555$	−2.56231	−	7.88597i	−0.108764	−	0.334741i
$556$	−26.9582	+	82.9687i	−1.14328	+	3.51866i
$557$	−10.6460			−0.451086			−0.225543	−	0.974233i	$-0.572416\pi$
$557$	−10.6460			−0.451086			−0.225543	+	0.974233i	$0.572416\pi$
$558$		0			0
$559$	25.4164			1.07500
$560$	−6.80902	+	20.9560i	−0.287733	+	0.885553i
$561$	−4.24264	−	13.0575i	−0.179124	−	0.551288i
$562$	−28.2984	−	20.5600i	−1.19369	−	0.867270i
$563$	9.76393			0.411501			0.205750	−	0.978605i	$-0.434037\pi$
$563$	9.76393			0.411501			0.205750	+	0.978605i	$0.434037\pi$
$564$	41.1884			1.73435
$565$	17.6631	+	12.8330i	0.743093	+	0.539889i
$566$	−50.8328	+	36.9322i	−2.13666	+	1.55238i
$567$	2.19098	−	1.59184i	0.0920126	−	0.0668511i
$568$	−3.39919	+	10.4616i	−0.142627	+	0.438960i
$569$	9.48683	+	6.89259i	0.397709	+	0.288952i	0.768607	−	0.639721i	$-0.220950\pi$
$569$	9.48683	+	6.89259i	0.397709	+	0.288952i	−0.370898	+	0.928673i	$0.620950\pi$
$570$	−1.58114	+	4.86624i	−0.0662266	+	0.203825i
$571$	−0.810272	−	2.49376i	−0.0339088	−	0.104361i	0.932670	−	0.360732i	$-0.117473\pi$
$571$	−0.810272	−	2.49376i	−0.0339088	−	0.104361i	−0.966578	+	0.256371i	$0.917473\pi$
$572$	43.6869	−	31.7404i	1.82664	−	1.32713i
$573$	−2.63715	−	8.11631i	−0.110168	−	0.339064i
$574$	1.19098	+	3.66547i	0.0497107	+	0.152994i
$575$		0			0
$576$	−6.01722	−	18.5191i	−0.250718	−	0.771629i
$577$	−9.27051	+	28.5317i	−0.385936	+	1.18779i	0.549862	+	0.835255i	$0.314680\pi$
$577$	−9.27051	+	28.5317i	−0.385936	+	1.18779i	−0.935799	+	0.352535i	$0.885320\pi$
$578$	6.97214	+	5.06555i	0.290003	+	0.210699i
$579$	5.59309	−	17.2138i	0.232441	−	0.715380i
$580$	4.74342	−	3.44629i	0.196960	−	0.143100i
$581$	−2.55834	+	1.85874i	−0.106138	+	0.0771135i
$582$	−12.9586	−	9.41498i	−0.537152	−	0.390263i
$583$	−58.2492			−2.41244
$584$	31.7016			1.31182
$585$	−10.6066	−	7.70615i	−0.438529	−	0.318610i
$586$	−1.85410	−	5.70634i	−0.0765922	−	0.235727i
$587$	−4.86163	+	14.9626i	−0.200661	+	0.617571i	0.799203	+	0.601062i	$0.205255\pi$
$587$	−4.86163	+	14.9626i	−0.200661	+	0.617571i	−0.999864	+	0.0165096i	$0.994745\pi$
$588$	25.4558			1.04978
$589$		0			0
$590$	69.9230			2.87868
$591$	0.291796	−	0.898056i	0.0120029	−	0.0369411i
$592$	12.9192	+	39.7612i	0.530976	+	1.63418i
$593$	−4.19098	−	3.04493i	−0.172103	−	0.125040i	0.498399	−	0.866948i	$-0.333921\pi$
$593$	−4.19098	−	3.04493i	−0.172103	−	0.125040i	−0.670502	+	0.741907i	$0.733921\pi$
$594$	50.8328			2.08570
$595$	−8.27895			−0.339404
$596$	52.6869	+	38.2793i	2.15814	+	1.56798i
$597$	16.4164	−	11.9272i	0.671879	−	0.488149i
$598$	−14.5623	+	10.5801i	−0.595497	+	0.432654i
$599$	1.87132	−	5.75934i	0.0764602	−	0.235320i	−0.905520	−	0.424303i	$-0.860519\pi$
$599$	1.87132	−	5.75934i	0.0764602	−	0.235320i	0.981980	+	0.188983i	$0.0605191\pi$
$600$		0			0
$601$	5.61745	−	17.2887i	0.229141	−	0.705222i	−0.768704	−	0.639604i	$-0.779098\pi$
$601$	5.61745	−	17.2887i	0.229141	−	0.705222i	0.997845	−	0.0656177i	$-0.0209018\pi$
$602$	7.84193	+	24.1350i	0.319613	+	0.983669i
$603$	10.8541	−	7.88597i	0.442013	−	0.321141i
$604$	18.7824	+	57.8062i	0.764244	+	2.35210i
$605$	4.83688	+	14.8864i	0.196647	+	0.605218i
$606$	4.13948	−	3.00750i	0.168155	−	0.122172i
$607$	4.67376	+	14.3844i	0.189702	+	0.583843i	0.999998	−	0.00217835i	$-0.000693391\pi$
$607$	4.67376	+	14.3844i	0.189702	+	0.583843i	−0.810295	+	0.586022i	$0.800693\pi$
$608$	3.35410	−	10.3229i	0.136027	−	0.418647i
$609$	0.381966	+	0.277515i	0.0154780	+	0.0112455i
$610$	25.2101	−	77.5887i	1.02073	−	3.14148i
$611$	−20.5942	+	14.9626i	−0.833153	+	0.605321i
$612$	32.5119	−	23.6212i	1.31421	−	0.954832i
$613$	−0.476422	−	0.346141i	−0.0192425	−	0.0139805i	0.578122	−	0.815950i	$-0.303786\pi$
$613$	−0.476422	−	0.346141i	−0.0192425	−	0.0139805i	−0.597365	+	0.801970i	$0.703786\pi$
$614$	63.1591			2.54889
$615$	2.87714			0.116017
$616$	25.6471	+	18.6337i	1.03335	+	0.750774i
$617$	−2.12461	−	6.53888i	−0.0855337	−	0.263246i	0.899138	−	0.437666i	$-0.144195\pi$
$617$	−2.12461	−	6.53888i	−0.0855337	−	0.263246i	−0.984671	+	0.174421i	$0.944195\pi$
$618$	−7.57184	+	23.3037i	−0.304584	+	0.937414i
$619$	25.8384			1.03853			0.519267	−	0.854612i	$-0.326205\pi$
$619$	25.8384			1.03853			0.519267	+	0.854612i	$0.326205\pi$
$620$		0			0
$621$	−12.0000			−0.481543
$622$	20.6074	−	63.4230i	0.826281	−	2.54303i
$623$	4.74342	+	14.5987i	0.190041	+	0.584886i
$624$	−18.2705	−	13.2743i	−0.731406	−	0.531397i
$625$	−25.0000			−1.00000
$626$	−30.1599			−1.20543
$627$	3.00000	+	2.17963i	0.119808	+	0.0870459i
$628$	−34.1976	+	24.8460i	−1.36463	+	0.991463i
$629$	−12.7082	+	9.23305i	−0.506709	+	0.368146i
$630$	4.04508	−	12.4495i	0.161160	−	0.496000i
$631$	19.1162	+	13.8888i	0.761005	+	0.552903i	0.899219	−	0.437500i	$-0.144136\pi$
$631$	19.1162	+	13.8888i	0.761005	+	0.552903i	−0.138213	+	0.990403i	$0.544136\pi$
$632$	−3.74186	+	11.5163i	−0.148843	+	0.458093i
$633$	1.35045	+	4.15627i	0.0536757	+	0.165197i
$634$	−55.5689	+	40.3732i	−2.20692	+	1.60342i
$635$	−6.55524	−	20.1750i	−0.260137	−	0.800619i
$636$	18.0000	+	55.3983i	0.713746	+	2.19669i
$637$	−12.7279	+	9.24738i	−0.504299	+	0.366394i
$638$	−1.85410	−	5.70634i	−0.0734046	−	0.225916i
$639$	1.01722	−	3.13068i	0.0402406	−	0.123848i
$640$	−1.97214	−	1.43284i	−0.0779555	−	0.0566380i
$641$	−2.62210	+	8.06998i	−0.103567	+	0.318745i	−0.989391	−	0.145275i	$-0.953593\pi$
$641$	−2.62210	+	8.06998i	−0.103567	+	0.318745i	0.885825	+	0.464020i	$0.153593\pi$
$642$	2.72526	−	1.98002i	0.107557	−	0.0781451i
$643$	3.76622	−	2.73632i	0.148525	−	0.107910i	−0.511041	−	0.859556i	$-0.670740\pi$
$643$	3.76622	−	2.73632i	0.148525	−	0.107910i	0.659566	+	0.751646i	$0.270740\pi$
$644$	−10.2971	−	7.48128i	−0.405763	−	0.294804i
$645$	18.9443			0.745930
$646$	9.69316			0.381372
$647$	−25.7109	−	18.6801i	−1.01080	−	0.734389i	−0.0464226	−	0.998922i	$-0.514782\pi$
$647$	−25.7109	−	18.6801i	−1.01080	−	0.734389i	−0.964377	+	0.264533i	$0.914782\pi$
$648$	6.25329	+	19.2456i	0.245652	+	0.756040i
$649$	15.6595	−	48.1950i	0.614690	−	1.89182i
$650$		0			0
$651$		0			0
$652$	69.9787			2.74058
$653$	7.61803	−	23.4459i	0.298117	−	0.917509i	−0.684040	−	0.729445i	$-0.739779\pi$
$653$	7.61803	−	23.4459i	0.298117	−	0.917509i	0.982157	−	0.188064i	$-0.0602214\pi$
$654$	0.913438	+	2.81127i	0.0357182	+	0.109929i
$655$	−13.4164	−	9.74759i	−0.524222	−	0.380870i
$656$	−14.5066			−0.566387
$657$	−9.48683			−0.370117
$658$	−20.5623	−	14.9394i	−0.801602	−	0.582398i
$659$	−20.0795	+	14.5886i	−0.782187	+	0.568292i	−0.905635	−	0.424059i	$-0.860605\pi$
$659$	−20.0795	+	14.5886i	−0.782187	+	0.568292i	0.123447	+	0.992351i	$0.460605\pi$
$660$	32.5623	−	23.6579i	1.26749	−	0.920883i
$661$	2.42047	−	7.44945i	0.0941455	−	0.289750i	−0.892885	−	0.450286i	$-0.851322\pi$
$661$	2.42047	−	7.44945i	0.0941455	−	0.289750i	0.987030	+	0.160536i	$0.0513221\pi$
$662$	−66.2710	−	48.1487i	−2.57570	−	1.87135i
$663$	2.62210	−	8.06998i	0.101834	−	0.313412i
$664$	−7.30175	−	22.4725i	−0.283363	−	0.872102i
$665$	1.80902	−	1.31433i	0.0701507	−	0.0509674i
$666$	−7.67501	−	23.6212i	−0.297401	−	0.915305i
$667$	0.437694	+	1.34708i	0.0169476	+	0.0521593i
$668$	4.24264	−	3.08246i	0.164153	−	0.119264i
$669$	−4.36068	−	13.4208i	−0.168594	−	0.518878i
$670$	10.8541	−	33.4055i	0.419331	−	1.29057i
$671$	−47.8328	−	34.7526i	−1.84657	−	1.34161i
$672$	2.93159	−	9.02251i	0.113089	−	0.348051i
$673$	−32.3449	+	23.5000i	−1.24681	+	0.905857i	−0.998032	−	0.0627044i	$-0.980027\pi$
$673$	−32.3449	+	23.5000i	−1.24681	+	0.905857i	−0.248773	+	0.968562i	$0.580027\pi$
$674$	32.5119	−	23.6212i	1.25231	−	0.909857i
$675$		0			0
$676$	−29.7295			−1.14344
$677$	−21.2132			−0.815290			−0.407645	−	0.913141i	$-0.633650\pi$
$677$	−21.2132			−0.815290			−0.407645	+	0.913141i	$0.633650\pi$
$678$	−18.0753	−	13.1325i	−0.694177	−	0.504349i
$679$	2.16312	+	6.65740i	0.0830129	+	0.255487i
$680$	19.1162	−	58.8337i	0.733074	−	2.25617i
$681$	−2.00310			−0.0767591
$682$		0			0
$683$	−41.1803			−1.57572			−0.787861	−	0.615853i	$-0.788811\pi$
$683$	−41.1803			−1.57572			−0.787861	+	0.615853i	$0.788811\pi$
$684$	−3.35410	+	10.3229i	−0.128247	+	0.394705i
$685$	−1.81182	−	5.57622i	−0.0692262	−	0.213056i
$686$	−27.5344	−	20.0049i	−1.05127	−	0.763792i
$687$	−3.70820			−0.141477
$688$	−95.5174			−3.64157
$689$	−29.1246	−	21.1603i	−1.10956	−	0.806142i
$690$	−10.8541	+	7.88597i	−0.413209	+	0.300214i
$691$	39.1697	−	28.4585i	1.49009	−	1.08261i	0.515957	−	0.856614i	$-0.327436\pi$
$691$	39.1697	−	28.4585i	1.49009	−	1.08261i	0.974128	−	0.225996i	$-0.0725637\pi$
$692$	27.0000	−	83.0975i	1.02639	−	3.15889i
$693$	−7.67501	−	5.57622i	−0.291549	−	0.211823i
$694$	−17.4713	+	53.7713i	−0.663203	+	2.04113i
$695$	−12.4184	−	38.2200i	−0.471058	−	1.44977i
$696$	−2.85410	+	2.07363i	−0.108184	+	0.0786006i
$697$	−1.68430	−	5.18376i	−0.0637976	−	0.196349i
$698$	4.85410	+	14.9394i	0.183730	+	0.565464i
$699$	−9.52624	+	6.92122i	−0.360315	+	0.261784i
$700$		0			0
$701$	−1.12868	+	3.47371i	−0.0426295	+	0.131200i	−0.970106	−	0.242681i	$-0.921973\pi$
$701$	−1.12868	+	3.47371i	−0.0426295	+	0.131200i	0.927477	+	0.373881i	$0.121973\pi$
$702$	25.4164	+	18.4661i	0.959280	+	0.696958i
$703$	1.31105	−	4.03499i	0.0494471	−	0.152183i
$704$	−29.8898	+	21.7162i	−1.12651	+	0.818460i
$705$	−15.3500	+	11.1524i	−0.578115	+	0.420025i
$706$	−20.2604	−	14.7200i	−0.762509	−	0.553995i
$707$	−2.23607			−0.0840960
$708$	−50.6753			−1.90449
$709$	33.3221	+	24.2099i	1.25144	+	0.909224i	0.998305	−	0.0582075i	$-0.0185385\pi$
$709$	33.3221	+	24.2099i	1.25144	+	0.909224i	0.253134	+	0.967431i	$0.418538\pi$
$710$	−2.66312	−	8.19624i	−0.0999451	−	0.307599i
$711$	1.11977	−	3.44629i	0.0419946	−	0.129246i
$712$	−114.697			−4.29847
$713$		0			0
$714$	8.47214			0.317062
$715$	−7.68692	+	23.6579i	−0.287474	+	0.884755i
$716$	19.9022	+	61.2525i	0.743778	+	2.28911i
$717$	8.56231	+	6.22088i	0.319765	+	0.232323i
$718$	37.2705			1.39092
$719$	−37.5648			−1.40093			−0.700465	−	0.713687i	$-0.747024\pi$
$719$	−37.5648			−1.40093			−0.700465	+	0.713687i	$0.747024\pi$
$720$	39.8607	+	28.9605i	1.48552	+	1.07929i
$721$	8.66312	−	6.29412i	0.322631	−	0.234405i
$722$	38.1246	−	27.6992i	1.41885	−	1.03086i
$723$	6.27051	−	19.2986i	0.233203	−	0.717724i
$724$	−34.1324	−	24.7986i	−1.26852	−	0.921634i
$725$		0			0
$726$	−4.94975	−	15.2338i	−0.183702	−	0.565378i
$727$	24.6074	−	17.8783i	0.912638	−	0.663070i	−0.0290430	−	0.999578i	$-0.509246\pi$
$727$	24.6074	−	17.8783i	0.912638	−	0.663070i	0.941681	+	0.336508i	$0.109246\pi$
$728$	6.05446	+	18.6337i	0.224393	+	0.690612i
$729$	1.83688	+	5.65334i	0.0680326	+	0.209383i
$730$	−20.0934	+	14.5987i	−0.743691	+	0.540323i
$731$	−11.0902	−	34.1320i	−0.410185	−	1.26242i
$732$	−18.2705	+	56.2308i	−0.675297	+	2.07835i
$733$	11.6631	+	8.47375i	0.430787	+	0.312985i	0.781964	−	0.623324i	$-0.214218\pi$
$733$	11.6631	+	8.47375i	0.430787	+	0.312985i	−0.351176	+	0.936309i	$0.614218\pi$
$734$	5.38676	−	16.5788i	0.198829	−	0.611933i
$735$	−9.48683	+	6.89259i	−0.349927	+	0.254237i
$736$	23.0250	−	16.7287i	0.848714	−	0.616627i
$737$	−20.5942	−	14.9626i	−0.758597	−	0.551153i
$738$	8.61803			0.317234
$739$	−35.1490			−1.29298			−0.646489	−	0.762924i	$-0.723763\pi$
$739$	−35.1490			−1.29298			−0.646489	+	0.762924i	$0.723763\pi$
$740$	−37.2553	−	27.0675i	−1.36953	−	0.995023i
$741$	0.708204	+	2.17963i	0.0260165	+	0.0800706i
$742$	11.1074	−	34.1850i	0.407765	−	1.25497i
$743$	−36.4844			−1.33848			−0.669242	−	0.743045i	$-0.733381\pi$
$743$	−36.4844			−1.33848			−0.669242	+	0.743045i	$0.733381\pi$
$744$		0			0
$745$	−30.0000			−1.09911
$746$	−7.51722	+	23.1356i	−0.275225	+	0.847055i
$747$	2.18508	+	6.72499i	0.0799479	+	0.246054i
$748$	−61.6869	−	44.8182i	−2.25550	−	1.63871i
$749$	−1.47214			−0.0537907
$750$	25.5834			0.934172
$751$	30.3713	+	22.0661i	1.10827	+	0.805202i	0.982390	−	0.186844i	$-0.0598259\pi$
$751$	30.3713	+	22.0661i	1.10827	+	0.805202i	0.125876	+	0.992046i	$0.459826\pi$
$752$	77.3951	−	56.2308i	2.82231	−	2.05053i
$753$	7.79837	−	5.66585i	0.284189	−	0.206475i
$754$	1.14590	−	3.52671i	0.0417311	−	0.128435i
$755$	−22.6518	−	16.4575i	−0.824382	−	0.598949i
$756$	−6.86474	+	21.1275i	−0.249668	+	0.768399i
$757$	2.86783	+	8.82628i	0.104233	+	0.320797i	0.989550	−	0.144192i	$-0.0460583\pi$
$757$	2.86783	+	8.82628i	0.104233	+	0.320797i	−0.885317	+	0.464989i	$0.846058\pi$
$758$	−15.7082	+	11.4127i	−0.570548	+	0.414527i
$759$	3.00465	+	9.24738i	0.109062	+	0.335659i
$760$	5.16312	+	15.8904i	0.187286	+	0.576407i
$761$	−32.5119	+	23.6212i	−1.17855	+	0.856270i	−0.992008	−	0.126177i	$-0.959729\pi$
$761$	−32.5119	+	23.6212i	−1.17855	+	0.856270i	−0.186546	+	0.982446i	$0.559729\pi$
$762$	6.70820	+	20.6457i	0.243013	+	0.747916i
$763$	0.399187	−	1.22857i	0.0144515	−	0.0444773i
$764$	−38.3435	−	27.8582i	−1.38722	−	1.00787i
$765$	−5.72061	+	17.6062i	−0.206829	+	0.636555i
$766$	13.5625	−	9.85377i	0.490035	−	0.356031i
$767$	25.3376	−	18.4089i	0.914889	−	0.664706i
$768$	−10.2971	−	7.48128i	−0.371565	−	0.269958i
$769$	54.1246			1.95178			0.975892	−	0.218255i	$-0.0700365\pi$
$769$	54.1246			1.95178			0.975892	+	0.218255i	$0.0700365\pi$
$770$	−24.8369			−0.895058
$771$	4.28205	+	3.11109i	0.154214	+	0.112043i

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.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 2.48990i) q^{2} +(-0.270091 - 0.831254i) q^{3} +(-3.92705 - 2.85317i) q^{4} +2.23607 q^{5} -2.28825 q^{6} +(0.809017 + 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(1.80902 - 1.31433i) q^{9} +(1.80902 - 5.56758i) q^{10} +(-3.43237 - 2.49376i) q^{11} +(-1.31105 + 4.03499i) q^{12} +(-0.810272 - 2.49376i) q^{13} +(2.11803 - 1.53884i) q^{14} +(-0.603941 - 1.85874i) q^{15} +(3.04508 + 9.37181i) q^{16} +(-2.99535 + 2.17625i) q^{17} +(-1.80902 - 5.56758i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-8.78115 - 6.37988i) q^{20} +(0.270091 - 0.831254i) q^{21} +(-8.98606 + 6.52875i) q^{22} +(2.12132 - 1.54123i) q^{23} +(5.28360 + 3.83876i) q^{24} -6.86474 q^{26} +(-3.70246 - 2.68999i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-0.166925 + 0.513743i) q^{29} -5.11667 q^{30} +10.8541 q^{32} +(-1.14590 + 3.52671i) q^{33} +(2.99535 + 9.21875i) q^{34} +(1.80902 + 1.31433i) q^{35} -10.8541 q^{36} +4.24264 q^{37} +(-2.11803 - 1.53884i) q^{38} +(-1.85410 + 1.34708i) q^{39} +(-13.5172 + 9.82084i) q^{40} +(-0.454915 + 1.40008i) q^{41} +(-1.85123 - 1.34500i) q^{42} +(-2.99535 + 9.21875i) q^{43} +(6.36396 + 19.5863i) q^{44} +(4.04508 - 2.93893i) q^{45} +(-2.12132 - 6.52875i) q^{46} +(-3.00000 - 9.23305i) q^{47} +(6.96790 - 5.06248i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(2.61803 + 1.90211i) q^{51} +(-3.93314 + 12.1050i) q^{52} +(11.1074 - 8.06998i) q^{53} +(-9.69316 + 7.04250i) q^{54} +(-7.67501 - 5.57622i) q^{55} -7.47214 q^{56} -0.874032 q^{57} +(1.14412 + 0.831254i) q^{58} +(3.69098 + 11.3597i) q^{59} +(-2.93159 + 9.02251i) q^{60} +13.9358 q^{61} +2.23607 q^{63} +(2.69098 - 8.28199i) q^{64} +(-1.81182 - 5.57622i) q^{65} +(7.85410 + 5.70634i) q^{66} +6.00000 q^{67} +17.9721 q^{68} +(-1.85410 - 1.34708i) q^{69} +(4.73607 - 3.44095i) q^{70} +(1.19098 - 0.865300i) q^{71} +(-5.16312 + 15.8904i) q^{72} +(-3.43237 - 2.49376i) q^{73} +(3.43237 - 10.5637i) q^{74} +(-3.92705 + 2.85317i) q^{76} +(-1.31105 - 4.03499i) q^{77} +(1.85410 + 5.70634i) q^{78} +(1.31105 - 0.952532i) q^{79} +(6.80902 + 20.9560i) q^{80} +(0.836881 - 2.57565i) q^{81} +(3.11803 + 2.26538i) q^{82} +(-0.977198 + 3.00750i) q^{83} +(-3.43237 + 2.49376i) q^{84} +(-6.69781 + 4.86624i) q^{85} +(20.5305 + 14.9162i) q^{86} +0.472136 q^{87} +31.7016 q^{88} +(12.4184 + 9.02251i) q^{89} +(-4.04508 - 12.4495i) q^{90} +(0.810272 - 2.49376i) q^{91} -12.7279 q^{92} -25.4164 q^{94} +(0.690983 - 2.12663i) q^{95} +(-2.93159 - 9.02251i) q^{96} +(5.66312 + 4.11450i) q^{97} -15.7082 q^{98} -9.48683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 18 q^{4} + 2 q^{7} - 26 q^{8} + 10 q^{9} + 10 q^{10} + 8 q^{14} + 2 q^{16} - 10 q^{18} - 2 q^{19} - 30 q^{20} - 12 q^{28} + 60 q^{32} - 36 q^{33} + 10 q^{35} - 60 q^{36} - 8 q^{38} + 12 q^{39}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 18 * q^4 + 2 * q^7 - 26 * q^8 + 10 * q^9 + 10 * q^10 + 8 * q^14 + 2 * q^16 - 10 * q^18 - 2 * q^19 - 30 * q^20 - 12 * q^28 + 60 * q^32 - 36 * q^33 + 10 * q^35 - 60 * q^36 - 8 * q^38 + 12 * q^39 - 50 * q^40 - 26 * q^41 + 10 * q^45 - 24 * q^47 + 12 * q^49 + 12 * q^51 - 24 * q^56 + 34 * q^59 + 26 * q^64 + 36 * q^66 + 48 * q^67 + 12 * q^69 + 20 * q^70 + 14 * q^71 - 10 * q^72 - 18 * q^76 - 12 * q^78 + 50 * q^80 + 38 * q^81 + 16 * q^82 - 32 * q^87 - 10 * q^90 - 96 * q^94 + 10 * q^95 + 14 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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